Talk:E=mc²

Place new sections at the bottom, please.

Units of E=mc²

I was wondering if someone could explain the units used in this equation. I have never seen an explanation which includes the units. It would seem that the equation would not hold if the units changed. jimaginator

I had the same question. For the unit of mass, it seems like electronvolt (eV) is normally used in particle physics.[http:// Units: E] c is a constant the speed of light(m/s). But when calculating the energy of a nucler fission of a chunk of plutonium for example, eV is not suitable to use because the unit is too small. According this website E=mc^2 The Basics, Kg is used in that instance. Both are SI units and are convertible, so I guess that explains it.--Nc622 16:58, 5 Nov 2004 (UTC)

Thanks for your response. The E=mc2 Basics website states that it's Energy in Joules, mass in kg, and speed in meters per second. So far so good. Now Wiki says a Joule is: "One joule is the work required to exert a force of one newton for a distance of one metre". ---So now we have: 1N x 1m = 1kg x (m/s) x (m/s) A newton is a SI derived unit defined as the amount of force required to accelerate a mass of one kilogram at a rate of one metre per second squared. ---So now we have: 1kg x m x s^-2 = 1kg x (m/s) x (m/s). So, both sides end up being defined with kg,m,s; the basis of the SI units in the first place. It all seems rather circular in structure to me. If the units are picked to have some inherent relationship in the first place, anything can be used. And I suppose the squaring of the right side is where the really big energy quantity comes from, but somehow it's not all that satisfying. I guess it's the nature of the concept of energy in the first place, since this is more abstract than a meter which we can pace out, or a second which we have all have a subjective feel for. I had always felt that the simplicity of the equation was due to something simple in the fabric of the universe. When I first heard the equation in junior high, it was a wow moment, how could it be so simple? But really it isn't. What would the equation look like in other measurement systems? I suspect not so elegant. I wonder if Einstein was using SI, or even if he was thinking in terms of any particular system at all at first. Jimaginator 14 Nov 2004 UTC

The equation would look exactly the same in any other measurement system. I'm having trouble envisioning a thought process that could possibly lead you to believe otherwise. Of course the units are picked because of their inherent relationship; that's why the equation is meaningful! E is any unit of energy, m is any unit of mass, and c is any unit of velocity: so long as the three units are consistently defined, the equation will look exactly the same.

Further, eV is most emphatically not a unit of mass. An electron-volt is a unit of energy. The figures you see quoted in particle physics texts are in units of eV/c^2 which, not coincidentally, is a direct consequence of E=mc^2.

Mote 04:43, 9 Jan 2005 (UTC)

Well, sorry about the old thought processes, but the equation being based on circular, intertwined units is the crux of the matter. If we use pounds, parsecs/hour, and BTUs or whatever, I believe the equation WILL look terrible. If Einstein did not invent the SI units, then the interelationship between the units somehow pre-cognitively anticipates the future equation. Why even bother with the ^2 element at all? Pre-define the interconnection of the units right, and the equation could be E=mc! Still not satisfied here Jimaginator 19:30, Mar 17, 2005 (UTC)

Think of it this way: energy equals a constant times mass multiplied by the square of the speed of light. These are all abstract concepts. This relationship between the abstract concepts of energy, mass, and the speed of light is the simple truth which struck you so in junior high. SI units are chosen so that the constant equals one. If you use imperial units or made up units, the abstract relation still holds. There will be a different constant in the equation, but energy always equals a constant times mass multiplied by the square of the speed of light. There is no way to measure speed such that energy equals mass times the speed of light. Speed is always a measure of distance traveled per unit of time. There is no way to define the "interrelationship" of units so that energy is not proportional to mass, or so that energy is not proportional to the square of the speed of light.

Many of the questions above illustrate confusion about how units and formulas work. Let's think for a minute about a simple, intuitive formula: the area of a rectangle as a function of its width and height:

$A=W\times H$

The important thing to understand is that when you plug in units, they are subject to the same mathematics as the numbers. If you plug in W and H in meters, you get A in meters times meters, or m². If you plug in W and H in feet, you get A in feet times feet, or square feet. If you plug in W in parsecs and H in nanometers, you get A in nanometer-parsecs, which is not a convenient unit of area, but is a legitimate one.

