One-Way Speed of Light: Is it Possible?

[kochanskij]

TL;DR Summary

If light travels at C+V in one direction and C-V in the other, could we detect that? How? If not, could this indicate something profound about light and spacetime?

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all directions. (I'm not talking about the speed of its source or detector. Assume everything is in the same inertial frame) Please correct me if I'm wrong.

If it goes at C+V in one direction, it must go at C-V in the opposite direction. We always measure an average speed of C. But we can never know what V is. Could this lead to something profound about light and space and time? Maybe light has no definite one way speed. Maybe it is in a superposition of all speeds. V is every velocity 0 < V < C. Is this possible? Has any physicist explored this? Or is the one way speed of light just a trivial curiosity?

 

[Dale]

It is just an arbitrary convention that can be chosen as desired. There are many, many threads on this topic already here.

https://www.physicsforums.com/threads/the-one-way-speed-of-light.1016771/
https://www.physicsforums.com/threads/sr-and-one-way-speed-of-light-tests.4602/
https://www.physicsforums.com/threads/how-to-measure-the-one-way-speed-of-light.461274/
https://www.physicsforums.com/threads/one-way-speed-of-light-measurement-proposal.584743/
https://www.physicsforums.com/threads/measuring-one-way-speed-of-light.750191/

just to give a few threads..

 

[FactChecker]

TL;DR Summary: If light travels at C+V in one direction and C-V in the other, could we detect that? How? If not, could this indicate something profound about light and spacetime?

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all directions. (I'm not talking about the speed of its source or detector. Assume everything is in the same inertial frame) Please correct me if I'm wrong.

If it goes at C+V in one direction, it must go at C-V in the opposite direction. We always measure an average speed of C. But we can never know what V is. Could this lead to something profound about light and space and time? Maybe light has no definite one way speed. Maybe it is in a superposition of all speeds. V is every velocity 0 < V < C. Is this possible? Has any physicist explored this? Or is the one way speed of light just a trivial curiosity?

The first thing to realize is that measuring the one-way speed of light requires that the clocks at both ends are perfectly and undeniably recording identical times. That opens a can of worms that is not possible to solve.
The next thing to realize is that Einstein's theory of Special Relativity solved some problems for the first time and made predictions (including atomic energy, physics happening slower for fast-moving objects, etc.) that have been convincingly confirmed. So, whatever he needed to assume for that theory is strongly supported.

 

[Mister T]

TL;DR Summary: If light travels at C+V in one direction and C-V in the other, could we detect that?

No.

If not, could this indicate something profound about light and spacetime?

It indicates that simultaneity is relative. I think that's pretty profound.

Time dilation makes synchronizing two separated clocks impossible.

That doesn't sound right to me. Do you have a reference for this claim?

Has any physicist explored this?

Of course. It's a well-understood phenomenon. For at least 100 years, I think.

 

[Ibix]

Or is the one way speed of light just a trivial curiosity?

I'd go with this option. You can choose to use coordinates in which the speed of light is anisotropic. In SR they just make all the maths messier so nobody does so, but you could. However, it's quite common to do in GR because it tends to be more convenient to pick coordinate systems adapted to the geometry of spacetime than worry about whether they're everywhere orthonormal.

 

[Sagittarius A-Star]

If it goes at C+V in one direction, it must go at C-V in the opposite direction.

No. The two-way-speed of light must be $c$.

If the distance is $L$ and the light moves with $c+v$ in one direction, because the 4D-reference coordinate-system was defined this way, then the time for both directions is
$t=\frac{L}{c+v}+\frac{L}{u}= \frac{2L}{c}$

Then light must go at
$u= \frac{c+v}{1+2v/c}$ in the opposite direction.

Calculation:
https://www.wolframalpha.com/input?i2d=true&i=Divide[L,\(40)c+V\(41)]+Divide[L,u]=2Divide[L,c]

 

[kochanskij]

No. The two-way-speed of light must be $c$.

If the distance is $L$ and the light moves with $c+v$ in one direction, because the 4D-reference coordinate-system was defined this way, then the time for both directions is
$t=\frac{L}{c+v}+\frac{L}{u}= \frac{2L}{c}$

Then light must go at
$u= \frac{c+v}{1+2v/c}$ in the opposite direction.

Calculation:
https://www.wolframalpha.com/input?i2d=true&i=Divide[L,\(40)c+V\(41)]+Divide[L,u]=2Divide[L,c]

Thank you for your correction. I feel silly that I forgot that you don't find an average velocity by adding the two velocities and dividing by 2. A very basic error on my part.

 

[cianfa72]

Sorry to resume this thread. Many times in PF has been discussed that the invariance w.r.t. inertial frames of one-way speed of light is just a matter of simultaneity convention employed to define it. In particular in SR inertial frames are defined in a such way that the one-way speed of light is actually the invariant $c$ (based on the Einstein synchronization convention).

However the two-way speed of light is actually measurable and experimentally it is the invariant $c$ as well.

A problem I see is that it is implicitely assumed that Einstein's synchronization convention can be always applied consistently.

What do you think about ?

 

[PeterDonis]

it is implicitely assumed that Einstein's synchronization convention can be always applied consistently.

No. In flat spacetime it is known that you can always apply Einstein synchronization between clocks at rest relative to each other.

In curved spacetime it is known that you can't always do that, and nobody assumes that you can.

 

[cianfa72]

No. In flat spacetime it is known that you can always apply Einstein synchronization between clocks at rest relative to each other.

Is it actually an experimental result ?

 

[PeterDonis]

Is it actually an experimental result ?

Where would you go to find a flat spacetime to experiment in?

It's a mathematical result using the known geometric properties of flat spacetime and inertial worldlines.

 

[cianfa72]

It's a mathematical result using the known geometric properties of flat spacetime and inertial worldlines.

Ok, so using for instance families of mutually "at rest" inertial worldlines in flat spacetime we can check that Einstein's synchronization convention holds consistently.

 

[PeterDonis]

Ok, so using for instance families of mutually "at rest" inertial worldlines in flat spacetime we can check that Einstein's synchronization convention holds consistently.

Yes.