-2

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?

Qmechanic
  • 201,751
Rijul Gupta
  • 5,463
  • 3
    Other questions regarding the same video: https://physics.stackexchange.com/q/590904/ and https://physics.stackexchange.com/q/590923/ – G. Smith Nov 01 '20 at 05:11
  • Have you read about how minuscule the deflection of light by a star is? If you are thinking about black holes, how long would it take to do an experiment where we send light to one and wait for it to come back? (And even if we had the time, we could not do this.) – G. Smith Nov 01 '20 at 06:18
  • 1
    Wouldn't this be the same as just bouncing it off a mirror? The black hole is just acting as a really big mirror. – user253751 Nov 03 '20 at 13:51
  • @G.Smith: It is a thought experiment to test whether it is at least theoretically possible or not. – Rijul Gupta Nov 05 '20 at 09:46
  • @user253751: No, as the light never changes direction merely the path it is following has been bent due to gravity; in this experiment the bending is so severe that the path leads back to point of origin. – Rijul Gupta Nov 05 '20 at 09:47
  • 1
    @RijulGupta So you agree that it goes away from the origin, and then something happens to it, and then it goes towards the origin? – user253751 Nov 05 '20 at 09:48
  • @user253751: No. Unless my understanding of bending of space-time through gravity is incorrect, nothing happens to the light in question, the path itself is bent. – Rijul Gupta Nov 05 '20 at 09:51
  • 1
    @RijulGupta okay, but... the light is still going in a different direction. It's like saying satellites don't go in ellipses or the moon goes in a straight line. If it was going left, and now it's going right, then it changed direction. – user253751 Nov 05 '20 at 10:04
  • @user253751: does the moon change its direction to come back to origin? – Rijul Gupta Nov 05 '20 at 10:09
  • yes? of course it does. it changes its direction every millisecond – user253751 Nov 05 '20 at 11:24
  • @user253751: I think there is some ambiguity in the use of "direction" here, as in one instance you are mentioning the movement of something from going left and then going right implying a reversal of motion, while in another (i.e. case of moon) you are referring to change in direction with no reversal of motion.

    The moon never reaches a point in it's orbit and then retrace it's path back to the origin. I am merely hypothesising a mechanism in which we measure the speed of light in a trajectory similar to that of the moon.

     – Rijul Gupta Nov 05 '20 at 12:10
  • 1
    "change in direction" implies a change in direction. It doesn't imply a reversal. However, a reversal is also a change. – user253751 Nov 05 '20 at 12:23
  • @user253751: can you please explain how reflection of light (or anything) from a surface is equivalent to the motion of the moon? As I understand it, it's not equivalent, and that's all I am hypothesising. – Rijul Gupta Nov 05 '20 at 12:29
  • 1
    @RijulGupta When something goes in one direction, and then a different direction, it changed direction. How you change the direction is not relevant. It doesn't matter whether it's a black hole or a mirror. If the light goes in one direction and then in the opposite direction, that's a two-way measurement. – user253751 Nov 05 '20 at 13:17
  • 3
    Does this answer your question? Can we use curved spacetime to measure the one-way speed of light? – Dale Feb 20 '21 at 16:50
  • 1
    @Dale I think that's the first relevant post I have read on this so far. I envy the OP of that question as they have clearly outlined what I meant to post and did not bother writing down. I'll continue the discussion there as this question seems to draw irrelevant comments. – Rijul Gupta Feb 20 '21 at 17:44

3 Answers3

0

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.

Brandon Herygers
  • 1
  • perhaps I should have emphasized it more, but I am attempting to ascertain if we have at least a theoretically sound way of measuring the speed of light. I am assuming my proposal should work but I haven't tested it rigorously (mathematically), which is why I am asking for other people's comment on it. – Rijul Gupta Jan 19 '21 at 01:17
0

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.

enter image description here

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.

jng224
  • 3,697
0

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

lukas123321
  • 1