Explaining Sagnac vs. SRT Violation & Reconciling Lorentz Transform

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Discussion Overview

The discussion centers around the apparent conflict between the Sagnac effect and Special Relativity Theory (SRT), particularly in the context of Sagnac ring laser gyroscopes and fiber-optic gyros. Participants explore the implications of the Sagnac effect on inertial navigation systems like GPS and the reconciliation of Sagnac's formula with Lorentz transformations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants question how the Sagnac effect appears to violate the second postulate of SRT, which states that the speed of light is constant in a vacuum for all observers.
  • Others argue that the Sagnac effect is a prediction of SRT and cannot be considered a violation, suggesting that misunderstandings arise from misinterpretations of SRT.
  • A participant raises concerns about the necessity of Sagnac corrections in GPS, noting that the Earth's frame is not inertial, which complicates clock synchronization.
  • Some participants discuss Ruyong Wang's experiments, highlighting that the travel-time difference of counter-propagating light beams in a moving fiber is independent of the type of motion, leading to further questions about the implications for SRT.
  • There are claims that the Sagnac effect is relevant for various wave phenomena, including electromagnetic waves and de Broglie waves, prompting discussions about its universality.
  • One participant expresses skepticism about the mathematical foundations of SRT, suggesting that the observations required to support it are lacking, and questions the objectivity of the underlying mathematics.
  • Another participant challenges the idea of circular reasoning in the mathematics of the Sagnac effect, asserting that the effect is based on measurable differences in travel distances for light beams.

Areas of Agreement / Disagreement

Participants express a range of views, with some asserting that the Sagnac effect does not violate SRT, while others maintain that there are unresolved questions regarding its implications for inertial navigation and the foundations of SRT. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Limitations include the dependence on specific definitions of inertial frames and the unresolved nature of the mathematical steps involved in reconciling the Sagnac effect with SRT. Participants also note the lack of consensus on the implications of experimental results for the broader understanding of relativity.

  • #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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