[Paper Review] Rethinking the Foundations of the Theory of Special Relativity: Stellar Aberration and the Fizeau Experiment

Anthony F. Maers, Randy Wayne|arXiv (Cornell University)|May 10, 2011

History and Developments in Astronomy44 references5 citations

TL;DR

This paper proposes a new relativistic wave equation based on the primacy of the Doppler effect, offering a framework that explains stellar aberration, the Fizeau experiment, and the Michelson-Morley null result without invoking the relativity of space and time. It claims superior quantitative accuracy over Special Relativity in modeling light propagation in moving media, particularly in predicting fringe shifts dependent on refractive index.

ABSTRACT

In a previous paper published in this journal, we described a new relativistic wave equation that accounts for the propagation of light from a source to an observer in two different inertial frames. This equation, which is based on the primacy of the Doppler effect, can account for the relativity of simultaneity and the observation that charged particles cannot exceed the speed of light. In contrast to the Special Theory of Relativity, it does so without the necessity of introducing the relativity of space and time. Here we show that the new relativistic wave equation based on the primacy of the Doppler effect is quantitatively more accurate than the standard theory based on the Fresnel drag coefficient or the relativity of space and time in accounting for the results of Fizeau's experiment on the optics of moving media - the very experiment that Einstein considered to be "a crucial test in favour of the theory of relativity." The new relativistic wave equation quantitatively describes other observations involving the optics of moving bodies, including stellar aberration and the null results of the Michelson-Morley experiment. In this paper, we propose an experiment to test the influence of the refractive index on the interference fringe shift generated by moving media. The Special Theory of Relativity, which is based on the relativity of space and time, and the new relativistic wave equation, which is based on the primacy of the Doppler effect, make different predictions concerning the influence of the refractive index on the optics of moving media.

Motivation & Objective

• To re-express the foundations of Special Relativity by prioritizing the Doppler effect over the relativity of space and time.
• To resolve inconsistencies in explaining light propagation in moving media, particularly in the context of the Fizeau experiment.
• To provide an alternative theoretical framework that accounts for the null result of the Michelson-Morley experiment without assuming relativistic spacetime.
• To propose a testable experiment distinguishing the new wave equation from Special Relativity based on refractive index effects on interference fringes.
• To challenge the foundational role of the Lorentz transformation and the invariance of the speed of light in favor of a Doppler-centric approach.

Proposed method

• Develops a new relativistic wave equation based on the Doppler shift as the primary physical principle, rather than the constancy of light speed.
• Applies the wave equation to model light propagation from a source to an observer in different inertial frames, emphasizing phase and frequency shifts.
• Uses the wave equation to quantitatively reproduce the Fizeau experiment's results, particularly the dependence of light speed on the refractive index of moving media.
• Compares predictions of the new model with those of Special Relativity and the Fresnel drag coefficient for interference fringe shifts in moving media.
• Proposes a new experimental setup to measure fringe shifts in interferometers with moving media, where the refractive index is systematically varied.
• Analyzes the implications of the model for the relativity of simultaneity and the speed limit of charged particles, linking them to Doppler-based dynamics.

Experimental results

Research questions

• RQ1 Can a relativistic wave equation based on the Doppler effect accurately reproduce the results of the Fizeau experiment without invoking the relativity of space and time?
• RQ2 How does the new model compare quantitatively with Special Relativity in predicting fringe shifts in moving media?
• RQ3 Does the new framework provide a consistent explanation for stellar aberration without requiring relativistic transformations of space and time?
• RQ4 What is the predicted dependence of interference fringe shifts on the refractive index of moving media according to the new wave equation?
• RQ5 Can a new experiment distinguish the predictions of the Doppler-based model from those of Special Relativity in moving media?

Key findings

• The new relativistic wave equation provides a more accurate quantitative description of the Fizeau experiment than the standard theory based on the Fresnel drag coefficient or relativistic spacetime.
• The model successfully explains the null result of the Michelson-Morley experiment without requiring the invariance of the speed of light in all inertial frames.
• The theory accounts for stellar aberration through Doppler-based phase shifts, offering an alternative to the relativistic aberration formula.
• The model predicts a measurable dependence of fringe shift on the refractive index of moving media, differing from Special Relativity’s predictions.
• The proposed experiment could test the influence of refractive index on interference patterns in moving media, providing a potential empirical distinction between the two frameworks.
• The framework naturally explains why charged particles cannot exceed the speed of light, linking this to Doppler shift dynamics rather than spacetime geometry.