Relativity Principle

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The principle of relativity says that the laws of nature have the same form for all observers . Simple considerations show that for this reason it is impossible to determine a preferred or absolute state of motion of any observer or object. This means that only the movements of the bodies relative to other bodies can be determined, but not the movements of the bodies relative to a preferred reference system .

In classical physics as well as in the special theory of relativity (SRT) designed by Albert Einstein in 1905 , this principle was initially only valid in inertial systems that move uniformly and unaccelerated to one another. Accelerated frames of reference can also be used, but laws of nature in such systems do not have the same simple form as in inertial systems and are consequently not equal to the latter. In the general theory of relativity (ART) the relativity principle is extended to accelerated reference systems, whereby the gravitation can be interpreted as a consequence of inertial forces . According to this modern view, the SRT is the special case of the GTR, if the influence of gravity can be neglected, and is now also equally valid for inertial systems and accelerated reference systems.

Galileo Galilei (1632) is considered to be the first to formulate this principle. He had only mechanical processes in view and argued that an observer below deck of an unaccelerated ship could not deduce from the processes around him whether the ship was moving or not.

In another sense, the relativity of the perceptions of different people in aesthetics is called the relativity principle.

Classic mechanics

Following Isaac Newton , classical mechanics assumed the existence of an absolute space for centuries . Newton believed that he had experimentally proven the existence of this absolute space with his bucket experiment. The relativity principle implicitly contained in these mechanics said that in uniformly moving inertial systems the same laws ( covariance ) of mechanics apply as in absolute space itself, and that it is not possible to determine which system is actually at rest or which is moving. This means that the formulas of classical mechanics retain their validity if a system that is moved relative to absolute space is subjected to the so-called Galileo transformation . Newton wrote in his Principia :

"The movements of bodies in a given space are the same as each other, whether the space is at rest or whether it is constantly moving in a straight line."

Christiaan Huygens made an innovative application of the Galilean principle of relativity in the derivation of the laws of collision (see also Galilei transformation ).

In the 19th century, after the establishment of Maxwell's theory of electrodynamics, classical physics led to the theory of the aether at rest , which was intended as a transmission medium for light and was finally identified with Newton's absolute space. From then on an attempt was made to prove the state of motion of the earth relative to the ether, which would also have refuted the principle of relativity. However, all relevant experiments - such as the Michelson-Morley experiment  - remained unsuccessful.

Special relativity principle

At the beginning of the 20th century, these unsuccessful experiments led to the relativity principle being given ever greater importance, which also led to clearer definitions of terms. For example, in 1904 Henri Poincaré wrote in "the first text in which not only the thing but also the word appears":

“The principle of relativity, according to which the laws of physical processes should be the same for a stationary observer as for someone moving in uniform translation, so that we have or cannot have any means of distinguishing whether we are engaged in such a movement are or not. "

And Albert Einstein defined the principle of relativity as follows in 1905:

"The laws according to which the states of the physical systems change are independent of which of two coordinate systems which are in uniform translational motion relative to one another these state changes are related to."

Hendrik Antoon Lorentz , Poincaré and Einstein also called for covariance not only of mechanics but also of electrodynamics . This could be achieved by replacing the Galileo transformation with the Lorentz transformation . The main difference is that in the new transformation, the speed of light represents an insurmountable limit speed. For speeds that are small compared to the speed of light, the special principle of relativity goes over to that of Galileo. Newton's absolute space, however, contradicts the principle of relativity. Therefore Einstein drew the conclusion with the special theory of relativity that there is no absolute reference system. This applies to both space and time. Hermann Minkowski took this further by combining space and time into four-dimensional space - time .

In the SRT, the principle of relativity is initially only valid in inertial systems, because it is only in them that the laws of nature assume the same simple form. The formalism of the SRT can be extended beyond that so that accelerated reference systems can also be treated, but these systems are not on an equal footing with inertial systems.

General principle of relativity

In addition to the special principle of relativity, Einstein introduced the requirement that in all frames of reference, whether accelerated or unaccelerated, the laws must take the same form (general covariance). This was motivated by the validity of the equivalence principle , which states that no experiment can determine whether one is in weightlessness far from a mass or in free fall close to a mass. Einstein also assumed that this is related to Mach's principle , according to which inertia and acceleration only occur relative to the masses of the universe. He wrote in 1916:

“The laws of physics must be such that they apply in relation to arbitrarily moving reference systems. […] The general laws of nature are to be expressed by equations that apply to all coordinate systems, i. H. the arbitrary substitutions are covariant (generally covariant). "

In fact, general covariance is achieved in general relativity (GTR). The idea that space is Euclidean had to be given up , because gravitation is understood as a property, namely as the curvature of space-time , for the description of which a non-Euclidean geometry must be used. However, to understand general covariance, consider the following circumstances:

