Measuring one-way speed of light with gravitational lensing

Question

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?

Answer 1

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.

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.

Answer 2

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.

Answer 3

For me, anisotropic light speed would intuitively have to be reflected in anisotropic space time. Since it is the curvature of spacetime due to gravity/acceleration that bends the rays of light, we can see that a change in "speed" (even if it is only the direction) is accompanied by space time curvature.

This reasoning shows that spacetime then would need to have different properties moving in different directions, but that would also affect gravity and interaction of masses. If space is isotropic for gravity, i would assume its isotropic for light.

I am not clever enough, but maybe there is a way to even mathematically proof this from general relativity ?

From special relativity we know that if we would have two light speeds, c1 and c2, we would have :

x/c1 + x/c2 = 2x/c in which we only know c. This is an equation with two unknowns, so unless we assume a relation between c1 and c2 (such as c1 = c2 ) or assume a value (equivalently, c1 = c) we can never solve it.

This shows we need some other equation combining c1 and c2, and I was wondering if such a thing could be generated from general relativity, relating gravity to the speed of light via space time curvature. I am not acquainted enough to understand if this would actually work, or if it would just produce equivalent equations, thus effectively not yielding a second equation and not solving the problem of solvability.

I think part of this is reflected in experiments involving the change in one way speed of light (accelartion) :

"Although experiments cannot be done in which the one-way speed of light is measured independently of any clock synchronization scheme, it is possible to carry out experiments that measure a change in the one-way speed of light due, for example, to the motion of the source. Such experiments are the de Sitter double star experiment (1913), conclusively repeated in the X-ray spectrum by K. Brecher in 1977;[39] or the terrestrial experiment by Alväger, et al. (1963);[40] they show that, when measured in an inertial frame, the one-way speed of light is independent of the motion of the source within the limits of experimental accuracy. In such experiments the clocks may be synchronized in any convenient way, since it is only a change of speed that is being measured."

https://en.wikipedia.org/wiki/One-way_speed_of_light