If you say, "What if W is in feet, H is in meters, and A is in acres?" the question doesn't make sense; it's like asking, "What if W is 3, H is 7, and A is 18?". The units of the three variables are no more independent than their values; specifying two of them tells you what the third is.

E=mc² works the same way. If m is in kilograms, and c is in meters/second (SI units), then E is in kg-m²/s². That's the SI units for energy, and it has another name: the joule. If m is in grams, and c is in cm/s (cgs units), then E is in g-cm²/s², which is also called an erg (the cgs unit for energy). If m is in slugs and c is in furlongs/fortnight, then E is in slug-furlong²/fortnight², which is an inconvenient but legitimate unit of energy. (Note, of course, that the numerical value of c is different in these different units, just like your car's speed is different in MPH and km/h.)

In summary, physical formulas are not tied to a particular system of units, but the formula tells you the relationship between the units, just as it does for the numerical quantities. They have to be in agreement, with the same units on both sides of the equals sign. -- Coneslayer 2005 June 30 21:12 (UTC)

Thanks one and all for your responses. I believe I am starting to get the abstract nature of the relationship and the changing constant. But still I wonder how that ^2 got in there. Why isn't it ^2.039874 or something? I can't help but think of Pi's transcendental nature (OK, maybe that's a bad example, but the relationship of the circumference of a circle to it's diameter does seem to be locked into the universe, as is the speed of light. Why isn't Pi 3.00000...?) E=mc^2 still seems amazingly elegant, which I suppose is a testament to Einstein's genius. Anyway, thanks very much for the increased understanding Jimaginator 18:33, 22 September 2005 (UTC)

For a better understanding, see the same article in the french wikipedia.--24.37.172.194 04:20, 23 August 2005 (UTC)

Equation and the bomb

I tried to make more accurate the connection between this equation and the bomb, which seems to often erroneously imply that the uranium itself can serve as the "mass" end of this equation (it refers to the binding energy of the nucleus, much smaller than the mass of the atoms themselves). But I'm not a physicist. If someone with more expertise here could look over what I've done and see if it is correct, I'd be very happy. --Fastfission 01:52, 15 Jan 2005 (UTC)

I'm currently reading Greene's The Elegant Universe, which states: "The world grasped the devastating power arising from the conversion of less than 1 percent of two pounds of uranium into energy at Hiroshima" (51) - which would seem to suggest that the uranium is what's converted. ~ Booyabazooka 01:57, 4 May 2005 (UTC)

Matter to energy

The mass which is converted into energy is not the fissionable material itself (i.e. the uranium or the plutonium), but related to the strong nuclear force of the bonds which holds the large nucleus all together.

Actually, then, it seems that a fission reaction doesn't convert any matter into energy at all; it just releases a lot of energy that was formerly "contained", correct? If incorrect, can someone explain this in some detail? The popular belief is that fission and fusion convert some amount of mass into energy. Thanks. Tempshill 17:33, 16 May 2005 (UTC)

Popular belief is correct: Fission product.

Yes, mass is converted into energy - however it is much easier to think of this concept if you understand that truly mass *is* energy. Energy *is* mass. A good example to drive this home is a frozen dinner - take a dinner out of the freezer, put it in the microwave and heat it up. The dinner will GAIN MASS. This mass comes in the form of heat, and yes I do mean energy as well, but if you weigh the dinner on a very sensitive scale, you will see that the dinner weighs more than it did before you heated it. Fresheneesz 07:46, 20 November 2005 (UTC)

---

See the article on rest mass to explain why this does not account for the modern understanding of mass.

The equation also proves one of the fundamental limiting factors of space travel - the inability for anything with mass to exceed (or even reach) the speed of light. As the speed of light squared is always constant, the two variables in the equation are energy on one side, and mass on the other.

Therefore, when energy (in this case velocity) increases, mass must increase. Conversely, the more mass an object has, the more energy it requires to accelerate even further. The speed of light (c = 299,792,458 meters per second) is the point where the energy required to reach it is infinite, and attaining such a speed becomes impossible.

