Talk:Centrifugal force (rotating reference frame)

What is a "scalar force"?

At the start of the current article there appears a list of pointers to other article, and the last item on the list says "For the scalar force that appears in polar coordinates, see the article on polar coordinates". I checked the article on polar coordinates, and the word "scalar" doesn't appear there. So, what exactly IS a "scalar force"? And why does the article point to another article for explanation of something that isn't even mentioned in the other article? Surely something is amiss.63.24.61.29 (talk) 20:48, 2 August 2008 (UTC)

Of course, you are correct in pointing out the absurdity of a "scalar" force. This pointer should be removed altogether, but I have only edited it to remove the absurdity. The history of this article shows that this pointer was a concession to a long, drawn out battle that apparently exhausted all parties and led to this compromise. Brews ohare (talk) 15:45, 3 August 2008 (UTC)

Any single dimension is a scalar- a scalar is simply a single number. There's nothing absurd about a scalar force any more than there is about a scalar acceleration. What is 9.81 m/s^2?- (User) WolfKeeper (Talk) 16:14, 3 August 2008 (UTC)

I don't understand the "corrected" version. The acceleration component that it refers to (i.e., the one that arises in stationary polar coordinates) is explicitly described and given the name "centrifugal force" in countless reputable references, including:

(1) "An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press.

(2) "Methods of Applied Mathematics" By Francis B. Hildebrand, 1992, Dover, p 156.

(3) "Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books.

(4) "Essential Mathematical Methods for Physicists" By Hans-Jurgen Weber, George Brown Arfken, Academic Press, 2004, p 843.

This has been pointed out previously, with the relevant quotations. I don't think there can be any dispute of the fact that this particular acceleration term is indeed among the terms that are called (in contemporary reputable sources) centrifugal force. Needless to say, it's entirely a matter of convention as to what names we give certain terms appearing in certain equations, but since Wikipedia articles are supposed to reflect verifiable facts from reputable sources, I can't see any justification for excluding this particular fact from the article. I think any discussion of the contemporary (let alone the historical) concept of centrifugal force is incomplete if it doesn't include this.

There are also other concepts that go under the name "centrifugal force" but that are not yet mentioned in this article. And conversely, there are lots of things discussed at length in this article that are only indirectly related to the concept of centrifugal force. I understand that much of this material has been added as part of a tutorial on general physics being given to placate some of the editors here, but ultimately I think it detracts from the readibility and relevance of the article.

Overall I think the present article has evolved into a lengthy set of notes that various people have made as they clarified in their own minds certain aspects and implications of the centrifugal force, as they responded to challenges from certain other editors. Sort of learning on the job. That's a commendable exercise, but it doesn't make for a very coherent article, and frankly, the "on the job learning" still has a long ways to go before it arrives at a fully consistent and complete account of centrifugal force. I'm not sure if this is really the best and most efficient way of authoring Wikipedia articles. (It may be... I'm really not sure.) If nothing else, I guess people are having fun.63.24.126.122 (talk) 16:34, 3 August 2008 (UTC)

The thing you're failing to understand is that fundamentally this is an encyclopedia, and encyclopedias have an article per definition, whereas a dictionary has an article/entry per word/phrase and has multiple definitions within that. So the wikipedia has to define a term and then describe it. We've decided that dividing the term up along these technical grounds is the way to go. Coordinate transformation centrifugal force goes in this article (sister article to coriolis effect), polar centrifugal force/effect is in the Polar coordinate system article, reactive centrifugal force is over there. Ultimately it is an editorial decision in conjunction with the various definitions that there are as to how the wikipedia is laid out, but this is the way it seems to be best to do it.- (User) WolfKeeper (Talk) 16:46, 3 August 2008 (UTC)

Scalar forces

I believe this pointer is better left out in the first place, or a separate discussion should be added in this article. The whole idea that the radial term in polar coordinates is a centrifugal force in any sense of the word is a stretch to begin with. Were it not for D Tombe, I doubt that this idea would ever surface. Brews ohare (talk) 16:39, 3 August 2008 (UTC)

Forget him, we need to do the right thing; we're narrowly swinging too far the other way, it deserves a link out- there is indeed a usage in polar coordinate systems, it's less common, and it's not the same thing. And because it's not the same thing, the description shouldn't be in this article, but we need to at least link it.- (User) WolfKeeper (Talk) 16:46, 3 August 2008 (UTC)

By calling it a "stretch" I agree with you that the polar coordinate thing is not a fictitious force in the sense of being related to a non-inertial frame of reference. Rather, it is a term that appears in even an inertial frame of reference when polar coordinates are used, and has been referred to in the literature (in a totally confusing way that brings with the confusion absolutely no advantages) as "centrifugal" only because of its formal similarity to the formula for centrifugal force. Brews ohare (talk) 16:54, 3 August 2008 (UTC)

Your point of view seems to be that terms arising from the use of curved temporal axes may be called fictitious forces, but terms arising from the use of curved spatial axes may not, or at least that the latter constitutes a sufficiently different meaning of the term "centrifugal force" that it doesn't belong in the same article. You're certainly entitled to that point of view, but I question whether you're entitled to impose it on this Wikipedia article, especially since it is contrary to multiple reputable contemporary sources.

At the risk of discussing the subject of the article (which we're not supposed to do on Discussion pages), just think for a minute about a particle moving around in a circle of radius r with constant angular speed w relative to a system of polar coordinates rotating with speed W. The radial equation of motion is r" = f + r(W+w)^2 where f is the centripetal force (per unit mass). The total absolute angular speed of the particle is W+w, and the "extra" term that appears in Newton's law is r(W+w)^2. We might choose to treat this acceleration term as if it was an outward force, balancing the inward-pointing force f. This is the whole concept of fictitious force. But your position is that the "true" centrifugal force consists only of rW^2, and the rest of the terms (2rWw and rw^2) you believe should be called something else. Essentially you are trying to impose the old pre-relativistic segregation between spatial and temporal components of spacetime coordinate systems, and there are certainly plenty of reputable texts that adopt the same pre-relativistic point of view (although most of them take this naive approach only because they don't think anyone cares, not because it's justified). Nevertheless, there are also many texts that take the more sophisticated relativistic point of view, and reject any segregation of spatial and temporal components as artificial and meaningless.

I guess the question is whether this Wikipedia article should recognize all of these reputable sourced views of the subject, or reject all but the naive pre-relativistic view (as you advocate). From my reading of Wikipedia policy, if there are multiple views of a subject to be found in a significant fraction of the reputable contemporary sources on that subject, then all of those views are to be represented in the article.63.24.99.40 (talk) 20:09, 3 August 2008 (UTC)

Only if they're within the scope of the article, at the moment the scope is Newtonian, and rotating reference frames, as with the Coriolis effect article.- (User) WolfKeeper (Talk) 20:18, 3 August 2008 (UTC)

If you want to create an article on relativistic centrifugal force, by all means go ahead.- (User) WolfKeeper (Talk) 20:18, 3 August 2008 (UTC)

There can be little doubt that fictitious forces are different from the so called centrifugal acceleration terms found in polar coordinates. Thus, whatever the history, utility and beauty of these last, they belong in this article only to say that they do not belong here. Brews ohare (talk) 21:04, 3 August 2008 (UTC)

Hmmm... I've presented a well-reasoned and well-sourced case for why the full meaning of the term centrifugal force in contemporary reputable sources ought to be included in the article, and even explaining in detail why those reputable sources say what they say, i.e., the rationale for regarding the fictitious forces arising from curved coordinates to be the same category of conceptual entity, regardless of whether the curved axes happen to be just the time axis or just the space axes or any combination of those. In response, you say "there can be little doubt" that I'm wrong. Well, based on the facts as I've described them, and on your inability (or unwillingness) to offer any subtantive rebuttal, I would say we can proceed to modify the article along the lines I've suggested, i.e., more in conformity with Wikipedia policy and less reflective of the personal POV of individual editors.

In answer to Wolfkeeper, the subject here isn't relativistic centrifugal force, it is centrifugal force as grasped by people who have learned the epistemological lessons of relativity (and the rest of modern science), even though these lessons haven't found their way into some introductory engineering texts. I would also point out that the present article claims to be based on relativity, and even quotes Einstein's first postulate, so I don't think you can rationally claim that the current article excludes what it regards as the relativistic view of the subject.

Well, I agree with this latter point, the article shouldn't include relativistic definitions and so I have removed it. This article is really a sister article to Coriolis effect and that doesn't discuss polar coordinate systems or relativistic mechanics either. I would encourage you to start an article on that particular, quite different topic, but on practical grounds, I don't see that this article can be stretched to include both.- (User) WolfKeeper (Talk) 21:38, 4 August 2008 (UTC)

Well, I think you two have given me a good indication of the level of discourse (and intellectual honesty) here, and I think I'm out of my league, so I'll bow out and leave you to it. Good luck.63.24.104.68 (talk) 21:34, 3 August 2008 (UTC)

I believe I have been responsive in describing exactly why the polar coordinate terms are not the same breed of cat as the fictitious forces. Your answers to this are not responsive. Instead, you drag in vague ideas like curved time axes, etc. without addressing specific items in the article, or replying to suggestions given. Brews ohare (talk) 21:47, 3 August 2008 (UTC)

Centrifugal force and polar coordinates

I'm going to support ip 63.34.xxx.xxx (btw, please register a user name it makes it easier to recognize your posts) on this. The term present in equations in polar coordinates and the term present in rotating reference frames are two sides of the same coin. (i.e. they are terms coming from the non-trivial connection coefficients involved in calculating the acceleration.) I think this article should cover both. Especially, since there is a whole bunch of textbooks that don't really distinguish between the two. (Marion and Thornton is one of them.) I do however see problems in providing a unified definition of the two, that distinguishes them from other fictious forces. (TimothyRias (talk) 16:47, 4 August 2008 (UTC))

They're not two sides of the same coin, because one centrifugal force is frame related (the force is proportional to the square of the rotation rate of the frame, and independent of the motion of the particle) whereas the polar coordinates is entirely object related (it depends on the rotation rate of the *object* around the origin). If you have a reference that says that they're the same thing, then we need that to make changes to the article, otherwise you're wasting our time. And quite frankly, that's the whole point, that they're not the same. Or, if all you're say is the trivial truth that the effect of centrifugal, coriolis etc. in both rotational frames of reference is the same as polar coordinates is the same as any other coordinate transformation that is equivalent to Newtonian Mechanics, then yeah, so? That doesn't mean that all coordinate transformations should be in this article, because the same argument applies to them also. And even that argument ignores the fact that this is a 3D vector treatment, whereas polar is only 2D.- (User) WolfKeeper (Talk) 20:19, 4 August 2008 (UTC)

I weigh in with Wolfkeeper on this: the mathematical terms in polar coordinates have not only no physical connection to fictitious forces, they also are completely unrelated mathematically to these forces except for the circular motion case, where you could argue that (when multiplied by a mass) they express terms that are the negative of the fictitious forces, but only in that limited case.

The reason for agreement in this singular case is that for circular motion the circle traversed happens to be the osculating circle for the entire path, and the center of polar coordinates happens to be the same as the center of the osculating circle. Remove either of these accidents and you lose any connection. I believe the distinction has been made very clearly and correctly in this article and in the polar coordinates article and again in the centripetal force article. Brews ohare (talk) 22:00, 4 August 2008 (UTC)

About polar coordinates being 2d, that's irrelevant the same term appears in 3d extensions of polar coordinates (i.e. spherical or cylindrical coordinates).(TimothyRias (talk) 08:13, 5 August 2008 (UTC))

I agree that dimensionality is irrelevant at a fundamental level. However, even in two dimensions a general planar motion does not lead to the polar coordinate expressions. You have to use the osculating circle. Have you thought about this point? It has come up earlier. See this. And this. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

That is only necessary if you want the motion to be tangential at every point of the curve, and is an approach that I would not recommend. But there is no reason you couldn't describe an arbitrary planar curve in a single set of polar coordinates. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: I'm left-adjusting the format of these comments so they are easy to find. The objective is not to describe a curve, but to describe a motion along a curve. Otherwise we are doing analytic geometry. not mechanics, and there is no "acceleration" and no "time dependence". If you track a motion, the kinematics of the motion must be referred to the osculating circle, a circle with time-shifting center in general, to determine the centripetal force in an inertial frame of reference. (See Curtis.) This centripetal force becomes the centrifugal force in the non-inertial frame of motion attached to the moving particle. See here. Brews ohare (talk) 15:34, 5 August 2008 (UTC)

About there being no physical connection I beg to differ. A change of frame is just a time dependent change of coordinates. That is it is just a change of coordinates in spacetime. (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

There are many meanings of "frame". See Frame of reference, for example. However, here is the key issue: there are inertial frames and non-inertial frames. In inertial frames there are no fictitious forces That includes no centrifugal force. However, in an inertial frame you can use a time dependent coordinate system, like a polar coordinate system that tracks the particle. That does not mean you left your inertial frame. It means only that you adopted a time-dependent description of what you see from your viewpoint. Just like you can adopt a teen-ager's vocabulary to describe life, but that doesn't make you a teen-ager: you'll still be talking about pensions, retirement, and health care. On the other hand, you can jump onto a particle and share the particle's motion. Then you are in a non-inertial frame. The particle is at rest in this frame. However, if you want to explain various matters, you need to introduce fictitious forces, like centrifugal force. Otherwise, you don't understand why you are being pushed around even though you are at rest in your frame.Brews ohare (talk) 11:38, 5 August 2008 (UTC)

(Since when are polar coordinates time dependent?)(TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: If you track motion, the motion is time dependent. And then the polar coordinates describing the motion are time dependent. (See here.) Brews ohare (talk) 15:34, 5 August 2008 (UTC)

Note that that is not what people usually mean with polar coordinates. (TimothyRias (talk) 08:39, 6 August 2008 (UTC))

Once you move into the general setting of (curved) spacetime the concept of a frame loses its (global) meaning. At best it has some local meaning. This because in a curved space the exponential map is not an isometry (as it is in flat minkoswki space.) The lesson from this is that viewpoints are inherently local. When comparing events at different points we must also account for the fact that we have to make a choice of "frame" at each point. If we have chosen coordinates, then this gives us an easy canonical way of choosing the local frame at each point, and thus of comparing events. In flat space choosing anything other than cartesian coordinates (with the usual SO(3,1) ambiquity) will lead to a non trivial comparison between points. Technically we will have non-zero connection coefficients. Going back to a 3d description by picking equal time slicings, will then give a description in which velocities and accelerations have picked up extra terms, which may or may not be interpretet as fictitious forces. From this point of view the centrifugal terms in rotating frames and polar coordinates arise exactly in the same manner. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Well said.130.76.32.15 (talk) 20:14, 5 August 2008 (UTC)

Hi Timothy: I have no ambition to discuss relativistic formulations. I'll bet Marion and Thornton don't do that either, in this context, eh? Brews ohare (talk) 15:34, 5 August 2008 (UTC)

For a more down to Earth connection. In a central force problem, integrating out the integral of motion connected to rotational invariance (i.e. conservation of angular momentum) leads to the same centrifugal term no matter what coordinates you started in.(TimothyRias (talk) 08:13, 5 August 2008 (UTC))

If you are talking about analyzing the problem in polar coordinates, you get the polar-coordinate expression for "centrifugal acceleration". If you did the problem in elliptical coordinates, or in arc-length coordinates you would not. If you are looking at angular momentum, a constant of the motion in the central force problem, it is coordinate system independent. But that is not the same discussion. If you want to call some contribution to the angular momentum in some particular problem a "centrifugal contribution" that is a confusing choice of terminology, but it is a different confusion than the discussion of the polar coordinate acceleration term. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

I'd also love to see you guys give an explicit citation backing up your claim that there is absolutely no physical connection between the two. Otherwise I don't think the wikipedia article should be making such a strong claim. (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

The discussion of inertial and non-inertial frames above explains why there is no physical connection. There are already citations in the articles that state clearly that centrifugal force is a fictitious force and does not appear in an inertial frame. The polar coordinate acceleration appears in all frames that employ polar coordinates, inertial or non-inertial. Brews ohare (talk) 12:01, 5 August 2008 (UTC)

That there isn't a connection in the scope of 'classical' classical mechanics (in which global frames have a meaning) does not mean that there is no physical connection, period. There are many examples where a more general theory is necesary to explain the connection between different seemingly different concepts. This is one of them. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: Well, in the big picture, maybe everything is connected. But within the framework of this corner of mechanics, with the usual definition of inertial frames (Lorentz or Galilean related), there is no basic connection; only an accidental connection in the case of circular motion. (The source of this accident already was described here.) Brews ohare (talk) 15:34, 5 August 2008 (UTC)

It is probably better to just mention the clear fact that both are referred as centrifugal force.(TimothyRias (talk) 08:13, 5 August 2008 (UTC))

The fact that the same name is used for both is already in the articles, and the differences are also pointed out. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

But the better argument may be that there is plethora of textbooks out there that treat them as the same.Mostly without actually explaining the deeper connection between the two. (An example of this is the Marion and Thornton book (again since it is the one that's on my desk) in the chapter on central forces it mentions that the term appearing in the (polar coordinate) formula is called the centrifugal force, but that it is not a force in the usual sense and then defers to the section about fictitious forces for a more detailed treatment.) (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

To treat them as the same is a shocker. However, the context of the central force problem may be the cause of confusion. It may be that in this problem a number of different items are accidentally similar. A more general case would show up differences. The "not a force in the usual sense" phrase sounds like a ducking of clear thought. I do not have access to this text. Can you find a comparable discussion that is available in some detail on googlebooks?? Brews ohare (talk) 11:38, 5 August 2008 (UTC)

I can have a look. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Here are a couple of references accessible online:

"An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press. "In this chapter we have faced the fact that there is something of a crisis in intuition that arises from the introduction of the polar coordinate system, even in a non-rotating system or reference frame. When we first use rectilinear coordinates to understand the dynamics of a particle, we commit our minds to the simple expressions x" = F_x, y" = F_y. We think of the accelerations as time rate-of change [per unit mass] of the linear momentum X' and y'. Then we express the same situation in polar coordinates that partly restore the wanted form. In the case of the radial component of the acceleration we move the r(theta')^2 term to the right hand side and call it a "centrifugal force."

"Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books. "Since the force here is radial, it is convenient to use polar coordinates. Taking x = r cos(theta) and y = r sin(theta) [i.e., stationary polar coordinates] then... If we interpret the term [r(theta')^2] as a force, this is the well-known centrifugal force..."Fugal (talk) 04:32, 6 August 2008 (UTC)

This means that a great many users (even those with physics degrees) reading this article are gonna assume they are (more or less) the same thing. Hence it should be discussed in the article. I don't think this would have to be a very lengthy discussion. The current not (with some further tweaking/sourcing) should probably suffice. (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

I can see that readers of Marion and Thornton could get the wrong idea: after all, I think you did. I don't see how the reader of the Wiki articles could get the wrong idea, however. I hope that you haven't. You do appear to see that there is a different view on Wiki, anyway, but just don't see why. I'd like to see the articles written so that you would see exactly what is going on. So before you lose your initial perception of the articles, please make a note of what could be done to lead a reader by the hand. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

Coming from a more general perspective, I think I've a clearer idea of what's going on than you. So, I'd appreciate a little less condecending tone. As for some suggestions on where to improve the article I'll come back to that later. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: Sorry for the appearance of condescension. I am just trying to explain things from a certain (apparently limited) viewpoint. However, this narrow perspective is the one commonly adopted for this topic. Brews ohare (talk) 15:34, 5 August 2008 (UTC)

The narrow perspective is probably OK for the article. However there appears to be a non negligible number of prominent sources that take an other perspective, hence the wikipedia article should at least mention it. And when mentioning it, it should probably refrain from making over the top strong statements such that there is no physical connection. A little bit of weaseling tends to be in order when the perspective of an article is limited. (TimothyRias (talk) 08:45, 6 August 2008 (UTC))

Fictitious vs polar centrifugal forces (Cont'd)

I am assuming that you are not referring to "weaseling" based upon "slices of space-time"? If that is what you mean, then please provide a reference (preferably one that can be read on googlebooks), and a quotation, and a summary of the issues. If instead, what you mean goes back to the confused state of terminology, that subject already has been adequately dealt with in Aside on polar coordinates, short of some inadvisable rant about authors that use a terminology in their topics on use of polar coordinates that is incompatible with their use of the identical terminology for fictitious forces in other sections of their very same book. Brews ohare (talk) 13:58, 6 August 2008 (UTC)

The terminology is incompatible (or rather, seems incompatible) only to readers who insist on imposing a pre-conceived but incomplete notion as to the meaning of "fictitious forces". The confusion is due mainly to the fact that authors of introductory texts sometimes split up the topic of fictitious forces into two parts, thinking that this will make it easier for students to understand if they present the consequences of curved space coordinate axes separately from the consequences of curved time coordinate axes. But unfortunately this pedagogical tactic tends to leave some students with a bifurcated view of what is really just a single concept. There is nothing more (or less) "physical" about the fictitious forces that arise in either case. Both are artifacts of using coordinate systems in terms of which the net applied force (per unit mass) does not equal the second derivative of the space coordinates with respect to the time coordinate. In both cases this coordinate effect can be corrected by the inclusion of additional acceleration terms (recognizing that the true absolute acceleration does not equal the second derivative of the space coordinates with respect to the time coordinate in these systems), or alternatively those extra terms can be negated and brought over to the other side of the equations and treated as if they were forces, hence fictitious forces. Some texts make the unity of this subject explicitly clear, whereas others obscure it, and still others present only the effect of curved time axes and never address the corresponding effect of curved space axes at all. Since Wikipedia articles are supposed to reflect the views published in reputable sources, I think the article should describe both the obscure disjointed view (which you advocate) and the clear unified view. It would be nice if the article could just be written giving the clear unified view, but since so many published texts present the outmoded and obscure view, I conceed that it needs to be represented as well. It may actually be useful, since it may help people avoid confusion.Fugal (talk) 15:18, 6 August 2008 (UTC)

Hi Fugal: In contrast to your viewpoint, I believe the article to provide a correct, well balanced and thoroughly documented viewpoint. That is, that there are multiple uses for the terms, and the one appropriate here applies to fictitious forces. It does not say that other uses are forbidden or "wrong", but that they are different. It does no good to lump them all together, when there are real physical differences between them. The most simple difference is that fictitious forces appear only in non-inertial frames of reference. Would you dispute this point? Consequently, the fictitious centrifugal force is different from the "polar coordinate" centrifugal term, which last appears in all frames, inertial and non-inertial. I find it difficult to debate this point; it is very well documented by the citations in the article. Brews ohare (talk) 04:32, 7 August 2008 (UTC)

Whenever acceleration terms appearing in the equations of motion due to non-linear coordinates are brought over to the other side of the equation and treated as forces, they are called fictitious forces (also known as inertial forces, pseudo forces, etc). This encompasses both accelerating coordinate systems and spatially curved coordinate systems, es explained in the numerous references that have been cited. Consider an isolated particle, free of any external forces (F=0), so it is following an inertial path, and suppose its motion is described in terms of a coordinate system x1,x2,x3,t. In terms of these coordinates we find that the second derivative of the space coordinates with respect to the time coordinate is not zero. In other words, the equation F = m d^xj/dt^2 = 0 is not satisfied. Nevertheless, we know the particle is following an inertial path, because no external forces are being applied, i.e., we know F = 0. One way of explaining this is to say that, in terms of our chosen coordinates, the absolute acceleration of the particle must not equal the second derivative of the space coordinates with respect to the time coordinate. There must be some other terms in the expression for the true absolute acceleration, and these terms must sum to zero. Alternatively we could choose to maintain the (sometimes convenient) fiction that the absolute acceleration equals d^2xj/dt^2 and we can still apply Newton’s law by bringing the extra acceleration terms over to the other side of the equation and pretending they are forces. Thus, as it says in Goodman and Warner’s “Dynamics”, the simple law F = m d^xj/dt^2 can be applied in terms of any system of coordinates, provided we include in F the sum of all fictitious forces, i.e., all acceleration terms (multiplied by mass) representing the difference between the true absolute acceleration and the vector d^xj/dt^2. Thus, fictitious forces arise in any non-linear coordinate system (i.e., any system in which the absolute acceleration does not equal the second time derivative of the space coordinates), and they arise in exactly the same manner, regardless of whether the non-linearity is of the time coordinate or the space coordinates or both.

It would be nice if you were able to understand this, but frankly, whether you understand it or not, the fact remains that this is how fictitious forces are comprehensively defined, as substantiated in the numerous references that have been provided, so there is simply no justification within the rules of Wikipedia editing for mis-representing these facts in the article.Fugal (talk) 15:05, 7 August 2008 (UTC)

Of course, in doing any mathematical manipulations, "convenient fictions" (your characterization above) may be introduced that suit the investigator's temporary conceits. However, the "fictitious" forces so introduced are not on a par with the much more fundamental issues that relate to the state of motion of the observer, that separate inertial from non-inertial frames, and that are not to be categorized as mere mathematical manipulations.

The choice of coordinate systems doesn't have any effect on actual physical phenomena. Fictitious forces are, by definition, artifacts of a particular choice of coordinate systems. They are all "mere mathematical manipulations". Also, the acceleration terms appearing with certain coordinates do not depend on the presence or state of motion of any observer. An accelerating observer can use inertial coordinates, and an inertially moving obvserver can use accelerating coordinates, and they can both use rectilinear or curved spatial coordinates. The choice of coordinate systems is arbitrary, and even with a given choice of coordinate systems, the choice of whether and which acceleration terms to bring over to the "force side" of the equation and treat as if they were forces is also arbitrary.Fugal (talk) 18:14, 7 August 2008 (UTC)

I don't think you understand fully the difference between a "coordinate system" (a mathematical concept) and a "state of motion" (a physical reality). It is a perversion of concept to suggest there is no difference between inertial and non-inertial observers. I find that virtually all texts on mechanics make a distinction. And fictitious forces appear only for non-inertial observers. See Frame of reference, Fictitious force and Inertial frame of reference for more detail on this. Brews ohare (talk) 22:31, 7 August 2008 (UTC)

It is you who plainly does not understand the difference between coordinate systems and states of motion. I can't comment on your "perversion of concept" statement, because it bears no relation to anything I've said. Likewise your follow-up statement that all texts distinguish between inertial and non-inertial is not pertinent to anything at issue here. Then you repeat your (thoroughly falsified) mantra that fictitious forces appear only for non-inertial observers. This is self-evidently false, and numerous references have been provided to you. You've read one of them, because you quoted it, when it specifically notes that coordinate systems in terms of which fictitious forces arise are not necessarily rotating. But by some truly bizarre psychiatric phenomena you've apparently convinced yourself that the book said just the opposite of what it actually says, so you continue to repeat your false claim. Weird.

And then to make this even better, you refer me to three Wikipedia articles for enlightenment, and a quick survery of the history of those pages shows that each of them was authored by (wait for it) Brews ohare! The fact that you're proliferating your fundamental misconceptions through multiple Wikipedia articles doesn't make you a reliable source. (See Wikipedia policies.)

Look, I've taken the trouble to provide you with SEVEN reputable published references from academic publishers, and all you've done is pointed me to three Wikipedia articles authored by yourself. Fugal (talk) 00:42, 8 August 2008 (UTC)

I don't appreciate your view of my limited abilities for understanding and your lofty validation of your own unsupported opinion. You might try less rhetoric and more communication. The views I have expressed are well-documented. Please, read the Wiki articles and the supporting citations. Brews ohare (talk) 16:22, 7 August 2008 (UTC)

The comments I've made here have not been "unsupported opinions", they have been accompanied with (so far) SIX different reference texts, all of which explicitly include the fictitious forces arising from curvilinear space coordinates. My comments have been honest attempts to convey the idea presented in those references. Undoubtedly it could be expressed better, but I'm doing my best. Having said that, I'm not sure what non-communicative "rhetoric" you are referring to.Fugal (talk) 18:14, 7 August 2008 (UTC)

Please provide me with links to these SIX supporting texts. Brews ohare (talk) 22:03, 7 August 2008 (UTC)

Links? Try reading a book from time to time. Here are the six references sources that have been provided to you (FOUR times now, so I hope you understand why I'm getting a little testy with you for insisting that you be spoon-fed repeatedly), plus a seventh for good measure:

(1) "An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press.

(2) "Methods of Applied Mathematics" By Francis B. Hildebrand, 1992, Dover, p 156.

(3) "Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books.

(4) "Essential Mathematical Methods for Physicists" By Hans-Jurgen Weber, George Brown Arfken, Academic Press, 2004, p 843.

(5) Marion and Thornton [ref by Tim Rais, "the term appearing in the (polar coordinate) formula is called the centrifugal force"]

(6) "Dynamics", Goodman and Warner, Wadsworth Publishing, 1965.

(7) "Statics and Dynamics", Beer and Johnston, McGraw-Hill, 2nd ed., p 485, 1972. —Preceding unsigned comment added by Fugal (talk • contribs) 00:25, 8 August 2008 (UTC)

I have reviewed the sources that I could access from your list. Those I looked at fall into two groups:

1. Authors whose main interest is polar coordinates and introduce the centrifugal force as "not real" and therefore "fictitious" in the sense of a mathematical convenience. These authors really are not interested in "fictitious forces" in the sense of classical mechanics, that is, in the relation to inertial and non-inertial states of motion. One cannot deny these authors their choice of terminology, but of course it is a different use of the term fictitious. Their point of view has been summarized in the present article and presented more fully in the article on polar coordinates.
2. Authors who do consider both the polar coordinate and the "state of motion" uses of the term. An example is Stommel and Moore, quoted at length earlier in these remarks. These authors use the term non-Newtonian instead of non-inertial to describe a rotating frame of reference, and repeatedly stress that rotation is different from simple use of polar coordinates in an inertial reference frame. This difference is exactly the distinction made in the present article.

So, I see no conflict with these references. Brews ohare (talk) 14:34, 8 August 2008 (UTC)

Fugal's sources

Stommel and Moore p. 4 "Sometimes the additional terms in the accelerations are transposed to the right side of the equation, leaving only the double-dotted terms on the left. So the acceleration terms on the right look like forces. They even acquire names such as "centrifugal force." As convenient as this may be from an intuitive, practical point of view, this transposition...can lead to confusion. ...So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system. p. 26: "you should be very clear in your mind not to confuse the idea of a plane polar coordinate system fixed in inertial space with the idea of rotation of coordinates. This chapter is entirely tied to one particular reference frame, fixed in inertial space – so don't get mixed up now, or later when we introduce rotating axes." p. 36: This immediately gives the components of acceleration in polar coordinates, [lists equations] Remember once again that all this has nothing to do with rotating coordinate systems. We are in a polar coordinate system that is at rest with respect to the stars....The term r ω² then looks like a force, and it actually has a name: "the centrifugal force". ... But it is really not a force at all, and so if we want to make use of it in a formal sense, then we could call it a virtual, fake, adventitious force." Following these various cautions, these authors later proceed to a rotating frame (p. 54) where they again introduce polar coordinates, these now are polar coordinates in a rotating frame, and derive what is now the true fictitious force by analogy with the formulas for the polar coordinates in a stationary frame. They rely upon their earlier cautions about confusion, but (in my view) have done things in the way most likely to actually cause confusion. Nonetheless, they are perfectly clear that the two cases are different, and that they are exploiting a mathematical analogy.

