Explaining Sagnac vs. SRT Violation & Reconciling Lorentz Transform

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SUMMARY

The discussion centers on the apparent conflict between the Sagnac effect and Special Relativity Theory (SRT), particularly in the context of Sagnac ring laser gyros and fiber-optic gyros. Participants assert that the Sagnac effect does not violate SRT, as it is a prediction of the theory, and emphasize the necessity of Sagnac corrections in systems like the Global Positioning System (GPS) due to non-inertial frames. The conversation also references Ruyong Wang's experiments, which demonstrate that the travel-time difference of counter-propagating light beams in moving fibers is consistent with SRT when analyzed from an inertial frame.

PREREQUISITES
  • Understanding of Special Relativity Theory (SRT)
  • Familiarity with the Sagnac effect and its implications
  • Knowledge of inertial vs. non-inertial frames of reference
  • Basic principles of fiber-optic technology and gyroscopic measurements
NEXT STEPS
  • Study the derivation of the Sagnac effect within Special Relativity from reputable sources.
  • Investigate Ruyong Wang's 2003 paper on modified Sagnac experiments for deeper insights.
  • Explore the implications of the Sagnac effect on Global Positioning System (GPS) accuracy and functionality.
  • Review historical experiments related to the speed of light, such as the Michelson-Morley experiment, to understand foundational concepts in relativity.
USEFUL FOR

Physicists, engineers, and students interested in the intersection of relativity and practical applications in navigation systems, particularly those working with gyroscopic technology and fiber optics.

  • #61
Your formula for SR is given in leading order of the ##v/c## expansion. You have to apply the same approximation also for the aether-theory result
$$\Delta t=\frac{2L v}{c^2} \frac{1}{1-v^2/(n^2 c^2)}=\frac{2L v}{c^2} (1+\mathcal{O}(v^2/c^2)),$$
i.e., you get the same leading-order result in SR an Aether theory.
 
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