# Round trip (two way) speed of light

1. Jul 24, 2008

### bernhard.rothenstein

Many approaches to "special relativity in the anisotropic space) make use of the concept of round trip (two way) speed of light. Do you think that we could avoid that concept. Is it physically motivated?
Thanks

2. Jul 24, 2008

### HallsofIvy

Staff Emeritus
In relativity, all measurements are to be done a one place in order to avoid "simultaneity" problems. That's the reason for the "roundtrip" speed. You can't measure the one-way speed of light since you would have to measure it leaving and arriving at two different places.

3. Jul 24, 2008

### bernhard.rothenstein

Thanks for your answer. Is there a physical basis for consideringt that light could propagate say forward with one of the speeds infinit>c(f)>c/2.

4. Jul 24, 2008

### Fredrik

Staff Emeritus
If space isn't isotropic, it isn't special relativity, and if there's more than one speed of light it isn't general relativity either.

5. Jul 24, 2008

### bernhard.rothenstein

6. Jul 24, 2008

### Fredrik

Staff Emeritus
In SR, the mathematical model of space and time is Minkowski space, and if you slice Minkowski space into a one parameter-family of space-like hypersurfaces that represent space at different times, those slices are isotropic. In GR, the mathematical model is a 4-dimensional smooth manifold with a Lorentzian metric, and the metric defines the speed of light to be 1 in the appropriate units. If you want to the speed of light to vary, you have to replace GR with something else, e.g. a theory with two metrics. See e.g. http://arxiv.org/abs/astro-ph/0305457v3. (I haven't read the whole article myself, so I probably won't be able to answer difficult questions about what it says).

7. Jul 24, 2008

### bernhard.rothenstein

Thanks. Have you seen the papers
H. Reichenbach, The Philosophi of Space and Time, Dover Publication. Inc. New York 1957
R. Anderson et al, Physics Report 295 93 (1958).
It is considered that if c represents the one way speed of light c, c(f) and c(b) representing the speeds of a light signal propagating in the positive direction of the OX and after reflection in its negatice direction then they are related by
(2/c)=(1/c(f))+(1/c(b)) where c(f) and c(b) could change in known limits.
Has all that some relationship to special relativity?

8. Jul 25, 2008

### DrGreg

Fredrik, this all depends on what you consider to be included within "SR".

Bernhard & I have had many conversations in this forum where you use non-orthogonal coordinates in flat spacetime. The flatness of spacetime arguably means this is SR. The coordinate non-orthogonality arguably means this is not SR.

(Do a Google search for DrGreg (Selleri OR Tanglerhini OR Reichenbach) site:physicsforums.com.)

This means abandoning Einstein's synchronisation convention and adopting one of several other possible conventions instead. Under such conditions, the two-way round-trip average speed of light (A-B-A) is still isotropic, as required by experiment, but the one-way coordinate speed of light (A-B), measured in such a non-standard coordinate system, is no longer isotropic.

The anisotropy is not a property of spacetime, but a property of the coordinate system.

Just to reiterate, any anisotropic "one-way speed of light" is always a coordinate speed, not what you might call a "physical speed" measured by the local clocks and rulers and Einstein sync convention of an inertial observer. As you should know, in GR the coordinate speed of light need not be c, except for local Einstein-synced inertial observers.
The isotropy of the local two-way speed of light is physically motivated: there is a wealth of experimental evidence to support it, and no credible evidence to refute it. Any theory that ignored this experimental fact would be incomplete, and any that contradicted it would be worthless. (This assumes, of course, that observers use proper local time and proper local length for measurement; you could construct theories that did not do so.)

Yes, if you believe in aether. No, if you do not. But there's no evidence to prove the existence of aether (though none to disprove it either), and even if aether did exist, it conveniently censors itself so it can't be detected, which makes it a rather pointless concept.

(Sorry, I will be off-line for the next week and a half, and will not be able to reply for a while.)