Special relativity with a preferred frame and the relativity principle: cosmological implications

Abstract: The modern view, that there exists a preferred frame of reference related to the cosmic microwave background (CMB), is in apparent contradiction with the principles of special relativity. The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relativity principle and universality of the (\textit{two-way}) speed of light. In the framework developed, a degree of anisotropy of the one-way velocity acquires meaning of a characteristic of the really existing anisotropy caused by motion of an inertial frame relative to the preferred frame. The anisotropic special relativity kinematics is developed based on the first principles: (1) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant and (2) A set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of space-time transformations between inertial frames. Applying the consequences of the transformations to the problem of calculating the CMB temperature distribution yields an equation in which the angular dependence coincides with that obtained on the basis of the standard relativity theory but the mean temperature is corrected by the terms second order in the observer velocity. From conceptual point of view, it eliminates the inconsistency of the usual approach when formulas of the standard special relativity are applied to define effects caused by motion with respect to the preferred frame.

• The paper introduces anisotropic transformations that integrate a preferred frame while preserving the two-way speed of light.
• The methodology employs Lie group analysis to derive modified transformation laws that align with classical mechanics in low-velocity limits.
• Implications include corrected cosmic microwave background temperature predictions and new experimental approaches using the universal constant q.

Special Relativity with a Preferred Frame and its Cosmological Implications

The paper by Georgy I. Burde addresses a significant conceptual discrepancy between the established tenets of special relativity and the observational evidence of a preferred cosmic frame related to the cosmic microwave background (CMB). Traditional special relativity dismisses a universal rest frame, while the existence of such a frame is suggested by the CMB. This work endeavors to resolve this conflict by extending the framework of special relativity to accommodate a preferred frame, thus preserving the relativity principle alongside the universality of the two-way speed of light.

Core Concepts and Methodology

The proposed theory leverages the flexibility in the assignment of one-way light speeds permissible within special relativity to include the notion of anisotropy, which is essentially the variable character of light speed when assessed from different inertial frames moving relative to the preferred frame. This introduces a parameter $k$, representing anisotropy, which varies with the motion's velocity vector concerning the preferred frame.

The theoretical developments hinge on several pivotal concepts:

• Anisotropic Transformations: Unlike the conventional Lorentz transformations that maintain interval invariance, the modified transformations here alter the interval through a conformal factor. This factor indicates that the standard interval invariance does not hold under actual physical anisotropy.
• Lie Group Analysis: Applying Lie group theory crucially facilitates the generation of transformation laws that maintain form-invariance of the anisotropic equation of light propagation, satisfying group closure properties while transitioning back to Galilean transformations in low-velocity limits.
• Correspondence Principle: This principle underpins the derivation of transformations, ensuring that as velocities diminish, transformations congruence with classical mechanics is retained, thus maintaining the continuity between new and old physics.

Results and Implications

Cosmological Insights

The framework presented predicts alterations in the perceived cosmic phenomena, specifically giving rise to a distinct formulation for the CMB temperature distribution observable from a moving frame. Crucially, while the angular dependence mirrors predictions by standard relativity, it corrects the mean temperature by terms quadratic in observer velocity. This rectification resolves inconsistencies arising from the application of standard relativistic formalism to effects induced by relative motion against the CMB frame.

Future Directions

The anisotropic special relativity theory proposed has potential far-reaching implications. It suggests new avenues of experimental validation centered around the universal constant $q$, integral in quantifying the anisotropy level. Moreover, the potential application of such a framework in interpreting astronomical observations — such as Doppler shifts from distant galaxies — holds promise to refine our understanding of cosmic motion.

The research initiates vital conversations surrounding fundamental physics principles, propelling us toward a unified theory that seamlessly integrates relativistic mechanics with cosmological observations. Continued exploration in experimental settings, perhaps involving precision astrophysical measurements or novel laboratory configurations, could provide further insights, potentially validating or challenging the proposed theoretical model. Such inquiries might ultimately propel more comprehensive reconciliation between general relativity and cosmological phenomena within a broader astrophysical context.