Test theories of special relativity

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Test theories of the special theory of relativity represent a theoretical scheme in order to be able to analyze experiments whose results may differ from the predictions of the special theory of relativity .

Before carrying out an experiment, it is usually not assumed that the results automatically agree with the theory to be tested, but it should also be indicated which alternative theories are used if the experiment gives a different result. This can be achieved by creating a test theory whose statements are somewhat broader than those of the theory to be tested. In relation to the special theory of relativity, these would be, for example, various postulates regarding the propagation of light, the existence of a preferred reference system such as ether , or other possibilities of violating the Lorentz invariance . The best-known test theories are those of Robertson (1949) and Mansouri-Sexl (1977), which, since they are equivalent to one another, together form the Robertson-Mansouri-Sexl test theory. Another, far more comprehensive model is the standard model extension , which is not limited to the special theory of relativity.

Robertson-Mansouri-Sexl (RMS) test theory

Overview

Howard P. Robertson (1949) extended the Lorentz transformation by adding further parameters. He assumed that a "preferred reference system " (or a stationary ether) exists in which the two-way speed of light (i.e. the speed from the transmitter to the Receiver and back) and the one-way speed of light is isotropic . It is also assumed that in all other reference systems the Poincaré-Einstein synchronization is used as a method for defining simultaneity, which means that the one-way speed of light is also isotropic in these systems. However, due to the presence of additional parameters in the transformation that represent the influence of the preferred frame of reference, the two-way speed of light is not isotropic.

A very similar model was developed by Reza Mansouri and Roman Sexl (1977). The difference to Robertson's model is that Mansouri and Sexl were by no means limited to the Poincaré-Einstein synchronization, but allowed any synchronization. For example, they used "external synchronizations", whereby time displays of clocks in a certain reference system are arbitrarily preferred and also used in all other reference systems. This means that in this model, not only the two-way, but also the one-way speed of light is anisotropic.

Since the two-way speed of light is anisotropic in both models, and only this speed can be measured directly without assuming a certain synchronization, both models are experimentally equivalent and are collectively referred to as the Robertson-Mansouri-Sexl test theory (RMS). Since the special theory of relativity, however, predicts a constant two-way speed of light, RMS differs experimentally from the special theory of relativity. If a result deviating from the Lorentz invariance is found in an experiment , the more detailed properties of any preferred reference system can be determined by analyzing the RMS parameters.

theory

The notation of Mansouri and Sexl is used below. Using units that make the speed of light equal to 1, they chose the following coefficients for the transformation between the frames of reference:

where are the coordinates measured in a preferred reference system and the coordinates measured in a moving reference system, and is a value dependent on the synchronization used. It follows that the time dilation and the length contraction represents. It is believed that , and automatically result in the Lorentz transformations. So the purpose of this test theory is to evaluate measurements of a ( v ) and b ( v ) and determine how close they come to the values ​​that exist if the Lorentz transformation is valid. In addition, they allowed arbitrary values ​​for , i.e. arbitrary synchronizations. These are:

  1. Internal clock synchronization: This includes the Poincaré-Einstein synchronization and the method of "slow clock transport" (different clocks are synchronized by a clock moving at an extremely low speed).
  2. External clock synchronization: They suggested the reference system in which the CMBR is isotropic as a test ether system and used the clocks of this reference system to synchronize the clocks of all other reference systems. This means that the clocks of all reference systems are synchronous (no relativity of simultaneity ).

They came to the result that all these synchronizations are only then equivalent to each other as long as the time dilation is exactly valid (i.e. ), regardless of whether an ether exists or not. Mansouri / Sexl established the “remarkable” fact that a theory based on “absolute” simultaneity can be equivalent to the SRT.

Mansouri / Sexl, and practically all modern physicists, are still of the opinion that the special theory of relativity and Lorentz symmetry are to be preferred, since otherwise the equivalence of the inertial systems would be destroyed, or more precisely, that the observed equivalence would otherwise only be an apparent one. This makes models such as Lorentz's theory of ether , taking Ockham's principle into account, so improbable that they are practically no longer represented in the professional world.