I was unable to access the second source: "Statistical Mechanics" By Donald Allan McQuarrie. Brews ohare (talk) 17:13, 7 August 2008 (UTC)

As a correction, the Stommel and Moore reference was not mine, it was provided by Tim (Actually, it wasn't mine either, but the noname ip 63.something. (TimothyRias (talk) 12:02, 8 August 2008 (UTC))). Having said that, it's a fine reference, explicitly refuting your claims and confirming mine. By the way, I enjoyed your statement that when they discuss rotating coordinates they "derive what is now the true fictitious force", presumably as opposed to the false fictitious force that they derived for curved spatial coordinates, and had the nerve to call "centrifugal force". Let me just conclude this comment by repeating from your quotation: "So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system."Fugal (talk) 18:37, 7 August 2008 (UTC)

Apparently we don't interpret these remarks the same way. Brews ohare (talk) 22:05, 7 August 2008 (UTC)

How about this... since you claim that Stommel and Moore support your position, I assume you have no objections to replacing your "Comment on Polar Coordinates" in the article with a direct repetition of the very words from Stommel and Moore you quoted above. Since you believe that the words "fictitious forces only appear in rotating frames" mean the same thing as "Remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system", you should have no objection to this substitution. And for everyone else in the world it reverses the meaning from being false to being true. So it's a win-win situation.Fugal (talk) 00:54, 8 August 2008 (UTC)

I personally make no such claim that fictitious forces only appear in rotating frames- clearly they appear in linearly accelerating frames and polar coordinates as well. The question is what the scope of this article should be. It has been agreed that it should be the radial force that appears in rotating frames, and in that way it forms the sister article to Coriolis effect. We have another article for polar coordinates. I also have no problem with including rotating polar coordinates here either. The question of scope is the most fundamental one, and this is not being addressed in the above discussion- and no reference to books can answer that- it is an editorial decision we have and must continue to make sensibly. I simply don't consider adding the 'centrifugal force' from fixed polar coordinates to be apropos in this article.- (User) WolfKeeper (Talk) 01:01, 8 August 2008 (UTC)

It might be helpful for you to review Wikipedia policies. When you say the decision of what to put in this article on "centrifugal forces" can't be answered by references to books (or presumably to any other verifiable sources), and instead should be determined by the personal "editorial decisions" of editors such as yourself, you are proposing a flagrant violation of Wikipedia policy. The article on subject X is supposed to accurately and faithfully represent the verifiable information about X to be found in reputable published sources. This is the cornerstone of Wikipedia. You're really not at liberty to impose your personal preference for the article to present only a partial and distorted version of what appears in reputable sources for this subject. The suggestion has been made that those editors who are fixated (for some unknown reason) on one particular aspect of the subject (such as fictitious centrifugal forces in rotating coordinate systems on Wednesdays and Saturdays, because by God there IS a clear distinction between the days of the week, and we've agreed to only consider Wednesdays and Saturday's in this article), then those people can start their own article on the subject "Fictitious Centrifugal Forces in Rotating Coordinate Systems on Wednesdays and Saturdays". I personally think that would be somewhat silly, but I certainly have no objection if you wish to do so. However, the article on centrifugal force needs to accurately represent the verifiable information to be found on this subject in the reputable literature. That is the Wikipedia rule. I trust no one here is advocating violating this basic Wikipedia principle.Fugal (talk) 06:10, 8 August 2008 (UTC)

There is no policy debate here. The article is about centrifugal force as treated in classical mechanics, and as it appears in common English usage (as in the centrifuge). The alternative (uncommon in everyday usage) use of the term as a catch-all for mathematical convenience in polar coordinates is properly outlined and referred to the appropriate article polar coordinates. The standard usage of "centrifugal force" as a fictitious force that appears in rotating reference frames is extremely well documented in the article using primary sources. Wiki policies have been scrupulously observed. Brews ohare (talk) 14:41, 8 August 2008 (UTC)

Fugal, you're right that I don't get decide alone. Ultimately it comes down to editoral consensus about what is normally meant by the term 'centrifugal force'- and whatever that is, it needs to be at centrifugal force in the same way that coriolis effect is what is meant there. I really don't think that centifugal force is just any force acting outwards, and I don't think that coriolis effect in polar coordinates is what is meant at coriolis effect.- (User) WolfKeeper (Talk) 03:26, 9 August 2008 (UTC)

While you're trying to understand the subtle nuances Fugal of the wikipedias policies you might like to try being less tendentious and offensive, and actually start to assume good faith.- (User) WolfKeeper (Talk) 03:26, 9 August 2008 (UTC)

Wolfkeeper. I suggest that you do the same for others. It has been a wikipedia policy to assume bad faith regarding everything that David Tombe does. Here you are acting in the same manner by berating Fugal. I thing that is a bit of a contradiction.72.64.63.178 (talk) 13:40, 9 August 2008 (UTC)

The difference is that Fugal understands thoroughly what the core of this topic is and is constructively discussing different ways to present the material, whereas David Tombe showed no signs at all of understanding at any point, and this lead him to waste considerable amounts of both his and other editors time.- (User) WolfKeeper (Talk) 14:00, 9 August 2008 (UTC)

Surely you are joking MR Wolfkeper. I didnt think humor was allowed. Maybe you are simply being dishonest in order to prove that what I said previously is true. You do treat Mr Tombe with disrespect. In any event, I cant see nothing wrong in repeating what has been said by Mr Tombe, concerning which you now seem to be agreeing with Fugal, when he says basically the same thing. "Citations are being ignored when it suits certain editors".

<duplicate of suspended user screed deleted>- (User) WolfKeeper (Talk) 15:39, 10 August 2008 (UTC)

It seems to me that Mr Tombe has been right all along and you simply just ignored and opposed his correct viewpoint, which now you seem to be agreeing with, since it is being advocated by a different editor. I certainly would like to know if you are now agreeing with Fugal and conceeding that he is right so that we can continue to complete this article?71.251.182.49 (talk) 12:27, 10 August 2008 (UTC)

You appear not to be assuming good faith. David Tombe paid lip-service to rotating reference frames, but was unable to explain why coriolis force is a vector quantity that can point in any direction perpendicular to the axis. This is inconsistent with the usage in weather systems, where the center of a cyclone or anticyclone is not aligned with the axis of the Earth. This shows pretty clearly that he didn't really get it, even if he says he did, even if you claim he did. They are similar, but *not* the same.- (User) WolfKeeper (Talk) 15:39, 10 August 2008 (UTC)

Sir, here you are attacking Mr Tombe, and that is not the point of this discussion. But if you seek to prove my point, I thank you for it. You have done so. You deliberately assume bad faith on the part of Mr Tombe, and so you have harassed him and unfairly blocked him and smeared his reputation. You continue to do that here by dead horse beating Mr Tombe who is unable to reply to your slanders. I think it is you who is being dishonest. You should frankly admit you have been wrong in this debate, and that Mr Tome and Frugal are correct in what they have said here. You and your supporters can then withdraw and let the article be completed without your blocking its progress towards completion.72.64.46.35 (talk) 20:55, 10 August 2008 (UTC)

Scalars and Vectors

On the subject of scalar forces. Please note that "scalar" does not simply mean single dimensional. It also implies being invariant under coordinate transformations. (A scalar is a rank 0 tensor, just as a vector is a rank 1 tensor) (TimothyRias (talk) 16:47, 4 August 2008 (UTC))

Well, it's invariant under rotation, who cares about translation in polar coordinates? And note that there's more than one definition of scalar anyway.- (User) WolfKeeper (Talk) 20:19, 4 August 2008 (UTC)

I weigh in with Timothy on this. "Who cares" is not an answer here. A vector has transformation laws under (for example) rotations, and just because you have a situation that does not explore this fact does not change the fact. Brews ohare (talk) 22:00, 4 August 2008 (UTC)

Centrifugal effect

Centrifugal effect redirects here. It's not a psychological effect (they're offtopic here anyway), it's an apparent acceleration in rotating reference frames, in the same way that coriolis effect is.- (User) WolfKeeper (Talk) 18:34, 3 August 2008 (UTC)

Actually, common usage is vague. In the case of Coriolis effect, it is very commonly used to mean Coriolis effect (perception). That refers to a lot of medical stuff about disorientation and nausea. Brews ohare (talk) 21:01, 3 August 2008 (UTC)

That's not the most common usage. The most common usage is in things like weather systems.- (User) WolfKeeper (Talk) 03:29, 9 August 2008 (UTC)

Suggested move/refactor to Fictitious forces in rotating frames

A radical suggestion: I propose that this article be moved to Fictitious forces in rotating frames, and that Coriolis force and Euler force be merged into it at the same time.

Rationale: the three "rotational" fictitious forces are all generated by the same physical phenomenon, and drop out as individual terms when the frame-transformation equation is differentiated and expanded. A detailed treatment of centrifugal force must necessarily include both of the others, and vice versa, and as a result both the Coriolis and Euler forces are already dealt with in this article.

After the merge we would thus end up with a single long fully-integrated article instead of one long article and two short ones with overlapping topics. Refactoring and copyediting work could then be more effectively applied to that single article, which I believe can be significantly shortened if a more general treatment is used, without treating centrifugal force as a special case that is separable from the other force terms.

At the same time, there are other related phenomena such as centripetal force and reactive centrifugal force and certain "centrifugal" terms in coordinate transformations which are not fictitious forces and not related to rotating frames, but are often confused with the rotational fictitious forces. Renaming this article will also make clear that the only topic being discussed is that of fictitious forces in rotating frames -- The Anome (talk) 12:11, 5 August 2008 (UTC)

You have stated the plusses of merger. However, one downside is that the combined article would be very, very long. That presents some questions of organization: it is tougher to make a clear, long article. Another downside is that "centrifugal force" is a magnet for dissension, and the other topics don't seem to attract so much attention. These debates might prove even more intractable in a longer article where they could spread like a grass fire. Finally, the reader who wants to find out about the individual topics will have to wade through a long, long table of contents to find what they want. My vote would be to leave things alone. Brews ohare (talk) 12:35, 5 August 2008 (UTC)

As Brews says, size is the big issue and there already is the article Fictitious force anyway.- (User) WolfKeeper (Talk) 15:43, 5 August 2008 (UTC)

I think it is a good very good idea. As I said before [1]: It is much easier to discuss centrifugal and Coriolis forces together than one at a time, since you rarely have one without the other. However, the existing articles should be kept and reduced to a more condensed and precise form. This would also give more room in the "centrifugal force" article for discussions about the etymology and historical perspective, and different uses of the term. The "fictitious force" article should only briefly state the results for rotating frames, and link to the new article for details. --PeR (talk) 20:37, 5 August 2008 (UTC)

I think it's a good suggestion. It would allow those who wish to restrict their attention just to the fictitious forces arising from the use of rotating coordinates to do so in the article devoted to that limited subject, while allowing the more encompassing meaning of "centrifugal force" as found in the literature to be fully represented in this article. I also agree with PeR that the existing article should be made more concise. (It has become nearly unreadable.)Fugal (talk) 04:24, 6 August 2008 (UTC)

I believe that the reason the article is so large is that it was expanded greatly during the recent phase of adversarial editing, to include a large number of worked examples. Many of these are very good, but they overlap one another, proving the same points over and over again in different ways. I believe that the article could easily be cut down to perhaps half of its current length by reducing the number of detailed worked examples, whilst retaining sufficient clarity and rigor of exposition. -- The Anome (talk) 08:20, 6 August 2008 (UTC)

User history indicates that you The Anome were actively editing during the adversarial phase in question. Did you make any attempt to control the adversarial expansion of the article? 86.141.250.16 (talk) 19:45, 10 August 2008 (UTC)

Even if so, I don't think it would be small enough to do much merging. And I completely disagree with the idea of re-merging reactive centrifugal force back here; the amount of usage of that concept is fairly low in the modern world, it gives it undue weight; and anyway it is logically quite distinct, under the wikipedias and general encyclopaedic rules it should not be merged here.- (User) WolfKeeper (Talk) 21:43, 6 August 2008 (UTC)

PeR- wikipedia articles are not about a term, they are about a topic or a concept. That's why reactive centrifugal force is not here- it's completely different, sharing only direction and having something to do with rotation.- (User) WolfKeeper (Talk) 21:48, 6 August 2008 (UTC)

The topic or concept in this case would be "force directed away from the center of rotation". It is not uncommon for Wikipedia to have articles on broad topics, optionally linking to more detailed articles on more specific sub-topics. The section on "reactive centrifugal force" would of course be relatively small, in order to avoid undue weight, and the longer discussion can stay in its own article.

The current state of the article will result in a steady influx of editors who want "their" definition of "centrifugal force" to appear in the article. Defending it vigorously against such edits will be counterproductive at best, and at worst scare new editors away from Wikipedia. --PeR (talk) 07:09, 8 August 2008 (UTC)

The notion of making the article noncontroversial is an interesting one. As a strategy, it would seem that what this means is that any article where debate may recur should be structured as a many-part article, with a part devoted to each perspective. That approach makes sense in some cases. Or, should we have centrifugal force (mechanics) and centrifugal force (polar coordinates)? I'd love to write the disambiguation page: For those of mathematical bent who do not see any difference between inertial and non-inertial frames, see centrifugal force (screwballs). To be more serious, it might be advantageous to have two pages for centrifugal force. My guess is that only the contributors to the present centrifugal effect page are really interested in the subject; the rest are interested in debate. So a narrowing (not broadening) of the subject will eliminate the phony dispute, or at least direct it to an insignificant minor topic page where it can go on and on and on and … who cares? Brews ohare (talk) 15:10, 8 August 2008 (UTC)

Well, centrifugal force (screwballs) would be a WP:POV FORK, and therefore, unfortunately, not allowed. The centrifugal force (polar coordinates) article doesn't need to be started until the section on polar coordinates becomes too large for the main article, and I don't think that's likely to happen. --PeR (talk) 18:25, 8 August 2008 (UTC)

Since wiktionary has 3 different definitions for the term, I've created centrifugal force (disambiguation).- (User) WolfKeeper (Talk) 03:47, 9 August 2008 (UTC)

This may be a good step toward straightening things out. Thanks. Brews ohare (talk) 04:15, 9 August 2008 (UTC)

Division of centrifugal effect into multiple pages

As a measure to limit useless debate over the proper content of the present page, I propose that the present centrifugal force page be renamed centrifugal force (classical mechanics) and new pages be started centrifugal force (general relativity), centrifugal force (polar coordinates) that are referred to by a disambiguation page: For the commonly used term centrifugal force and for the term as used in classical mechanics, see centrifugal force (classical mechanics). For the term as used as a mathematical convenience in polar coordinates, see centrifugal force (polar coordinates). For a very general approach useful to those with a background in general relativity see centrifugal force (general relativity).

Personally, I expect the other pages to develop very slowly as the main debaters on these issues have no real interest in contributing pages, and probably cannot bring enough muscle to bear to write these pages themselves. Brews ohare (talk) 15:27, 8 August 2008 (UTC)

This debate here has entirely been over centrifugal force in classical mechanics, so your suggestion doesn't really address the issue. (Also, your repeated reference to "polar coordinates" indicates that you don't have a clear understanding of what the issue.) All of the references that have been provided to you are concerned solely with classical mechanics. Of course, references don't do much good for people who can read a sentence like "Remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system" and interpret it as confirmation of their belief that such unreal forces appear only in rotating coordinate systems. I'm honestly not sure how to deal with such people, if we can't even agree on what a simple English sentence means. I think the only viable approach is what I outlined previously, i.e., we have to take the quotations you claim to agree with (like the statement that "the appearance of this type of unreal force does not necessarily involve a rotating coordinate system") and include them in the article verbatim. Then you can interpret them as confirming your beliefs, and all other readers can get an accurate and complete explanation of the subject.Fugal (talk) 16:02, 8 August 2008 (UTC)

Well, of course, that is an incorrect view of the situation. Within classical mechanics, the whole polar coordinate thing has at best a very subsidiary and limited role as a mathematical device, and no physical importance at all. As witness to the unimportance of polar coordinates, none of the examples presented depend upon polar coordinates, and a formulation entirely in terms of vector notation emphasizes the physics, again with no need for polar coordinates. Inasmuch as polar coordinates are such a source of confusion, it would be a relief to remove them entirely from consideration in this article and put that remote, derivative subtopic elsewhere. Brews ohare (talk) 23:38, 8 August 2008 (UTC)

No need to fork an article on relativistic effects until that section grows too large for the main article. At present it's about zero bytes, so there's no rush. --PeR (talk) 18:25, 8 August 2008 (UTC)

Hi Per: I am not concerned over the length of the present article, but would like to shunt discussion of the polar coordinate version away from this page, where frankly I don't care what happens to it. Brews ohare (talk) 22:33, 8 August 2008 (UTC)

The change proposed by The Anome, which received supportive comments from PeR and myself, and dissenting comments from Brews and Wolf, was significantly different than what Wolf has now implemented. (The proposal was to create an article called Centrifugal Forces in Rotating Frames, and then the article on simply Centrifugal Force could adopt a more comprehensive approach reflecting the full range of views in the published literature.) I don't think that 3:2 constitutes consensus for the "2" position. As I understand it, Brews & Wolf are adament about excluding any mentions (other than perhaps dismissive and derogatory ones) of the more comprehensive view of the subject of this article taken by numerous reputable reference sources. Would it be possible for Brews and/or Wolf to summarize their reason(s) for taking this position? Unless they can provide some valid justification, it seems to me that their position is prima facie contrary to Wikipedia policy. I think it would help if their answer(s) could be phrased in terms of (for example) why certain references are not actually from reputable sources, and so on, rather than in terms of "well, I think the most sensible definition of fictitious force is such and such", since, as we all know, our own personal POVs are not relevant.Fugal (talk) 17:32, 9 August 2008 (UTC)

My reasoning has been explained already. Fugal's view that a "more comprehensive" article is necessary is a ploy to include a digression on a specific use of the same term in a mathematical, rather than a physical, context. The use of the same term by the mathematically inclined to mean something else is not a reason to add an extensive discussion of this occurrence to this article, which is about physics, not about polar coordinates. Although I expect Fugal to dispute the ability to divorce this physics-related phenomena from polar coordinates, in fact that has been done in the present article by focusing upon the physics, and not upon polar coordinates. Of course, any physics phenomena can be explained in a manner independent of any specific coordinate system, for example, by the use of vector analysis. That is the approach taken. Reference to the mathematicians' use of the term in connection with polar coordinates has been made for the sake of completeness, but that is all the billing it deserves in this physics article. Brews ohare (talk) 23:43, 9 August 2008 (UTC)

I was hoping your justification wouldn't just consist of your own original research concerning what you regard as a distinction between what is "physical" and what is "mathematical". If the basis vectors of a coordinate system change in time, you call the resulting terms appearing in the equations of motion "physical", whereas if the basis vectors of a coordinate system change in space, you call those same terms arising in the equations of motion "mathematical". This is unfortunately an only too familiar attitude among a certain well-recognized kind of individual, who, when pressed to justify his beliefs, falls back on meaningless and misguided assertions of a profoundly important distinction (which, alas, only he can see) between "physical" and "mathematical", e.g., the Lorentz transformation is dismissed as being "only mathematical, not physical", and professional physicists are accused of failing to distinguish between mere math and genuine physics. Experience has shown that it is never productive to engage such individuals in a discussion of their views, so I don't propose to do that here. I will just repeat my request that you present a justification of your position, not in terms of your personal beliefs and Point of View, but in terms that address the existing literature in reputable published sources. Thanks.Fugal (talk) 02:50, 10 August 2008 (UTC)

Fugal: Well you have indeed raised the level of discourse. I cannot improve upon your own rhetoric: " This is unfortunately an only too familiar attitude among a certain well-recognized kind of individual, who, when pressed to justify his beliefs, falls back on meaningless and misguided assertions. Experience has shown that it is never productive to engage such individuals in a discussion of their views. I will just repeat my request that you present a justification of your position, not in terms of your personal beliefs and Point of View, but in terms that address the existing literature in reputable published sources. Thanks." Despite your excellent advice just quoted, I have made another effort below. Brews ohare (talk) 19:16, 10 August 2008 (UTC)

I don't understand your point. My position is entirely based on the existing literature in reputable published sources, several of which have been provided, in which is presented a view of the subject of this article that is presently not accurately represented in the article. My position is that this is not an insignificant minority or fringe viewpoint, but is in fact a view represented in a significant fraction of the literature, and hence merits inclusion (accurately) in the article. You, on the other hand, are arguing for the exclusion of this view (or a derisive POV dismissal of it), and your basis for this position is (correct me if I'm wrong here) that you believe one view is "physical" and the other view is "merely mathematical". I don't think your personal philosophical ideas about what is "physical" and what is "mathematical" constitute a valid basis for deciding what qualifies for the article. If you could cite some reputable source explaining that one view of this subject is physical and the other merely mathematical, then your position would be legitimate, but you haven't cited any such source. That's why I call your comments "original research". I don't think the attitude will get us very far. I'm trying to articular a well-reasoned argument here, and what I get in return is "I'm paper and you're glue; everything you say bounces off me and sticks to you!". Sheesh.Fugal (talk) 18:48, 10 August 2008 (UTC)

3:2 isn't a consensus at all. Look, this isn't merely a question of the editorial opinion, we're supposed to be making an informed decision about what is NPOV, based on evidence. For example, I did a google on 'centrifugal force', ignoring the wikipedia I got:

• [2] - talks about rotating reference frames
• [3] rotating reference frames
• [4] rotating reference frames
• [http://hyperphysics.phy-astr.gsu.edu/HBASE/corf.html[ rotating reference frames/mach principle
• [5] doesn't exist at all
• [6] rotating reference frame
• [7] copy of columbia encyclopedia reactive centrifugal force
• [8] dunno, vague "inertia"
• [9] rotating reference frame
• [10] spam
• [11] not specified, reactive?
• [12] fictitious doesn't really exist
• [13] rotating frames of reference

Feel free to check these to make sure I've classified them correctly, and do your own googles or other kinds of searches.- (User) WolfKeeper (Talk) 00:00, 10 August 2008 (UTC)

You say "3:2 isn't a consensus at all." Could you expand on that comment? Your views were in the minority, and yet you went ahead and made your change, so I pointed out that you couldn't justify your edit based on a clear consensus of the editors. Now your answer is to tell me that "3:2 isn't a consensus at all". I know it isn't a consensus, even less so for the 2 position than for the 3 position, and yet you implemented an edit based on the 2 position. How do you justify this?

As to your web search results, you unfortunately overlooked one or two, such as

http://math.ucr.edu/home/baez/classical/inverse_square.pdf

http://www.scar.utoronto.ca/~pat/fun/NEWT3D/PDF/CORIOLIS.PDF

http://www-math.mit.edu/~djk/18_022/chapter02/section04.html

http://www.phy.umist.ac.uk/~mikeb/lecture/pc167/gravity/central.html

http://www.cbu.edu/~jholmes/P380/CentralForce.doc

http://www.myoops.org/twocw/mit/NR/rdonlyres/Mechanical-Engineering/2-141Fall-2002/1BEBB815-1441-4698-8D09-3C0E378291F3/0/spring_pendulum.pdf

This is just from about 60 seconds worth of browsing. All of these explicitly present as "centrifugal force" the term arising from the basis vectors changing in space, e.g., stationary spherical, cylindrical, polar, parabolic coordinates. I also found a cite that carefully stated centrifugal force appears only in rotating coordinates, and then proceded to derive the centrifugal force in terms of stationary polar coordinates, so one has to be careful to distinguish what people think they are doing from what they are actually doing.

Careful here. I just gave the top-hits from google, because it's the most unbiased way I know to quickly get a feel for what most people think on a subject (using multiple search engines would improve this further). Clearly there are a variety of views, but the majority are to do with rotating reference frames. Absolutely, absolutely you can come up with many references that talk about other ways of dealing with it, but rotating reference frames seems to be the most common, and this is compatible with the wikipedia's article layout. Your links above don't deal with the commonality angle at all.- (User) WolfKeeper (Talk) 15:46, 10 August 2008 (UTC)

But in this game of dueling web links you are at a distinct disadvantage, because clearly there is a sizeable set of links that advocate each of the views under discussion, i.e., those that think only when the basis vectors change with time can the accelerating terms properly be called fictitious forces, and those who think it is just as legitimate to regard as fictitious forces terms arising from the basis vectors changing in space. This is consistent with my position here; I content that both views of the subject are represented by a significant portion of the reputable sources. Your position, on the other hand, is that ONLY sources that agree with your POV exist, so your task is to deny the existence of all the sources, both on the web and more importantly in published texts, that present the more comprehensive and unified view of the subject. I don't see how exactly you expect to be able to prove the non-existence of things whose existence is really beyond dispute... but I'm keeping an open mind. In view of all the published texts that have been cited, along with the web pages (and the lists could be extended indefinitely), could you tell me how you justify your belief that what I call the more comprehensive view of this subject is NOT represented by a significant number of reputable sources?Fugal (talk) 02:50, 10 August 2008 (UTC)

You'll have to point towards where I made any such claim, because I have never done so, and that your claim that that my "position, on the other hand, is that ONLY sources that agree with your POV exist, so your task is to deny the existence of all the sources", here your assumption of bad faith could not be made any clearer. Indeed I have added links to the articles to other definitions and have discussed the commonalities and differences endlessly.- (User) WolfKeeper (Talk) 15:46, 10 August 2008 (UTC)

Ironically, it was my assumption of good faith that led me to infer that you believe the more unified and comprehensive view is not represented in a significant fraction of the literature. According to Wikipedia policy, the only justification for excluding some view of a subject is if that view is either not to be found in a verifiable reputable source or is only found in an insignificant fraction of the literature (i.e., "held by only one person or a small number of people"). Since your position is that the more comprehensive view is to be excluded from the article (or dismissed as ridiculous sophistry, as it is in the present blatently POV note in the article), I inferred that this was because you, in good faith, were following Wikipedia policy. If I was wrong about that, and if in fact you are trying to keep this view of the subject out of the article even though you acknowledge that it is the view taken by a significant part of the reputable literature on the subject, then I stand corrected. But in that case I think your edits are contrary to Wikipedia policy. Am I missing some subtlety of your position that somehow makes it justifiable?Fugal (talk) 18:33, 10 August 2008 (UTC)

This is not about views, this is about article scope, which in turn is to do with the definition. Since the most common technical definition of the term 'centrifugal force' is to do with rotating frames of reference, the article on that subject should be found here. Your allegedly 'more comprehensive views' are in no way excluded from the wikipedia, and please feel very free indeed to create such an article or add it one other than this one, and I'm sure we would happily link it from this one.- (User) WolfKeeper (Talk) 23:47, 10 August 2008 (UTC)

If you don't mind an outsider's opinion - Statements such as "create such an article or add it one other than this one" imply a sense of ownership in this article, which is understandable given the lengthy history with David Tombe, but not advisable. I think Wolf and Brews should be more willing to accept input from non-fringe, sourced opinions provided by other editors. Also, we already have enough forks from this article; further forking isn't necessary. Plvekamp (talk) 01:20, 11 August 2008 (UTC)

I honestly don't think there's any forks right now at all, nor should there be. If you look a term up in the dictionary, and there's 3 different definitions, then there should be 3 different articles. That's essentially the primary difference between an encyclopedia (which has one article per definition) and a dictionary (which has one article per term). Failure to understand this can cause problems with structuring as well as totally unnecessary battles.- (User) WolfKeeper (Talk) 01:56, 11 August 2008 (UTC)

It's also necessary, but not sufficient to have sourced opinions when editing. We also have to deal with questions of undue weight. And again, failure to understand how some neat idea or other is perhaps being given undue weight is very frequently highly problematic. Still, a well sourced argument should nearly always be included somewhat if it's in the scope of the article.- (User) WolfKeeper (Talk) 01:56, 11 August 2008 (UTC)

Well, hmmm... I really dislike the condescending tone of your replies, but I'll leave you to your views. I still think it might be best for you and Brews to take a break and let some of the other competent editors have a chance. This talk page is a battlefield, and it shouldn't be. Plvekamp (talk) 03:05, 11 August 2008 (UTC)

There is no tone.- (User) WolfKeeper (Talk) 03:15, 11 August 2008 (UTC)

The Anome made a good suggestion, which was to put the treatment that focuses on rotating coordinates into an article entitled "Centrifugal force in Rotating Coordinates", which would then allow the article on "Centrifugal Force" to be more representative of the full range of published views of this subject. I think you're trying to appropriate the top-level name ("Centrifugal Force") for the particular definition of centrifugal force that is of most interest to you, and even restricting it further to one particular view of the fictitious force definition, and relegate the views of that subject that appear in other reputable sources to subsidiary articles, refering to them from this main article with dismissive back-of-the-hand derision. I don't think that is editing in good faith, and I don't think it conforms with Wikipedia policy. The suggestion of The Anome, which received supporting comments from PeR and myself, was more suitable (in my opinion). The "voting" was 3:2 in favor of that proposal over yours and Brews's, but you went ahead and carried out your proposal. I can only repeat that I don't think your edits are justified under Wikipedia policy.

Surely it's not indicative of good faith to try wiggling out of Wikipedia policies, which require accurately reflecting all verifiable views on a subject, by simply declaring that you aren't trying to exclude views, you're just trying to exclude definitions. Please. That argument might have some validity for distinguishing between, say, the reactive force and the fictitious force, but it’s the height of sophistry to try to apply that argument to a restricted view and a more comprehensive view of the fictitious force interpretation. If one "definition" of a topic completely encompasses and subsumes another, to say that the more comprehensive definition is to be excluded from the top-level article on the subject is rather odd. If anything, the more restricted view should be relegated to a subsidiary article. This would seem (to me) to be more rational, and apparently the majority of editors agree.

This is just your normal weasel worded nonsense. The topic and article scope is determined by the definition. If there is more than one definition there is simply more than one article. The definitions here are varied, and this article currently covers the most common definition and hence is the one that people get when the type 'centrifugal force', and I have provided evidence of that above. If you wish to cover other definitions then you need to create or edit new articles.- (User) WolfKeeper (Talk) 09:44, 11 August 2008 (UTC)

Look, I will extend to you the same offer you extended to me. (Please excuse the tone of the following... they are your words.) “Your views are in no way excluded from the Wikipedia, and please feel very free indeed to create such an article or add it to one other than this one, and I'm sure we would happily link it from this one.” How does this proposal strike you? Fugal (talk) 05:05, 11 August 2008 (UTC)

I already did create this article, I defined it and edited it over a long period, and Brews did even more work to it. We did the work. You didn't. But nevertheless I'm quite happy with your suggestion.... but if and only if you can show that the current definition isn't the most common and most notable definition.- (User) WolfKeeper (Talk) 09:44, 11 August 2008 (UTC)

Just out of curiosity, are you consciously mimicking Coriolanus there?

