# One-way speed of light

1. Aug 27, 2009

### Saw

In the page about Experimental Basis of SR, there is this comment, preceding the references to experiments on the one-way speed of light:

I am not sure I understand the message. When the author says several times (especially in the last sentence) "these theories", is he always referring to "aether theories"? If the answer is yes, does it mean that all the experiments mentioned below are consistent with aether theories and that is why the experiments in question are "unable to rule out" aether theories?

In other words, is it correct to say that, actually, SR only requires the 2-way speed of light to be isotropic?

2. Aug 27, 2009

### Hurkyl

Staff Emeritus
You can use whatever system of coordinates you like -- SR places no restriction on that.

Speed, as you're using it, is not a physical quantity on its own -- it depends on your choice of coordinate system.

3. Aug 27, 2009

### DrGreg

To measure the round-trip 2-way A-B-A speed of light requires only a clock at A and can be measured experimentally.

To measure the 1-way A-B speed of light requires two clocks at A and B which have to synchronised somehow. The standard SR method of synchronisation guarantees the 1-way speed equals the 2-way speed by definition, as we use light to perform the synchronisation.

But you are free to use some other method of synchronisation, and if you do, the equations of physics no longer take the isotropic form we are familiar with, and, depending on which definition you use, you may well be able to distinguish one observer's coordinate system from another's, i.e. the principle of relativity relative to these non-standard coordinates appears not to hold.

In particular, there is one non-standard method of synchronisation which chooses one (arbitrary) frame as a reference ("aether") frame and all observers synchronise to that single frame instead of the standard way. You end up with an "aether theory" which is really "relativity in non-standard coordinates". Either formulation is valid because it's just a different choice of coordinates to describe the same thing.

If (t,x,y,z) are the coordinates of an observer synchronised in the standard way, define "aether coordinates" by

T = t + vx/c2
X = x
Y = y
Z = z

where v is the velocity along the x-axis of the observer relative to whatever you arbitrarily choose to be "the aether".

4. Aug 27, 2009

### Hurkyl

Staff Emeritus
(The time certainly. But how to decide what distance was travelled involves your choice of coordinates)

5. Aug 27, 2009

### Saw

Hulkyl, thanks for your comment, though I didn´t quite catch where you are pointing at.

Thanks, DrGreg, as usual. I am familiar with that and I believe I understand it. My way of visualising it is thinking that the same light pulse has a double role: (i) it is the one whose speed is measured and (ii) also the one used for synch and length measuring purposes. The pulse is sent away, bounces back somewhere and when it returns to the origin, the clock located there marks 2 seconds. So we assume that the pulse bounced back at a place located 1 ls from the origin and that the clock situated at the place where the pulse bounced back must be set at 1 s. Hence, the 1-way speed of this very same light pulse is measured as c, by defnition.

I've also read that another method like slow clock transportation (a clock is transported from one place to another at extremely low velocity, so that the effect of time dilation is made negligible) renders equivalent results.

I also assume that if, instead of a light pulse, you use for synch purposes an elastic material ball, the results would be the same. (Is that right?).

My question, however, arose because I've just read in the book "Einstein's mistakes", by the physicist Hans C. Ohanian (who does look quite in line with mainstream physics), a criticism on the importance that Einstein gave to the synch issue. He claims that nowadays the 1-way speed of light is accurately measured by atomic clocks that need not be synched ala Einstein-Poincaré. In particular, he says this is done by sending a signal, for instance, from Lucerne to Berne but not returning it immediately, only 12 hrs later, when the Earth has rotated and so the light takes the same direction as in the go-trip.

This has disconcerted me. The trick looks very clever, but I see two possibilities. One, this system gives a different result than the Einstein method and then I do not see how it can match with the rest of the theory. Second, it gives the same result, in which case I do not understand how that can happen. On the other hand, what about the motion of the solar system, of the galaxy...?

I must admit that, not "believing" or "adhering to" aether (how can you believe in something that is undetectable?), I do use Lorentz relativity as a pedagogical help or test method to teach myself SR: from time to time I switch to LR and if something is consistent therein, I feel satisfied. However, this sort of experiments seem to suggest that SR predicts results different from LR (a constant 1-way speed of light, totally independent of synch method...) and that puzzles me. I often read in the forum that SR and LR are experimentally indistinguishable. Isn't that the final word? If it is, then it seems that Ohanian himself would not be right... What do you think?

6. Aug 27, 2009

### DrGreg

Fair point. I was thinking in terms of what time measurements are needed rather than distance. In the realm of inertial observers in SR we can assume some sort of rigid ruler to measure distance. In GR it's not so easy. But that's not the modern way we measure distance. In fact we now measure distance using light so that even the 2-way speed of light, for inertial observers, is guaranteed to be constant by definition. (And, in fact, locally for non-inertial observers, too.)

(I'm sure you know all this Hurkyl; I'm saying this for the benefit of other readers.)

7. Aug 27, 2009

### DrGreg

Yes, in the mathematical limit as the velocity tends to zero (and so the time taken to perform the transportation goes to infinity!) slow clock transport is equivalent to the standard "Einstein synchronisation" method. (So, as it's essentially the same method, two "slow-clock-transport-synchronised" clocks will be out of slow-clock-transport-sync according to some other observer at a different velocity.)
Well, I suppose if the bounce at the other end was truly elastic (no loss of kinetic energy) and a 100% immovable wall to bounce off, and no friction, yes. Light would be more reliable, though.

Without having read the details of this, I suspect the flaw in this argument is that your two clocks have moved and effectively "swapped places" during the 12 hours, which is equivalent to the slow clock transport mentioned above. So all you would be doing, I think, is verifying that slow clock transport is equivalent to Einstein synchronisation, which is what theory predicts anyway.

8. Aug 28, 2009

### Saw

Could the following be added: if you measure 1-metre rods (= the basic unit of distance) with a two-way trip of light, as we in fact do, it's also guaranteed that if you use those rigid rulers to measure distance, you get the same result, by definition, as if you used light, since now the rulers are just a sort of material representation of the light measurement?

9. Aug 28, 2009

### Saw

That's a nice approach. I wonder if we could say, in view of this, that the two-way trip of light returns through the back door...