Experiments with RMS

Test theories of special relativity are currently often used to evaluate experimental tests of violations of the Lorentz invariance, which may result from quantum gravity . The parameters according to the RMS scheme take the following form for quantities of the second order in v / c :

, Time dilation
, Length in the direction of movement
, Length perpendicular to the direction of movement

Deviations from the two-way speed of light result with

where the speed of light in the preferred system, the speed of light in the moving system is in angle . The values ​​when the special theory of relativity is valid are , and consequently .

Some fundamental and frequently repeated experiments that play a particular role in these assessments are as follows:

  • Michelson-Morley experiment , with which the directional dependence of the speed of light is tested with respect to a preferred reference system. Current precision: .
  • Kennedy-Thorndike experiment , with which the dependence of the speed of light on the relative speed of the apparatus with respect to a preferred reference system is tested. Current precision: .

The combination of all three experiments, together with the Poincaré-Einstein synchronization, is necessary to derive all parameters of the Lorentz transformation. Michelson-Morley experiments test the combination of β and δ, Kennedy-Thorndike experiments test the combination of α and β. In order to obtain the individual values, however, one of the variables must be measured directly. This is done, for example, with the Ives-Stilwell experiment, whereby α is measured in accordance with the time dilation. β can now be determined by means of Kennedy-Thorndike, and consequently δ by means of Michelson-Morley.

In addition to these experiments measuring second-order effects in v / c , Mansouri and Sexl also discussed experiments measuring first- order effects in v / c . They called these tests "one-way speed of light measurements". The aim is to check the equivalence of the two internal synchronizations, namely that caused by slow clock transport and that caused by light. However, they emphasized that the negative results even of these tests are compatible with ether theories, in which bodies moving relative to the ether are subject to time dilation. However, many no longer speak of " one-way speed of light " with these measurements , because the results are also compatible with external synchronization and anisotropic one-way speed of light. This means that they are compatible with all models in which the two-way speed of light is isotropic and the two-way time dilation of moving bodies assumes the same value.

Standard Model Extension (SME)

Another, much more far-reaching model for checking experimental deviations from various standard theories is the standard model extension (SME = Standard Model Extension). a. was developed by Alan Kostelecky . In contrast to the test theory of Robertson-Mansouri-Sexl (RMS), which is of a kinematic nature and is limited to the special theory of relativity, the formalisms of the dynamic effects of the standard model and the general theory of relativity are expanded in the SME by introducing additional parameters that violate Lorentz. The RMS test theory is completely contained in the SME, but the latter contains a much larger number of parameters with which possible violations of the Lorentz invariance and the CPT theorem can be assessed.

All experiments carried out so far have confirmed the Lorentz invariance, i. H. no deviations from it were found, regardless of which parameters of the test theories were used. For example, a group of SME parameters was checked with the simultaneous use of different Michelson-Morley resonators at different geographical latitudes ( Berlin and Perth ) to an accuracy of 10 −16 . A large number of other parameters were also checked in a number of other tests, for example the Hughes-Drever experiments .