Anyway, there are some genuinely disparate concepts that go under the name “centrifugal force”, but there are also single concepts that have multiple distinct but equivalent (or overlapping) definitions. If a certain individual thing can be (and often is) defined in different ways, these represent different views of the same subject. This is not the same as (say) the difference between the various definitions of “bark”, where one definition refers to the sound of a dog, and another refers to the skin of a tree, and another refers to a boat. Those are distinct meanings, distinct subjects, and properly would deserve their own articles. But when talking about "centrifugal force", defined as an extra acceleration term (treated as a force) that arises when equations of motion are expressed in terms of certain coordinate systems, we don’t really have such different subjects. The various ways of defining the “fictitious force” concept are really just different ways of viewing one and the same subject. It just so happens that one definition, while entirely encompassing the other, also unifies it in a conceptually coherent way with a somewhat larger range of things that also, fortuitously, go under the name of centrifugal force.

Compare this with coriolis force, which is mentioned in the current article 35 times. No one claims that coriolis force is the same as centrifugal force (by any definition), so why is it in this article? Well, presumably it’s in this article to provide context for understanding centrifugal force by comparing and contrasting it with similar and related concepts. So, even though all the discussion of coriolis force in this article is arguably off-topic, no one objects, because it is understood to be providing useful context. But surely it is even more useful to point out that centrifugal force (and coriolis force) are just special cases of a more general unified concept, one that explains how they fit in the context of all fictitious forces, and is consistent with the more sophisticated literature on the subject, and that unifies them with other concepts that also (fortuitously) happen to be known in many reputable sources as “centrifugal force”. Surely if all the discussion of coriolis force is justified based on providing useful context for understanding, then this more fundamental context is even more justified.... and yet the article breathes not one word about it, except to mock it derisively, based on misunderstanding and some original research notion about fictitious forces being "physical". (Apparently the definition of “physical” is “Whatever Brews says it is”.) I really think you two guys should take a break. Read the Wikipedia policy on “ownership” and take the advice to heart.Fugal (talk) 19:56, 11 August 2008 (UTC)

< outdent ------------------------

IMHO any completely general treatment needs to be in fictitious forces.- (User) WolfKeeper (Talk) 21:44, 11 August 2008 (UTC)

And I hope you're not serious about coriolis force being offtopic here. We're allowed to talk about directly related topics in an article and how they relate, and centrifugal force and coriolis forces go around in pairs- they're joined at the hip. And notably the polar coordinate coriolis force and the rotating reference frame coriolis forces are surprisingly different. In polar coordinates the coriolis term is always strictly rotational, whereas in rotating reference frames it can point in any direction at all perpendicular to the frame rotation axis. You'll also notice that there's only one definition of the coriolis force in the coriolis effect article. If you were being in any way consistent you should be commenting on that talk page as well.- (User) WolfKeeper (Talk) 21:44, 11 August 2008 (UTC)

You're misunderstanding his point. He's pointing out how the coriolis force comments provide context, not proposing their removal from the article. His "why is it in this article?" question is rhetorical, not literal. Fugal's not a crank, he has valid concerns. I wish you guys would quit trying to bash every point he makes. Again, I point you towards WP:OWN. Plvekamp (talk) 00:41, 12 August 2008 (UTC)

Nah, not me anyway. It all comes down to scope really. Personalities are usually irrelevant in the long run, the wikipolicies usually work it out in the end.- (User) WolfKeeper (Talk) 03:34, 12 August 2008 (UTC)

Evidently you didn't read what I wrote. I carefully explained the rationale for including comments on the coriolis force in this article (for context and relationships), and you responded by informing me that there are reasons for including comments on the coriolis force in this article. That's non-sequitur #1.Fugal (talk) 03:47, 12 August 2008 (UTC)

That's not a non-sequitor, you were arguing that there was no true relationship between coriolis force and this article, but that there is a stronger one to other forms of centrifugal force. For inertial polar coordinates, the main relationship is a similar name, and the equation looks similar, but really isn't, the symbols mean different things. I don't think that that argument can be sustained. It's at best a family relationship, but coriolis and centrifugal are cohabiting.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

But the core of your argument is that: If a certain individual thing can be (and often is) defined in different ways, these represent different views of the same subject. This is not the same as (say) the difference between the various definitions of “bark”, where one definition refers to the sound of a dog, and another refers to the skin of a tree, and another refers to a boat. Those are distinct meanings, distinct subjects, and properly would deserve their own articles. But when talking about "centrifugal force", defined as an extra acceleration term (treated as a force) that arises when equations of motion are expressed in terms of certain coordinate systems, we don’t really have such different subjects.

I honestly think it's a good definition. It's completely wrong for this article though, if necessary we should move this article to one side, rewriting this article to try to meet it would be nuts. There's also the question of article layout within the wikipedia- what article the users get when they search for particular terms. I personally think that the current choice is a good one.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Then you expounded on how centrifugal and coriolus force are "joined at the hip" and therefore must be treated together, but in the same message you informed us of your humble opinion that any "general treatment" needs to be in the fictitious force article. It's perfectly clear that what you really mean is, YOUR general treatment (mixing centrifugal and coriolus forces willy-skelter) is fine for this article, but the general treatment of centrifugal force contained in the published literature must be excluded from this article. So that's non-sequitur #2.Fugal (talk) 03:47, 12 August 2008 (UTC)

It's not my treatment, it's a perfectly standard treatment, and we're knee-deep in sources that use it, and it appears to be the most common treatment.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Then you scold me for not correcting the mistakes that you and Brews have spawned into a multitude of other related articles. You mentioned the article on the coriolis effect (which is actually less relevant for a variety of reasons), but you might also have mentioned the article on Inertial Frames, etc. But is it really MY fault that you two have spread your sophomoric misunderstandings into all these articles? Science crackpots are always more energetic in the promotion of their crackpottery than other people are in the debunking of it. For you to berate me for not having corrected more of YOUR errors, and to attribute this to "inconsistency" on my part, well, I'd call that non-sequitur #3.Fugal (talk) 03:47, 12 August 2008 (UTC)

You've never actually edited anything, any article in the wikipedia have you Fugal?- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

As to your lastest original research on coriolus force in polar and rotating coordinates, forgive me, but considering that you announced just a few days ago that there is no such thing as three-dimensional polar coordinates (!), I hardly think you're qualified to be lecturing on this subject. Suffice it to say that you have no clue what you're talking about. And let me remind you again that these Discussion pages are not for the discussion of the subject of the article, they are for discussion of editing the article. Your original research (like that of Brews) is irrelevant. Fugal (talk) 03:47, 12 August 2008 (UTC)

I said that the treatments were different, 3D here, 2D in polar coordinate system. Sure you can generalise, but nobody had, and nobody has since come up with a 3D treatment either, it's not difficult, but nobody has. And what original research? The coriolis term in polar coordinates applies only to the angular term, are you seriously arguing that it doesn't? The arguments against doing OR don't apply in talk, we're supposed to be doing research for the article. And you're continuing to fail to assume good faith.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Let's just take stock for a minute: You continue to promote original research, exclude views of the subject that are well represented in a large fraction of the literature on the subject, make edits against the majority of editors, and assert ownership of this article, all in violation of Wikipedia policy. Not bad for a day's work.Fugal (talk) 03:47, 12 August 2008 (UTC)

Let's just take stock for a moment, we're discussing what to do about a difficult topic/article structure in a talk article and OR is perfectly OK in talk (I haven't engaged in it anyway), I've excluded no views at any time, and the wikipedia is not a democracy it works on consensus.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Quite frankly, the more I look at this, the better having more articles looks. Some people have called this fragmentation, and perhaps expect that there would be massive duplication, but in reality that rarely happens, the hypertext nature of the wikipedia makes it easy to link to where detailed treatments are. There's also the user-centered point that people are usually looking for a particular topic that is for them, at their current education level and purposes, and right now we've not catered well to those different levels, and using a more general definition in this article would only make that worse, generality always implies greater complexity, even if it ultimately looks simpler.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Centrifugal force as a physical concept, and as mathematics

Fugal characterizes the view of the present article that centrifugal force is a concept of physics is "original research". That arbitrary statement is rejected by all the citations in the article. There also is another meaning for "centrifugal" sometimes introduced in the limited context of polar coordinates as a mathematical device in that coordinate system. This different usage also is recognized in the article, but is obviously not the subject of the article. A full discussion of this other use is in the article on polar coordinates. What else needs to be said? Do we need a google search to count usages for each interpretation? This article is about the physics, not about math. Does an article on bridgework refer to the Golden Gate?

According to Fugal: "If the basis vectors of a coordinate system change in time, you call the resulting terms appearing in the equations of motion "physical", whereas if the basis vectors of a coordinate system change in space, you call those same terms arising in the equations of motion "mathematical"." And in later discussion, Fugal says: "…those that think only when the basis vectors change with time can the accelerating terms properly be called fictitious forces, and those who think it is just as legitimate to regard as fictitious forces terms arising from the basis vectors changing in space.". This characterization is incorrect. The contrast is not between different types of coordinate system (time varying vs. space varying, or whatever), but between a coordinate system (which provides a mathematical description of observations in space and in time) and a state of motion; and how that state of motion affects one's observations. Thus, an observer in an inertial frame can use a polar coordinate system, and so can an observer in a non-inertial frame. And both also can avoid doing so altogether and use Cartesian coordinates, or arc-length coordinates, or use vector analysis. Whatever approach they choose to describe their observations, it may be pointed out, the inertial observer finds only "real" forces enter Newton's laws of motion (forces that originate between physical bodies), while the non-inertial observer finds it necessary to add fictitious forces, among them the (physical) centrifugal force of this article. That (physical) centrifugal force is not the so-called "fictitious force" of mathematical manipulation. The so-called "fictitious force" of mathematical manipulation occurs for either observer if they choose polar coordinates, and is an artifact of polar coordinates, not a consequence of the state of motion of the observer. If citations are needed to support these explanatory remarks, please see the article proper.

As a mathematical point, the acceleration in polar coordinates is

${\frac {d^{2}\mathbf {r} }{dt^{2}}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+{\frac {1}{r}}\quad {\dot {\overbrace {r^{2}{\dot {\theta }}} }}\quad {\hat {\boldsymbol {\theta }}}$

The term $r{\dot {\theta }}^{2}$ is sometimes referred to as the centrifugal term as a mathematician's idea of picturesque vocabulary. In this equation, one component points in the radial direction (unit vector ${\hat {\mathbf {r} }}$) and the other component in the direction normal to this one (unit vector ${\hat {\boldsymbol {\theta }}}$). These two directions are not along and normal to a particle's trajectory except in unusual cases, such as circular motion about a fixed center coinciding with the origin of the polar coordinates. However, the (physical) centrifugal force (from the particle's viewpoint) is always normal to the particle's trajectory; in general, not in direction ${\hat {\mathbf {r} }}$. Consequently, regardless of the mathematical conceit that the polar equation terms include a "centrifugal term" that terminology is at best poetic license from a physical context based upon the moving particle. Of course, if the polar coordinate system is that of an inertial observer, there is in fact zero (physical) centrifugal force; despite whatever the mathematical conceit chooses to call "centrifugal"; rather, there is a (physical) centripetal force, which is normal to the path of the particle, and not directed toward the center of polar coordinates; that is, unrelated to either term in the mathematical expression for acceleration above. Again, the mathematical conceit is only poetic license.

Again, none of this explanatory material is controversial. For citations, see the articles on polar coordinates, centripetal force, fictitious force and of course centrifugal force. I have had a lot to do with these articles, but I am not citing myself: rather, I'm suggesting you look up the citations in these articles.

Although planar polar coordinates are used in the mathematical example above, the same ideas apply to spherical or cylindrical coordinates. Only the form of the mathematical terms alters; the variously identified, mathematically picturesque "centrifugal" terms still are at best only very indirectly related to the (physical) centrifugal force, except for particular trajectories. Brews ohare (talk) 19:21, 10 August 2008 (UTC)

Let me start by saying that, notwithstanding the attempts to suggest an affiliation with published sources, the narrative above constitutes original research. Brews has energetically filled several Wikipedia articles with his own POV on a set of related subjects, and is trying to leverage off of those to continue enlarging his empire of confusion. I really think it's time for some fresh air on these topics. Plenty of Brews's statements are uncontroversial, but also have no bearing on the issue at hand. The only relevant passage in the above rambling is:

“The contrast is not between different types of coordinate system … but between a coordinate system (which provides a mathematical description of observations) and a state of motion; and how that state of motion affects one's observations.”

That’s utterly incorrect, and contains so many implicit fallacies that it's hardly worth de-constructing it. Look, the “observations” (i.e., raw sense impressions) of an observer are related only indirectly to the higher level conceptual framework of three-dimensional Euclidean space plus time. There’s a huge epistemological distance between primitive “observations” and “states of motion in space and time”, which would take a long time to explain. Fortunately that’s unnecessary, because the theory of epistemology is irrelevant to this discussion. The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force. Every reputable source explains that fictitious forces arise when motions are described in terms of certain kinds of coordinate systems. Needless to say, the very same motions can be described in terms of infinitely many different systems of coordinates, and in some of those systems the absolute accelerations will equal the second time derivative of the space coordinates, whereas in others the absolute acceleration will consist of that second derivative plus some additional coordinate-dependent terms. These are the terms that, if it’s convenient, we may choose to bring over to the other side of the equation and pretend they are “forces”, hence fictitious forces. Brews’s ideas about “observers” versus coordinate systems are original research and don’t belong in Wikipedia. (Those ideas also happen to be quite wrong, but it’s pointless to argue that here. It suffices to say they are original research and hence irrelevant to this discussion.)

Maybe I should also point out that the business about things in curvilinear coordinates only corresponding to fictitious forces in certain specialized configurations is totally bogus. As explained in (for example) Beers and Johnston’s Statics and Dynamics, “The tangential component of the inertia vector provides a measure of the resistance a particle offers to a change in speed, while its normal component (also called centrifugal force) represents the tendency of the particle to leave its curved path.” In general, the inertia vector represents the “inertial forces”. In rectilinear unaccelerated coordinates the inertia vector of a particle always points along the “straight lines” of the coordinate system, so there are no fictitious forces. But if the coordinate system is accelerated or non-rectilinear or both, the “straight lines” of the coordinate system veer off from the inertia vector. If we choose to adopt the fiction that the “straight lines” of our coordinate system are actually straight, then we conclude that the inertial particle is actually accelerating, and we attribute this to the presence of fictitious forces. This is in no way limited to special configurations. We merely consider the inertial tangent vector at each point along the path of the particle.

Furthermore, even under the limited partial approach to dynamics that Brews favors, he understates the ambiguity, because the axis of rotation of a coordinate system (or an observer if you wish) may be continuously changing, both in position and orientation, so the decomposition of the acceleration terms into easily classifiable components involves just as much complexity as it does when basis vectors change in space.

One last point: The equality of the fictitious forces in cases when the basis vectors are changing in time versus when they are changing in space is not at all just a fortuitious coincidence. For example, if a particle is moving absolutely in a circle, and we describe it in terms of a coordinate system rotating at the same speed as the particle, then the fictitious force is due to the changing basis vectors with time. But if we describe the same particle in terms of stationary polar coordinates, in which the direction of the basis vectors change in space, we see that the particle is changing its spatial position with time, and hence the relevant basis vectors are (again) changing in time, and we arrive at exactly the same acceleration term. It’s just two ways of looking at exactly the same thing. But the main point is that this isn’t just Fugal talking, this is the view of the subject taken in a very sizeable fraction of the published literature on the subject.63.24.52.50 (talk) 22:03, 10 August 2008 (UTC)

I am afraid 63.24.52.50 has made only a lot of pronouncements that do not withstand scrutiny and have not been supported by citation. In effect, 63.24.52.50 has not carefully addressed the detailed discussion he attacks (nor the various articles) in an orderly manner. That does not encourage the view that real discussion can take place.

I point at one sentence from the above rant: "The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force." This statement contradicts virtually all references cited in centrifugal force, and if it really is what this editor means, suggests an ignorance of the subject that is quite amazing. Here is only one citation (of many from googlebooks) that contradicts this remark Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…". Brews ohare (talk) 05:26, 11 August 2008 (UTC)

Here's just one more high-quality citation (on top of the seven I've already provided). Take a look at the very clear discussion of this topic in Michael Friedman's "The Foundations of Space-Time Theories", Princeton University Press, 1989. I've not doubt that you will find his ignorance of the subject as amazing as mine.

I looked up Friedman's book, but unfortunately it is not excerpted on googlebooks, so I cannot say whether his understanding or your interpretation of his words will prove the more amazing. Brews ohare (talk) 16:18, 11 August 2008 (UTC)

You say I have not carefully addressed your detailed discussion, but that's not true, I clearly explained above why your discussion is wrong. And your statement that my comments are unsupported by citation is also false, as I'm simply re-iterating the statements for which numerous citations have already been provided. Furthermore, these pages are not for discussions of the subject of the article, they are for discussion of the article itself, focusing on material from verifiable sources. The things that I'm "attacking" are things like your statement in the article where you say the unified and comprehensive modern view of fictitious forces "has no connection to the physics", and that it is purely mathetical rather than physical, or some such nonsense. That is original research (not to mention wrong), and does not belong in the article. I'm not interested in trying to convince a crackpot that he's wrong... I know very well that it's impossible to do. I'm just trying to bring Wikipedia policies to bear, to eliminate the original research that you have inserted into this article. As far as I can tell, you and Wolf are violating those policies, and acting as if you "own" this article. You don't.Fugal (talk) 05:41, 11 August 2008 (UTC)

I have provided chapter and verse on these matters; you have not. Brews ohare (talk) 16:18, 11 August 2008 (UTC)

Brews this assertion of yours: Of course, if the polar coordinate system is that of an inertial observer, is somewhat illustrative of the argument here. The thing is polar coordinates do not necessarily refer to an inertial frame.(TimothyRias (talk) 08:46, 11 August 2008 (UTC))

The word "if" means that the assumption is not necessary, but suppose it were true. Brews ohare (talk) 16:08, 11 August 2008 (UTC)

As I've explained above the physical notion of a frame is inherently local. (this is somewhat obscured by the Poincare symmetry of flat space but is also true in flat space.) Besides an global choice for an inertial frame, you can also make a other natural choice for the local frames. I like to refer to this as the "Muslim" frame choice, namely the one that is always oriented in the direction of a central point (Mecca), in this choice the centrifugal term in the polar coordinates gets a very clear physical interpretation as the centrifugal force. As for your assertion that the centrifugal term in polar coordinates "only arises as a result of mathematical differentiation." Yes, thats true, but the same is true for the centrifugal term in a rotating frame of reference. The centrifugal force always arises as extra terms introduced in the covariant derivative. (TimothyRias (talk) 08:46, 11 August 2008 (UTC))

In an inertial frame of special relativity, which includes Newtonian mechanics as a special case, there is zero physical centrifugal force, regardless of the coordinate system selected. There is, however, inward normally directed centripetal force if the observed trajectory is curved. In general relativity, I do not understand the theory well enough to say exactly what the situation is. However, general relativity is outside the scope of the article. Do you need citations to support my statement here? Brews ohare (talk) 16:08, 11 August 2008 (UTC)

In general relativity (or in any covariant approach to classical mechanics) there never is any physical centrifugal force. (there also is no physical gravity) All terms normally called centrifugal force are just acceleration terms for some particular choice of coordinates. (or alternatively choice of local frames, coordinates are not really necessary but tend to be a convenient way to define the local frames.) And this really is not beyond the scope of this article because this epistemoligical lesson (which doesn't really need GR/the einstein equations) has long since trickled back into out understanding of fictitious forces. Among others this has lead to the realisation that there is really logical difference between the centrifugal force as it appears in rotating frames and as it appears in polar coordinates. Both may be interpretated (in that is all that is happing; interpretation) as fictious forces resulting from a certain choice of local frames and insisting that the connection remains trivial. (TimothyRias (talk) 08:32, 12 August 2008 (UTC))

Timothy: To expect the notions of general relativity to be understandable by use of a few sentences and no background or mathematics is to make a mockery of a lifetime's work by many. I cannot see how introduction of these concepts in an unsupported zero-context fashion can assist the reader without general relativity background. To do justice to such a treatment, you should write a stub about it, where appropriate space and citations can be presented. It can be linked to the present article for those with the interest and capacity to pursue this topic. Brews ohare (talk) 14:58, 12 August 2008 (UTC)

My main point is that you should not be stating (here or in the polar coordinates article) that there is no physical connection between the centrifugal term in polar coordinates and that in a rotating frame, as physically they are in fact pretty much the same. You seem very keen on stressing that there is no connection. I'm not sure why. A much simpler approach would be to leave it in the middle what the connection between the two is and simply not that both are the centrifugal force. This is the approach of many notable textbooks, so why should it be so bad for wikipedia. (TimothyRias (talk) 15:53, 12 August 2008 (UTC))

Within classical mechanics the two concepts are completely different. I cannot say what happens in general relativity. However, it does not seem to serve the reader to suggest they are the same concept in an article that has no pretensions at general relativity, when in this limited context the two ideas are totally separate, both logically and physically.

That clear distinction makes me wonder if you are not smearing together separate ideas in general relativity as well, where matters are much more likely to become murky as not only the observer has the (mathematical) opportunity to change local coordinate systems, but space-time also is local and curvilinear for physical (not mathematical) reasons. The two aspects might become coupled, but I frankly am skeptical that they are truly identical even in this context. For example, the Schwarzschild solution uses polar coordinates, showing that a choice of coordinate systems still is possible in general relativity, and space-time geometry does not tie one's hands entirely. After all, it would be odd if matters that were logically distinct and with different origins (arbitrary naming in the mathematical formula for acceleration of a few coordinate-system-dependent terms that are independent of any particular state of motion vs. physics involving state of motion) were to become exactly the same thing in a more general context.

Anyway, that connection is best left for a separate article where the merging of two unrelated concepts can be shown to occur as gravity becomes stronger (supposing that actually to be the case). Brews ohare (talk) 18:58, 12 August 2008 (UTC)

With this statement as background, in a curvilinear coordinate system, as you note, there is always some metric tensor, not just the simple diagonal tensor of ones found in the Cartesian system. These functions invariably lead to "fictitious forces" in the picturesque mathematical sense. However, they do not lead to physical centrifugal force in inertial frames. The polar coordinate example spelled out in detail here is a particular example with everything worked out in detail. Do you need citations on this? Brews ohare (talk) 16:08, 11 August 2008 (UTC)

Your concept of "physical fictitious forces" is pure original research, as is your belief that there are “physical fictitious forces” and “mathematical (or poetic) fictitious forces”. I don’t believe you can cite any reputable source to back up this “physical versus mathematical” dichotomy. This alleged dichotomy is, of course, quite common among a certain class of original thinkers, but it doesn’t appear in reputable sources, so it doesn’t belong in Wikipedia. All reputable sources agree that fictitious forces are not really forces at all, let alone “physical forces”. They are extra acceleration terms (beyond the second time derivative of the space coordinates) that appear when the absolute acceleration of an object is expressed in terms of various coordinate systems. There's nothing more or less "physical" about fictitious forces depending on whether they are due to basis vectors changing in time or in space (or both). You've been provided with numerous high-quality sources that explain all this. I don't think your repeated denials, based on your original research regarding "physicality" versus "mathematicality", are very productive.Fugal (talk) 19:28, 11 August 2008 (UTC)

We may have a semantic problem here: I have used the terms "physical" and "mathematical" to distinguish between the fictitious force due to a state of motion and that fictitious force due to the mathematical exercise of identifying a few terms in the mathematical expression for acceleration as expressed in polar coordinates regardless of the state of motion. I thought this meaning was pretty clear, but maybe now it is is clearer still? So your remarks about "All reputable sources agree that fictitious forces are not really forces at all" are wide of the mark, as I do not disagree at all with the fact that what I have called physical fictitious forces are fictitious forces in the sense of state-of-motion, eh? However, I believe your point is that both the type of fictitious force I have called "physical" and the type I have called "mathematical" are the same. I already have provided you with citations that indicate that they are not the same, and that what I have called "physical fictitious forces" that is , fictitious forces related to state-of-motion disappear in inertial frames, while the "mathematical" type of fictitious forces do not. Below I repeat an exchange with a citation that you have chosen to ignore:

Fugal: "The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force."

Brews_ohare: Here is only one citation (of many from googlebooks) that contradicts this remark Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…".

Here's a few more: "The reason the centrifugal force is fictitious is because it involves a noninertial frame of reference" Bergethon The physical basis of biochemistry

"Centrifugal force is a fictitious or "phony" force that we introduce to correct for the acceleration of our rotating frame of reference" Oliver: Collected papers

"The centrifugal and Coriolis force are called fictitious forces because they are needed only by an observer in a rotating reference frame." Armstrong Mechanics waves and thermal physics

"In a non-inertial rotating reference frame, centrifugal force is defined as a d'Alembertian inertial force, a fictitious force acting on the moving body." Sneddon Encyclopaedic Dictionary of Mathematics for Engineers and Applied Scientists

"If we insist on treating mechanical phenomena in accelerated systems, we must introduce fictitious forces, such as centrifugal and Coriolis forces." Meirovitch Methods of Analytical Dynamics

It is clear to me that these quotations directly and unequivocally contradict your claim as to the irrelevance of state of motion to the concept of fictitious forces. Brews ohare (talk) 06:11, 12 August 2008 (UTC)

Personally, I've never seen a constant speed rotating polar coordinate reference frame being discussed in a book, so I'm not sure it's particularly notable, but I've no objection to it having a section, provided it's a short one, and it's well referenced, since it would meet the definition.- (User) WolfKeeper (Talk) 10:08, 11 August 2008 (UTC)

Fugal's positions

Fugal

My position is that [the mathematical terminology for certain terms in the acceleration of a body as viewed in curvilinear coordinates] is not an insignificant minority or fringe viewpoint, but is in fact a view represented in a significant fraction of the literature.

Brews-ohare

My view is that it is not a viewpoint, but a different use of terminology. That these terms constitute a different usage is shown (in part) by the fact that these terms are an artifact of the coordinate system, and therefore appear in every state of motion, every frame of reference, in both inertial and non-inertial frames. That is not true of centrifugal force as defined in this article. As a different subject, a reference to this alternative usage is all that is needed. I believe Wolfkeeper has the same view. Brews ohare (talk) 14:41, 12 August 2008 (UTC)

Fugal

The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force.

Brews_ohare

Here is only one citation (of many from googlebooks) that contradicts this remark: Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…". Brews ohare (talk) 15:55, 12 August 2008 (UTC)

Fugal

Also, the acceleration terms appearing with certain coordinates do not depend on the presence or state of motion of any observer.

Brews_ohare

My point exactly: however, centrifugal force (as used in this article) does depend on the state of motion of the observer. In Newtonian mechanics, a state of acceleration (a state of motion) identifies a non-inertial frame of reference. A citation: "If we insist on treating mechanical phenomena in accelerated systems, we must introduce fictitious forces, such as centrifugal and Coriolis forces." Meirovitch Methods of Analytical Dynamics . Brews ohare (talk) 15:37, 12 August 2008 (UTC)

Fugal

Fictitious forces are, by definition, artifacts of a particular choice of coordinate systems. They are all "mere mathematical manipulations".

Brews_ohare

In fact there are two meanings for fictitious force: one depends on the state of motion of the observer (see above) and one is a mathematical act of poetic license, applying picturesque language to certain terms that arise in the acceleration when calculated in curvilinear coordinates, without regard for the observer's state of motion. Are we going 'round and 'round here?!? Here are two quotes relating "state of motion" and "coordinate system":

We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted ${\mathfrak {R}}$, is said to move with the observer.… The spatial positions of particles are labelled relative to a frame ${\mathfrak {R}}$ by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame ${\mathfrak {R}}$, can be considered to give a physical realization of ${\mathfrak {R}}$. In a frame ${\mathfrak {R}}$, coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

— Jean Salençon, Stephen Lyle Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9

and from J. D. Norton:

…distinguish between two quite distinct ideas. The first is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events in spacetime neighborhoods. The second, the frame of reference, refers to an idealized system used to assign such numbers … To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions. … Of special importance for our purposes is that each frame of reference has a definite state of motion at each event of spacetime.

— John D. Norton: General Covariance and the Foundations of General Relativity: eight decades of dispute, pages 835-836 in Rep. Prog. Phys. 56, pp. 791-858 (1993).

Assuming it is clear that "state of motion" and "coordinate system" are different, it follows that the dependence of centrifugal force (as in this article) upon "state of motion" and its independence from "coordinate system", while the mathematical version of "fictitious force" has exactly the opposite dependencies, indicates that two different ideas are referred to by the same terminology. The present article is about one of these two ideas, not both of them.

In summary, the article has focussed on the physical view based upon "state of motion", while Timothy and Fugal are more focussed on the mathematical manipulations within a curvilinear coordinate system, independent of the observer's state of motion. Some arguments given are more or less correct from one stance, some from the other, but the article quite properly treats the usual "state-of-motion" meaning, and refers the other to the appropriate mathematical treatment of whatever coordinate system you might like to pick, e.g. polar coordinates.

I have rewritten the section on "Aside on polar coordinates" in a way that I hope meets everybody's approval.

Brews ohare (talk) 16:54, 13 August 2008 (UTC)

Some comments on recent edits

There is something wrong with the following line introduced in one of the recent edits (at the end of first paragraph of the "Centrifugal force in general curvilinear coordinates" section):

The component of any such fictitious force normal to the path of the particle and in the plane of the path’s curvature is then called centrifugal force.

This attempt at a general definition seems to fail to include the case of a rotating reference system (the one case we all agree is the most commonly treated one), in which the centrifugal force is not necessarily normal to the trajectory of a particle. It would also include the coriolis force in such a case, since that is always perpendicular to the particles velocity. (well as long as the particle is moving in a plain perepedincular to the axis of rotation, anyway.) The sentence cites a source which I haven't been able to check. But I highly doubt that this sentence is conveying what that text was saying. (TimothyRias (talk) 14:00, 14 August 2008 (UTC))

The cited reference is Beers and Johnston’s "Statics and Dynamics", which says “The tangential component of the inertia vector provides a measure of the resistance a particle offers to a change in speed, while its normal component (also called centrifugal force) represents the tendency of the particle to leave its curved path.” In the general treatments of this subject it is recognized that the decomposition into the commonly named components called centrifugal, Coriolis, Euler, and the "fourth" fictitious force that appears in the general case becomes ambiguous. Remember, the Christoffel symbols are not even tensors, and the mapping of its various components (in terms of various coordinate systems) to the simplistic categories of centrifugal, Coriolis, etc., is ambiguous. The approach most commonly taken is as described in Beers and Johnston and represented in the article. [The ambiguity is already obvious in the simple example given in the article, of a particle moving in a circle, where the extra terms consist of mr(w+W)^2. This is the most natural and meaningful quantity, since w+W is the absolute angular speed, whereas w and W individually are artifacts of our choice of coordinate system. If we expand the expression it becomes mrw^2 + 2mrwW + mrW^2, in which case we could call mrW^2 the centrifugal force and 2mrwW the Coriolis force and mrw^2 a contribution of the fourth fictitious force. But none of these is individually meaningful (except by convention for a given choice of coordinates). Only the combination of all of them has absolute significance.]