Roadrunner 04:08, 4 Jun 2005 (UTC)

Alternative view on E=mc^2

This is undoubtedly rubbish but would like to have it confirmed. Sure the 'c' is only valid as a function of time. So could time be an alternative form of energy and mass? It would answer a few of questions that seem to float around. E.g. the universe doesn't have enough mass - but it does have lots of time. In the instant after big bang a huge amount of mass, energy and time were created - which implies a strong relationship. What is at the centre of an atom/proton/quark - perhaps concentrated time. What is gravity and why does it distort space/time? - gravity is a function of mass which correlates to time and therefore attracts other time as it tries to return a singular point of time. The universe is only infinite for as much time as is available for it to exist. What's beyond the universe is no time. This is not the linear time that we experience day to day but time the essence. -unsigned

I can confirm "This is [...] rubbish". WAS 4.250 20:03, 9 October 2005 (UTC)

Time, space, mass, energy, the particle-like nature of reality (e.g. interactions occur at definite places in space-time), and the wave-like nature of reality (e.g. between interactions particles can pop into and out of existence and lack a definite location or momentum) are all one indivisible THING. None can exist without all of them existing. The expansion of the univrse since the big bang is NOT matter flying into space; but space-time being CREATED between the particles (that's why the expansion is not limited to being below the speed of light). As you read this, space-time is being created between the particles that make up your body (and everything else). WAS 4.250 20:03, 9 October 2005 (UTC)

Celeritas

I have written a new article on Celeritas which I feel should be linked to from this article but can't really figure out how. Any input would be welcomed. Majts 00:03, 12 October 2005 (UTC)

I added "Celeritas is said to be the c in E=mc²." to the See also section. WAS 4.250 00:51, 12 October 2005 (UTC)

thanks, that works, although I took the liberty of making a change to the wording Majts 01:12, 12 October 2005 (UTC)

Energy to mass?

Is this even theoretically possible? Would a giant discharge of energy produce a miniscule amount of matter? JD79 04:31, 5 November 2005 (UTC)

Well... yes... and it was first done in 1932. You can see the picture here [1]

Cultural Significance

Unfortunately I don't have the time to do it, but may I suggest perhaps a section to the article stipulating the cultural significance of the famous equation aswell as notable references that allude to it in various forms of popular culture.

Equation is an approximation

I think it should be noted that the equation E=mc^2 is an approximation good only when v<<c . My edit in this respect was reverted as being *wrong* - while it is quite clear (and is shown later down the page) that it most certainly *is* an approximation. Fresheneesz 07:04, 21 November 2005 (UTC)

Provide a source and we'll talk. WAS 4.250 11:57, 21 November 2005 (UTC)

You aren't confusing m with rest mass, are you? In relativity that's usually denoted m0. - 172.135.179.230 17:03, 21 November 2005 (UTC)

Well, actually m is the standard way to write mass - and it usually means rest mass. m0 is used to differentiate rest mass from "relativistic mass" - a term that many physicsists (including einstein) think is a "wrong" way to think about it. The point is that in the equation E=mc^2 - m is REST mass. And in any case, the page *should* indicate that m is relativistic mass if it is such.

But you're right, if m indicated relativistic mass - then it would be correct - but it would be very misleading for those who are used to m being rest mass, namely almost every physicist out there. - As for a source, how bout THIS PAGE. WAS 4.250 - have you even read the article? Do you understand the meaning of the relativistic part of this page? It is OBVIOUS that E=mc^2 is an approximation, and I don't appreciate this constant nagging for a source when the source is on the same damn page. Just because I don't provide an ISBN number doesn't mean that my information is incorrect. - Not to mention, I find it infinitely irksome that you don't even explain your stance - you just want a fucking source. Try *THINKING* for once. E=mc^2 only works when m is relativistic mass. And given that that is NOT the case (as of yet the page never mentions that that is the case), the equation must be an approximation. I believe I already explained this on your talk page WAS - so TALK to me. Fresheneesz 18:28, 21 November 2005 (UTC)

I plan on either noting that m is relativistic mass - or changing the equation back to an approximation. Please, anyone whos interested discuss. Fresheneesz 01:45, 22 November 2005 (UTC)