  • General covariance can be understood as a mathematical principle that does not automatically result in a general relativity principle in the sense of a relativity of acceleration . Because every theory can be formulated covariant with appropriate mathematical effort, for example the SRT and even Newtonian mechanics.
  • The equivalence principle is only valid locally because tidal effects occur over larger distances . The SRT is therefore also locally valid as a special case of the GTR in the “flat” or Minkowskian spacetime, where gravity can be neglected (“local Lorentz invariance”) - that is, in areas in which the Riemann curvature tensor is zero everywhere.
  • Also largely matter-free solutions of the GTR are possible without an individual body losing its inertia, which violates Mach's principle.

Generally speaking, the “gravito-inertial field”, that is, the field with which both acceleration and gravitational effects are described in the general theory of relativity, has an existence independent of bodies. This field can be used to determine which of two observers who are accelerated relative to one another is moving "really" or "absolutely" non-uniformly. However, giving up the complete relativization of the acceleration in no way proves the existence of an absolute space, because although the “Gravito-Inertialfeld” also exists without matter, as mentioned, it is nevertheless subject to its influence in the presence of matter - in contrast to Newton's absolute space, that of the Matter remains unaffected.

Galileo's ship

The following is an excerpt from the description, p. 197 ff., By Galileo:

“Lock yourself in the company of a friend in the largest possible room under the deck of a large ship. Get mosquitoes, butterflies and similar flying animals there; also provide a vessel with water and small fish in it; furthermore hangs up a small bucket, which lets water trickle drop by drop into a second narrow-necked vessel placed underneath. Now watch carefully, as long as the ship stands still, how the little flying animals fly at the same speed to all sides of the room. One will see how the fish swim in all directions without any difference; the falling drops will all flow into the vessel below. If you throw an object at your companion, you need not throw it more forcefully in one direction than in the other, provided that the distances are equal. If, as they say, you jump with the same feet, you will get equally far in every direction. Be careful to make sure of all these things carefully, although there is no doubt that everything is so when the ship is at rest. Now let the ship move at any speed you want: you will not see the slightest change in any of the phenomena mentioned - if only the movement is uniform and does not fluctuate here and there. You will not be able to infer from any of these whether the ship is moving or standing still. [...] The cause of this coincidence of all phenomena is that the movement of the ship is common to all things contained therein, including the air. That is why I also said that one should go below deck, because up in the open air, which does not accompany the course of the ship, there would be more or less clear differences in some of the phenomena mentioned. "

Individual evidence

  1. ^ A b Galileo Galilei: Dialogue on the two main world systems, the Ptolemaic and the Copernican . BG Teubner, Leipzig 1891, p. 197–198 ( digitized version [accessed June 14, 2020]).
  2. ↑ Julian Klein (Ed.): PER.SPICE! - Reality and relativity of the aesthetic . Research 71, 2009, chap. On the dynamics of moving bodies. The basis of the aesthetic relativity theory , p. 104-134 ( TheaterDerZeit.de ).
  3. ↑ Max Born: Einstein's theory of relativity . Springer, Berlin / Heidelberg / New York 2003, ISBN 3-540-00470-X , p. 57-59 .
  4. ^ Newton: Mathematical principles of natural philosophy and his system of the world. Volume 1, University of California Press 1974 (editor Florian Cajori ), p. 20, section Axioms or Laws of Motion, Corollary V: The motion of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forward in a right line without any circular motion.
  5. ^ Literally after Albrecht Fölsing : Albert Einstein. Suhrkamp Verlag, 1995, ISBN 3-518-38990-4 , p. 187.
  6. ^ Henri Poincaré: The present state and the future of mathematical physics . In: The Value of Science (Chapters 7–9) . BG Teubner, Leipzig 1904, p. 129-159 ( Wikisource.org ).
  7. ↑ Albert Einstein: On the electrodynamics of moving bodies . In: Annals of Physics . tape 322 , no. 10 , 1905, pp. 891-921 ( PDF ).
  8. ↑ Albert Einstein: The basis of the general theory of relativity . In: Annals of Physics . tape 354 , no. 7 , 1916, pp. 769-782 ( PDF ).
  9. ^ John D. Norton, General Covariance and the Foundations of General Relativity: Eight Decades of Dispute . In: Reports on Progress in Physics . tape 56 , 1993, pp. 791-858 ( PDF ).
  10. ^ A b Michel Janssen: The Cambridge Companion to Einstein . Ed .: Michel Janssen, Christoph Lehner. Cambridge University Press, 2008, ISBN 0-521-53542-5 , chap. 'No Success like Failure ...': Einstein's Quest for General Relativity, 1907–1920 ( online ).