See also

Individual evidence

  1. ↑ a b c d e Robertson, HP: Postulates versus Observation in the Special Theory of Relativity . In: Reviews of Modern Physics . 21, No. 3, 1949, pp. 378-382. doi : 10.1103 / RevModPhys.21.378 .
  2. ^ A b c d e Mansouri R., Sexl RU: A test theory of special relativity. I: Simultaneity and clock synchronization . In: General Relat. Gravit. . 8, No. 7, 1977, pp. 497-513. bibcode : 1977GReGr ... 8..497M . doi : 10.1007 / BF00762634 .
  3. ↑ a b c d e Zhang, Yuan Zhong: Test theories of special relativity . In: General Relativity and Gravitation . 27, No. 5, 1995, pp. 475-493. doi : 10.1007 / BF02105074 .
  4. ^ A b c Zhang, Yuan Zhong: Special Relativity and Its Experimental Foundations . World Scientific , 1997, ISBN 9789810227494 .
  5. ↑ a b c Anderson, R .; Vetharaniam, I .; Stedman, GE: Conventionality of synchronization, gauge dependence and test theories of relativity . In: Physics Reports . 295, No. 3-4, 1998, pp. 93-180. doi : 10.1016 / S0370-1573 (97) 00051-3 .
  6. ↑ a b c d e Lämmerzahl, Claus; Braxmaier, Claus; Dittus, Hansjörg; Müller, Holger; Peters, Achim; Schiller, Stephan: Kinematical Test Theories for Special Relativity . In: International Journal of Modern Physics D . 11, No. 7, 2002, pp. 1109-1136. doi : 10.1142 / S021827180200261X .
  7. ↑ Giulini, Domenico; Straumann, Norbert: Einstein's impact on the physics of the twentieth century . In: Studies In History and Philosophy of Modern Physics . 2005, pp. 115-173. arxiv : physics / 0507107 . doi : 10.1016 / j.shpsb.2005.09.004 .
  8. ^ A b Mansouri R., Sexl RU: A test theory of special relativity: II. First order tests . In: General Relat. Gravit. . 8, No. 7, 1977, pp. 515-524. bibcode : 1977GReGr ... 8..515M . doi : 10.1007 / BF00762635 .
  9. ↑ a b c d e Mansouri R., Sexl RU: A test theory of special relativity: III. Second-order tests . In: General Relat. Gravit. . 8, No. 10, 1977, pp. 809-814. bibcode : 1977GReGr ... 8..809M . doi : 10.1007 / BF00759585 .
  10. ↑ Herrmann, S .; Senger, A .; Möhle, K .; Nagel, M .; Kovalchuk, EV; Peters, A .: Rotating optical cavity experiment testing Lorentz invariance at the 10 −17 level . In: Physical Review D . 80, No. 100, 2009, p. 105011. arxiv : 1002.1284 . bibcode : 2009PhRvD..80j5011H . doi : 10.1103 / PhysRevD.80.105011 .
  11. ↑ Tobar, ME; Wolf, P .; Bize, S .; Santarelli, G .; Flambaum, V .: Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser . In: Physical Review D . 81, No. 2, 2010, p. 022003. arxiv : 0912.2803 . doi : 10.1103 / PhysRevD.81.022003 .
  12. ↑ Reinhardt, S .; Saathoff, G .; Buhr, H .; Carlson, LA; Wolf, A .; Schwalm, D .; Karpuk, S .; Novotny, C .; Huber, G .; Zimmermann, M .; Holzwarth, R .; Udem, T .; Hänsch, TW; Gwinner, G .: Test of relativistic time dilation with fast optical atomic clocks at different velocities . In: Nature Physics . 3, No. 12, 2007, pp. 861-864. bibcode : 2007NatPh ... 3..861R . doi : 10.1038 / nphys778 .
  13. ^ Roberts, Schleif (2006): Relativity FAQ, One-Way Tests of Light-Speed ​​Isotropy
  14. ↑ Bluhm, Robert: Overview of the SME: Implications and Phenomenology of Lorentz Violation = Lect. Notes. Phys. . In: Springer . 702, 2005, pp. 191-226. arxiv : hep-ph / 0506054 . doi : 10.1007 / 3-540-34523-X_8 .
  15. ^ Kostelecký, V. Alan; Mewes, Matthew: Electrodynamics with Lorentz-violating operators of arbitrary dimension . In: Physical Review D . 80, No. 1, 2009, p. 015020. arxiv : 0905.0031 . doi : 10.1103 / PhysRevD.80.015020 .
  16. ↑ Mattingly, David: Modern Tests of Lorentz Invariance . In: Living Rev. Relativity . 8, No. 5, 2005.
  17. ↑ Müller, Holger; Stanwix, Paul Louis; Tobar, Michael Edmund; Ivanov, Eugene; Wolf, Peter; Herrmann, Sven; Senger, Alexander; Kovalchuk, Evgeny; Peters, Achim: Relativity tests by complementary rotating Michelson-Morley experiments . In: Phys. Rev. Lett. . 99, No. 5, 2007. arxiv : 0706.2031v1 . bibcode : 2007PhRvL..99e0401M . doi : 10.1103 / PhysRevLett.99.050401 .
  18. ↑ Kostelecký, VA; Russell, N .: Data tables for Lorentz and CPT violation . In: Review of Modern Physics . 83, No. 1, 2011, pp. 11-32. arxiv : 0801.0287v5 . bibcode : 2011RvMP ... 83 ... 11K . doi : 10.1103 / RevModPhys.83.11 .

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