[Physics] Sagnac experiment interpretation

[Doug Marett]

Hi Olivier,

   The simplest explanation for the difference is that with the Sagnac
device the interferometer paths enclose an area, whereas with the Michelson
interferometer they do not. The Sagnac effect equations is:

[image: Inline image 1]where w = angular velocity and A = enclosed area. L
= circular path length, R = radius

So if you want to detect rotation, the counter-propagating paths need to
enclose an area. So the Michelson configuration is not suitable. But again
the Sagnac device will only detect rotation with respect to the fixed
stars, not translational velocity.

The Sagnac experiment behaves as if light speed is constant in the frame of
reference of the fixed stars. So the rotating observer measures a speed of
light difference of +/- wR for each beam which manifests as a fringe shift,
and this is a first order difference. You could argue that the path each
beam of light has traveled is longer or shorter due to the rotation of the
observer, but it is longer or shorter with respect to absolute non-rotating
space, not the lab.
http://www.conspiracyoflight.com/Sagnac_webapp/Sagnac_interferometer.htm

With the Michelson interferometer, the propagation time in each arm is:
approximately  t = L * LC/ (c/n +/- v/n^2 ) where L is the length of the
path, LC is the Lorentz contraction, n = refractive index of path, v =
translational velocity, c = stationary frame speed of light. Because the
Michelson interferometer doesn't enclose an area, there is no path length
difference between the two paths due to rotation with respect to the fixed
stars, and the translational velocity exactly cancels (after factoring in
the Lorentz contraction), so the result is zero as is explained here:
http://www.conspiracyoflight.com/M%26M.html

Hope that helps.

Doug




On Sat, Nov 5, 2016 at 7:34 AM, O. Serret <o.serret at free.fr> wrote:

> Hi Doug,
>
> Thank you for having made known Sagnac experiment, it looks very
> interesting.
>
> Michelson experiment looks like Sagnac experiment without rotational
> movement ; except than both experiments are done within the rotational
> referential frame of Earth.
>
> The point I don’t clearly understand is the difference with Michelson
> interpretation. I mean :
>
> A) From the GR point of view, if there is no change of shift interference
> with Michelson experiment, it is because light is independant of the Earth
> rotation. So, why shift interference would depend of the Sagnac rotational
> movement ?
>
> B) From the Aether point of view, if there is a change in shift
> interference in Sagnac experiment, it is because light is slowed down by
> aether. So, why it is not slowed down within Michelson experiment ?
>
> Thank you for your explanation (with a draft if possible)
>
> Best regards
>
>
>
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