By the way, the sentence that worries you is saying essentially the same thing as the later sentence at the end of the section (which was adapted from the pre-existing text, which talks about referring the fictitious forces to the osculating frame of a curved path. If that view was unobjectionable before, it ought to be unobjectionable now. The only difference is that I've actually provided a reference to a reputable source.Fugal (talk) 14:48, 14 August 2008 (UTC)

Centrifugal force in general curvilinear coordinates

The way this new section was introduced has a number of shortcomings, as does its content.

As to its manner of introduction, it was placed on the page without any discussion on this talk page, despite a very careful attempt on my part to resolve a number of issues on this page. My efforts, involving a simply stated contrast of views, my citations supporting these views, and my attempt to resolve these matters in a compromise, all were ignored entirely.

As to its content:

The subsection states:"This article is primarily concerned with the view of centrifugal force (and other fictitious forces) presented in introductory texts, which typically rely on intuitive though somewhat imprecise notions of concepts such as reference frames, forces, observations, and so on. In more advanced and abstract treatments of dynamics, the definitions of all these things are more general and explicit." I interpret these remarks as a dismissal of all citations opposing the author's views, which citations are in fact very numerous and include major authorities in the field such as Arno'ld, Lanczos, Landau and Lifshitz, Born, Einstein, Newton, etc. This statement is an unsupported and unsupportable slap at most of the texts on the subject, and should be deleted.

The article states: "In particular, an inertial coordinate system is defined as a system of space and time coordinates x1, x2, x3, t in terms of which the equations of motion of a particle free of external forces are simply d2xj/dt2 = 0.[51] " This definition of an inertial frame is not that of special relativity or of Newtonian mechanics. A clear counterexample is simply a frame moving with an accelerating particle: in this frame the second derivatives of position of this particle are all zero, but no-one would call this an inertial frame. The reference provided for this incorrect viewpoint is [Friedman] without page number or quotation. Given this editor's proclivity for taking things out of context, and given the clear citations for the contrary standard definition at inertial frame, this revisionist version of "inertial frame" should be removed from the page.

The article states "When equations of motion are expressed in terms of any non-inertial coordinate system (in this sense), extra terms appear, called Christoffel symbols." It is not helpful to introduce out of the blue an advanced concept like Christoffel symbols without explanation (or definition). Also, this article is not the place to introduce these technicalities, which belong (if they do belong) in a more technical article devoted to the subject of dynamics in curvilinear coordinates. It might be noted that a very large fraction of books on this subject, advanced and simple, never even mention Christoffel symbols, which apparently are not critical to the subject of centrifugal force.

The article states "Strictly speaking, these terms represent components of the absolute acceleration (in classical mechanics), but we may also choose to continue to regard d2xj/dt2 as the acceleration (as if the coordinates were inertial) and treat the extra terms as if they were forces, in which case they are called fictitious forces.[52] " The Christoffel symbols are connected to "forces" only in the limited mathematical sense of reinterpretation of mathematical terms by moving them from one side of the equation for acceleration to another, and have absolutely no connection to the state of motion of the observer. The reference cited says nothing about Christoffel symbols, and simply points out that the "mathematical device" of transferring terms from one side of an equation to the other can be described as introducing "fictitious forces". These authors are very, very careful to distinguish between the interpretation of this device in an "inertial frame" and its interpretation in a rotating frame. These sentences in this subsection distort the position of the cited source, and should be removed.

The article states "The component of any such fictitious force normal to the path of the particle and in the plane of the path’s curvature is then called centrifugal force.[53]" Timothy has objected to this statement, and Fugal's support for this statement is (i) a quotation stripped from context and (ii) some unsupported remarks about Christoffel symbols and (iii) some remarks about ambiguity and "absolute significance" in the case of circular motion that are nonsense. One problem with this sentence is that what is called centrifugal force depends on the state of motion of the observer of the particle, and so cannot be categorically given a unique definition independent of the observer.

The subsection also contains incomplete references (no links, isbn's, or page numbers), mainly to subsidiary topics (like curvilinear coordinates as an abstract mathematical topic, unrelated to physics) that are peripheral to the main thrust of the arguments. There are no definitions of terms and notation, and equations are poorly formatted.

I have removed this subsection. Before it is reintroduced, I suggest a return to the discussion opened on the talk page under the heading "#Fugal's positions", where simple courtesy demands formal response. At a minimum, there must be a proper discussion of the issues. Brews ohare (talk) 15:51, 15 August 2008 (UTC)

I think the topic is just about valid, since it discusses relationships between rotating reference frames and curvilinear reference frames which don't necessarily rotate. However, I think I would argue that this section is too large, and hence giving undue weight. I've also pruned many of the unsupported claims that rotating reference frames are in some sense vague or merely intuitive, I don't believe that, if properly defined, that that is true in any way, and as it was unreferenced, I removed it. If it can be referenced (and please make it a good reference to a factual way that this is true, rather than somebody talking hyperbolically in a book), then it may of course be reintroduced.- (User) WolfKeeper (Talk) 17:07, 15 August 2008 (UTC)

Brews, Please read WP:OWN. Demanding that people discuss additions on the talk page first is a clear sign that you have become too attached to the article. This is Wikipedia. Editors are encouraged to be bold. I am no expert at curvilinear coordinates, so I will say nothing about the actual content of the edit. --PeR (talk) 18:02, 15 August 2008 (UTC)

Mediation?

I think it might be helpful to get some fresh perspectives on this article. Several people have suggested that two individuals are showing signs of "ownership", and I have to agree. It seems that two editors have a very specific idea of exactly what this article must say, no more and no less, despite well sourced inputs from other editors. These two editors have made edits when opposed by the majority of other editors, and have repeatedly claimed ownership of this article (pointing out that THEY created it, THEY put the work into it, so any other views MUST go into other articles, not this one.) How does one go about requesting mediation in cases such as this? Fugal (talk) 21:40, 15 August 2008 (UTC)

Well, I don't know. If we were really trying to own it, we would have deleted it out of hand or moved it to a more appropriate article. I do know that you have just removed multiple largely non controversial edits, and reinserted several unreferenced statements, and made notation changes so that they don't match the rest of the article and so forth.- (User) WolfKeeper (Talk) 22:04, 15 August 2008 (UTC)

I would like to remind you that a precondition for editing the wikipedia is that other people can make changes to your work, and that you have to follow the policies on verifiability.- (User) WolfKeeper (Talk) 22:04, 15 August 2008 (UTC)

Coming from you, that is simply laughable. The only edits I have made are (1) removing the phrase referring to "out of body experiences", and (2) re-writing a brief seven-sentence ASIDE to make it more general and accurately reflect numerous referenced reputable sources. It was summarily deleted. And now you remind me that I must allow people to make edits and mind verifiability. Honestly, and I say this in complete seriousness, I believe you and Brews and genuinely lost your minds. Seriously. I think dealing with David Tombe has driven you both into clinical states of dementia. I know neither of you can see this, but others around you can see it very plainly. For your own good, take a break. Look, if it helps any, I'll promise not to have anything more to do with this article. Seriously, you two need to take a break. Seriously. S.e.r.i.o.u.s.l.y. Fugal (talk) 00:23, 16 August 2008 (UTC)

I find it impossible to reconcile your description of your edits with [14] which appears to be a general revert. And you are violating both the letter and spirit of WP:CIVIL with your above comments, and in the wikipedia this will typically overwhelm any genuine point or grievance you may have.- (User) WolfKeeper (Talk) 00:55, 16 August 2008 (UTC)

As a case in point, note the latest challenge from one of these owners: "If it can be referenced (and please make it a good reference to a factual way that this is true, rather than somebody talking hyperbolically in a book..." I think this gives a good idea of what is going on here. Since numerous references from the most reputable published sources have been provided for the views that this editor wishes to keep out of the article, he now demands that a reference be provided, but not just "somebody talking hyperbolically in a book". I think that speaks for itself. Clearly this editor will not accept any view that differs from his pre-conceived views. He simply dismisses all published works from reputable sources as "somebody talking hyperbolically in a book". And this is the more reasonable of the two owners. Some kind of mediation is badly needed here.Fugal (talk) 21:49, 15 August 2008 (UTC)

I would like to remind you that the edit you made essentially implied that it was impossible to precisely define a rotating reference frame, and the edit was unreferenced. Unreferenced material can be removed at any time in the wikipedia. If you HAVE a reference for this, then produce it and you can reinsert it.- (User) WolfKeeper (Talk) 22:04, 15 August 2008 (UTC)

Centrifugal force in polar coordinates

I have attempted to eliminate erroneous concepts that fail to distinguish between coordinate systems and reference frames. Quotations with relevant citations are given earlier on this talk page, and Fugal has been invited several times to comment. (For example, see Fugal's positions, and Fugal's sources). All the math and the statements made in the new article are non-controversial and are supported in mathematical detail by the citations. Brews ohare (talk) 22:45, 15 August 2008 (UTC)

In this connection, I suggest that the links to Stommel and Moore be followed and the work read closely. These authors are very, very careful to distinguish the cases of polar coordinates in inertial frames from that in non-inertial (rotating) frames. For example:

p. 4 "Sometimes the additional terms in the accelerations are transposed to the right side of the equation, leaving only the double-dotted terms on the left. So the acceleration terms on the right look like forces. They even acquire names such as "centrifugal force." As convenient as this may be from an intuitive, practical point of view, this transposition...can lead to confusion. ...So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system. p. 26: "you should be very clear in your mind not to confuse the idea of a plane polar coordinate system fixed in inertial space with the idea of rotation of coordinates. This chapter is entirely tied to one particular reference frame, fixed in inertial space – so don't get mixed up now, or later when we introduce rotating axes." p. 36: This immediately gives the components of acceleration in polar coordinates, [lists equations] Remember once again that all this has nothing to do with rotating coordinate systems. We are in a polar coordinate system that is at rest with respect to the stars.... Brews ohare (talk) 23:49, 15 August 2008 (UTC)

Scope of the article & disambiguation and article name

OK, we're still battling the scope issues I think.

The disambiguation page has 4 different definitions:

• physics: In a rotating reference frame, Centrifugal force is an apparent force that seems to push a body away from the axis of rotation of the frame and is a consequence of the body's mass and the frame's angular speed.
• physics: In circular motion, the reactive centrifugal force is a real force applied by the accelerating body that is equal and opposite to the centripetal force that is acting on the accelerating body.
• physics: In polar coordinates, the apparent radial force that seems to push a rotating body away from the centre of rotation of the frame and is a consequence of the body's angular speed around the origin.
• in everyday understanding, centrifugal force is the effect that tends to move an object away from the center of a circle it is rotating about (i.e. inertia).

I'm hoping that this classification is fairly non controversial (although other people may want to add other examples of centrifugal force as well perhaps, and by all means).

I would like to move this (Centrifugal force) article to Centrifugal force (rotating reference frame) and I would propose to leave a redirect to it from Centrifugal force. This better clarifies for the users what the article is about in the name, and gives us more flexibility to change things if that should be decided later. It also gives us a specific name to link to from Coriolis effect that refers directly to the associated type of centrifugal force that that article is associated with.

I'm hoping that this too is relatively non controversial, but I welcome comments. I feel that there are people who wish to put a more general article at Centrifugal force, if anything this renaming should make that easier to do later if this type of article were created and there was consensus to change the redirect.- (User) WolfKeeper (Talk) 22:57, 15 August 2008 (UTC)

I support this change. However the description:

• physics: In polar coordinates, the apparent radial force that seems to push a rotating body away from the centre of rotation of the frame and is a consequence of the body's angular speed around the origin.

needs to be modified. It could read:

• physics: In polar coordinates, one of several terms that appear when acceleration of a particle is expressed in polar coordinates. These terms are mathematically related to the change of coordinate system basis vectors with change in the coordinates themselves.

Unfortunately, the belief advanced by some editors that these terms are closely related to physical phenomena are unsupported by close reading of the authorities on the subject. Brews ohare (talk) 23:27, 15 August 2008 (UTC)

You should discuss those IMO relatively minor changes to the terms used on the talk page of the disambiguation page if you wish to make them, and perhaps approach to the optimally imperfect phraseology can be made.- (User) WolfKeeper (Talk) 23:52, 15 August 2008 (UTC)

OK; Whether or not my view is accepted, the disambiguation I've suggested is beyond controversy, and any thoughts about physical interpretation can be left to the article proper. Brews ohare (talk) 23:54, 15 August 2008 (UTC)

Nah. ;-)- (User) WolfKeeper (Talk) 00:27, 16 August 2008 (UTC)

Given that there were no dissenting voices I have done the move.- (User) WolfKeeper (Talk) 14:33, 20 August 2008 (UTC)

Polar coordinates

While the curvilinear coordinates can be seen as a generalisation of the rotating reference frame, the polar coordinates section talks only about inertial frames of reference. It therefore isn't the same centrifugal force, and very probably needs to go.

The difference is obvious- if an object is stationary in polar coordinates, then there is no centrifugal force. In a rotating reference frame, there is a centrifugal force when the object is stationary. They are not the same thing at all, and the associated coriolis forces are completely different also, they act in different directions and are of different magnitudes.

More or less polar centrifugal force is to rotating reference frame centrifugal force as the magnetic force is to electrostatic force. And they are special cases of curvilinear equations and electromagnetism, respectively.

Magnetism and Electrostatics have almost the same form of equations, but they are completely different in reality, and the same thing applies here. Too many people aren't really getting this. Similar mathematics is just not enough.

Just like I don't think we would really want a big section on magnetism in an electrostatics article, we don't really want a big section on polar coordinates in a rotating reference frame article.

But we also don't really need too much on general electromagnetism in a magnetic article either, the curvilinear stuff is a bit OTT at the moment, it needs to mostly go in its own article, but in my opinion having something here is quite valid.- (User) WolfKeeper (Talk) 02:40, 16 August 2008 (UTC)

I am confused by your remarks. Are they about the subsection Centrifugal_force#Centrifugal_force_in_polar_coordinates? This subsection does refer to centrifugal force. It derives this force for a rotating frame, using polar coordinates in that frame. The resulting centrifugal force is Ω² r directed outward, which I believe you will agree is no surprise. The discussion parallels very closely the discussion cited in Stommel and Moore. Brews ohare (talk) 05:21, 16 August 2008 (UTC)

Centrifugal force in general curvilinear coordinates (again)

Wolfkeeper: You do not seem to have read my comments upon this wording when it first appeared. There are defects that must be fixed. Whether or not you have taken the time to really look at it, this section contradicts some very basic facts, and is completely opposite to much of what is said in the Polar coordinate version, which is, after all, a special case of curvilinear coordinates. It also only appears to have citations, as many of the citations apply only to peripheral matters and do not document what is asserted in the sentence they are attached to.Brews ohare (talk) 16:03, 16 August 2008 (UTC)

This section has been completely rewritten and the relevant math included. An excellent exposition by Silberstein with a full view on google straightens out the entire mess. Brews ohare (talk) 15:41, 17 August 2008 (UTC)

Besides the text NOT being available on google books. (but elsewhere online), I am not sure that a text from the period (1922!) that the interpretation of GR was still under hot debate, and well before the proper definition of frame in GR (Weyl 1929) will really help resolve the issues. Since that text was written our understand and interpretation of what was really going on has increased dramatically. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

When I click on the link provided above (Silberstein), the book immediately opens. Of course, the general theory of relativity itself has evolved over time. Please indicate, however, how Silberstein's discussion of the issue at hand (lumping different types of forces together and calling them all by a single name: "fictitious forces") has "evolved". Notice that he treats the case of polar coordinates explicitly as an example of the general approach. Brews ohare (talk) 15:32, 18 August 2008 (UTC)

"State of motion" vs. "coordinates"? It is all about frames.

I find the difference being made made between "coordinate" and "state of motion" fictious forces being made in this article to be somewhat artificial. It seems to complete ignore the fact both just define a particular frame. (Or rather tetrad as the properly defined concept is called.) (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

If your introduction of the term tetrad indicates an aim to provide a discussion valid for general relativity, please say so. I'd be happy to see such a thing, but in another article.

Your description of "artificial" distinctions is dealt with in more detail shortly. Brews ohare (talk) 16:22, 18 August 2008 (UTC)

The introduction of no-flat geometries in general relativity has forced us to reevalute what exactly we mean with frame since the old naive approach often figuring hypothetical physical realizations using rigid rods and clocks. It was realized that the proper way to fix a frame is to assign an "state-of-motion" and orientation to each event in spacetime. The mathematical way to describe such an assignment is a tetrad. (note that a state of motion is described by a single timelike vector and an orientation by three spacelike vectors, togehter they form an orientation in spacetime.) This concept in itself has nothing to do with GR, it is just the proper description of something which wasn't very rigidly defined in the past. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Hi Timothy: I have looked at the articles Frame fields in general relativity Dirac_equation#Curved_spacetime_Dirac_equation and Atlas (topology) in pursuit of more information about your remarks above. My reaction (please excuse me) is that this material should not affect this article on this basis:

1. It is (I'd say) too abstruse for simple exposition.
2. It is not used by the vast majority of textbooks or monographs, even at a graduate level. Which is to imply that the views I have expressed may be less profound, but are definitely more accessible and in common use throughout physics, engineering, robotics and meteorology.
3. A careful exposition of these ideas on Wikipedia requires several new pages to be written by an expert. The existing pages Frame fields in general relativity Dirac_equation#Curved_spacetime_Dirac_equation and Atlas (topology), while pertinent, are not oriented toward the discussion of fictitious forces, and their application to this topic is presently not developed.

Just what the implications of these topics may be for the topic of fictitious forces is unclear. I have no doubt that one can assign a tetrad, and a team of observers already has been suggested as more appropriate than a single observer at Observer (special relativity) and family of observers. I am not clear that this elaboration of the term "observer" has any direct impact on what has been said in the present article. We have your exposition above, but you have not shown its implications for the topic of fictitious forces. Are you interested in fleshing all this out with appropriate references and quotations in some kind of accessible language? Brews ohare (talk) 16:11, 19 August 2008 (UTC)

I'm not advocating talking about tetrads in this article. That would way too technical for the intended audience. The main point I'm arguing is that the article should not try so hard to explain the perceived difference between "state-of-motion" and "coordinate" fictitious forces. Especially since the last isn't anymore related too coordinates than the first. It is also related to the use of a different frame. But one that fails to be inertial in a slightly different way, then the first. I guess the main implication for this article is that you should not be making a fuss about such a subtle difference. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

First of all let me point out that "state of motion" alone is not enough to get centrifugal force even in a rotating frame, an orientation also needs to be specified. (An easy example of this is given by the origin in a rotating frame. Its state of motion is "stationary", centrifugal force is caused by the fact that the orientation of the origin is continuously changing (with respect to the orientation defined in an "inertial" frame). Specifying a "state of motion" and orientation at every point in space, is in fact specifying a tetrad.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

There is no statement that "state-of-motion" is "all that is needed". The statement is rather that "state-of-motion" is a factor deciding whether or not the fictitious force is zero in "state-of-motion" fictitious forces, while "coordinate" fictitious forces can be non-zero even in an inertial frame of reference. That is not an artificial difference. Brews ohare (talk) 15:23, 18 August 2008 (UTC)

A frame being inertial is not in any way fixed by the state-of-motion of any single observer. (again envision the observer at the center of a rotating frame, his state-of-motion is constant, yet the frame is not inertial.) It is determind by the state-of-motions and orientations of ALL events being "aligned". In traditional classical mechanics the alignment of the orientations was pretty much always assumed (implicitly exploiting the poincare symmetry of flat space and hence somewhat of a mathematical slight of hand), and kept in dependent of the choice of coordinates. Doing this in polar coordinates leads extra terms in the velocities and accelrations (as we all know well). Choosing to view these extra terms as fictitious forces is related to a certain choice of orientations which are not aligned, just as choosing to view the extra terms in a rotating frame as fictitious forces is related to the states-of-motion not being aligned. Both choices are a deviation from the inertial frame. The first one is just one that you (seem to be) are not familiar with. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Hi Timothy: Well again I'd say a team of observers already has been suggested as more appropriate than a single observer at Observer (special relativity) and family of observers. I am inclined to discount this notion that the whole idea of a connection between "inertial frame" and "state-of-motion" is disqualified because a single observer can't determine the meaning of the word "orientation" and needs a team of observers to do so. The observer in Newton's example of two tethered rotating spheres had no difficulty determining they were rotating, and not the fixed stars. And Newton's observer did not need a coordinate system, never mind a tetrad. Whatever the tetrad approach may bring to this problem, it has to result in pretty much the same picture. That means, among other things, that centrifugal force vanishes in inertial frames, in stark contrast to the "coordinate" version of centrifugal force, which is non-zero in inertial frames. Your definition of "observer" may be too narrow to encompass the classical observer, and replacing that observer by a team of observers has little consequence for the present article. Brews ohare (talk) 19:23, 19 August 2008 (UTC)

The thing is that you already need a team of observers to describe the states-of-motion in a rotating frame. We are however very much used to exploiting the flatness of space to generate such a family from the state-of-motion and orientation of a single observer. This method is very much embedded in the classical idea of a global frame as Newton was using. But even a global frame needs to specify its orientation. (although this is usually done implicitly as a hidden assumption.)

I'd also like to stress that consider the acceleration terms in polar coordinates is connected to attaching the coordinates to a non-inertial frame. Just like viewing the acceleration terms in a rotating coordinate system as ficitious forces is related to attaching them to a rotating frame. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

A practical manner of assigning a tetrad is by first defining a coordinate system, and then using the coordinates basis at each point to define the tetrad. (This approach is commonly taken in GR.) An other approach, frequently taken in classical mechanics, is to assign assign "states of motion" everywhere but orientations only at one point in space, and using parallel transport assisted by flatness of space to extend this orientation to the entirity of space. This approach leads to a choice of orientation that is independent of the choice of spacial coordinates. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

Depending on the problem being solved, of course a variety of methods may be "practical". How do your remarks relate to the quotation in the article, repeated below:

We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted ${\mathfrak {R}}$, is said to move with the observer.… The spatial positions of particles are labelled relative to a frame ${\mathfrak {R}}$ by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame ${\mathfrak {R}}$, can be considered to give a physical realization of ${\mathfrak {R}}$. In a frame ${\mathfrak {R}}$, coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

— Jean Salençon, Stephen Lyle. (2001). Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9

Please relate your remarks to the article at hand. Brews ohare (talk) 16:18, 18 August 2008 (UTC)

Well very simple with the terms "rigid body" the author is implying that he uses the translation spacial symmetry to extend the orientation of the observer to the entire spacial slice. He thus gives a limited definition of frame which suffices for his purpose. (much in the way that many mathematical authors will define functions to continuous, simply because at the present they do not wish to concider noncontinuous functions. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Timothy: Might not the present Wiki article on centrifugal force also be "limited" but "suffice for its purposes"? Brews ohare (talk) 19:03, 19 August 2008 (UTC)

I have very little problem with keeping the scope somewhat limited. My gripe is with the amount of weight being given to discerning between "coordinate" and "state-of-motion". (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

For polar coordinates these approaches lead to different choices of frame. Insisting that these frames are "straight" leads to the inclusion of fictious forces in the first while it does not in the second. Brews has systematicly tried to label this difference as purely mathemtical, while in fact it is the direct result of the very physical choice of frame. (well, at least just as physical as the choice between a rotating and an inertial frame.)(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

You are using the term "frame" in your sense of the word, not in the sense used in the article and in the usual discussion of this topic. The standard meaning of frame refers to a state of motion of the observer, and leads to the distinction between inertial and non-inertial frames. Brews ohare (talk) 16:37, 18 August 2008 (UTC)

Again the state-of-motion of an observer is not sufficient to establish wether a frame is inertial. You will also need his orientation and a way of extending this to the rest of space. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Just how the extension from "observer" to a "family of observers" changes the exposition is unclear to me. The idea of "extending orientation to the rest of space" sounds a bit like the introduction of Christoffel symbols, and this approach is subject to the same issues about two types of fictitious force, as was discussed by Silberstein. Brews ohare (talk) 17:05, 19 August 2008 (UTC)

Using parallel transport (which is basically defined by the christoffel symbols) to extend the orienation to the rest of space, is one (very much geometry based) systematic approach to this extension. However any arbitrary choice of extension is, a priori, valid. It basically specifies how the observer would imagine his orientation (and state-of-motion) to be were he at the other position. The parallel transport approach is basically the one that is physically realized of you use as hypothetical system of rigid rods to define your frame of reference. You might even argue that such an approach is physically favoured. However the same arguments favour the same approach for extending the orientation and state-of-motion to extend it to the whole space time, leading to an inertial frame. Letting go of one, but not the other is a somewhat arbitrary choice made (sometimes unconsciencelessly) in many physics texts. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

Now, does this make the centrifugal force in a rotating frame and the one in the polar coordinate frame the same? Yes and No.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

This sentence misuses vocabulary: a rotating frame is a non-inertial frame and implies an observer accelerating relative to (say) the fixed stars. The term "polar coordinate" is a mathematical descriptor of a particular type of coordinate system, and is not in and of itself attached to any observer, and may be used in both inertial frames and non-inertial frames. In fact, exactly this is done in the article. Polar coordinates are used first in an inertial frame, and then in a rotating (non-inertial) frame, and then the two are compared. Brews ohare (talk) 16:37, 18 August 2008 (UTC)

As I have explained before polar coordinates can be used to define a non-inertial frame simply by picking the coordinate basis at each point as the orientation for that point. These orientations are not aligned hence the resulting frame is not inertial. It is not necesary to use this frame when using polar coordinates, but when doing so pretending that the orientations are in fact aligned leads to concidering the the extra acceleration terms as ficitious forces. Obviously with "polar coordinate frame" I mean the frame that can be naturally defined by polar coordinates. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Timothy: Apparently you have introduced a definition of "inertial frame" here in terms of the connection between the orientations adopted at different points in space time. Some more detail would be nice. How does this definition connect with the notion of "real" vs. "fictitious" forces? Some forces can be transformed away, and others cannot? And if your frame contains "fictitious forces" can it still be "inertial"? I suspect that you have in mind the formalism using Christoffel symbols. That is exactly the quagmire explored in the Silberstein citation provided in the article, and does not lead us away from the distinction between two types of "fictitious force". Brews ohare (talk) 18:46, 19 August 2008 (UTC)

In the (admittedly somewhat ad hoc) definition for inertial frame, no fictitious force would ever be present in an inertial frame. That is if we accept the convention that fictious forces are the force that are introduced by simply assuming that a reference frame is aligned. This is obviously somewhat of tautology, due to the definition of fictitious. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

Clearly they appear in different choices of frame, hence they are different. Yet, they arise as a result of the same physical reasoning (they are both fictious forces resulting from think of a "nonstraight" frame as "straight") and are both "outward pointing", making them very similar. With the difference and simularities being so subtle most textbooks choose the circumventing the issues (or just plain ignore it and just label both as "the" centrifugal force) adopting a "who cares where you put those acceleration terms, just put them somewhere and analyse the differential equations" additude.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

It is not a difference in choice of "frame" that is involved here. The subsection on polar coordinates shows that describing the movement of a particle in an inertial frame the equation for acceleration is:

${\frac {d^{2}\mathbf {r} }{dt^{2}}}={\boldsymbol {a}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}\ ,$

and is used directly in Newton's second law as:

${\boldsymbol {F}}=m{\boldsymbol {a}}\ ,$

where F is the real external net force. The frame is inertial so no fictitious force is recognized because this is simply Newton's law in polar form. The Stommel reference makes the very same point.

However, in the "coordinate" approach in this exact same inertial frame the term $-r{\dot {\theta }}^{2}$ is called a "fictitious force": same frame, different "fictitious forces"; one approach zero forces, the other approach non-zero forces even though the frame is inertial. Newton's law in the coordinate view becomes:

${\boldsymbol {F}}+mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-2m{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}=m{\boldsymbol {a}}\ ,$

with

${\boldsymbol {a}}=({\ddot {r}}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}){\hat {\boldsymbol {\theta }}}\ ,$

That is, the "acceleration" in the "coordinate view" contains only the second-order time derivatives of the coordinates, and all the other polar contributions are taken as fictitious forces to the force-side of the equation, and are non-zero even in this inertial frame of reference. Brews ohare (talk) 16:04, 18 August 2008 (UTC)

You do realize that you can repeat this whole rant for a rotating frame, right? (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

This exposition is applied to a rotating frame in the article, and the two are compared. I don't see why this argument is a "rant": what do you object to here? Brews ohare (talk) 16:11, 19 August 2008 (UTC)

My objection is that you can do exactly the samething with a rotating coordinate system attached to an inertial frame. You get an expression of Newton's law in rotating coordinates. Sticking to this frame it is unnatural to move the extra terms to force side of the equation. Doing so (in some sense) implies moving to the rotating frame defined by the coordinates. In the same way choosing to view the extra accelaration terms in polar coordinates as ficitious forces implies moving to a different frame. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

These observations are sensible, but the actual practice as exemplified by (but not limited to) Stommel is to follow this unnatural procedure. As indicated below in my remarks to Fugal, that means the introduction of non-zero fictitious forces in an inertial frame of reference, a no-no in the standard discussion of inertial frames. The same approach is used extensively in the design of robotic manipulators, which follows your "throw everything into the pot, who cares about terminology, and solve the DE's" approach. I speculate that this attitude evolves from using a Lagrangian formulation that leads naturally to equations with only second-order time derivatives on one side of the equations. See R. Kelly, V. Santibáñez, Antonio Loría (2005). Control of robot manipulators in joint space. Springer. p. p. 72. ISBN 1852339942. {{cite book}}: |page= has extra text (help)CS1 maint: multiple names: authors list (link) and Shuzhi S. Ge, Tong Heng Lee, Christopher John Harris (1998). Adaptive Neural Network Control of Robotic Manipulators. World Scientific. p. p. 48. ISBN 981023452X. {{cite book}}: |page= has extra text (help)CS1 maint: multiple names: authors list (link)

Brews ohare (talk) 15:39, 20 August 2008 (UTC)

(As a side note: in Lagrangian formalism all terms end up on the side of the equation of motion. (i.e. you get something of the form PDE = 0) I think you are however right in suspecting that this leads to a who cares what we call the individual terms attitude, just solve the damn thing already.)

