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Mentz114

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After the recent discussion here about the Sagnac effect** I wanted to see if there is any frequency shift if light is sent from one point on a rotating worldline to another a small distance away. It looks like this cannot happen because ##\gamma=dt/d\tau## is the same at every point on the curve.

Thinking of the scenario as an Einstein elevator (a box) circling a point so that the 'roof' is the closest to the center and the 'floor' is furthest, the observer in the elevator can send a light beam from one side to the other with the beam parallel to the roof and see no deflection or frequency change ( first posulate).

In the non-comoving frame ( say at ##r=0##) the elevator is rotating and when the light gets the other wall, the wall is receding/approaching so there is a frequency shift. (second postulate).

These postulations seem to contradict each other. The obvious solution is that the elevator observer sees the frequency shift and attributes it to the gravitational analog of the centripetal acceleration. But then every point still has the same 'potential' ( or does it ?).

Any ideas ?**

A good reference for rotation is http://www.projects.science.uu.nl/igg/dieks/rotation.pdf

and elevators

Juergen Ehlers and Wolfgang Rindler

http://pubman.mpdl.mpg.de/pubman/item/escidoc:152994:1/component/escidoc:152993/330688.pdf

Thinking of the scenario as an Einstein elevator (a box) circling a point so that the 'roof' is the closest to the center and the 'floor' is furthest, the observer in the elevator can send a light beam from one side to the other with the beam parallel to the roof and see no deflection or frequency change ( first posulate).

In the non-comoving frame ( say at ##r=0##) the elevator is rotating and when the light gets the other wall, the wall is receding/approaching so there is a frequency shift. (second postulate).

These postulations seem to contradict each other. The obvious solution is that the elevator observer sees the frequency shift and attributes it to the gravitational analog of the centripetal acceleration. But then every point still has the same 'potential' ( or does it ?).

Any ideas ?**

A good reference for rotation is http://www.projects.science.uu.nl/igg/dieks/rotation.pdf

and elevators

Juergen Ehlers and Wolfgang Rindler

*Local and Global Light Bending in Einsteins and other Gravitational Theories*http://pubman.mpdl.mpg.de/pubman/item/escidoc:152994:1/component/escidoc:152993/330688.pdf

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