Special relativity — Wikipedia.

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:

1. The laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference).

2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

Special relativity is restricted to flat spacetime, i.e., to all phenomena without significant influence of gravitation. The latter lies in the domain of general relativity and the corresponding tests of general relativity must be considered.



Lorentz ether theory — Wikipedia.


What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century. Lorentz's initial theory was created between 1892 and 1895 and was based on a completely motionless aether. It explained the failure of the negative aether drift experiments to first order in v/c by introducing an auxiliary variable called "local time" for connecting systems at rest and in motion in the aether. In addition, the negative result of the Michelson–Morley experiment led to the introduction of the hypothesis of length contraction in 1892. Many aspects of Lorentz's theory were incorporated into special relativity (SR) with the works of Albert Einstein and Hermann Minkowski.

Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. The introduction of length contraction and time dilation for all phenomena in a "preferred" frame of reference, which plays the role of Lorentz's immobile aether, leads to the complete Lorentz transformation. Because the same mathematical formalism occurs in both, it is not possible to distinguish between LET and SR by experiment. However, in LET the existence of an undetectable aether is assumed and the validity of the relativity principle seems to be only coincidental, which is one reason why SR is commonly preferred over LET.


Tests of special relativity — Wikipedia.


The strength of the theory lies in its unique ability to correctly predict to high precision the outcome of an extremely diverse range of experiments. Repeats of many of those experiments are still being conducted with steadily increased precision, with modern experiments focusing on effects such as at the Planck scale and in the neutrino sector. Their results are consistent with the predictions of special relativity.



What is the experimental basis of Special Relativity?

There has been a renaissance in tests of Special Relativity (SR), in part because considerations of quantum gravity imply that SR may well be violated at appropriate scales (very small distance, very high energy). It has been seven years since the last update of this page, and there are over 60 new experiments, many of which are recent, ingenious, and improve bounds on violations of local Lorentz invariance by several or many orders of magnitude.

General relativity — Wikipedia.


Tests of general relativity — Wikipedia.

The Confrontation between General Relativity and Experiment. (Clifford M. Will) (2014)

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them are reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational-wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

We find that general relativity has held up under extensive experimental scrutiny. The question then arises, why bother to continue to test it? One reason is that gravity is a fundamental interaction of nature, and as such requires the most solid empirical underpinning we can provide. Another is that all attempts to quantize gravity and to unify it with the other forces suggest that the standard general relativity of Einstein is not likely to be the last word. Furthermore, the predictions of general relativity are fixed; the theory contains no adjustable constants so nothing can be changed. Thus every test of the theory is either a potentially deadly test or a possible probe for new physics. Although it is remarkable that this theory, born 90 years ago out of almost pure thought, has managed to survive every test, the possibility of finding a discrepancy will continue to drive experiments for years to come.

The Lorentz-covariance — Wikipedia


Aether is back? The "Fifth Element": history and contemporary outlook. Does the aether contradict Einstein’s theory? (About Lorentz’ symmetry, invariance). (K. Zloschastyev) (2007)   (in Russian) 

Einstein’s STR postulated that physical laws remain unchanged for all observers in inertial systems, and a Lorentz transformation can be used to pass from one system to another. Such “Lorentz invariance for observers” (LIO) should never be violated in the frame of the STR.


However, in Einstein’s theory, there is also a “Lorentz invariance for particles”  (LIP), whose violation isn’t written in the STR, but on the other side, there is no need to radically revise the theory subject to matching the LIO.


It is possible to demonstrate that LIP and LIO are not identical : hence when LIO is preserved, the LIP may be violated in some cases (spontaneously or in full), and there are quite a lot of corresponding theoretical examples.


​While equations compatible for the theory of relativity preserve the Lorentz symmetry, some of their solutions violate this same symmetry ! Thus we can easily explain why we have been unable to observe any deviation for the GTR : most of solutions, factually corresponding to events or effects observed by us, preserve symmetry, and only a few of them  do not (or the deviations are very small and remain out of reach for our contemporary measurement devices). The aether could in fact be such a LIP-violating solution of certain field equations, which are fully compatible with the LIIO. There are plenty of experiments searching for violations of Lorentz symmetries, there are all different, and many of them give only indirect indications, not direct.


Some think that Einstein’s theory did grow up so fast within contemporary science, that scientists already lost any thoughts about its possible discarding. But in fact, a large number of specialists throughout the world are hunting for facts, theoretical or experimental, which could limit the area of applicability of the theory of relativity. So far without success, the theory is in full line with observations. But, sooner or later, this will happen (for instance, a full theory of quantum gravitation has still not been built yet), and another theory, more general, will replace Einstein’s one. Who knows, maybe the aether will have a place in such theory ?...


New Symmetries in the space-time and non-linearity in nature (V. G. Zhotikov) (2006)  (pdf, in Russian

It has been demonstrated that the group of relativistic invariance should be a group of Lorentz-Caratheodory, and not a group of Lorentz transformation (equivalent to a group of Poincaré)


The group of Lorentz-Caratheodory contains two sub-groups: the group of Lorentz and the group of Caratheodory, which introduced an invariant value in the theory: the fundamental length.


In this way the problem of divergences in the quantum field theory can be solved.


It has been shown that these transformations are an example of non linear transformation, and that they give simple explanations for many non linear phenomena in nature.


Hence, all the fundamental equations in physics should be invariant, in addition to the invariance according the group of Lorentz, also according the group of transformations of Caratheodory.

About the violation of Lorentz’ symmetry (short analysis of consequences)  (pdf, in Russian

Relativity in physical theories (in Russian) 

A Lorentz-invariant theory of gravitation (in Russian)

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