As a more to the point response. What I was saying was that you can in fact introduce rotating coordinates in a inertial frame. When this is done you get the acceleration terms that you call "state-of-motion" centrifugal force, however we are still in the inertial frame. Really interpreting these terms as actually fictitious forces however requires us to switch to the frame that is natural to the coordinates, a rotating frame. This switch is often done implicitly when changing coordinates. This seems to be what Marion and Thornton do in their book; they forgo the distinction between coordinate systems and reference frames and just assume the convention that changing coordinates automatically means changing frames to the corresponding coordinate frame.

And I stress again that the coordinate frame corresponding to polar coordinates is not inertial. The problem of having non-zero fictitious forces in an inertial frame only exists if you attach polar coordinates to an inertial frame (instead of their coordinate frame), but that problem also exists for rotating coordinates when attached to an inertial frame. (TimothyRias (talk) 09:31, 21 August 2008 (UTC))

Timothy: Thanks for the comments. Your observations about Marion and Thornton are illuminating, and the obliquity of these authors is the source (I believe) of all the fuss raised by Fugal and Paolo.dL. Brews ohare (talk) 13:54, 21 August 2008 (UTC)

What does this mean for the wikipedia article? I see two options:

• Both are treated in a single article centrifugal force and it is just noted that both are "outward pointing" fictious forces in a nonstandard choice of frame.
• Two article are created (centrifugal force (rotating frame) and centrifugal force (polar coordinates) and centrifugal force becomes a disamb. page linking to the two. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

A similar idea is at centrifugal force (disambiguation). You might wish to comment on its formulation on its talk page. Brews ohare (talk) 15:43, 18 August 2008 (UTC)

Some options that I think should be avoided:

• Extensive treatment of centrifugal force in polar coordinates. Physical equations of motion are really beyond the scope of that article. Polar coordinates find use an all sorts of (non physics related) situations. It might get a small mention there as an application, but it should not get much more.

I really wish that we can stop arguing so much about this. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

Please read the article with more attention to detail. Brews ohare (talk) 15:23, 18 August 2008 (UTC)

Please start being a little less condescending for somebody who clearly has a very limited understanding of the development of the concept of reference frame in the 20th century. I realy am starting to get the feeling that I'm communicating with a 19th century brickwall paradigm. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Trying to explain my viewpoint is not condescension, but is, in fact, a compliment. My request that you read the article more closely is simply my reaction that some of your remarks are addressed in the article, and you didn't notice that. Were you to propose some change in wording, it would serve the purpose of telling me that you had actually read the material, eh?

I find your exposition about inertial frames and "state-of-motion" and orientation to each event in spacetime interesting, and would like to see you undertake a contribution to an article (maybe a new one) about this topic.

Somewhere above you say:

With the difference and similarities being so subtle most textbooks choose to circumvent the issues (or just plain ignore them and just label both as "the" centrifugal force) adopting a "who cares where you put those acceleration terms, just put them somewhere and analyze the differential equations" attitude.

This quote suggests you do think there is a "subtle" distinction between the two designations of fictitious force, and not simply no distinction. Is that so? Could you express this distinction from the tetrad viewpoint? Brews ohare (talk) 19:55, 19 August 2008 (UTC)

Well clearly there is some difference. Due to the fact that spacetime is pseudo riemanian a tetrad splits into a timelike vector field (which in this discussion has been refered to as the state-of-motion) and a triple of spacelike vectorfields (which we have called orientation). The so called "state-of-motion fictitious forces" are related to the timelike part of the tetrad not being "aligned", while the so called "coordinate ficititious forces" are related to the spacelike part of the tetrad not being aligned. Hence there is a minor distinction between the two and regarding them as different is somewhat inline with other ways that we treat time and space assymmetrically.

And because we treat time and space differently in many situations the two "types" of fictious forces may sometimes manifest differently. For example, due to the habit in classical mechanics of regarding time as an external absolute parameter, different choices for the spacelike part may always be connected to a choice of coordinates, making it seem that a simple coordinate transformation is all that is needed to transform the related fictitious forces away. (while it becomes impossible to do simple time dependent coordinate changes, and those get a somewhat special status.)

But in the end the distinction is a somewhat arbitrary one induced by our methods of discribing physics, while the connection between the two as actually quite physical. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

Suggestion for Resolution

It occurs to me that the current article would be just fine if only it was given the more accurate name "Brews Ohare's Personal POV and Commentary on Centrifugal Force and Other Miscellaneous Topics". If this were the article's title, there would be much less dispute over the content, since it would be, by definition, whatever Brews wants it to be (although it might then be more appropriately hosted somewhere other than Wikipedia). The current article is brimming over with neoligisms like "coordinate fictitious force" and "state-of-motion fictitious force", and elaborate attempts to rationalize Brews' personal (and evolving) ideas about what these newly minted terms ought to mean. From the standpoint of Wikipedia, this article has become truly pathological, bloated to the point of being unreadable. And whenever someone makes the slightest attempt to modify it, they are bombarded with ten or twenty counter-edits from Brews, coupled with an equal number of interminable rants on the discussion page, where we are informed that his beliefs are "beyond controversy". Several people have suggested (independently) that Brews should relinquish ownership and take a much needed break, but he shows no signs of taking this advice. The entire article has become a novel narrative interwoven with original research and highly POV rationalizations, all aimed at trying to justify why Brews' somewhat naive and unsophisticated view of the subject is superior to all other views. This kind of exercise in polemics really isn't appropriate for a Wikipedia article (in my opinion).Fugal (talk) 13:39, 20 August 2008 (UTC)

Hi Fugal: The issue that is troubling on this page is very simply put: there are two definitions in use for fictitious force. Because they both use the same term "fictitious force" it is hard to talk about the two meanings without distinguishing between them. Hence, the "neologisms" of coordinate fictitious force and state-of-motion fictitious force. I am not tied to these terms: do you think type A fictitious force and type B fictitious force would be more suitable?

A controversy arises whether there are in fact two different meanings. On this subject Timothy is of the mind that there is a difference, but it so subtle that it requires recognition of our prejudices about space-time differentiation and would require a five-year doctorate in general relativity and differential geometry to understand the distinction between the meanings. Therefore, the distinction is not worth bringing up, and we would be advised to ignore the difference and just label both as "the" centrifugal force, adopting a "who cares where you put those acceleration terms, just put them somewhere and analyze the differential equations" attitude.

My response to this view is very, very simple: one definition leads to fictitious forces that vanish in an inertial frame of reference; the other definition leads to forces that do not vanish in an inertial frame of reference. I do not find that to be subtle difference at all. For the case of polar coordinates, explicit mathematical forms for the forces in the two cases are presented that show exactly how the difference in the two definitions leads to two different sets of mathematical terms.

To spell this remark out as it is stated in the article, in an inertial frame of reference the force is simply the net real force F on a moving particle, and the "state-of-motion" fictitious force is zero regardless of the choice of coordinate system. The force in the "coordinate" view is:Stommel

${\boldsymbol {F}}+mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

in which F is the real net force just mentioned, and the other terms are the "coordinate" fictitious forces, which have a form that varies depending upon which type of curvilinear coordinates you want to use. Obviously, as this is an inertial frame, these extra "coordinate" fictitious forces are not only "fictitious", they also do not vanish in an inertial frame of reference, which is contrary to all discussions in the literature about inertial frames of reference and their relation to fictitious forces.

These are not subtleties; they are real differences that cannot be ducked.

Where do you weigh in on this? Brews ohare (talk) 14:34, 20 August 2008 (UTC)

I repeat:

1. Polar coordinates naturally attach to an non-inertial frame.
2. You can introduce a rotating coordinate system in any inertial frame. Doing so will lead to additional acceleration terms, which may be interpreted as fictitious forces (although such an interpretation is unnatural without changing frames) and which are non-zero in the inertial frame. (TimothyRias (talk) 09:38, 21 August 2008 (UTC))

Hi Timothy: So, from these remarks I take it that you agree entirely with these latest comments of mine, and find them unsurprising? You might (I'm guessing) simply add that this approach is either (i) unnatural because it is not accompanied by a switch of frame as well as adoption of polar coordinates or (ii) implicitly anticipates such a switch but, unfortunately, often does not point out such anticipation. Brews ohare (talk) 13:37, 21 August 2008 (UTC)

(I'm not sure which latest remarks you are refering to, but I certainly disagree with "they are real differences that cannot be ducked" as the issue you raised exists for both "types" of centrifugal.) Yes, you could add that and (ii) is one of the things I have been trying to point out. (TimothyRias (talk) 14:56, 21 August 2008 (UTC))

Let me try again. You say:

which may be interpreted as fictitious forces (although such an interpretation is unnatural without changing frames) and which are non-zero in the inertial frame

which I take as not in conflict with my statement:

Obviously, as this is an inertial frame, these extra "coordinate" fictitious forces are not only "fictitious", they also do not vanish in an inertial frame of reference, which is contrary to all discussions in the literature about inertial frames of reference and their relation to fictitious forces.

Your remark:

the issue you raised exists for both "types" of centrifugal

is unclear to me. I will elaborate next on the two different uses of the term "fictitious force".

The "state-of-motion" centrifugal force is zero in an inertial frame of reference (by definition of an inertial frame), regardless of whether the coordinate system is Cartesian or curvilinear, as is stated in the article. To elaborate: in the inertial frame, Newtons' law in polar form is:

${\boldsymbol {F}}=m{\boldsymbol {a}}=m({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+m(r{\ddot {\theta }}+2{\dot {r}}\ ,$

and the force on the left is the real net force. The terms on the right are not interpreted as fictitious in the "state-of-motion" viewpoint, but simply as artifacts of the curvilinear coordinate system. Bluntly put, in the "state-of-motion" viewpoint, all fictitious forces are zero by definition of an inertial frame of reference. There simply are no fictitious forces in an inertial frame. I believe this viewpoint to be very basic to the connection between inertial frames and fictitious forces, as expressed, for example, by V. I. Arnol'd (1989). Mathematical Methods of Classical Mechanics. Springer. p. p. 129. ISBN 978-0-387-96890-2. {{cite book}}: |page= has extra text (help)

The equations of motion in an non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.

— V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129

A slightly different tack on the subject is: Iro

An additional force due to nonuniform relative motion of two reference frames is called a pseudo-force.

— H Iro in A Modern Approach to Classical Mechanics p. 180

It seems clear to me that terms introduced not by relative motion, but by change in coordinate system (say from Cartesian to polar coordinates in the same frame of reference, same origin, same state of motion) do not qualify as "pseudo-forces".

That viewpoint is different from the "coordinate viewpoint", where Newton's law (still in an inertial frame of reference) is rearranged to put some terms on the force-side: see Stommel

${\boldsymbol {F}}+mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}=m{\tilde {\boldsymbol {a}}}=m{\ddot {r}}{\hat {\mathbf {r} }}+mr{\ddot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

where a "coordinate" version of the "acceleration" is introduced:

${\tilde {\boldsymbol {a}}}={\ddot {r}}{\hat {\mathbf {r} }}+r{\ddot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

consisting of only second-order time derivatives of the coordinates r and θ. A "coordinate" fictitious force is thereby introduced:

${\boldsymbol {F_{fict}}}=mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

that is non-zero in the inertial frame.

Do you have any issues with this formulation of the difference between the two uses of the term "fictitious force"?

Parenthetically I would add that this problem does not go away by changing terms from "fictitious" to "apparent" or to "pseudo", because the ambiguity extends to two uses of the terms "centrifugal" and Coriolis". Brews ohare (talk) 18:27, 21 August 2008 (UTC)

Suggestion for Resolution(Cont'd)

A fictitious force derived in an inertial frame implies switch to non-inertial frame

Comment by TimothyRias:

You seem to have missed my point:

Let's do it a bit more explicitly. Suppose we have an inertial frame with cartesian coordinates x and y. (for convenience we drop de third coordinates). In this frame we can adopt new (time dependent) coordinates: (disclaimer any equations should be read module missing/extra signs)

$X=\cos(wt)x+\sin(wt)y\;$

$Y=\cos(wt)y-\sin(wt)x\;$

If we do so we get the following acceleration:

${\vec {a}}=({\ddot {X}}-2w{\dot {Y}}-w^{2}X){\hat {X}}+({\ddot {Y}}+2w{\dot {X}}-w^{2}Y){\hat {Y}}$

We can introduce a "coordinate acceleration"

${\tilde {\vec {a}}}={\ddot {X}}{\hat {X}}+{\ddot {Y}}{\hat {Y}}$

By which we introduce a coordinate fictitious force:

${\vec {F}}_{fict}=(2w{\dot {Y}}+w^{2}X){\hat {X}}+(-2w{\dot {X}}+w^{2}:Y){\hat {Y}}$

You will recognize these as the regular expressions for the fictitious forces in a rotating frame. However we are still an inertial frame, hence by definition (of fictitious force) these cannot be fictitious forces. Interpreting these as fictitious forces implies going to the corresponding rotating frame; the coordinate frame of the choosen coordinates. This is quite general, interpreting the extra acceleration terms in certain coordinates as fictitious forces always implies adopting the coordinate frame. When these extra terms are non-zero it also implies that the coordinate frame in non-inertial. The polar coordinate frame fictitious forces being non-zero when applying the coordinates to an inertial frame doesn't make them different from the rotating frame fictitious forces. The rotating frame fictitious are also non-zero if you apply the corresponding coordinates to an inertial frame. Hence the thing that you described above as a real difference that cant be ducked is a not difference at all. It is just a difference in the way you have been treating the two cases, but each treatment can be applied to both cases. (TimothyRias (talk) 09:09, 22 August 2008 (UTC))

Thanks much for becoming specific. I now understand what you are saying. From this perspective, I'd add the following remarks:

1. Unless one adopts your view that calling certain acceleration terms in an inertial frame "fictitious" definitely implies ipso facto that a change of frame to a non-inertial frame is made, the idea that these terms are fictitious forces in the common meaning of that term (as per the quotations above from Arnol'd and Iro) is nonsense.

Yes, this is true both for the acceleration terms in rotating coordinates as those in polar coordinates. You might even turn it around. The definitions of fictitious force given by Arnol'd and Iro imply that calling anything a fictitious force must imply adopting some non-inertial frame. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

Glad we agree on this point. Brews ohare (talk) 16:03, 25 August 2008 (UTC)

2. If a change to a non-inertial frame is implied, one must face the prospect that there are an infinity of non-inertial frames, and one must choose which one is implied . Thus, mere implication of the switch of frames is very ambiguous. It would be pertinent to specify which frame is implied.

Not so ambigious actually. The implied change is toward the coordinate frame of the chosen coordinates. This convention for defining your frame is commonly adopted in GR, because it is by far the easiest way to specify a frame in a more general context. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

Point to be clarified. A switch to polar coordinates is not in itself unique. For example, is it a switch to a rotating set of polar coordinates? If so, at what rate does it rotate. what is its Ω? Clearly, the centrifugal force depends upon Ω and cannot be specified without it. Taylor Classical Mechanics p. 358 suggests the co-rotating frame, by which is meant a frame selected at a specific time t to have the rate of rotation of the observed particle Ω = dθ/dt at that moment. In this instantaneous frame that must be reselected at every moment, he suggests easy identification of terms at that moment is possible. I added this to Polar_coordinate_system#Centrifugal_and_Coriolis_terms and removed your . Brews ohare (talk) 00:36, 26 August 2008 (UTC)

I would not normally call rotating polar coordinates, "polar coordinates", I would instead just call them "rotating polar coordinates". It is also clear that "rotating polar coordinates" and normal "polar coordinates" imply different frames.(TimothyRias (talk) 09:54, 27 August 2008 (UTC))

No problem with this; do you think I have said differently? Brews ohare (talk) 19:54, 27 August 2008 (UTC)

Once a particular set of coordinates is chosen, this identifies a unique adapted frame.(TimothyRias (talk) 09:54, 27 August 2008 (UTC))

No agreement here; the frame refers to e.g. inertial or non-inertial, not to coordinate system. Brews ohare (talk) 19:54, 27 August 2008 (UTC)

Simply take the coordinate base as the tetrad. (Note this only works directly for coordinate systems in which the coordinate base is already orthonormal such a Cartesian or polar coordinates. For more general coordinates a more advanced recipe may be required orthonormalizing the base.) (TimothyRias (talk) 09:54, 27 August 2008 (UTC))

You say :I would not normally call rotating polar coordinates, "polar coordinates", I would instead just call them "rotating polar coordinates". What? I have been very careful to distinguish between polar coordinates in inertial and in non-inertial frames. Your notion that the coordinate system implies a frame is incorrect: a frame can be chosen and then a variety of choices is available for coordinate system. The reverse order of events is not germane here. Brews ohare (talk) 15:38, 27 August 2008 (UTC)

Of course, you can use any set of coordinates with any frame, the two are, a priori, independent concepts. We both agree on this, so I tier from having you imply that I imply otherwise. (I suggest that you aren't even trying to understand what I'm saying here.) This works both ways, you can first select coordinates and then a frame of visa versa. There is however a well known procedure for obtaining a choice of frame from a choice of coordinates (see for example Norton): (In the definition of frame used by Norton:) take the congruence of timelike curves defined by constant spacelike coordinates as your frame. Note that in this definition, indeed polar and cartesian coordinates yield the same choice of frame. Taking the slightly more general definition of frame that also includes a specification of the orientation of at each event, then these two coordinate systems will yield different frames. Easy. (TimothyRias (talk) 16:26, 27 August 2008 (UTC))

Hi Timothy. How about sticking to the context of classical mechanics? Or do you really want to write a whole subsection on tetrads and fictitious forces using a "congruence of time-like curves"?? After that you could connect this digression back to the topic of this article based upon classical mechanics. I'd prefer to settle the issues in the classical setting first, and then digress. Brews ohare (talk) 19:54, 27 August 2008 (UTC)

3. If switching is implied, the variables must be redefined by implication as well. For example, using the fictitious force ${\boldsymbol {F_{fict}}}=mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$, the original meaning of the variables r, θ refer to the position of a moving particle, and are only indirectly related to the rotation Ω of any frame of reference (because the particle is moving in some curved path, it has its own angular velocity in any frame). This point is noted by Stommel, for example, who distinguishes between Ω and the full angular velocity of the particle dθ/dt .

Actually this is not necessary. This change was done by the change of coordinates already. Adopting the corresponding coordinate frame just makes it easier to interpret the coordinate values. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

I don't follow you here: if the polar coordinate values r and θ are the coordinates of the particle observed in polar coordinates in the inertial frame, a particular rotating frame must be selected before the corresponding variables r' and θ' in that frame can be set up. That is, one must select a particular rotating frame before one can proceed. Are we talking about the same thing here? Brews ohare (talk) 16:03, 25 August 2008 (UTC)

We don't need a rotating frame in polar coordinate case. We need a frame in which the orientation is dependent on the (spacial) position. Specifically, we need the frame to which polar coordinates are adapted namely the one in which the orientation is always aligned with the radial direction (and the state-of-motion does not vary with time or space). Changing to this frame does not change the coordinate expressions in polar coordinates, it merely changes their interpretation. (Just like adapting a rotating frame when already using rotating coordinates, just changes the interpretation of the coordinates and coordinate expressions.) (TimothyRias (talk) 09:54, 27 August 2008 (UTC))

The connection between "frame" and "orientation" is lacking in a classical framework: one can choose a Cartesian coordinate system in a chosen frame with any orientation. As another example, a polar coordinate system (classically) has orientation only for the z-direction. I'd suggest that if a "deeper" concept of orientation based upon differential geometry in a general relativistic framework is necessary to understanding "orientation" that at a minimum it is necessary to make a separate subsection to develop the notion, and that most probably it should not be part of this article at all. And I am unclear that there is any bearing at all upon what is being discussed. Brews ohare (talk) 15:33, 27 August 2008 (UTC)

4. No author that I can find has said either that a frame change is implied, or provided any guidance as to just what frame and what variable changes might be implied.

You might wanna check your old pal Norton on this. He clearly mentions the convetnion of letting the frame be specified by the coordinates. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

Norton mentions this "convention" (p. 836) only as a position that he does not agree with and that has problems associated with it (particularly in rotating frames) that are the subject of a long discussion in his paper. Following his introduction of this viewpoint he says (p. 837) "More recently, to negotiate the obvious ambiguities of Einstein’s treatment, the notion of frame of reference has reappeared as a structure distinct from a coordinate system."

Additional citations by many different authors supporting the distinction between frames of reference and coordinate systems are found in frame of reference. Brews ohare (talk) 16:55, 25 August 2008 (UTC)

Sigh, did I say they were the same? No, I didn't, did I? What I said was that a particular coordinate system can be used to define a frame of reference. This specifically alluded to be Norton when discussing the alternative version of the definition of a frame using equivalence classes of coordinate systems adapted to some congruence of curves. (As a small aside: not all coordinate systems will allow this, at least in Norton's sense, since not all coordinate systems will have clear timelike and spacelike coordinates. Take an form of lightcone coordinates, which do not have any timelike coordinates, but instead of two lightlike coordinates.) He also mentions the convention in GR of always assuming the frame corresponding to the coordinates. What he critizes is the notion that this convention implies that er is no difference between the two concepts.

Sigh away; If there is a deeper meaning here, instead of sighing, you might try explanation. And there is a distinction between "can be used" and "must be used". You have a lot of technical blah-blah here that seems beyond the scope of the article and only vaguely related to the issues at hand. Brews ohare (talk) 15:33, 27 August 2008 (UTC)

On the same page, he also mentions that in the definition of frame that he will be using the properties of the metric to identify changes of rotation (i.e. he uses paralell transport to assign orientations to each timelike curve.) He also mentions that you can have a more general definition of frame by adding a continous specification of the orientation to curves (or rather a spacelike triad to the timelike vectorfield to form a tetrad). It is this more general definition of frame that I have been referring to as needed to make physical sense of the centrifugal force in polar coordinates. (TimothyRias (talk) 09:36, 27 August 2008 (UTC))

And the implication and conclusion is? Can you package these observations of yours in some way meaningful to the article? The objective here is to relate two approaches to finding "fictitious forces", which may sometimes agree, but as commonly used, often do not. Brews ohare (talk) 12:52, 28 August 2008 (UTC)

Perhaps support by reference to a source can be found for the idea that frame change is implied by adoption of the words "fictional force"?

Supposing that can be done, the article could be modified to say:

"Sometimes authors intend the use of "fictional force" in the "coordinate" sense to imply ipso facto a change of frame to a non-inertial frame where these forces are in fact "fictitious forces" in the sense of standard classical mechanics. For example , see authors A, B, C, who indicate that the correct way to introduce "fictitious forces" by implication is to follow the recipe below to insure a correct choice of non-inertial frame (among the infinity of possible such frames) where in fact these particular terms become the correct fictitious forces."

If sources to cite cannot be found, an alternative revision is based upon finding a recipe that leads to versions of "coordinate" fictional forces that are the same as the "state-of-motion" fictional forces. To set up some such revision, take the example of the rotating frame in the article where the "coordinate" fictitious force is:

${\boldsymbol {F_{fict}}}=mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}}+m\left(2r\Omega {\dot {\theta }}'+r\Omega ^{2}\right){\hat {\mathbf {r} }}-m\left(2{\dot {r}}\Omega \right){\hat {\boldsymbol {\theta }}}$

The first two terms are contributed by motion of the particle as seen in the rotating frame, and are the terms seen even when Ω = 0. The last two terms are the fictitious forces of classical mechanics. Thus, a possible recipe for determining fictitious forces is to write out Newton's laws in the inertial frame for a particular case of a particle motion, namely, in this case, one where $mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}}=0$. For example, if one picks a particle that will be seen as stationary in the inertial frame one wishes to switch to, the correct centrifugal force will result (but the Coriolis force requires something else). Can it be done? Basically, one needs to calculate the trajectory of a particle in the selected non-inertial frame that is (apparently) in free motion, and use that trajectory in the inertial frame when finding the forces. That's a guess.

Assuming the recipe can be found, a possible revision would then be:

"It is possible to use the "coordinate" fictional forces approach in a manner that leads to the same "fictional forces" as the "state-of-motion" fictional forces. Here is the recipe: blah -blah -blah. Although this careful use of the "coordinate" fictional forces approach leads to the same fictional forces as those of standard classical mechanics, it must be recognized that the literature often does not follow the above recipe. Consequently, versions of "coordinate" fictitious forces frequently are derived that violate the above prescription, and therefore are not "fictitious forces" in the "state-of-motion" sense in any frame of reference."

The objective here is to relate two approaches to finding "fictitious forces", which may sometimes agree, but as commonly used, often do not. Brews ohare (talk) 18:53, 22 August 2008 (UTC)

Fugal's commentary

The current article is getting filled up with attempts to rationalize the personal POV of one editor. It appears to me (although I haven't taken a formal vote) that the majority of other editors believe the neoligisms and novel narratives being woven by that editor are not reflective of any published reputable source. To some extent, this is probably unavoidable, because the topic in dispute is not considered to be significant enough (or difficult enough) to warrant being discussed explicitly in very many reputable sources. Most scientists understand what Christoffel symbols mean, and the fact that none of them are "more physical" than the others, but they don't feel it necessary to make a point of this obvious fact.

Maybe the best way forward is to move the last half of this article, beginning with the discussion of polar coordinates, to its own article, which could be on the general subject of centrifugal force, allowing this article to be focused just on Brewsian centrifugal force in rotating coordinates. I seem to recall that Brews said not long ago that he advocated moving this "insignificant side topic" to its own article, where he felt certain it would languish for lack of interest. If I remember rightly, he said once it was move from his page, he didn't care what happenned to it. So he is presumably all in favor of my proposal.Fugal (talk) 01:36, 24 August 2008 (UTC)

Hi Fugal: Everything in the article is well documented, while your comments and views are not. Earlier attempts to engage you in a documented discussion have been ignored by you: for example, here. So you now are simply stating your POV with far less justification than the views in the article. You claim the article says "some Christoffel symbols are more physical than others", which may be only sloppy reading of the article or may be poor polemic. Perhaps, instead of vague slaps at your undefined notion of a "Brewsian centrifugal force", you might attempt to provide valid, detailed, specific criticism backed up with real citations? In other words, perhaps you could be constructive? Brews ohare (talk) 16:27, 24 August 2008 (UTC)

A clear, complete, and concise explanation, fully supported by references from high quality published sources, was added to the article, and you summarily deleted it, and proceeded to replace it with your own novel narrative, which consists of whole sections without a single reference, in which neoligisms and novel notions and original research are introduced. And now YOU ask ME to be constructive and provide real citations? Sheesh. Look, your original research about "state of motion fictitious forces" and "coordinate fictitious forces" simply does not belong in Wikipedia. You know very well it is original research, and every other editor here knows it is original research. If you really want me to be constructive, I'll be happy to go in and delete all your original research and novel narrative and replace it with well-sourced and accurate material. Is this what you are asking me to do?

I also note that you declined to comment on my proposal above, which is that, now that this article is specifically about rotating coordinates, the other material discussing the more general view really belongs in another article, devoted to the general topic of centrifugal force and other fictitious forces. This material certainly doesn't belong here in this rotating frames article. Fugal (talk) 18:49, 24 August 2008 (UTC)

I really don't care about the curvilinear section with Christoffel symbols: it is there because Wolfkeeper asked for such a section.

The section on polar coordinates is about a comparison between polar coordinates in rotating and in inertial frames. So it reasonably belongs here. It is somewhat lengthy in order to present clearly that "ficititous force", in particular centrifugal and Coriolis force, are used in two different meanings. These two meanings crop up most obviously in polar coordinates, although they also arise in the use of curvilinear coordinates. I think you do not subscribe to the idea of two meanings, but it is far from original research. Citations are provided where the use of "ficitious forces" is suggested in inertial frames, in clear contradiction to the quotations from Arnol'd and Iro you can find higher on this page. This contradiction can be viewed (most reasonably) as two uses of the same term or, if you prefer, a misuse of the terminology by a large number of writers (not my choice for description). You are attached to one meaning at the exclusion of the other, or possibly wish to conflate the two meanings. Brews ohare (talk) 20:17, 24 August 2008 (UTC)

It isn't for Wikipedia editors to pass judgement on whether published reputable sources are "mis-using" terminology, we are just to accurately represent what those sources say. What we have here is one set of introductory texts that give a simplified and restricted view of the subject, and then several advanced grown-up references that give a more general and comprehensive view of the subject, so both deserve to be accurately represented (per Wikipedia policy), although most editors would tend to lean toward the more general and comprehensive view..Fugal (talk) 21:04, 24 August 2008 (UTC)

The idea that there is a simplisitic and a more general view is undocumented. Also, you have not stated just what exactly is the general view, nor cited sources, nor provided any quotes. Brews ohare (talk) 21:20, 24 August 2008 (UTC)

In this situation there are multiple sources that seem superficially to say contradictory things, but as has been explained to you previously, they are contradictory only if you insist on imposing the Brewsian myopia onto them, and have only a sophomoric level of understanding of physics. Introductory texts tend to give a simplistic description of things, and unfortunately some students become embittered later when they learn, upon discovering more advanced material, that they were given a simplified view earlier in their education. They feel betrayed. Well, that's understandable, but we're not here to debate the merits of various pedigogical strategies in our educational system, we're here to present a topic accurately on the basis of the best available sources..Fugal (talk) 21:04, 24 August 2008 (UTC)

Well, you are very unkind to me. And do not document anything you say. Brews ohare (talk) 21:20, 24 August 2008 (UTC)

You mentioned the "most reasonable" interpretation is that terms are being used with different meanings, which to some extent is true, but one is just an informal and simplified version of the other. You seem to be intent on enshrining the simplistic 4th grade version as some kind of dignified and preferred "alternative" to the grown-up complete and treatments of the subject, and you seem to be intent on denigrating the latter. This is just motivated by your personal POV (in my opinion)..Fugal (talk) 21:04, 24 August 2008 (UTC)

That is exactly what it is: Your undocumented opinion. Brews ohare (talk) 21:20, 24 August 2008 (UTC)

I suspect it's all because you were given, by well-meaning teachers and text book writers in 4th grade, an overly simplified explanation of dynamics. The problem is, very few 4th grade students are prepared to absorb a treatise on the epistemology of scientific knowledge, so they are taught in terms of intuitive notions, despite the fact that those notions are ultimately untenable. The irony here is that you're intent on perpetuating the very over-simplification that was perpetrated on you.Fugal (talk) 21:04, 24 August 2008 (UTC)

Your fourth-grade education was more advanced than mine. However, you still have no documentation for your "grown-up" interpretations.

Look, we have very clear quotes from Arnol'd (an impeccable authority on the subject at a very sophisticated level) and Iro (a textbook, author's rep unknown to me, but a very standard statement) that fictitious forces do not arise in inertial frames. I do not see you challenging these authors. On the other hand, there are very clear quotes showing that some authors have defined fictitious forces so they do exist in inertial frames. What is there to argue about? Cited sources have used different meanings for the same terminology. All we can do is recognize the fact and point it out to the reader.

