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Measuring one-way speed of light with gravitational lensing

Physics Asked by Rijul Gupta on March 12, 2021

This recent video from Veritasium (https://youtu.be/pTn6Ewhb27k), explored the problem of measuring one way speed of light and covered a few possible (and practical) solutions. However my understanding of the problem from that video and the other questions on stack overflow suggests that the crux of the problem lies with reflection (retracing the path).

Hypothetically, couldn’t we use refraction through gravitational lensing on astronomical scale to have the light refracted back to the observer so that it only travels in a single direction and hence determine one way speed of light?

2 Answers

Changing the direction with gravitational lensing wouldn’t slow down the speed of light,as gravity does not affect the speed at which light travels. A mirror however is reflecting the light back not bending it. The problem lies in that we have no way to measure the speed of light that has not already been reflected off of a surface. Gravity is not a surface and bends the space time that light travels through instead of reflecting it. So hypothetically it would work. In reality the human lifespan (even the lifespan of our planet) is far to short for us to fire a beam of light at a black hole and wait for it to return. Not only that but imagine trying to keep track of a single beam of light that has to go behind a black hole in order to make its way back to us.

Answered by Brandon Herygers on March 12, 2021

Following the reasoning from the video, this would not work - it is similar to the example of letting light travel through a cable, returning it to its starting point. If one assumes that only the actual spatial direction influences the magnitude of $c$, the light would have to change directions in order to return. One could thus still not be certain about the velocity in a specific direction.

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In the above example, the speed of light could be something like $0.5c$ in Direction 1 and instantaneous in direction 2 and one would have no way to know.

TL;DR: The problem of measuring the one-way speed of light as presented in the linked vide does not depend on two different paths (e.g. through reflection), but on the actual spatial direction the light is travelling.

I should perhaps add that this is just my assumption from watching the video and is not based on actual mathematics or similar.

Answered by Jonas on March 12, 2021

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