Noting that the m refered to here OF COURSE refers to the actual mass rather than the Newtonian mistaken concept of mass is appropriate. "Relativistic" mass is the real mass - the only mass - when equating mass to energy. Equating the Newtonian concept of mass to energy is ridiculous. As velocity increases the mass increases. The REAL mass. Not some funny special definition mass. Relativistic mass is that REAL mass. WAS 4.250 02:07, 22 November 2005 (UTC)

about Fresheneesz and physics article edits from my user talk page

Hey WAS, thanks so much for reverting those ridiculous edits on the Entropy page. Is there some way to prevent this kind of ridiculous editing in the future? The same guy totally messed up the Arrow of Time article (I reverted that) - he seems to mean well but... These are nontrivial subjects that should probably not have fundamental changes made to them by individuals without formal training in the subject matter. Heck, I don't even remember enough of my physics classes to edit this stuff without looking it up in a book! - JustinWick 18:01, 20 November 2005 (UTC)

Wikipedia:Vandalism in progress WAS 4.250 12:03, 21 November 2005 (UTC)

Hi, its fine you think my edits are ridiculous - but did you guys actually go and *look* it up in a book before you reverted my changes? E=mc^2 is most definately an approximation - have you heard of relativity? I'm editing these pages to match current theory, and current knowlege - as is the entire point of wikipedia. I am most definately *NOT* trying to match text books, or in any way parallel the idiotic way our society goes about teaching us science. E=mc^2 only works when the velocity of an object is near 0. What is so hard about understanding that? Fresheneesz 20:40, 20 November 2005 (UTC)

You say "E=mc^2 only works when the velocity of an object is near 0." Provide a source and we'll talk. WAS 4.250 12:03, 21 November 2005 (UTC)

Max Plank apparently said so: [2], tell me - is the m in that equation relatvistic mass? Because if it is, that needs to be explained on that page and a link to relativistic mass given. Fresheneesz 18:37, 21 November 2005 (UTC)

There are good sources and there are bad sources. The author of the piece you referenced doesn't know what he's talking about. Please read this. Changes to the article to reflect knowledge contained in it but not in the wikipedia article MIGHT be appropriate, and probably ARE, if done in the right way. I myself am much better at facts than the best way to present those facts. Maybe the talk page of the article would be a good place to suggest additions to the article to present what you discover at the source I just suggested you read. But make sure you understand something before you jump in and change stuff. Saying you don't believe in entropy and making changes to the entropy article seems, well, vandal-like... WAS 4.250 21:30, 21 November 2005 (UTC)

I didn't say I don't understand enropy. I said I don't understand it fully - and i doubt many chemists do either. Its a difficult subject. I edit things I *do* understand, and I am most definately correct in the relationship between free energy and entropy.

- secondly, your constant crying for sources is getting ridiculous - a source is not what makes something correct. I would urge you to think about what *is* and what *isn't* correct before you revert an edit. When I see edits I don't understand - I ignore them, because I can't say whether its right or wrong. I'll only corect something in cases where i'm sure i'm right.

- I think your statement "A little knowlege is a dangerous thing" is a horrible outlook, and completely contrary to the ideas on which wikipedia is based. The point of Wikipedia is not to put people through the rigamarole we went through in school, but to teach the full depth of a concept - with all its knowlege in full view.

- all that said, If you want me to take the m in E=mc^2 as relativistic mass - I will note that on the page myself. If you want me to take m as rest mass (as it should be - agreed upon by most physicists - see the page for rest mass, its the same page as relativistic mass), then I will reinstate my approximation claim. So please choose what you want. Fresheneesz 01:39, 22 November 2005 (UTC)

Fresheneesz, you have run afoul of several issues at once. (1) The simplest is the question of a proper understanding and statement of the physics. Assuming good faith and civil discussion, there's a fair chance we can sort that out to everyone's satisfaction. (2) A little knowledge is a dangerous thing; however, it has never been established how much knowledge is safe. The Wikipedia approach to resolving questions draws heavily on the concept of no original research. Pragmatically, this often comes down to citing sources. For example, suppose I have just completed a rock-solid proof of the Riemann Hypothesis, at home in my study. Further suppose twenty trustworthy mathematician editors here vouch for it. Can I put that on Wikipedia? The answer is no; it must first appear in a reputable journal. Or suppose the two of us witness the landing of an interstellar craft, chat with its occupants, and obtain unique tangible items from them that prove it happened. Can that incident be reported in Wikipedia? Again, no; not until it has been published elsewhere. So WAS 4.250 is merely following standard protocol by asking you to cite sources. (3) A century has passed since Einstein published the equation, but Wikipedia is very young. There is a growing awareness of a need for better quality control, and poorly written articles like this are a symptom. The unfortunate truth is that an excellent article requires a rare combination: subject knowledge, expressive skill, free time, adequate motivation, editor consensus, and constant vigilance. And to obtain editor consensus, you may need outstanding political skills coupled with extraordinary patience. Don't expect Wikipedia to be something it is not. --KSmrq^T 16:00, 22 November 2005 (UTC)