Timothy has suggested that using differential geometry in general relativity a somewhat more unifying approach can be found (just how unifying, or just how it is accomplished is unclear and undocumented). That idea is (i) unsupported so far by citation or quotation (ii) very advanced and beyond the average reader, and (iii) must reduce within the less heady atmosphere of classical mechanics to the same inglorious result of two different meanings. Brews ohare (talk) 21:39, 24 August 2008 (UTC)

You continue to say that no explanation or documentation for the grown-up unified version has been given, but that is not true. As stated above, a clear, complete, concise, and fully sourced explanation was added to the article, only to be deleted within hours by Brews ohare, replaced with his POV novel narrative and original research. You should read what you deleted, and pay particular attention to the definition of an inertial coordinate system. You may also need to work on your understanding of how coordinate systems are related to "frames", and challenge yourself to understand the difference between a frame and an observational frame.Fugal (talk) 01:03, 25 August 2008 (UTC)

I don't agree that a "clear, complete, concise, fully sourced explanation" was given. I don't agree that my understanding is limited in the ways you suggest. And I do not find anything that is germane to contradictory quotes indicating different usages of the same terms. Brews ohare (talk) 05:31, 25 August 2008 (UTC)

Anyone who cares to check the history of the article can see plainly that you're wrong. If you had read what was written, instead of simply deleteing it, you would have learned something. For example, you would understand that what seems to be contradictory usages of the same terms are really the same usage. But this would require you to read and comprehend, neither of which you seem inclined to do.

I repeat, the current article contains, in the sections beginning with polar coordinates, neoligisms and novel narrative and original research which is not appropriate for Wikipedia. The thesis that there are "state-of-motion fictitious forces" and "coordinate fictitious forces" is the fabrication of just a single editor here, as is all the nonsense about "attaching coordinate systems to frames", and none of this original research belongs in Wikipedia. This material is not verifiable from any reputable source, and should be removed.

The editor who inserted this material opposes its removal (surprise), and shows every sign that he intends to continue opposing its removal, but it nevertheless needs to be removed, per Wikipedia policy. These policies were specifically designed to restrain the contributions of individuals like this. The policies against original research and novel narratives need to be upheld.Fugal (talk) 05:57, 25 August 2008 (UTC)

You seem unwilling to say anything concrete or contributory and are simply focussed upon being nasty. State your case that I am "wrong" and provide your citations. Where material is not readily available on-line, add some quotations from the sources. Brews ohare (talk) 14:37, 25 August 2008 (UTC)

You're mistaken. I provided a perfectly concrete and contributory explanation, with reference, and you deleted it within 60 minutes of its appearance, and since then you've denied that I ever provided it. I repeat, you should go and read what you deleted. It answers all your questions, and clears up all your confusions.Fugal (talk) 17:27, 25 August 2008 (UTC)

Perhaps you refer to your Revision as of 21:30, 15 August 2008? It was removed with extensive comments at Reasons for removal to which no response was received. In addition, many of the issues already were presented at Fugal's positions, so far ignored by you.

Initially, you took the view that of course fictitious forces were non-zero in inertial frames: frames had nothing to do with it. That view is accurate for the "coordinate" terminology, but contradicts the meaning of an "inertial" frame in the sense of standard classical mechanics (above quotes from Arnol'd and Iro). So, let's relax and just look at the statement of the issue as given below. I don't think you really object to it. Brews ohare (talk) 05:31, 26 August 2008 (UTC)

Simple statement of the issue

Clear quotes from Arnol'd (an impeccable authority on the subject at a very sophisticated level) and Iro (a textbook, author's rep unknown to me, but a very standard statement) state that fictitious forces do not arise in inertial frames. No-one challenges these authors. On the other hand, there are very clear quotes showing that some authors have defined fictitious forces so they do exist in inertial frames. Among them are many in the area of design of robotic manipulators (for example, Ge et al. and Teshnehlab & Watanabe) and some standard works as well. Stommel, Shankar, and McQuarrie for example. What is there to argue about? Cited sources have used different meanings for the same terminology. All we can do is recognize the fact and point it out to the reader.

It seems to me that it is impossible to dispute the above facts. If dispute is attempted, it must show that in fact authors do not define fictitious forces that are non-zero in an inertial frame. Obviously, examples of this activity are already cited and cannot be made to go away. Brews ohare (talk) 17:46, 25 August 2008 (UTC)

The problem is that you fail to grasp the different contexts in which various texts make various statements. Understanding context is essential to a meaningful and accurate understanding of the literature... and this applies to the literature on any subject. Failure to understand the context can easily lead one to believe that authors are saying contradictory things, when in fact they are just stipulating different things and taking normal linguistic shortcuts for the purposes of their own discussions.

Let me give a concrete example from a reference source that is easily accessible to all: Einstein’s 1905 paper on special relativity. This paper talks a lot about coordinate systems and frames, but notice that at the beginning of section 3 the author introduces them by saying “Let us in stationary space take two systems of coordinates, i.e., two systems, each of three rigid material lines, perpendicular to each other and issuing from a point.” Note that he says “i.e.,” meaning “that is”, and not “e.g.” meaning “for example”. He is stipulating that hereafter when he says “coordinate system” in this context he means a rectilinear system of coordinates.Fugal (talk) 00:06, 29 August 2008 (UTC)

At this point, certain editors here may enter a state of panic, because they know full well that other reputable sources discuss “coordinate systems” that are not restricted to being rectilinear Cartesian coordinates, so we have two inconsistent usages!! Oh my God, what will we do??!! Does this mean we need two separate articles on coordinate systems, one devoted to the views of people who focus on rectilinear Cartesian systems, and another devoted to the “insignificant side topic” of people who "erroneously mis-use" the term “coordinate system” to refer to more general things like polar coordinates? After all, this isn’t a dictionary, it’s an encyclopedia. Just one definition per article. Blah Blah Blah.Fugal (talk) 00:06, 29 August 2008 (UTC)

Of course not. There’s no “inconsistency” here. No one supposes that Einstein would have disputed the existence of coordinate systems that do not conform to the attributes of the systems he described, and which he chose to call “coordinate systems”. He was simply defining the term for purposes of his discussion, and making certain stipulations to avoid dealing with issues that arise when discussing coordinate systems in full generality, since those issues were not the focus of his concern. It would be a gross misrepresentation to assert, on the basis of that paper, that Einstein advocated a restricted definition of the term "coordinate system", and it would be an even worse misrepresentation to assert that he believed all his subsequent statement, predicated on the noted stipulation, must apply in general. But this is precisely how a certain editor here is interpreting all the cited references.Fugal (talk) 00:06, 29 August 2008 (UTC)

It should be noted that another common way of stipulating the restricted view is to talk in terms of “frames”, which are just equivalence classes of mutually stationary coordinate systems, so they “mod out” any differences in the spatial coordinates. This applies to many texts on classical dynamics, where there is a (often tacit) stipulation that unless specifically noted to the contrary, the “default” coordinate system is rectilinear and Cartesian. Introductory books often make statements that are true within the limited context that they have described for the student, but that are not true in a more general context. Not all of those texts are careful enough to explicitly define the context (as Einstein did), but it would be silly to conclude that they dispute the existence of other kinds of coordinate systems. Nor are we entitled to infer from their failure to discuss the more general coordinate systems what they would say about them if they had chosen to discuss them. (Some students, upon discovering that they were taught simplified versions sometimes become embittered, and even turn into physics crackpots.)Fugal (talk) 00:06, 29 August 2008 (UTC)

Naturally if we stipulate that our statements about coordinate systems assume spatially rectilinear coordinates, or if we talk in terms of “frames”, thereby stipulating that we are choosing to "abstract away" any differences in spatial coordinates, then we can say without further ado that extra acceleration terms appear only in accelerating coordinate systems (or frames). But if we consider more general coordinate systems we must account for the fact that extra acceleration terms (for moving objects) may appear even in unaccelerated systems. Does this imply that authors who limit their discussions to Cartesian coordinates (or to “frames”, which implicitly entail a decision to "mod out" any difference in spatial coordinates while not modding out differences in time coordinates) are unaware of the existence of curvilinear coordinate systems, or that they would dispute the existence of such systems, or that they would dispute that extra acceleration terms appear in such systems even when not accelerated, or that they would dispute that those terms can be brought over to the “force” side of the equation of motion, just as can any other extra acceleration term? Of course not.Fugal (talk) 00:06, 29 August 2008 (UTC)

Does it imply that those authors believe that one extra acceleration term is somehow more physical or more “real” or more “mathematical” than any other acceleration term arising from the use of a coordinate system whose basis vectors diverge from inertial paths, whether it be in the spatial direction or the temporal direction or both? Of course not.Fugal (talk) 00:06, 29 August 2008 (UTC)

Does it imply that those authors fail to recognize that when an object moves relative to a given coordinate system, the extra terms that arise due to the variations in the basis vectors are literally the same terms, regardless of whether the basis vectors change in space at constant time or change in time at constant position (or both)? Of course not.Fugal (talk) 00:06, 29 August 2008 (UTC)

So, for this article to be written as if there are two inconsistent definitions is just a sophomoric misunderstanding, and just plain silly. The plain fact is that there is a fully general treatment of the subject, and then there are some fairly common simplified and restricted treatments of the subject, aimed at people who have no interest in the epistemological issues. This article goes out of its way to denigrate the more general and comprehensive treatment, and to dignify the simplified restricted treatment as the only “correct” one. That’s just a silly POV of one particular editor here, in support of which the article has become bloated with his own novel narrative and original research. I think (as others have suggested) that it would be helpful if that editor would take a break, and let people who have a mature understanding of the literature on this subject edit the article without being forced to engage in endless polemical discussions with someone who is has clearly lost perspective on this subject.Fugal (talk) 20:19, 28 August 2008 (UTC)

So you appear to be saying that Brews displays 'sophomoric misunderstanding' is 'just plain silly' and lacks a 'mature understanding' i.e. is immature. Please read and follow WP:CIVIL. Otherwise you may be taking a break soon yourself.- (User) WolfKeeper (Talk) 23:00, 28 August 2008 (UTC)

Brews has stated that my "ignorance of the subject is quite amazing". I don't recall you threatening him with blocking for such comments, nor would I wish you to do so. I do not take offence at these statements on this discussion page, because when someone believes that someone else is wrong, he has to say so. I ask no one to block him for saying what he thinks, even if he thinks I'm amazingly ignorant.Fugal (talk) 00:06, 29 August 2008 (UTC)

In comparison, I've stated here that it's "just plain silly" for the article to be written the way it is (for reasons which I explained at length), and I've stated that the current article represents a sophomoric misunderstanding of the subject, rather than a mature understanding of the subject. This is my essential critique of the article, and I explained in detail why I think this.Fugal (talk) 00:06, 29 August 2008 (UTC)

Now, it seems to me that your comment is intended to inhibit criticism of the way this article is written. If someone thinks an article is written based on misunderstanding, then they ought to be able to say so, and hopefully they will go on to explain what the misunderstanding is. And may I add that a majority of the editors have expressed views that are at least somewhat similar to mine, in terms of how the article seems to be slanted toward making some POV argument about the illegitimacy of the more general comprehensive view of the subject. There have also been multiple comments from multiple editors that two of the editors here have shown clear signs of thinking they have some ownership of this article, and ought to take a break, per the wiki guidance on "ownership".Fugal (talk) 00:06, 29 August 2008 (UTC)

I continue to think that some kind of mediation is needed here, i.e., some additional administrative oversight, before any real progress can be made. This latest attempt to intimidate editors and suppress comment on the quality of the article is a good case in point.Fugal (talk) 00:06, 29 August 2008 (UTC)

Your comments, Fugal, would be ever so much more interesting if they actually addressed the point. Of course, you can set up imaginary misinterpretations that are clearly so, and then claim that is what is happening here also. That approach of analogy to a "straw-man" is a rhetorical device used in debate, where the objective is to make one's point regardless of the strength of one's position. I'd suggest these gimmicks are out of place here. Address the actual situation; deal with the actual sources and citations.

It is impossible to dispute that there are two distinct usages for centrifugal. If dispute is attempted, it must show that in fact authors do not define fictitious forces that are non-zero in an inertial frame. Obviously, examples of this activity are already cited and cannot be made to go away.Brews ohare (talk) 14:10, 29 August 2008 (UTC)

Tags

{{Disputed|date=August 2008}} {{very long}} I think these tags should be removed. The first tag was placed by Fugal, and the issues he raised have been dealt with in the section of the article linked here. (He hasn't signed off on them, but also has not responded to suggestions for further discussion.) The second tag was placed by Timothy, who has not explained what exactly is too long about it, or what to do about it, and seems continually to insist upon exploration of advanced issues, with a tenuous (or, at least, vaguely identified) relation to the subject, requiring a still longer article to explain technical jargon (e.g. "tetrads", "congruence of timelike curves defined by constant spacelike coordinates", "continuous specification of the orientation of a spacelike triad to the timelike vectorfield"). Brews ohare (talk) 17:09, 28 August 2008 (UTC)

Strongly disagree with removing the tags with the article in its present condition. The majority of editors have expressed the view that the article is significantly too long, and that it contains misrepresentations and misunderstandings of the reputable literature. These have been fairly thoroughly explained on this discussion page.

One particular editor continues to misunderstand and misrepresent, and it seems clear to the majority of editors that this editor will never relinquish his position, no matter how clearly his misunderstandings are explained to him. This particular editor has adopted the tactic of filabustering, by reverting every edit that doesn't conform to his point of view, and justifying these reverts by posting endless repetitive objections to this discussion page based on his own misunderstandings, which he will never relinquish. Eventually every well-meaning editor simply gives up trying to reason with an obviously unreasonable person, at which point he declares victory and reverts their improvements back to his own misunderstandings.

Numerous editors have independently suggested that this particular editor appears to have strong feelings of "ownership" over this article, and they have suggested that it would be helpful for the article (not to mention for himself) if he would take a break. He shows no sign of taking this advice. As a result, the current tags on the article are necessary, and probably another should be added, about non-neutrality, since the article contains so much POV novel narrative and original research (all from this particular editor).Fugal (talk) 19:58, 28 August 2008 (UTC)

My own edits to this article are in direct response to this discussion page. They also have been supported in detail on this page, with repeated requests for commentary (as opposed to undocumented opinion). Brews ohare (talk) 05:39, 29 August 2008 (UTC)

Does the very long tag need explanation? The article is over 100k long! Note that the target is to try to keep article under 32k, for especially broad topics longer articles are exceptable. This article clearly does not fall in this last category. The fact that you couldn't figure that one out on your own says a lot about your loss of perspective with respect to this article. (TimothyRias (talk) 20:17, 28 August 2008 (UTC))

Not much help to say the article is long with no suggestions as to what should be changed to shorten it. Besides suggesting what might be cut, you might also suggest (i) why it should be cut and (ii) what might replace what is cut in the way of a more succinct explanation. Although you might debate the point, I'd say a good many of the additions to the article were provoked by the need for clarifications that you have occasioned yourself. Brews ohare (talk) 05:39, 29 August 2008 (UTC)

Wolfkeeper has adopted the policy of unilaterally deciding whether and when a dispute has been resolved, and/or whether it merits a dispute tag on the article. I believe this is contrary to Wikipedia policy. This behavior is especially egregious in the present case, because the majority of editors have expressed opposition to the POV that Wolfkeeper is promoting, and in fact at least FOUR editors have independently indicated that Wolfkeeper and/or Brews have lost their perspective and should take the advice given in the "ownership" article. In these circumtances, when a majority of editors have stated that an administrator has lost his or her perspective on a certain article, it seems to me that the administrator ought not to be exercising administrative functions related to that article (e.g., blockiing people who make unfavorable comments about the article). I wouldn't be surprised if there is already a Wikipedia policy stating as much, but even if there isn't, it sure seems like a reasonable idea. I'll try to contact some admin facilitators to see what they think, and report back.Fugal (talk) 04:57, 29 August 2008 (UTC)

A majority of editors??? Brews ohare (talk) 05:39, 29 August 2008 (UTC)

I forgot to mention that the inclusion of references in an article doesn't innoculate it against charges of being novel narrative. In fact, the description of novel narrative explicitly says that it consists of stringing together a bunch of references, but weaving them into a narrative whose meaning and intent differs from that of the sources. Hence it gets back to having a representative treatment, not simply citing references. The treatment must be accurate, and this is what is disputed in the present article.Fugal (talk) 05:01, 29 August 2008 (UTC)

Fugal: Your claim of narrative is totally unsupported by any documentation, and is simply invalid. The references are cited at enough length to show clearly that they are not misinterpreted in any way. Even longer excerpts can be read on line at the provided links.

In addition, your suggestions that a dispute exists on this talk page is not valid. A dispute implies dialog, and not just your own repeated statements. You have refused time and again to respond to all objections to your POV, and simply repeat yourself. And you have made no substantial, specific, documented objection to the article. Brews ohare (talk) 05:39, 29 August 2008 (UTC)

In my experience in 95+% of cases where an article is being tagged for POV, a general tag is completely inappropriate, and it's just a hissy fit of one editor to one or a few points being raised. This article is certainly no exception.- (User) WolfKeeper (Talk) 14:26, 29 August 2008 (UTC)

Concrete suggestions for reducing the length of the article.

OK, this article has grown way out of proportion. The current article size is over 100k. Not all of this is readable prose, but most of it is. (certainly at least 80k) We need to get this article back to readable proportions. Here are somethings that I think can be done to reduce the length:

1. The first 4 sections "Analysis using fictitious forces", "Choice of observational frame of reference", "Are centrifugal and Coriolis forces "real"?" and "Fictitious forces" contain a lot of overlap. Many of these sections repeat what has been said in the other section for a slightly different point of view. The sections can probably be rewritten to about 1 or 2 sections of about half the total length.
2. The discussion of artificial gravity from the "Are centrifugal and Coriolis forces "real"?" section can probably be removed. It doesn't really add anything to that section. It also opens up the more subtile subject of gravity itself being a fictitious force, which should probably be kept well beyond the scope of the article. It may be useful to re-add a small section on the subject of "artificial gravity" in the now very small "applications" section.
3. The "Moving objects and observational frames of reference" contains a long technical explanation of what local coordinates are, which is not within the scope of the article. The section would be better off referencing the appropiate article and skipping the long technical derivation.
4. On a similar note, a remark about the style of the article in general. Wikipedia as an encyclopedia not a textbook. The article has the strong tendency to try to explain and/or teach things. A more encyclopedic style of reporting facts about the subject would probably increase the readability of this article. This holds especially for long mathematical derivations to make a point. This will deter most potential readers. (mathematics may be a second (or first :)) language to (most) editors here, it certainly isn't for most readers) As a rule of thumb we should try to keep the use of formulas down to where the formulas themselves are the subject.
5. The "Uniformly rotating reference frames" is largly a paraphrase of the first section, but adds some actual formulas. (Which in this case are actually illustrative.) It should probably be taken along when rewriting/restructuring the first few sections.
6. The "Examples" section is probably a bit bloated. It should probably be condensed a little. It at least needs another look when the preceding sections have a more structured form.
7. The "Centrifugal force in polar coordinates" and the sections directly following it are a prime example of an editor falling in the pitfall of trying explain something. In this case it has lead to an essay several pages long trying make his point. The fact that a long the way the need arises to introduce new nomenclature should be seen as writing on the wall. Nowhere in the cited literature is connection/difference between the two "types" of centrifugal discussed, hence the wikipedia article should not either. Any attempt to discuss either - without any direct reference to a reputable source discussing this precise topic - will result in some form of original research.

(I'm out of time for the moment, I'll be back to elaborate on this last point some more.) (TimothyRias (talk) 10:31, 29 August 2008 (UTC))

I agree. Timothy has presented a good plan for trimming the article down to a more manageable size without losing any crucial content. In particular, I agree that the entire "centrifugal force in polar coordinates" major section can be removed entirely, for the reasons he states above: I have therefore WP:BOLDly done so. -- The Anome (talk) 11:57, 29 August 2008 (UTC)

Anome: Well, advancing matters to an edit war with absolutely no discussion is a very forward step. Your failure to remove the curvilinear section which logically also should go for the same reasons (although improper reasons) shows your lack of care in looking at this matter before so BOLDLY stepping into this matter. I fixed that for you. I congratulate Fugal and Timothy for having achieved their goal of censoring a very clearly argued case, never responded to in any way by these two editors, who have merely ranted on and on. Great editing Anome. Great. Real leadership. Glad you are so BOLD as to simply cut the knot, grasp the nettle etc. etc.. Brews ohare (talk) 14:43, 29 August 2008 (UTC)

Thanks for that: the curvilinear section was the next to go, and I'm glad you've preempted me by removing it as well. My intention was just as you said: to grasp the nettle and cut the knot. I'd be glad to help work on the rewrite of the rest of the article, as per Timothy's plan. -- The Anome (talk) 01:12, 30 August 2008 (UTC)

Many of Timothy's suggestions bear examination. I hope his later contributions undertake to explain just what he suggests in more detail. A massive rewrite like this is an undertaking, and as what is being replaced has been through numerous revisions, I suspect any replacement will as well. Brews ohare (talk) 13:57, 29 August 2008 (UTC)

all these forks

While I admit that I haven't looked at them in extreme detail, all these disambiguated "centrifugal force" articles, as far as I can tell, are discussing the same thing, just from different perspectives (or perhaps different philosophical viewpoints). That's not good; it's bordering on the policy/guideline against POV forks. Of course if there's enough to say about a philosophical perspective on a concept, then that perspective can get its own article with a link/summary in the main article, but there should be only one main article, which should summarize all current viewpoints. These badly need a merge into a single centrifugal force article.

I'm getting the impression that you may be having problems with a particular editor with a strong POV, though I haven't looked in enough detail to be sure which editor or which POV. If that's the case then WP ways need to be explained to him; he shouldn't be allowed to perpetuate the current mess, which is not a good situation for anyone. --Trovatore (talk) 22:50, 10 September 2008 (UTC)

Uh huh. How about you look at it in extreme detail, and get back to us if and when you actually have an informed point of view?- (User) WolfKeeper (Talk) 23:05, 10 September 2008 (UTC)

You also might like to read WP:NOTADICT which explains why two or more things that happened to be termed Centrifugal force do not automagically get to go in the same article. The relevant part is: 'Topics with the same or similar titles for different things are found in different articles'.- (User) WolfKeeper (Talk) 23:09, 10 September 2008 (UTC)

If -- and I am not persuaded that this is the case -- the different articles are actually discussing different things, rather than different ways of looking at the same thing, then why is it that centrifugal force redirects here, rather than being a disambiguation page? If this article is in fact the primary among the four (which I would think it would be) then it should just be named centrifugal force, with a hatnote for the dab page. If, on the other hand, the four articles discuss truly different things and none of them is clearly primary, then centrifugal force itself should be dab page. --Trovatore (talk) 23:23, 10 September 2008 (UTC)

Your proposal about disambiguation makes sense.

However, combining pages doesn't look like a good idea. History shows that centrifugal force is a magnet for confused debate, partly because there are conflicting terminologies for it, and half the world believes only one or the other of the two. Partly also because everyone has an intuitive notion of centrifugal force that gives it a reality not easily supplanted by abstract arguments about "frames of reference". The present set-up is a device to limit this unending debate that historically has recycled every few months as different new-comers to the page raise the same old issues.

The page divisions mean that debate focuses upon more specific issues, and that some of the arguments that arise again and again can be dealt with in a succinct manner by reference to specific examples within the limited context of the page where debate flares.

It may evolve that this separation of topics has not ended the problem, but so far so good.

It isn't inconceivable that some such sacrifices are necessary concessions to the reality of an encyclopedia that is modifiable by anyone. No-one wants to ride herd on the education of the English-speaking world via Wikipedia Talk pages.Brews ohare (talk) 14:53, 11 September 2008 (UTC)

Just for the record, I don't consider this to be in any way a sacrifice, the Wikipedia's rules actually do push you towards this layout.- (User) WolfKeeper (Talk) 15:06, 11 September 2008 (UTC)

I'd add to these remarks that the different pages do discuss different aspects of "centrifugal force". For example Centrifugal force (rotating reference frame) discusses examples based upon observations of a general nature in frames rotating about fixed axes, while Centrifugal force (planar motion) describes centrifugal force as it arises in the specific observation of a particle traveling a planar trajectory from the viewpoint of various observers that are using different types of coordinate systems. There is some common text of a general nature, for the sake of easy reading, but it is pretty minimal. Brews ohare (talk) 15:35, 11 September 2008 (UTC)

I have some sympathy for the idea that a single article could probably encompass all of the more-or-less related concepts that go under the name of "centrifugal force". Admittedly, there are some genuinely distinct concepts that go by that name... such as the reactive force versus the inertial force. But these two concepts are not entirely un-related (even though they are distinct).

As an aside, I recently found an scholarly paper written in 1898 in which the author ranted about the mis-use of the term "centrifugal force", and he had compiled about a dozen references, tabulating how many defined it "correctly" (in his opinion), and how many defined it "incorrectly". (His idea of "correct" was the reactive force definition.) I just mention this to point out that people have had issues with this for a long time, and it isn't just in Wikipedia talk pages that this has been an on-going topic of discussion/debate.

Recognizing that the reactive force really is a distinct definition of the term, I think most editors found it acceptable (though perhaps not all considered it desirable) to segregate that into a separate article. But then the really tricky part begins, because even within the "fictitous/inertial force" definition, there are different approaches that can be taken, different views of the subject, ultimately arising from different conceptions of the very foundations of science (intuitive, informal, and specialized versus abstract, rigorous, and general). The literature is mixed with regard to how these different views are presented, and naturally the intuitive/informal/specialized approach is to be found in the majority of texts, simply because the majority of texts are written at an introductory level and tend to rely on the intuitive informal and specialized approach to things, because it's simpler.

To be honest, I think the main reason we've been unable to consolidate the entire subject of centrifugal force (within mechanics), or even just the inertial/fictitious force part of the subject, into a single article is that some editors feel very strongly (just as did the guy back in 1898) that there is only ONE "correct" usage and interpretation of the term, and they don't want to sully their article with any hint or suggestion that there might be any other permissible usages within mechanics. Unfortunately the literature contains a variety of treatments of the subject, usually in sources that are not really focused on this as their main subject, and we have to try to derive a reasonable overall article from these somewhat disparate sources. I think it could be done (probably in less space than the current article), but only if the editors decided that the subject is large and contains many distinct but aspects, and it isn't necessary (or appropriate) to denigrate all but one particular aspect.Fugal (talk) 07:27, 12 September 2008 (UTC)

The different pages present different aspects of the term "centrifugal force", not different interpretations or points of view. Specifically, centrifugal force (rotating reference frame) is restricted to discussion of centrifugal force as it appears in reference frames rotating about a fixed axis, while centrifugal force (planar motion) treats centrifugal force as it occurs in the observation of a particle in planar motion (a restricted example) as seen from several different non-inertial frames. It also might be noted that centrifugal force (planar motion) presents two terminologies, not "one correct usage". Discussion of that page probably should appear on its discussion page, not here. Brews ohare (talk) 12:25, 12 September 2008 (UTC)

By the way, the forked article about "planar" motion is, I believe, very mis-named, because there is no need for any restriction to planar motion. There have been some mis-understandings expressed on these discussion pages about things like whether there is even such a thing as three-dimensional polar coordinates, and this kind of view seems to underly the mis-naming of that fork. Also there has been a persistent resistance to the introduction of the fully general formalism that emcompasses all aspects of fully general motion (as opposed to rotation about a fixed axis, which is really more of a text book exercise, as compared with most real applications that involve general motion), with fully general systems of reference. Within that context, the entire subject of centrifugal force is very simple, unified, and coherent, but without making use of that formalism (which requires a level of abstraction that is unfamiliar to some), it splits into seemingly disjoint subjects, hence all the forking. It occurs to me that perhaps what's needed is an article specifically on the subject of the many meanings and interpretations of the term "centrifugal force" in dynamics. This could be the main article on centrifugal force, with branches to sub-articles where individuals could expound at greater length on their own preferred views of the subject.Fugal (talk) 07:27, 12 September 2008 (UTC)

The article centrifugal force (planar motion) does treat planar motion, and the math on that page is restricted to that case. Of course, more general, non-planar trajectories along 3-dimensional curves could also be treated by extending the formalism to include things like torsion. But it is not a misnaming of the page to say what it actually describes.: Discussion of that page probably should appear on its discussion page, not here.

A more general treatment, e.g. based upon concepts of differential geometry and general relativity would be an interesting page in itself, but, as Fugal has pointed out, it would be consulted mainly by specialists because that kind of background is not general, restricted to mathematicians and physicists with specialized training.

By broadening the discussion to treat fictitious forces in general, rather than the very particular centrifugal force, a very general treatment for the case of particle motion in both inertial and non-inertial frames employing Cartesian coordinates is provided at fictitious force. It does not, however, treat general relativity and curvilinear coordinate systems. Brews ohare (talk) 12:39, 12 September 2008 (UTC)

We shouldn't confuse the introduction of general curvilinear coordinates with general relativity. I think there's common agreement among all the editors that this article (or these articles) are restricted to classical (i.e., pre-relativistic) dynamics. Within that context, general curvilinear coordinates are the most comprehensive, and when the discussion is framed in those terms, the entire subject becomes unified, and one sees that what had seemed to be distinct concepts are really just different ways of looking at exactly the same thing. This is why the disagreement over dictionary versus encyclopedia is so ambiguous, because what seems to be different definitions from one point of view are really just different points of view from another point of view.Fugal (talk) 13:40, 12 September 2008 (UTC)

Unification of viewpoint seems to me a bit more complicated than using curvilinear coordinates. Math connected to general formulas and their simplification to apply to specific coordinate systems is unrelated to the physics, which is concerned with relating the results of observers in disparate states of motion (inertial cf. non-inertial) regardless of what coordinate system they choose to employ. I'd agree that "just the same thing" can be described in various coordinate systems. However, the fictitious forces and the classification of the various contributions as "centrifugal", "Coriolis", or "Euler" depends strongly upon the observer's state of motion (e.g. are they rotating? and about what axis, oriented how?) and not upon their selection of coordinates (Cartesian, arc-length, etc.) to describe what they see. Perhaps a detailed statement of just what could be unified and just how that could be done might be provided? Brews ohare (talk) 18:11, 12 September 2008 (UTC)

It's already been provided (several times, by at least two different editors), so I'm unsure if provided it again will be productive. The other editor commented that you didn't seem to be really trying to understand, and I'd have to endorse that impression. However, I'll think about possibly posting a detailed summary statement of the unified view, maybe later today if I get around to it. But before you would be in a position to understand it, I think you need to clarify some misunderstandings that you've expressed in your latest message.

