Test theories of special relativity

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Test theories of special relativity are frameworks, which are used for examinations about the validity of Lorentz symmetry and the existence of a preferred frame of reference. A well known example was created by Reza Mansouri and Roman Ulrich Sexl in 1977.[1]

[edit] Theoretical framework

By setting the speed of light to unity Mansouri/Sexl chose the following coefficients of the transformation between reference frames:

t=aT+\varepsilon x
x = b(X − vT)

Where T, X are coordinates measured in the (preferred) ether frame, and t, x are coordinates measured in a moving frame, and therefore 1 / a(v) is time dilation and b(v) is length contraction. By supposing 1/a(v)=b(v)=1/\sqrt{1-v^2} the Lorentz transformation follows. Then they discussed different methods of clock synchronisation.

  1. Internal clock synchronisation including the Poincaré-Einstein synchronisation and synchronisation by slow clock transport. If it is assumed that time dilation has the exact relativistic value, both methods are equivalent in all reference frames, independent of the question if there is an ether or not.
  2. External clock synchronisation by choosing a "preferred" reference frame (like the CMB) and using the clocks of this frame to synchronize the clocks in all other frames. This means that in all frames the clocks are synchronous, nevertheless also in this case the ether theory is equivalent to special relativity, if the effects of time dilation and length contraction have the exact relativistic value.

So Sexl/Mansouri spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and Lorentz ether theory of Hendrik Lorentz, Joseph Larmor and Henri Poincaré and wrote:

“ In this theory measuring rods show the standard Fitzgerald-Lorentz contraction and clocks the standard time dilatation when moving relative to the ether. Such a theory would have been the logical consequence of the development along the lines of Lorentz-Larmor-Poincaré. That the actual development went along different lines was due to the fact that "local time" was introduced at the early stage in considering the covariance of the Maxwell equations. ”

However, Sexl/Mansouri preferred SRT over an ether theory, because the latter "destroys the internal symmetry of a physical theory".

[edit] Breaking Lorentz symmetry?

Modern measurements empirically seems to discredit Lorentz violating models. A 2007 study sensitive to 10-16 employed two simultaneous interferometers over a year's observation: Optical in Berlin, Germany at 52°31'N 13°20'E and microwave in Perth, Australia at 31°53'S 115°53E. Such an aether background (leading to Lorentz violation) could never be at rest relative to both of them. [2]

Affine (Einstein-Cartan theory), teleparallelism (Weitzenböck) and noncommutative (Alain Connes) gravitation theories wholly contain General Relativity as a restricted case (isotropic vacuum, Equivalence Principle = true). They also allow a Lorentz-violating chiral vacuum background (anisotropic vacuum) in which the Equivalence Principle has parity violations in the mass sector (e.g., enantiomorphic mass distributions - atom locations - in opposite parity space groups P3121 and P3221 chemically identical crystals). This is experimentally unexamined.

[edit] References

  1. ^ Mansouri R., Sexl R.U. (1977), “A test theory of special relativity. I: Simultaneity and clock synchronization”, General. Relat. Gravit. 8 (7): 497–513 
  2. ^ Wolf et al.: Recent Experimental Tests of Special Relativity (2005) and Relativity tests by complementary rotating Michelson-Morley experiments (2007)