See Internet troll. WAS 4.250 01:49, 22 November 2005 (UTC)

By the way, there is a Wikipedia talk:WikiProject Physics and Wikipedia talk:WikiProject Mathematics where you can ask for comment on this kind of stuff. Oleg Alexandrov (talk) 06:01, 22 November 2005 (UTC)

e=mc^2 is not an approximation

Hi Fresheneesz. I came here from Oleg's house. E=mc^2 is not an approximation within its domain of applicability. Perhaps the reason that you think it is an approximation is because this article shows you an approximation where E is approximately mc2 for low v. That's true: in the case that the kinetic energy is negligible, the total energy is approximately equal to mc2. However, the equation E=mc2 is meant to apply to the case of rest energy (not total energy), or else to total energy with the m understood to be relativistic mass. The former case is more standard, but in neither case is the equation an approximation. -lethe ^talk 08:26, 22 November 2005 (UTC)

Thank you for the clarification. I think some clarification of this sort should appear in the article. Perhaps noting that E is "rest energy" ? Fresheneesz 08:41, 22 November 2005 (UTC)

I was going to add some text, but this article is in bad shape: explaining the technical details of the equation should not go into the "background" section, nor should it go into the "approximation" section. I couldn't figure out a clean place to add something. This article needs a section devoted to the equation, its derivation, and its meaning. When I finish everything on my to-do list (haha). -lethe ^talk 10:24, 22 November 2005 (UTC)

I'd happily stand corrected if adequate sources were provided. I hate this arguing. But the subject in question is the meaning of the "m" in Einstein's "E=mc squared" and the sources provided AGREE that the equation when written ("outdated") meant relativistic mass. That it is also true when velocity equals zero is a subset. Please read this. Dumbing it down for students doesn't change the meaning of the equation. Further discussion at Talk:Relativistic mass. WAS 4.250 17:54, 22 November 2005 (UTC)

Arguing? Who's arguing? I explained something to Fresheneez, and he thanked me. You probably could have done this yourself, instead of reverting with "cite sources". Do you know see how this can be confusing for the beginner? And you won't be corrected by any sources, because you are not incorrect. The equation is not an approximation.

Anyway, I seem to have another issue that I want to talk about with you. Is m in the equation rest mass or relativistic mass? You want to claim relativistic mass (in which case the formula is exact for all v) . I said above that rest mass is standard (in which case the formula is exact only for v=0, and wrong for other v), so we do appear to have a bona fide disagreement on our hands. Furthermore, I see that you've editted several pages to bring them into agreement with your position on this matter. I am inclined to revert, but let's discuss first, shall we?

Firstly, are we talking about the historical usage of the equation E=mc2? The more modern equation is m²=(E/c²)²−(p/c)². In this equation, there can be no doubt that m is rest mass (it's the Casimir invariant of the Poincaré group, aka the magnitude of the 4-momentum). The simpler formula can be viewed as a special case of this one for p=0. But that doesn't mean it has to be so viewed. It can also be viewed with the relativistic mass in mind. While it is not done today, perhaps it was in the past. I argue that not even that is true.

From the physics FAQ:

"The first record of the relationship of mass and energy explicitly in the form E = mc² was written by Einstein in a review of relativity in 1907. If this formula is taken to include kinetic energy, then it is only valid for relativistic mass, but it can also be taken as valid in the rest frame for invariant mass. Einstein's conventions and interpretations were sometimes ambivalent and varied a little over the years; however an examination of his papers and books on relativity shows that he almost never used relativistic mass himself. Whenever the symbol m for mass appears in his equations it is always invariant mass. He did not introduce the notion that the mass of a body increases with velocity--just that it increases with energy content. The equation E = mc2 was only meant to be applied in the rest frame of the particle. Perhaps Einstein's only definite reference to mass increasing with kinetic energy is in his "autobiographical notes"."

