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- TL;DR Summary
- Proper time identical for any beams sent in opposite directions (Sagnac style experiment)

Hello,

I have recently come across this article by Rizzi and Ruggiero, called "The Relativistic Sagnac Effect: Two Derivations": https://arxiv.org/pdf/gr-qc/0305084.pdf

In section 3, the authors derive the Sagnac proper time difference for all beams (light beams and matter beams, including muons, neutrinos, electrons, acoustic waves, etc).

I feel like I have misread or not understood something from the paper, because it seems to me that:

Whatever the angular velocity of the matter beams (be it 0.001c or 0.1c or 0.8c) when we read the time lapse between the counter-propagating beams, we'll register it as being a constant on the rotating clock.

They say this condition holds only if the rotating clock is Einstein synchronized. So, can this be actually tested? Or has it? Do we actually have the possibility to Einstein synchronize the rotating clock and, in this case, will we indeed ALWAYS obtain the same time lapse for matter beams, no matter how slow (or fast) these are?

The math in their derivation adds up nicely, but I find this statement counterintuitive.

Can someone explain it to me in a simple way and suggest the experimental setup for testing it?

Thank you in advance.

I have recently come across this article by Rizzi and Ruggiero, called "The Relativistic Sagnac Effect: Two Derivations": https://arxiv.org/pdf/gr-qc/0305084.pdf

In section 3, the authors derive the Sagnac proper time difference for all beams (light beams and matter beams, including muons, neutrinos, electrons, acoustic waves, etc).

I feel like I have misread or not understood something from the paper, because it seems to me that:

Whatever the angular velocity of the matter beams (be it 0.001c or 0.1c or 0.8c) when we read the time lapse between the counter-propagating beams, we'll register it as being a constant on the rotating clock.

They say this condition holds only if the rotating clock is Einstein synchronized. So, can this be actually tested? Or has it? Do we actually have the possibility to Einstein synchronize the rotating clock and, in this case, will we indeed ALWAYS obtain the same time lapse for matter beams, no matter how slow (or fast) these are?

The math in their derivation adds up nicely, but I find this statement counterintuitive.

Can someone explain it to me in a simple way and suggest the experimental setup for testing it?

Thank you in advance.

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