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My understanding is being thwarted by something basic I am missing. One starts with a light beam that is split into two perpendicular paths. There are two light paths that travel some distance. The light bounces off each respective mirror and returns back to the beam splitter/recombiner. If the phase of the light has been shifted in one arm, we should see negative interference when they recombine.I can imagine how one might get phase shifting for example if one mirror was moving relative to the beam splitter. We would have doppler shifting of the frequency coming off the moving mirror. So for an interferometer to work properly, the distance between the beam splitter and each mirror has to stay fixed.

But can this kind of interferometer be used to analyze a process occurring in one of the paths of light? Consider a big diamond sitting in front of one of the mirrors. When light enters a denser medium (like from air to glass) the speed and wavelength of the light wave decrease while the frequency stays the same. But the exact opposite change happens after the light leaves the diamond after having bounced off the mirror. So the interferometer should not be able to detect whether there is anything in the light path. Similarly, any change in spacetime geometry in one of the light paths should not be detectable. (if one light path for example was collinear with the gravitational field of a nearby black hole). Even though space is compressed in one direction, the actual distance is not changed because any 'ruler' you use to measure distance is also likewise compressed.

So how can LIGO measure a gravitational wave?

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Yes, it's true that if you put a diamond in the way of one of your interferometer arms, then pulses of light sent simultaneously on both tracks will always have the same phase at every moment, because entering a diamond doesn't change the frequency.

But this doesn't matter. In interferometry, you measure the phase difference between pulses of light when they arrive back at the detector. The pulse of light that goes through the diamond interferes with a pulse of light that was emitted by the light source earlier, because light moves slower through diamond. So there can be a phase difference.

This is fundamental to how hundreds of experiments work. LIGO is a bit more subtle, but it's covered well in this answer.

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  • $\begingroup$ Thank you for your answers. Sorry about duplicating an old question. $\endgroup$ – aquagremlin Sep 22 '19 at 17:14

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