You refer to "the results of observers in disparate states of motion", but observers don't have results. Measurements have results. This may seem like an unimportant quibble, but it isn't. It’s vitally important to be clear and precise. What you most likely mean is something like "the results of measurements performed by observers in disparate states of motion". But as soon as you state this explicitly, it is apparent that what you’re describing is nothing other than a coordinate system (or perhaps an equivalence class of coordinate systems, i.e., a system of reference, or a reference frame). In order to quantify the measured (i.e., observed) positions and motions of a particle, there must be a system of measure, which extends over the region of interest, and this is tantamount to a system of coordinates.

The Wikipedia article on Reference Frames, which I gather was written mostly by you, contains the your characteristic focus on “observers”, as if there is some kind of anthropomorphic quality of an “observational frame of reference” distinct from a plain old “frame of reference” (system or systems of coordinates). The source that you cited for this point of view is a quaint little introductory book entitled “How and Why in Basic Mechanics” by A. Kumar and Shrish Barve. That book does indeed refer to observers, but please (please!) make note of the following words from that very book, which it presents in the form of a dialogue between a professor and a clueless newbie:

I used words like 'relative to some observer'. The word 'observer', however, can be very misleading. It gives an impression that we are talking of a person looking at the phenomena, making appropriate measurements and possibly comparing them with those of another person. I suggest you banish this picture from your mind.

I am surprised. What is wrong with it?

Physics deals with numbers—measurements cairied out by impersonal Instruments. The person behind the instruments is irrelevant for physics; that is what one means by objectivity in science. So it is best to deseribe phenomena without invoking the notion of an observer...

We replace the image of an 'observer' by an impersonal abstract object; we simply imagine a frame of long rigid rods extending out from a point (origin) in space in three independent directions… [Please note that this amounts to the stipulation of rectilinear Cartesian coordinates, so all subsequent statements are restricted to this sub-class of coordinate systems. You may recall that I previously advised you to check your sources for stipulations of this kind.] Thus. for example, the frame of reference of a train is an abstract aitifact which has the same motion as thal of thc train. Therefore, instead of saying, for example, that the trajectory of a stone dropped out of a running train is a straight line for a train observer and a parabola for a ground observer, it is better to say that the trajectory is a straight line in the train's frame of reference and a parabola in the ground's frame of reference.

I realize this is somewhat repetitive, because I've explained this very same thing to you before, but your response was to disregard it because I'm "amazing ignorant". So my hope is that showing you that even your own source, which you've cited as the source for your belief in the paramount important of the concept of an "observer", actually goes to great lengths to disavow that of view, and to corroborate what I told you.

Now, having said all this to explain why these concepts can only be formulated in terms of coordinate systems, it's obviously true that we could choose to work only with quantities (such as absolute acceleration) that are invariant, regardless of the system of reference, but on this basis there are no fictitious forces. The introduction of fictitious forces entails a decision to forego absolute coordinate-independent acceleration, and to work with a coordinate-dependent acceleration. Hence the very subject that we're dealing with requires us to treat coordinate-dependent quantities.

The main point is that your alleged bifurcation between "mathematical descriptions" and "physical descriptions" does not exist. It won't be possible to make much progress with this article (or with any of the other articles that you've edited) until you relinquish the idea of such a bifurcation. From the standpoint of Wikipedia, your bifurcation is novel narrative, and is unsupporeted even by your own cited references (as shown above). I challenge you to cite a single reputable reference that distinguishes between mathematical descriptions and physical descriptions. If you're unable to find such a reference, I think you should stop making that point of view the basis for your editing of Wikipedia articles.Fugal (talk) 17:52, 13 September 2008 (UTC)

Response to Fugal

You refer to "the results of observers in disparate states of motion", but observers don't have results. Measurements have results. This may seem like an unimportant quibble, but it isn't. It’s vitally important to be clear and precise.Fugal (talk) 17:52, 13 September 2008 (UTC)

"Observer" is a technical term, but it does not imply any particular coordinate system or any specific measurement apparatus. It is not "anthropomorphic" and is a term in good standing in the literature. The quote you provide suggests the term "observer" be avoided only because of certain misconceptions related to the carry-over of popular meaning to a context where a technical meaning exists. The authors use the term "observer" themselves in answers to the student on the same page. I can produce quotes employing "observer" in a technical sense that already are present in various Wiki articles (see Frame of reference) in case you missed them. A googlebook of phrase "inertial observer" provides 647 books with this term. Brews ohare (talk) 00:21, 14 September 2008 (UTC)

Now, having said all this to explain why these concepts can only be formulated in terms of coordinate systems, it's obviously true that we could choose to work only with quantities (such as absolute acceleration) that are invariant, regardless of the system of reference, but on this basis there are no fictitious forces. The introduction of fictitious forces entails a decision to forgo absolute coordinate-independent acceleration, and to work with a coordinate-dependent acceleration. Hence the very subject that we're dealing with requires us to treat coordinate-dependent quantities.Fugal (talk) 17:52, 13 September 2008 (UTC)

Well, we are totally at odds here. The adoption of a non-inertial frame automatically introduces fictitious forces, regardless of any subsequent adoption of a particular coordinate system. Moreover, the definition of "absolute acceleration" probably will involve the definition of an inertial frame of reference, although this term is sometimes applied as follows: if a point P in frame ʕ is fixed relative the frame, the absolute acceleration of point Q in frame ʕ is its acceleration relative to P. What is your meaning?

I'd note that physical quantities like vectors and tensors are commonly considered to refer to entities that exist independent of coordinate systems, although coordinate systems can be introduced to make their manipulation more mechanical. The velocity vector of a particle, as an example, is coordinate-system independent, but it is not independent of the velocity of the frame of reference: it is "observer's state-of-motion" dependent in a manner that is independent of the observer's choice of coordinate system; for example, independent of the observer's choice for orientation of their coordinate system.

Perhaps you would wish to enter a detailed debate on this point? Brews ohare (talk) 00:32, 14 September 2008 (UTC)

The main point is that your alleged bifurcation between "mathematical descriptions" and "physical descriptions" does not exist.Fugal (talk) 17:52, 13 September 2008 (UTC)

This point needs further discussion, I'd guess. For example, the "physical description" provided by the phrase "the kid is sliding down the water slide" could be expressed mathematically in terms of the position s along the slide at time t or as the coordinates of the kid (x, y, z) at time t, or, instead of time, in terms of the distance the moon has orbited during the slide, or how far a certain beam of light traveled. That would be several mathematical descriptions of the same physical event. What is only "alleged" in this bifurcation? The mathematical description is many-to-one in relation to the physics. Brews ohare (talk) 19:40, 13 September 2008 (UTC)

Response to Fugal (cont'd)

You say the quote I provided from your source (e.g., “it is best to deseribe phenomena without invoking the notion of an observer... I suggest you banish this picture from your mind”) doesn’t dismiss the term “observer”. You go on to say that the quote disapproves of certain misconceptions related to the term, and that is certainly true. Unfortunately, it is precisely those misconceptions to which you have fallen prey, and which you are promoting in your edits here. For example, you say

The adoption of a non-inertial frame automatically introduces fictitious forces, regardless of any subsequent adoption of a particular coordinate system.

That’s a partially true statement, but to the limited extent that it’s true, it supports my position rather than yours. A frame is an equivalence class of coordinate systems,Fugal (talk) 02:18, 14 September 2008 (UTC)

The statement that a frame is "an equivalence class of coordinate systems" is interesting. Question 1: What are the rules for membership in this class? Question 2: Any references for this? Question 3: Is it more natural or easier to talk of "an equivalence class of coordinate systems" than to say that an observer has a choice of coordinate systems; actually any of the standard mathematical choices (curvilinear, polar, Cartesian, …); and whichever is chosen, it must adopt the observer's state of motion inasmuch as it travels with the observer? Thus, the "equivalence class" is simply all possible mathematical coordinate systems that travel with the observer, no? Brews ohare (talk) 04:48, 14 September 2008 (UTC)

and by selecting a particular frame we are partially specifying a system of measure which, combined with the pretense that the second derivative of spatial position with respect to time represents the true absolute acceleration in Newton’s law, does indeed entail the treatment of the remaining components of the true acceleration as fictitious forces.Fugal (talk) 02:18, 14 September 2008 (UTC)

I believe you are reverting to the "coordinate definition" of fictitious force here:that is, the approach that drags all contributions to the acceleration except the second derivative to the force-side of the equation; the physical or "state-of-motion" definition (appropriate to the discussion of fictitious force in the setting of inertial vs. non-inertial frames) does not do this, and does not imply all terms other than the second time derivative are fictitious. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

But this contradicts your position for two reasons:

First, this is already a blatently “mathematical” development, because we are choosing to pretend that the absolute acceleration of an object equals a particular mathematical function of our chosen coordinates (remember, the choice of a frame specifies the absolute shape of the time axis), despite the fact that we know full well that this function of our coordinates does not equal the absolute acceleration. It amounts to pretending that a family of curved lines are straight, even though we know they are really curved. This occurs because the inertial basis vectors at a given location in space change with time. Fugal (talk) 02:18, 14 September 2008 (UTC)

This all may be true of the "coordinate system" approach, but I regard that, as apparently you do also, as simply a device of mathematical convenience. The approach basic to the centrifugal force article is the "state-of-motion" approach that states that inertial forces appear only in non-inertial frames. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

Second, we have so far only partially specified a system of measure, by narrowing the choices down to the members of a certain equivalence class of mutually stationary coordinate systems. Within this class there are a variety of spatial coordinate systems, for some of which the inertial basis vectors at a given instant of time change with spatial position. The selection of these systems of measure entails additional fictitious forces in exactly the same sense that the specification of the temporal variation in the inertial basis vectors does.Fugal (talk) 02:18, 14 September 2008 (UTC)

Here I'd disagree. The distinction between fictitious forces in the "state-of-motion" sense and in the "coordinate-system" sense is lost, and the two usages are being smeared together. To repeat, "state-of-motion" fictitious forces are always zero in an inertial frame, while "coordinate-system" fictitious forces may or may not be, and in general curvilinear coordinate systems are non-zero in inertial frames. Brews ohare (talk) 06:06, 14 September 2008 (UTC)

Again, this is because we choose to pretend that the absolute acceleration of an object equals a particular mathematical function of our chosen coordinates, despite the fact that we know full well that this function of our coordinates does not equal the absolute acceleration. Just as before, it amounts to pretending that a family of curved lines are straight, even though we know they are really curved.Fugal (talk) 02:18, 14 September 2008 (UTC)

Here we return to the "coordinate-system" definition of fictitious forces. Brews ohare (talk) 05:58, 14 September 2008 (UTC)

Some of the spatial systems of measure within a given frame consist of rectilinear Cartesian coordinates, in which the basis vectors at a given instant of time do not change with spatial position. As has been shown by explicit quotations, the text books and papers that neglect the spatial variation in basis vectors do so by stipulating that they exclude from consideration any spatial coordinate systems whose basis vectors change with position. They usually do this tacitly, by saying that a spatial system of measure consists of three rectilinear Cartesian axes. (I’ve given you the quotations in which two of your own sources make this stipulation.) On this restricted and asymmetric basis, it is of course correct to say that fictitious forces are uniquely determined by the choice of a reference frame. But the point is that this is a restricted and asymmetric basis, because spatial coordinate axes need not be absolutely straight, just as temporal axes need not be absolutely straight.Fugal (talk) 02:18, 14 September 2008 (UTC)

Again, the restriction to Cartesian coordinates does simplify things, inasmuch as all the phony terms in the fictitious force due to the spatial and temporal variation of the unit vectors go away. However, I have no issue with your gripes over what I consider a mere mathematical gimmick in the "coordinate-system" terminology.

References have been cited which present the unrestricted and symmetrical treatment, in which we do not stipulate in advance that curved temporal axes are allowed but curvilinear spatial axes are excluded. This gives a unified and symmetrical treatment of the entire subject in general, which I can outline for you (again) if you wish.Fugal (talk) 02:18, 14 September 2008 (UTC)

I regret prevailing upon you, but yes, I'd like that outline. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

You say “That would be several mathematical descriptions of the same physical event. What is only "alleged" in this bifurcation? The mathematical description is many-to-one in relation to the physics.” The bifurcation you've alleged is between different choices from among the many possible mathematical descriptions of events. There is nothing absolute about fictitious forces. They are a purely artificial concept that arises when we choose a particular system of coordinates (or a class of systems) and then decide that if our chosen coordinate axes are curved we are going to pretend they are straight, which we do by pretending that a particular mathematical function of our coordinates represents the true acceleration of an object (even though we know it doesn’t).Fugal (talk) 02:18, 14 September 2008 (UTC)

As I have tried to explain above, I do not subscribe to the system you denigrate, and so will not try to support it. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

You allege a bifurcation between two different sets of mathematical descriptions, those that are familiar to you, and those that aren’t. You call the former descriptions “physical” and the latter “mathematical”. My point is that this bifurcation represents nothing but your personal prejudices and the limitations of your understanding, rather than any real bifurcation of the conceptual subject, and moreover that this bifurcation leads to the "forking" in the subject, which several editors consider undesirable.Fugal (talk) 02:18, 14 September 2008 (UTC)

I do not understand these remarks. I suspect they stem from supposing I am arguing for the "coordinate-system" mathematically convenient approach, which I do not support. I would agree we do not understand each other, but laying all the blame upon my limitations is ungraceful, to say the least.

The distinction between "physical descriptions" and "mathematical descriptions" is not as you describe it. The physical description in my first example is "sliding" (familiar to me and to you) and the mathematical descriptions consist of describing the succession of space-time points using various different choices of variables. The physical description in my second example is the observed vector velocity of a particle, a physically distinct entity that depends upon the state-of-motion of the observer, but not upon the observer's coordinate system. These examples provide very simple, clear distinctions, attributable to neither prejudice nor ignorance, I'd say.

The real issue probably comes down to the distinction between the two usages for fictitious force, what I have termed "state-of-motion" and "coordinate-system" fictitious forces. You have argued before that there is no such distinction, and maybe that is where matters rest? Is that the issue? Is that the only issue? Are we back to the discussion at Fugal's positions? Brews ohare (talk) 06:26, 14 September 2008 (UTC)

To make it handy, here is the earlier summary:

Fugal's positions

Fugal

My position is that [the mathematical terminology for certain terms in the acceleration of a body as viewed in curvilinear coordinates] is not an insignificant minority or fringe viewpoint, but is in fact a view represented in a significant fraction of the literature.

Brews-ohare

My view is that it is not a viewpoint, but a different use of terminology. That these terms constitute a different usage is shown (in part) by the fact that these terms are an artifact of the coordinate system, and therefore appear in every state of motion, every frame of reference, in both inertial and non-inertial frames. That is not true of centrifugal force as defined in this article. As a different subject, a reference to this alternative usage is all that is needed. I believe Wolfkeeper has the same view. Brews ohare (talk) 14:41, 12 August 2008 (UTC)

Fugal

The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force.

Brews_ohare

Here is only one citation (of many from googlebooks) that contradicts this remark: Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…". Brews ohare (talk) 15:55, 12 August 2008 (UTC)

Fugal

Also, the acceleration terms appearing with certain coordinates do not depend on the presence or state of motion of any observer.

Brews_ohare

My point exactly: however, centrifugal force (as used in this article) does depend on the state of motion of the observer. In Newtonian mechanics, a state of acceleration (a state of motion) identifies a non-inertial frame of reference. A citation: "If we insist on treating mechanical phenomena in accelerated systems, we must introduce fictitious forces, such as centrifugal and Coriolis forces." Meirovitch Methods of Analytical Dynamics . Brews ohare (talk) 15:37, 12 August 2008 (UTC)

Fugal

Fictitious forces are, by definition, artifacts of a particular choice of coordinate systems. They are all "mere mathematical manipulations".

Brews_ohare

In fact there are two meanings for fictitious force: one depends on the state of motion of the observer (see above) and one is a mathematical act of poetic license, applying picturesque language to certain terms that arise in the acceleration when calculated in curvilinear coordinates, without regard for the observer's state of motion. Are we going 'round and 'round here?!? Here are two quotes relating "state of motion" and "coordinate system":

We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted ${\mathfrak {R}}$, is said to move with the observer.… The spatial positions of particles are labelled relative to a frame ${\mathfrak {R}}$ by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame ${\mathfrak {R}}$, can be considered to give a physical realization of ${\mathfrak {R}}$. In a frame ${\mathfrak {R}}$, coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

— Jean Salençon, Stephen Lyle Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9

and from J. D. Norton:

…distinguish between two quite distinct ideas. The first is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events in spacetime neighborhoods. The second, the frame of reference, refers to an idealized system used to assign such numbers … To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions. … Of special importance for our purposes is that each frame of reference has a definite state of motion at each event of spacetime.

— John D. Norton: General Covariance and the Foundations of General Relativity: eight decades of dispute, pages 835-836 in Rep. Prog. Phys. 56, pp. 791-858 (1993).

Assuming it is clear that "state of motion" and "coordinate system" are different, it follows that the dependence of centrifugal force (as in this article) upon "state of motion" and its independence from "coordinate system", while the mathematical version of "fictitious force" has exactly the opposite dependencies, indicates that two different ideas are referred to by the same terminology. The present article is about one of these two ideas, not both of them. Brews ohare (talk) 06:30, 14 September 2008 (UTC)

The core of the entire problem here is your novel narrative related to "state of motion" as opposed to "coordinate system". Note that your reference says a frame specifies a state of motion at every point; it does not say that a state of motion at a single point specifies a frame. The reason it doesn't say this is because it's not true, but unfortunately this is the proposition on which you've based your entire view of this subject.

Look, as Tim Rias and I have both explained to you - repeatedly, at great length, and in several different ways - a state of motion does not suffice to unambiguously establish a system of measure over a region of space and time. Your intuitive notion that a "state of motion" (e.g., of an "observer") possesses an unambiguous extension to surrounding regions is simply incorrect. None of the references you repeatedly quote gives any support to this misunderstanding of yours. When I read any of your cited references, I think "yes, exactly right", and when I read any of Tim Rias's comments I think "yes, exactly right", and when I read any of the rest of the vast literature on this subject I think "yes, exactly right", but when I read any of your comments my reaction is "No, completely and utterly wrong". Why do you suppose this is?

I'm really not sure how any progress can be made here. You appear (to me) to be either unable or unwilling to let go of the mistaken idea that a state of motion possesses an unambiguous "physical" mapping from one place to another (an idea that you associate with an "observer", as if the word "observer" somehow magically enables two plus two to equal five). This imaginary unambiguous mapping is what you call physical, and all other mappings are what you call mathematical. As I said before, this false dichotomy simply represents the limitations of your understanding. I've explained what is wrong with your beliefs in great detail, (as have others), and have tried expressing it in various ways, hoping that one of these ways would turn on the light bulb for you, but nothing seems to help. How do you suggest we proceed?Fugal (talk) 07:33, 14 September 2008 (UTC)

Proposed procedure for resolution

1. Move the discussion to Talk:Centrifugal force (planar motion).
2. Further details on a proposal for resolution of differences are there. Brews ohare (talk) 17:02, 14 September 2008 (UTC)

That page has been split off from this "rotating reference frame" page so as not to be fixated on the rotating reference frame simplifications, but unfortunately you have based your discussion on that page explicitly on the text in the section entitled (wait for it...) "Rotating Reference Frames" in Stommel and Moore. You ignore the section where that reference addresses centrifugal force in the more general context.Fugal (talk) 17:25, 14 September 2008 (UTC)

What have I ignored by these authors that is pertinent? Brews ohare (talk) 17:37, 14 September 2008 (UTC)

The part where they discuss centrifugal force in stationary systems of reference.Fugal (talk) 19:33, 14 September 2008 (UTC)

Any specific items? Any page numbers? Brews ohare (talk) 21:03, 14 September 2008 (UTC)

Yes indeed. The items and page numbers that were presented months ago when the reference was first introduced, and the quotes explicitly contradicting your views were presented.Fugal (talk) 17:25, 14 September 2008 (UTC)

Your reply contains no data. It is a vague reference to the past, where my recollection is that you quoted Stommel and Moore out of context, and were corrected. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

And you (yet again) insist on inserting your own original research about a distinction between "coordinate-system fictitious forces" and "state of motion fictitious forces", which is not contained in any of the references you cite in support of it. As has been pointed out previously by others, the very fact that you find it necessary to coin these neoligisms is prima facie evidence that you are constructing novel narratives. Fugal (talk) 17:25, 14 September 2008 (UTC)

I am simply distinguishing between different usages. That different usages are used in the literature is supported by direct quotations. Brews ohare (talk) 17:37, 14 September 2008 (UTC)

The explanation for what you call "different usages" has been given to you repeatedly, by multiple editors. It is simply different contexts, e.g., once someone has stipulated that they are restricting their spatial coordinate systems to the class of rectilinear Cartesian coordinates, the statements limited to curved time axes then are correct, but they are conditional statements, within the specified context. So your novel narrative and neologisms, both of which violate Wikipedia policy, are not appropriate.Fugal (talk) 19:33, 14 September 2008 (UTC)

It is not a question of context: formulas for exactly the same situation produce different results for fictitious forces. These formulas are derived in the subsection proposed for critique, and are clearly different. You refuse to engage. Brews ohare (talk) 21:03, 14 September 2008 (UTC)

Once again, your conception of what consistites "the same" or "different" "situations" is fallacious. Fictitious forces are not absolute entities, they are dependent on the chosen system of reference (as well as on the arbitrary decision to conflate the identities of certain mathematical functions of those terms of reference). I do not refuse to engage, and I have engaged, but I do decline to be repetitive, and in particular to continue presenting explanations to issues concerning the foundations of physics over and over again to someone who has demonstrated an unshakeable determination to avoid understanding. Look, Wikipedia is not intended to be a venue where original researchers can come to extort discussions from experts on their pet ideas.Fugal (talk) 23:31, 14 September 2008 (UTC)

We're not talking foundations of physics here. We're talking about failure to critique planar motion observed from a rotating frame, which embodies at a very simple and concrete level the issues at stake in a context where rant could be avoided and real ideas discussed. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

Also, the naming of that forked article (planar motion) is itself part of your novel narrative, because the whole point of the other page was to write about the LESS restricted view of the subject, whereas by giving it the bizzare name "planar motion" you are implying that the page presents a MORE restricted view. And so on. All this has been explained to you over and over (and over) again, and not just by me.Fugal (talk) 17:25, 14 September 2008 (UTC)

Since I wrote the other page entirely, its purpose is obviously what I have made it. Brews ohare (talk) 17:37, 14 September 2008 (UTC)

Please see the Wikipedia policy on "ownership". You do not own any article, nor are you the sole arbiter as to the purpose or content of any article. Multiple editors here have suggested that you seem to be violating the Wikipedia policy in your attitude of "ownership", as exemplified by the statement above.Fugal (talk) 19:33, 14 September 2008 (UTC)

Fugal, that you would distort my remarks in this way is unconscionable. What I said was that your notion about what was the original purpose of this page is erroneous because I originated the page and selected the subject. That does not preclude anyone editing the page. What is the matter with you? Brews ohare (talk) 21:03, 14 September 2008 (UTC)

It isn't a distortion. Once again, you mis-understand. I was referring to your re-direct of my question, when I asked if you had any suggestions for how we should proceed, after both I and another editor had explained to you, over and over and over, the general unified view of this subject. You re-directed the discussion of THAT topic to your "planar motion" page, despite the fact that THAT topic has nothing to do with "planar motion".Fugal (talk) 23:31, 14 September 2008 (UTC)

And how does the subject of "redirection" relate to the misconception you raised about "the whole point of the other page was to write about the LESS restricted view of the subject". Can't you stay on topic? Brews ohare (talk) 13:00, 15 September 2008 (UTC)

From your perspective, the "matter with me" is that I decline to engage with an "original researcher" on the subject of his own original research. Such individuals should post their ideas on Usenet discussion groups. I realize it's tempting for an original researcher to come to Wikipedia and try to engage experts and professionals in discussions of their novel ideas, but that isn't the purpose of Wikipedia.Fugal (talk) 23:31, 14 September 2008 (UTC)

Well, as an "expert and professional" I suppose that "discussion of novel ideas" is one of your forté's. But we are just talking about two uses of the same terminology, something more prosaic. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

My proposal for making progress is for you to focus your efforts on this rotating reference frame page, and for the "planar motion" page to be renamed something like "Centrifugal force (general)", and for that page to be edited by people who understand the general concept of centrifugal force, which includes as a subset - but is not limited to - the "rotating reference frame" aspects. At some point, the redundancy will become clear, and I'd expect the "rotating reference frame" page to be removed, but in the mean time it may serve a useful purpose, allowing the editing of the "general" page to proceed on a reasonable basis.Fugal (talk) 17:25, 14 September 2008 (UTC)

Well, these "other people" can write "Centrifugal force (general)" if they can be rounded up. There is no need to re-write or re-name the existing page on planar motion, as that is a particular topic with its own discussion.Brews ohare (talk) 17:37, 14 September 2008 (UTC)

There is, in my judgement, no need or justification for a separate fork to a page on "planar motion", because it is contained as a subset of the full spatial motion discussion. On the other hand, the content of the page which you named "planar motion" really isn't planar motion, as anyone who cares to take a look can see for themselves. (Note that you yourself just moments ago recommended re-directing all discussion of the more general view of centrifugal force to that page, so you are obviously aware that the content of that page is not "planar motion".)Fugal (talk) 19:33, 14 September 2008 (UTC)

There is presently no "full spatial motion discussion". There is no reason at present to change the specific and limited discussion pages on "rotation about a fixed axis" and "planar motion" to become such a general page: a general page can stand on its own whenever it comes along.

You say "the page which you named "planar motion" really isn't planar motion". That statement is hogwash: look at the math. It all applies to planar motion of a particle, and will not work for a more general 3D motion. What is the matter with you?Brews ohare (talk) 21:03, 14 September 2008 (UTC)

Anyone who is interested can view that article for themselves, and decide for themselves if the subject is "planar motion".Fugal (talk) 23:31, 14 September 2008 (UTC)

And how did you decide this article is not about planar motion? Brews ohare (talk) 13:00, 15 September 2008 (UTC)

Again, you distort matters by saying I "recommended re-directing all discussion of the more general view of centrifugal force". What I did do was recommend that a discussion of a particular subsection of the page Centrifugal force (planar motion) be moved to that talk page. What is the matter with you? Brews ohare (talk) 21:03, 14 September 2008 (UTC)

Again, that isn't the re-direct I'm referring to. I'm talking about your latest re-direct of the discussion pertaining to the general unified approach to the overall subject, which of course has nothing to do specifically with "planar motion".

This event is a creation of your imagination. It never happened. Brews ohare (talk) 13:11, 15 September 2008 (UTC)

I interpret your vague general remarks, as opposed to specific textual and mathematical criticism of the proposed section, as a desire to pontificate rather than contribute. Brews ohare (talk) 17:51, 14 September 2008 (UTC)

The specific textual and mathematical criticism has been presented on this discussion page many many (many) times.Fugal (talk) 19:33, 14 September 2008 (UTC)

Fugal: That simply is untrue – no-one has reviewed the subsection proposed or made any concrete proposal. Brews ohare (talk) 19:46, 14 September 2008 (UTC)

You're mistaken. The novel narrative, neoligisms, and original research aspects have all been specifically and repeatedly pointed out. Also, a correct, concise, and complete version was added to the article, and you deleted it.Fugal (talk) 23:31, 14 September 2008 (UTC)

Reasons for deletion provided at #Centrifugal force in general curvilinear coordinates were never responded to. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

Your reason for deleting it is that you did not understand it and you found that I would not engage with you in a discussion of your original research, misrepresentations, and neoligisms.Fugal (talk) 23:31, 14 September 2008 (UTC)

I think you mean you have ranted a lot in vague context about "novel narrative, neologisms, and original research", but you disdain to critique in any more specific way. That applies to the reasons for deletion above, to #Fugal's positions_2 and, in particular, to the subsection planar motion observed from a rotating frame. Brews ohare (talk) 14:11, 15 September 2008 (UTC)

Wikipedia discussion pages are specifically NOT intended to be a venue for the discussion of the subject of an article. They are supposed to be where editors discuss the suitability of various edits in terms of the criteria established by Wikipedia policy. This consists of determining things like whether something is original research, novel narrative, neoligisms, and whether it accurately represents the views presented in reputable sources (verifiability). It does NOT consist of proving something to be "true" or "false". It's unfortunate that the policy had to be adopted, but it was prompted as the only practical way of dealing with individuals who are fixated on a certain topic and are absolutely convinced that their novel narrative on the topic is correct, and they can PROVE it. No amount of discussion or "engagement" with such individual will do any good. Hence the following official Wikipedia Policy:

begin quote-------------

Wikipedia's founder, Jimbo Wales, has described original research as follows: The phrase "original research" originated primarily as a practical means to deal with physics cranks, of which of course there are a number on the Web. The basic concept is as follows: It can be quite difficult for us to make any valid judgment as to whether a particular thing is true or not. It isn't appropriate for us to try to determine whether someone's novel theory of physics is valid; we aren't really equipped to do that. But what we can do is check whether or not it actually has been published in reputable journals or by reputable publishers. So it's quite convenient to avoid judging the credibility of things by simply sticking to things that have been judged credible by people much better equipped to decide." (WikiEN-l, December 3, 2004).