Apparently the notion of relativistic mass was introduced by the chemist Lewis much later. Here are some more quotes from the FAQ:

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion." -A. Einstein

"The concept of `relativistic mass' is subject to misunderstanding. That's why we don't use it. First, it applies the name mass--belonging to the magnitude of a four-vector--to a very different concept, the time component of a four-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of space-time itself." -Tayler and Wheeler

Relativistic mass is used in a lot of pop science books, for example books by Hawking or Kaku or the like. There are also some scientists who advocate their use in their work (for example the link you provided by Flores). However, it is hard to disagree with the fact that today, m always means rest mass. It is also likely that in Einstein's time in the equation E=mc², m also means rest mass. Your friend Flores is in a minority, and for Wikipedia to espouse his view is to breach NPOV. We should mention as often as is reasonable, that m usually means rest mass, but there are some who use it to mean relativistic mass, and what the difference is, and who uses what.

Those are my arguments. I disagree with the following edits of yours:

• this edit
  • Unilateral "since mass increases with velocity" may be OK in relativistic mass, but is no good in mass.
• this one
  • It is not only for teaching purposes. mass is rest mass in all kinds of research contexts. Really. Most practicing physicists in many theoretical branches don't ever consider the notion of relativistic mass. It is nearly impossible to do field theory, for example, with relativistic mass instead of rest mass.
• more
  • It is not inaccurate to call things with zero rest mass "massless". It is not NPOV to change all occurrences of the word "massless" to the phrase "with zero mass". "Massless" is standard usage among physicists, we are not here to redefine the language of the field, merely to display it. Let's be absolutely clear that the word massless refers to rest mass, but then use the term.
• [3]
  • This gives NPOV preferential treatment to relativistic mass: "since mass depends on velocity..." I think rest mass should be given primary standing, but failing that, there should be at least parity.
• [4]
  • I disagree with your source Flores, and don't think he should be taken as canon for wikipedia.
• [5]
  • equality of gravitational and inertial mass is not a theory. It's a hypothesis (synonymous with assumtion?) this edit also includes an enormous deletion of text with the edit summary "correct mistakes". I haven't followed the history of that article, so I can't say what's going on there, but I'm nervous.
• [6]
  • In this one you claim to be "removing POV", and you delete the suggestion that relativistic mass is used in popular science books, as well as several equations showing the benefits of relativistic mass. WTF?
• [7]
  • Another massive deletion of text without even an edit summary. What is going on here?

I feel that I have to revert all these edits. -lethe ^talk 19:26, 22 November 2005 (UTC)

I think Lethe has covered anything I could add. I agree, especially on your edits on the page mass - your edits there most defintately need discussion before they can be permenantly done. I hope that, although my actions have been rather distructive (to people's free time) I hope good change will come out of it when discussing the standard use of the word mass. Fresheneesz 20:57, 22 November 2005 (UTC)

A physicist's view

OK, I can't even read the mess above without hurting my head, so here area couple of facts to help you:

1. Physicists rarely use the "relativistic mass"—usually m just denotes the rest mass.
2. E=mc² is incomplete. The full version, as it is usually written out, is

   $E^{2}=p^{2}c^{2}+m^{2}c^{4}$.

3. E = mc² is thus valid only in the reference frame where the object is stationary.

Yes, you can do this other ways, but they are much less common in modern physics. -- SCZenz 00:53, 23 November 2005 (UTC)

That being said, if the article is presenting Einstein's original treatment, and is clear about it, that's not a problem. But it definitely is different than how the material would be presented today. -- SCZenz 00:56, 23 November 2005 (UTC)

I agree 100% with SCZenz, including the head-hurting part, and I'm glad someone else said all this so I don't have to. (go Bears!) Melchoir 01:04, 23 November 2005 (UTC)

Blame the professors. I think introductory, undergraduate relativity is often taught so that students learn the formula $M=m{\sqrt {1+v^{2}/c^{2}}}$ with $m$ the rest mass and M the relativistic mass. Yes, real physicists never use this formula, yes, Einstein may have thought it was a bad idea to word it this way ... yet, none-the-less, this is a part of the undergrad curriculum, and some fraction of WP readers will expect to see this formula when they go searching for it. I can only suggest that it needs to be explained in some mind-numbing way, i.e. that its just a whiz-bang variant of SCZenz's formula 2. Or, I duuno, maybe we can just banish it from WP, based on principles. linas 04:48, 23 November 2005 (UTC)