The phrase "original research" in this context refers to untested theories; data, statements, concepts and ideas that have not been published in a reputable publication; or any new interpretation, analysis, or synthesis of published data, statements, concepts or ideas that, in the words of Wikipedia's founder Jimbo Wales, would amount to a "novel narrative or interpretation" ... regardless of whether it's true or not; and regardless of whether you can prove it or not.

end quote----------------

Those last words are intended for people who demand that others "engage" with them in a discussion of what is "true". Bottom line: It doesn't matter. We're not here to decide what is true. We're just here to accurately report what has been published in reputable sources on this subject. If a reputable published source says centrifugal force appears in stationary polar coordinates (for example), then this must be reflected accurately in the article. Period.Fugal (talk) 20:39, 15 September 2008 (UTC)

Hi Fugal: Glad you got that off your chest. However, the discussion I'm looking for is a precise, well documented contribution to the articles. I do think that is what Wiki Talk pages are for. Brews ohare (talk) 21:13, 15 September 2008 (UTC)

You're not lacking an explanation. You're lacking an understanding.Fugal (talk) 19:33, 14 September 2008 (UTC)

Fugal, thanks. Same to you. Brews ohare (talk) 19:46, 14 September 2008 (UTC)

Unfortunately, all any of the other editors here can do is provide you with explanations, not with understanding. You can obviously continue to not understand indefinitely, and you can continue to edit this and other articles based on your lack of understanding, which manifests itself in misrepresentations, novel narratives, original research, neologisms, and a persistent attitude of ownership, all of which are inappropriate for editing Wikipedia articles.Fugal (talk) 19:33, 14 September 2008 (UTC)

Fugal, I see. You can lead a horse to water, but you can't make him drown. Unsubstantiated pejorative remarks certainly advance things. Brews ohare (talk) 19:46, 14 September 2008 (UTC)

My remarks have been fully subtantiated, as have been the remarks of others who have explained the same things. You're not lacking for explanations or substantiation, you're just lacking in understanding. I think I've done more than part to help, but at some point it becomes clear that you simply are determined not to understand... and you're equally determined to prevent any understanding from entering these articles, which I think is unfortunate, although I suspect it will eventually be remedied.Fugal (talk) 23:31, 14 September 2008 (UTC)

Many assertions, no back-up. A case of revisionist history. Brews ohare (talk) 14:42, 16 September 2008 (UTC)

Suggestions

Fugal, your rewriting of history on Talk:Centrifugal force (rotating reference frame) contains no specifics, no engagement, and no facts. Two simple examples are your complete lack of response to Fugal's positions and to the subsection planar motion observed from a rotating frame. If you are serious, you must get down to brass tacks and stop lecturing. Brews ohare (talk) 13:03, 15 September 2008 (UTC)

As a "brass tacks" approach, take the subsection Polar coordinates in a rotating frame of reference and explain why (in your mind) the two different treatments of the terms $(mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}})$ (as fictitious force in one case, but not in the other) do not constitute two different usages of the terminology "fictitious force". It is not a case of different contexts inasmuch as both approaches describe exactly the same phenomena in exactly the same coordinate system and in exactly the same frame of reference. Brews ohare (talk) 19:07, 15 September 2008 (UTC)

The general unified solution to the very example you're talking about has been presented three or four times on this discussion page already, explicitly and in full, with equations and detailed explanation. There is obviously no point in duplicating it yet again.Fugal (talk) 20:39, 15 September 2008 (UTC)

Perhaps you refer to your Revision as of 21:30, 15 August 2008?

It was removed with extensive comments at Reasons for removal to which no response was received. In addition, many of the issues already were presented at Fugal's positions, so far ignored by you.Brews ohare (talk) 21:13, 15 September 2008 (UTC)

No I am not. I am referring to the explicit and detailed treatment of the specific example you have asked about, namely, a particle described in terms of a rotating system of polar coordinates.Fugal (talk) 03:12, 16 September 2008 (UTC)

Please bend a little and point out this discussion, or repeat if need be. Brews ohare (talk) 04:56, 16 September 2008 (UTC)

I am not looking for a "general unified solution"; just an exploration of a simple direct example. For example, take the subsection Polar coordinates in a rotating frame of reference. The derivations closely parallel those in the cited sources, viz: Taylor, and also Stommel and Moore, so it is hardly "narrative, neologism and whatever". Please explain why (in your mind) the two different treatments of the terms $(mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}})$ (as fictitious force in one case, but not in the other) do not constitute two different usages of the terminology "fictitious force". It is not a case of different contexts inasmuch as both approaches describe exactly the same phenomena in exactly the same coordinate system and in exactly the same frame of reference. Brews ohare (talk) 21:13, 15 September 2008 (UTC)

Already presented multiple times here on this discussion page.Fugal (talk) 03:12, 16 September 2008 (UTC)

Excuse me, but I can find not even one discussion (besides my own) of the terms $(mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}})$ on this page. Brews ohare (talk) 04:56, 16 September 2008 (UTC)

And I say again, by humoring you to this extent, we have been abusing the purpose of this discussion page, which is not to (in your words) "explore" the subject of the article. As I said, some of us have made the mistake of trying to explain a bit about the subject to you, in hopes that it would make the editing go more smoothly, but the folly of trying to reason with an "original researcher" has been demonstrated once again.Fugal (talk) 03:12, 16 September 2008 (UTC)

Sorry I used the word "explore" in a sense you misunderstood; how about "suggest revisions to"? Your use of the words "humoring", "abusing", "folly" etc. is very much in keeping with Wiki guidelines for this Talk page, eh? "Do as I say, not as I do"? Brews ohare (talk) 17:30, 16 September 2008 (UTC)

Look, as I said above, Wikipedia discussion pages are not intended to be a venue for discussing the subject of the article. As a courtesy, some people have been abusing the intent of these pages by trying to discuss the topic with you, hoping that if you understood it a little better, the editing would go more smoothly. But that obviously hasn't worked. The wisdom of the Wikipedia policies has been borne out yet again. We must simply eliminate all neoligisms and novel narrative from the article(s) (i.e., any statements that cannot be directly traced to a verifiable reputable source), and then we must add all the directly verifiable statements concerning centrifugal force in the context of curvilinear coordinates, with full citations and quotes where necessary. That's the only way forward that is consistent with Wikipedia policy.Fugal (talk) 20:39, 15 September 2008 (UTC)

Glad you have identified "the only way forward". It's good to know where you are headed. Please start a page to "add all the directly verifiable statements concerning centrifugal force in the context of curvilinear coordinates, with full citations and quotes where necessary." I'd suggest it as a separate page until it is thoroughly examined and its relation established to existing pages that do not aspire to be a "general unified approach to the overall subject". So far as I have seen, it will be thin pickings to find sources for this fundamental work, as all treatments of centrifugal force that I have seen avoid it entirely, except in the field of robotics where a Lagrangian approach is common. That field uses fictitious force in the unusual sense where centrifugal force is present (non-zero) even in inertial frames (the "coordinate" sense). (BTW, so does your Revision as of 21:30, 15 August 2008.) Besides being inappropriate for an article fundamentally based upon a centrifugal force that is zero in inertial frames, a curvilinear, unified, general approach probably falls into the category of an advanced page for specialists. If that is so, the "unified" page will stand on its own, rather than modify the existing pages. Brews ohare (talk) 23:56, 15 September 2008 (UTC)

Once again, please see the Wikipedia policy on "ownership". Verifiable material on the subject of any given article belongs in that article. Likewise, novel narrative and neoligisms do not belong in any Wikipedia article, so they should be removed from any article in which they appear.Fugal (talk) 03:12, 16 September 2008 (UTC)

As the existing pages are of narrow scope, and deliberately so, introduction of a "general unified approach", which most probably includes Christoffel symbols and metric tensors and maybe a little differential geometry, becomes a large overhead on these simpler examples. For that reason I merely suggested (see the word if ? ) that a separate page would be a better course. Brews ohare (talk) 14:39, 16 September 2008 (UTC)

Neologisms?

I would argue that the use of the terms "state-of-motion" fictitious force and "coordinate" fictitious force does not constitute introduction of neologisms, but is simply the application of adjectives to a noun, very parallel to the distinction "red dog" compared to "black dog".

The term "state-of-motion" fictitious force refers to the standard case of fictitious forces that vanish in an inertial frame of reference, as does the centrifugal force of this article. The second term "coordinate" fictitious force refers to the artificial forces introduced by treating all the terms introduced by a non-Cartesian coordinate system as "fictitious forces". The "coordinate" fictitious forces are present in every frame, including an inertial frame of reference. One might propose better names, of course. Maybe "classical-mechanical" fictitious force & "geometrical" fictitious force, for example. Brews ohare (talk) 20:01, 16 September 2008 (UTC)

None of the numerous verifiable sources found it necessary to make use of these expressions. The fact that you have found it necessary to invent neoligisms in order to express your alleged “dichotomy” in the subject demonstrates that your idea is original research. This research and the associated novel narrative and neoligisms do not belong in Wikipedia, per the established policies.

The term "black dog" is suitable for an article on dogs because the term appears in reputable and notable sources on the subject of dogs. But (for example) the term "cloudy dogs" would not be suitable, because it doesn't appear (as far as I know) in the literature on dogs.

More to the point, an article on dogs would be expected to acknowledge that dogs have different colors. If someone were to try to dominate the Dog article, flooding (spamming?) it with edits and discussion, claiming that this is two different usages of the word "dog", and asserting that the only real physical dogs are red dogs, and the things that are confusingly called "black dogs" in some fringe references of no importance are not really physical dogs at all, they are just mathematical dogs, then it would be appropriate for other editors to object, because this alleged dichotomy is not found in any reputable source.

And if the individual actually alleged a physical/mathematical dichotomy, not between red and black dogs, but between cloudy and non-cloudy dogs... i.e., alleging a dichotomy based on terms that don't even appear in the literature at all, well, again, it would be appropriate for other editors to object, and to strive to get this individual to respect Wikipedia policies.Fugal (talk) 15:11, 17 September 2008 (UTC)

That "fictitious force" is subject to two usages is well documented. I have chosen to select one obvious difference between usages: the requirement that fictitious force be zero in an inertial frame for those fictitious forces that also are called inertial forces, pseudo-forces, and d'Alembert forces, and the lack of this requirement for the fictitious forces defined as all but the second-time-derivative terms in the acceleration expressed in curvilinear coordinates.

As a reminder of the role of inertial frames; this quote from Arnol'd:

The equations of motion in an non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.

— V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129

As a reminder of the second usage of fictitious force, here is a quote from Ge et al.

In the above [Lagrange-Euler] equations, there are three types of terms. The first involves the second derivative of the generalized co-ordinates. The second is quadratic in $\mathbf {\dot {q}}$ where the coefficients may depend on $\mathbf {q}$. These are further classified into two types. Terms involving a product of the type ${{\dot {q}}_{i}}^{2}$ are called centrifugal forces while those involving a product of the type ${\dot {q}}_{i}{\dot {q}}_{j}$ for i ≠ j are called Coriolis forces. The third type is functions of $\mathbf {q}$ only and are called gravitational forces.

— Shuzhi S. Ge, Tong Heng Lee & Christopher John Harris: Adaptive Neural Network Control of Robotic Manipulators, pp. 47-48

Divert yourself from "cloudy" dogs to treat this issue directly. Brews ohare (talk) 16:58, 17 September 2008 (UTC)

As always, your comments are based on your fundamental misconceptions as to the meanings of frames and coordinate systems. For the billionth time, a frame is simply an equivalence class of mutually stationary coordinate systems, and as such it may include both inertial and non-inertial coordinate systems. An inertial coordinate system is defined as one in which the space coordinates of any inertial path are linear functions of time. In introductory texts (and works that are not concerned with the dependence on spatial coordinates) a simplification is often introduced, by stipulating that the representative of any frame will be a rectilinear Cartesian coordinate system, which enables those works to then say without ambiguity that fictitious forces arise only in non-inertial frames. But this is a conditional statement, i.e., it is true only under the simplifying stipulations that those works present on the first few pages. (Unfortunately, beginning students are often unaware that they have only been presented with a simplified version. Some of them turn into physics cranks later in life, when they become exposed to the more general subject.) In more advanced works the general unsimplified view is taken, and in this context one must speak of specific coordinate systems, rather than of equivalence classes of coordinate systems, in order to avoid ambiguity. In this general context, one says that fictitious forces arise in non-inertial coordinate systems, which include systems with curved space axes or curved time axes or both. The point is that this general treatment of the subject does not contradict the simplied "Dynamics for Dummies" version, nor does it represent a different definition of the terms. It simply represents a more general view, sans the simplifying stipulations made in the introductory presentations.

Incidentally, since you were the one who introduced the red dog and black dog analogy, it seems odd that you would immediately admonish me for commenting in those terms. As to your wish (now) for the issues to be addressed directly, I can only say (again) that the issue has been addressed directly many many times. You aren't lacking explanations, nor substantiation, you are lacking only understanding of the subject ... and respect for Wikipedia policies.Fugal (talk) 19:42, 17 September 2008 (UTC)

Inertial frames

Fugal : An inertial coordinate system is defined as one in which the space coordinates of any inertial path are linear functions of time.

Isn't this definition circular? At a minimum we need a definition of an "inertial path". Maybe, a path followed by a particle subject to no forces (fictitious or otherwise)?(talk) 20:40, 17 September 2008 (UTC)

Of course it's circular. This is exceedingly well known, and has been pointed out and thoroughly discussed by every author on the foundations of science from Newton's day until today. Of course, one refers to "isolated" bodies, but that just begs the question of what is a sufficiently isolated body. As Einstein commented, "The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration." And of course this wasn't original to Einstein. For example, Mach pointed out that Newton's laws aren't really laws of motion, they are essentially the definition of inertial coordinate systems, but then this leads to the general problem of inductive knowledge, and so on. Newton himself was well aware of these issues, so there's nothing new here. Scientific knowledge is inherently provisional.Fugal (talk) 02:37, 18 September 2008 (UTC)

Thanks for that quotation. I was aware of this problem, but not of the quote. However, it seems to me that the orthodox way out this is DiSalle, who says in summary: Robert DiSalle (Summer 2002). "Space and Time: Inertial Frames". In Edward N. Zalta (ed.). The Stanford Encyclopedia of Philosophy.

The original question, “relative to what frame of reference do the laws of motion hold?” is revealed to be wrongly posed. For the laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing them.

— Robert DiSalle Space and Time: Inertial Frames

I hesitate to ask for you digress upon this "solution"; but perhaps you have another useful quote or source?? Brews ohare (talk) 04:44, 18 September 2008 (UTC)

My understanding is that a focus upon transformation properties of the laws of physics shows certain frames have simpler laws (because fictitious forces don't drop off rapidly with distance, for instance, and transform oddly, in fact vanishing in certain frames), and therefore are preferred. The alternative seems to be to suggest we don't know an inertial frame from any other frame: we can identify frames that are in uniform translation relative to one another as belonging to one family of frames, but in no way is such a specimen family preferred over another family exhibiting a common acceleration wrt the specimen family. For example, we cannot distinguish a rotating frame from a stationary frame; all we can say is that one rotates relative to the other. In particular, the rotating sphere experiment won't work. Assuming we stick within special relativity, which is your view? Brews ohare (talk) 05:14, 18 September 2008 (UTC)

Fugal : In this general context, one says that fictitious forces arise in non-inertial coordinate systems, which include systems with curved space axes or curved time axes or both.

Isn't this conclusion in contradiction with the classical mechanical view of the quote above from Arnol'd?(talk) 20:40, 17 September 2008 (UTC)

No, it isn't. You have to read carefully, and note the difference between frame and coordinate system, and recognize that Arnol'd has already "modded out" the variations in spatial coordinate systems within any given frame by stipulating (as in the two quotes that I provided to you previously) that we will take as THE representative of any frame a rectilinear Cartesian coordinate system, which just amounts to "modding out" any spatial coordinate effects, leaving only the temporal coordinate effects. This is just a simplification, so that almost all of the Christoffel symbols vanish, and the few that remain can be given cute names like centrifugal and Coriolis. The temporal coordinate effects are just as much "coordinate effects" as are spatial coordinate effects. There is nothing more or less "physical" or "mathematical" about them. And when it comes to simplicity, we can just as well (and often do) suppress variations in the time coordinate and put all the variations into the spatial coordinates, as is done in the numerous references that have been provided.Fugal (talk) 02:37, 18 September 2008 (UTC)

Here is the quote from Arnol'd once more:

The equations of motion in an non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.

— V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129

On p. 130 (the very next page to the above quote) Arnol'd says (vector variable Q is the radius vector of a moving point in the moving coordinate system):

Motion in a rotating coordinate system takes place as if three additional inertial forces acted upon every moving point of Q of mass m:

1. the Euler force of rotation: $m{\begin{bmatrix}\mathbf {\dot {\Omega }} ,\ \mathbf {Q} \end{bmatrix}}\ ,$
2. the Coriolis force: $2m[\mathbf {\Omega } ,\ \mathbf {\dot {Q}} ]\ ,$
3. the centrifugal force: $m{\begin{bmatrix}\mathbf {\Omega } ,\ {\begin{bmatrix}\mathbf {\Omega } ,\ \mathbf {Q} \end{bmatrix}}\end{bmatrix}}\ .$

Thus, $m\mathbf {\ddot {Q}} =\mathbf {F} -\mathbf {F_{Euler}} -\mathbf {F_{Coriolis}} -\mathbf {F_{centrifugal}} \ .$

— Arnol'd, p. 130

where the Euler force exists only in nonuniform rotation. [I've introduced the name "Euler force" following Lanczos]. The question is how these two quotes are to be combined.

I'd say the first quote requires that the inertial forces of the second quote to vanish in an inertial system, thereby distinguishing a system that is rotating from one that is not. (Obviously, they do vanish when Ω = 0. ) The entire formulation is in vector notation, and therefore independent of coordinate system (Cartesian or polar). If the radius vector Q is expressed in polar coordinates, $m\mathbf {\ddot {Q}}$ will contain a variety of terms related to the curvilinear coordinates (see here), and these are on the left side of the equation, not included in the inertial forces on the right side of the equation. Thus, the criteria for an inertial frame based upon vanishing of inertial forces is not affected by a switch to polar coordinates.

If instead the curvilinear terms in $m\mathbf {\ddot {Q}}$ are taken to the right side of the equation and all the terms on the right are called "fictitious forces", the resulting "fictitious forces" are clearly not the same as the original "inertial forces" and these newly coined "fictitious forces" do not vanish in an inertial frame. Hence, the need to recognize two usages for the term "fictitious force". Brews ohare (talk) 19:56, 18 September 2008 (UTC)

And finally, it seems to me you might be suggesting (particularly in your second statement above) that in a curvilinear system the second-time-derivatives of the coordinates are the applied force. In a curvilinear coordinate system that is what I've called the "coordinate" definition as exemplified by the quote above from Ge.(talk) 20:40, 17 September 2008 (UTC)

See above. All inertial forces are due to coordinate effects, so it's incorrect to call just some of them (the ones you've never thought about very much) "coordinate" effects while referring to others as "state of motion" effects. (It's also incorrect, and doesn't make sense, to refer to acceleration as a "state of motion", and you can't unambiguously extrapolate accelerations ... but this isn't the place for a tutorial on Fundamentals of Physics.)Fugal (talk) 02:37, 18 September 2008 (UTC)

It seems that you may be agreeing there are two terminologies, one you call the "simplification for beginning students" and one you call the "general unsimplified view ". Are we simply arguing over semantics? Is the difference just one of what merit is assigned to the two usages? Brews ohare (talk) 20:40, 17 September 2008 (UTC)

There are not two "terminologies". I went to the trouble of taking two of your own references, on which you've based your claims about two terminologies, and showed specifically with the exact quotes where they stipulated that they were restricting their considerations of spatial coordinates to rectilinear spatial coordinate systems, while allowing the temporal coordinate to be non-linear, in which case the statements they subsequently make about frames and inertial forces are correct. They are not correct, however, if the stipulation about spatial coordinates is removed, and the authors would surely not have objected to this statement. By the same token, the references that have been cited in which fictitious forces are derived in terms of stationary coordinate systems are also correct, because they have not stipulated rectilinear spatial coordinates. Of course, we could just as well stipulate that ALL our coordinates be rectilinear, in which case there are no fictitious forces at all.

Look, the explantion was contained in the edit to the article that you deleted. It specifically explained how the simplifed way of viewing of the subject, which is taken in the rest of the article, fits into the larger context of the general treatments, and how this also unifies the reputable references that derive centrifugal and other fictitious forces in terms of stationary coordinates. Viola, the so-called "confusing terminoligies" and "conflicting usages" evaporate when the subject is simply viewed clearly and correctly. It was all summarized in a paragraph or two, explaining, based on explicit quotes from numerous reputable sources, how all these pieces fit together. And you deleted it.Fugal (talk) 02:37, 18 September 2008 (UTC)

Discussion of Arnol'd

I wrote that “Newton's laws aren't really laws of motion, they are essentially the definition of inertial coordinate systems”, and you counter with “However, it seems to me that … the laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing them.” You do realize that you just repeated what I said, right?.Fugal (talk) 15:47, 19 September 2008 (UTC)

You present (yet again) a quote from page 129 of Arnol'd. Unfortunately you jumped straight to page 129 without understanding pages 1 through 10, which is where the context is established for the rest of the book. Please look at page 6, where “inertial coordinate systems” are defined <not> by a “state of motion”, but by the condition that the law of inertia takes the simple form x” = F(x,x’,t), where primed symbols represent derivatives of the coordinates with respect to time. Near the same page it says the only transformations between inertial frames are translations, rotations, and uniform motions. Both of these (along with all the rest of the discussion) explicitly signify that he is restricting “coordinate systems” to orthogonal rectilinear spatial coordinates? The transformation from Cartesian to polar coordinates (for example) is not just a translation, rotation, or uniform motion, so according to Arnol'd it is not an inertial coordinate system. He just isn't considering curvilinear spatial coordinates, so he is speaking in the restricted sense. This is exactly what I’ve been telling you. I’ve pointed out where this restrictive stipulation is introduced in all THREE of your sources.Fugal (talk) 15:47, 19 September 2008 (UTC)

The rest of your comments are just repetitions of your previous erroneous comments. Please note that the thing you call the “equation of motion in polar coordinates” on your “planar” page is not even a coherent equation of motion, it’s just a disguised version of the rectilinear vector equation with some of the appearances of the position vector replaced with the angular coordinate. You essentially have one vector equation in three unknowns (namely, the two components of the position vector and the scalar angle). If you actually tried to integrate this equation you would immediately see the fallacy of what you’ve written. Again, the correct treatment of that very problem has been presented here on these discussion pages multiple times. Obviously the use of curved spatial axes introduces terms in addition to those introduced by the use of curved time axes, but it’s just as obvious that the same terms can be introduced by just one or the other. We are free to choose whatever system of coordinates we like. The point is that all the references you habitually cite have explicitly restricted themselves to rectilinear spatial coordinates, so no terms involving the spatial coordinates arise, whereas other (more sophisticated) references discuss the unrestricted view.Fugal (talk) 15:47, 19 September 2008 (UTC)

You wrote that “The entire formulation is in vector notation, and therefore independent of coordinate system (Cartesian or polar).” Well duh. The equation F = ma is a vector equation, and it contains no fictitious forces, so according to your “reasoning” there are no fictitious forces in terms of any system of coordinates. Now, in one sense that’s true, i.e., if we use the true acceleration vector for “a”, then “F” will consist of just the true forces, and we can do this in terms of ANY coordinate system, regardless of whether it is accelerating or curvilinear or anything else. Of course, the expressions for “a” in terms of our chosen coordinates will depend on those coordinates. For some systems the vector “a” is just the second time derivatives of the space coordinates, whereas for other systems there are additional terms. Regardless of our coordinate system, the true acceleration “a” can always be expressed. But the subject of this article is a fictitious force, which arises when (and only when) we decide to use a fictitious acceleration rather than the true acceleration in the equations of motion. In other words, we use a fictitious acceleration A in place of the true acceleration “a”, but then the equation of motion becomes F+f = mA where f equals m(A-a). If we want, we can call f the fictitious force, which compensates for whatever fictitious acceleration we’ve chosen to use. Now, we have lots of choices, e.g., we can choose A = 0, in which case we get dynamic equilibrium and d’Alembert’s principle. On the other hand, we can choose A = second time derivatives of our space coordinates, which leads to the conventional fictitious forces. Of course, in the fully general context, the difference between this A and the true “a” will consist of terms that arise due to curved space axes as well as curved time axes. In a more restrictive context, with the stipulation that we will only use rectilinear space axes, the extra terms will then consist only of those arising from curved time axes. This is the restricted treatment that you were taught in Dynamics for Newbies. The point is that this is just a specialized treatment of a general subject.Fugal (talk) 15:47, 19 September 2008 (UTC)

Again, these discussion pages are not to be used for discussions of the subject of the article. My best advice to you is to read a real book devoted specifically to this subject, say Friedman’s “Foundations of Space-Time Theories”, specifically Section III on Newtonian physics. This clearly describes the general context that encompasses all the discussions of “centrifugal force” to be found in the reputable literature.Fugal (talk) 15:47, 19 September 2008 (UTC)

I will look into your remarks further. An immediate question, however, is how do you react to the Rotating spheres example? In particular, that example seems to say that it is possible to determine one is in an inertial frame by comparing the tension measured in a string with the tension calculated using the laws of physics including only real forces. In other words, fictitious forces are zero in the inertial frame (and non-zero in a rotating frame). It would not matter what coordinate system was used. In contrast, if the curvilinear additions to the acceleration introduced by using curvilinear coordinates are treated as additional fictitious forces, this scheme will not work. Brews ohare (talk) 18:21, 19 September 2008 (UTC)

Principle of inertia functions as an organizing principle

Well, I react by saying you're completely and utterly wrong, as usual. First, the issue here is not the epistemological problem of how inertial coordinate systems are identified. That relates to the general issue of inductive knowledge and how the principle of inertia functions as an organizing principle for our knowledge... not relevant to this article. Second, the recognition of the fact that space-time coordinate systems contain space coordinates as well as time coordinates (either or both of which may diverge from inertial paths, does not in any way impede us in the identification of inertial coordinate systems (whether by the revolving globes or any other means). To the contrary, this recognition is an essential part of accomplishing such an identification. You keep saying things like "it doesn't matter what coordinate system you use", oblivious to the fact that the very same thing applies to time coordinates as to space coordinates. If you want to exclude the use of fictitious (coordinate dependent) acceleration, then there are no fictitious forces. On the other hand, if you allow the use of fictitious acceleration, then there are fictitious forces associated both with curved time axes and with curved space axes (unless you stipulate that you are considering only rectilinear space axes for simplicity).Fugal (talk) 22:04, 19 September 2008 (UTC)

Fugal: You definitely have put your finger on an important issue that underlies all this: the epistemological problem of how inertial coordinate systems are identified. Maybe it belongs in Inertial frame of reference. Anyhow it belongs somewhere. Maybe you could do something helpful here? If we take up this problem, what is your take on using the tension in the string joining rotating identical spheres to define inertial frames? Brews ohare (talk) 22:41, 19 September 2008 (UTC)

This article has been falsified (so strongly POV that it is even incorrect)

I notice a colossal difference between this version which appears to be mainly the work of one person and the consensus version of only half a year ago: http://en.wikipedia.org/w/index.php?title=Centrifugal_force_(rotating_reference_frame)&oldid=196032047

In particular, the old version provides reiable sources that shows that the current version is already incorrect in the opening sentence. Moreover, the old version was very much NPOV while the new one only expouses a single POV and even falsely suggests that that POV is required for mapping to rotatitng frames.

This is the worst thing that can happen to a Wikipedia article - thus I'll put up the required banners. Harald88

Harald: You haven't said what you object to specifically. What changes would make you happy?

Contrary to your view, the opening (accurate) sentence is supported by numerous references that appear in the first paragraph.

In addition, you seem to be unaware that several other pages have been created that incorporate much of the material on centrifugal force from the ancient version you prefer. They are found at Fictitious force & Reactive centrifugal force. I believe you have over-reacted. Brews ohare (talk) 13:34, 19 September 2008 (UTC)

The splitting of the article into multiple articles is somewhat problematic, and it's also been done incompletely and inconsistently. I suspect what Harald objects to (among other things) in the current article is that, even though the article has a disambiguation suffix (rotating reference frame), the text of the article contradicts this disambiguation. The first sentence says "In classical mechanics, centrifugal force is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a rotating reference frame." Recognizing the other articles, the first sentence here ought to say something like "In classical mechanics, the term "centrifugal force" has several different meanings, one of which is a fictitious force arising from the use of non-inertial coordinate systems, and a subset of these are the fictitious forces arising in rectilinear Cartesian coordinates rotating about a fixed axis. This limited subset is the subject of this article. For a discussion of centrifugal force in general, see Article "Centrifugal Force (General)". Then similar caveats would have to be included in the remainder of this article, replacing the existing assertions of universality for this small subset of the meaning.Fugal (talk) 16:31, 19 September 2008 (UTC)

I've tried to remedy this matter by modifying the lead. Brews ohare (talk) 18:07, 19 September 2008 (UTC)

That's not the way it's done in the wikipedia Fugal. We're not defining all forms of centrifugal force. We are defining and scoping the term centrifugal force for this article. The name of the article and the links at the top link to other 'centrifugal force's that there are. The general principle is that the wikipedia is and encyclopedia is NOT a Dictionary. It is inappropriate to have reactive centrifugal force in this article as it is physically distinct in every important respect, but simply shares the same name (and points in the same direction... but even then only sometimes.) The wikipedia's rules are quite clear on this. See WP:NOTADICT. The old article that Harrald refers to simply wasn't scoped correctly for the wikipedia.- (User) Wolfkeeper (Talk) 18:59, 19 September 2008 (UTC)

I think we should follow Wikipedia policy in editing these articles, and provide an accurate and well-reasoned presentation of the subject based on verifiable sources. This article begins with what seems to be a disambiguation statement by saying "In classical mechanics...". The problem is that all the other meanings described in the other related articles are also in classical mechanics, so it is incorrect to say (as the article currently does) that "In classical mechanics, centrifugal force is.. such-and-such". In order for the introductory statement to be accurate, it needs to not conflict with the fact that (for example) the reactive centrifugal force is also a concept in classical mechanics.Fugal (talk) 21:43, 19 September 2008 (UTC)

The unit of English meaning is the sentence. If you read the entire sentence rather than cherry picking phrases from it, then I don't believe that that criticism has any merit at all. None of the other sentences around it support this interpretation of yours in any way ether, and the links to other meanings of the term 'centrifugal force' are as clear as could be.- (User) Wolfkeeper (Talk) 22:30, 19 September 2008 (UTC)

Fugal and Harald: The introductory sentence is In classical mechanics, centrifugal force (from Latin centrum "center" and fugere "to flee") is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame. This is a pretty clear identification of centrifugal force in general terms. As such, regardless of what the rest of the article may say, what is wrong with it? It is supported by numerous citations. Brews ohare (talk) 22:36, 19 September 2008 (UTC)

Do you mean, what's wrong with it in addition to the thing wrong with it that had already been identified? How many things have to be wrong with it before you will conceed that it is wrong? Once again, the sentence says "In classical mechanics, centrifugal force is such and such". But in classical mechanics centrifugal force is also other things, so the sentence is misleading, and conflicts with the other articles. The irrelevance of the cited references to this point has already been explained at length. An equal number of equally reputable references on the subject of classical mechanics have been cited which describe other things under the name "centrifugal force". Hence to say "In classical mechanics, centrifugal force is such and such" is self-evidently misleading. It ought to say something like what I suggested above, or something like "In classical mechanics, with rectilinear coordinates rotating about a fixed axis, centrifugal force is such and such".Fugal (talk) 01:16, 20 September 2008 (UTC)

The complete quote down to end of the first sentence goes:

For centrifugal force that isn't due to rotating reference frames, see centrifugal force (disambiguation).

For the external force required to make a body follow a curved path, see Centripetal force.

For general derivations and discussion of fictitious forces, see Fictitious force.

In classical mechanics, centrifugal force (from Latin centrum "center" and fugere "to flee") is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame."

This is clear, and follows WP:LEAD and the other norms of the wikipedia to the letter.- (User) Wolfkeeper (Talk) 02:31, 20 September 2008 (UTC)