# On the one way speed of light...

1. Jun 20, 2015

### rede96

If I have two clocks in space at rest wrt each other and just a meter apart, I could synchronise them. If they were far enough away from any other mass so gravitational forces are nullified, then if I just let these clocks sit there for a few million years, expansion will separate them but without effecting synchronisation.

Then at some time in the future we have pre-set clock A for example, to send a light signal to clock b. We compare the two times and we would have a measure for the one way speed of light.

Everything I have read says the one way speed of light is impossible to measure. So where does the above thought experiment break down?

Would gravity between the clocks be enough to stop them receding from each other with expansion? I can't think of any thing else.

2. Jun 20, 2015

### Staff: Mentor

It is not impossible to set up an experiment to measure a value that you attribute to the one way speed of light. What is impossible is to do so without assuming a synchronization procedure or a logically equivalent geometric assumption.

Here you explicitly synchronize them. So your result depends on your synchronization.

3. Jun 20, 2015

### rede96

I think I understand. I'd have to assume a speed of light in order to synchronise them as they are separated by a distance. But as I am synchronising them over a very short distance (1 meter) then wouldn't any error to the actual one way speed of light assumed be really insignificant over large cosmological distances?

For example I could set both clocks to send a signal to the other at the same pre-set time in the future, (by their clock) any error in synchronisation would be very small compared to the potential difference I might get in measuring the speed of light over many light years.

4. Jun 20, 2015

### PAllen

Let's say you build two atomic clocks right next to each other, get them exactly synchronized, and move them slowly 1 meter apart, with exactly symmetric acceleration profile. You assume this keeps them synchronized. And it does - exactly equivalently to as if you synched them using Einstein's clock sync based on assuming isotropy plus invariance of two way light speed. Maybe not emphasized enough is that any procedure that relies on any assumption of isotropy is informationally worthless for resolving one way light speed, because it builds in the answer given invariance of two way light speed. The assumption that slow separation with the same acceleration profile (in opposite directions) leaves the clocks synched is an isotropy assumption [it also builds in a homogeneity assumption].

As to cosmological expansion, the assumption that this leaves clocks synched is also an isotropy assumption. [Note, for your proposal to be even right in principle, it would have to be done far away from any galaxies, and the clocks would have to be very light in relation to initial distance. For expansion to be a primary factor, the clocks can not be part of any gravitationally bound system, including their own slight gravity.]

Personally, I find a lot of harping on this to be more philosophical than physical. For all branches of physics besides SR, isotropy operationally means: "does assuming isotropy in physical law lead to simplification?" If so, we call this result confirmation of isotropy and don't care about the fact that conspiratorial anisotropy has not been formally ruled out. Only in SR has there historically been an obsession with this distinction.

5. Jun 20, 2015

### Staff: Mentor

Sure. You could make it even less by putting them right next to each other. This approach is called slow clock transport. Assuming that slowly transported clocks remain synchronized is equivalent to assuming Einstein's clock synchronization.

6. Jun 20, 2015

### rede96

Yes, I wouldn't disagree. But hope people realise that my intention is never to disprove current theories. I am just trying to understand some of the basic principles (with as little math as possible!) and this is often done by testing / challenging limits, which my not be ideal but seems to be my personal learning style.

Yes of course, but I was just ignoring gravity for now as if the thought experiment falls down else where, then I don't have to worry about this right now.

I think I understand this point. But the point I was trying to make is that I can minimise the effects of that error to a point where the error is guaranteed to be less than any difference I measure in the one way speed of light. For example, moving the clocks apart to a distance where their own gravity doesn't effect them will cause lead to a small error in clock synchronisation. But this error could ONLY be micro seconds assuming a small transportation distance. If I was to measure the one way speed of light from clock A to Clock B and then Clock B to Clock A, which were separated by one light year, if I found one trip measured 364 days and the other 366 days, then I could say categorically that the difference was not down to clock synchronisation.

If you mean by this I have assumed expansion is the same in both directions then yes, I understand what you mean. But I can test for a difference in the rate of expansion in different directions that doesn't rely on any synchronisation convention.

7. Jun 20, 2015

### harrylin

This was already answered by PAllen and Dalespam; here's a little elaboration, very simple (and ignoring cosmology):

According to SR you may assume that your "rest" frame is a "moving" frame. So, consider your measurement from the perspective of a "rest" system relative to which your system is moving.

You should find that no matter at what speed you transport your clocks, there will be an asymmetry because the time dilation formula is non-linear. To make it very clear by means of an extreme, look at it from a frame in which your system is moving at 0.99c, and you move your clocks at 0.1c according to you. Obviously you will be seen to move your one clock (the one that moves faster than your system) much slower than the other one. That results in a difference in clock rate during the time of transport.
There will be a smaller difference for slow moving clocks, but it takes correspondingly longer to reach the desired distance. Calculation shows that the resulting synchronization error (according to the "stationary" frame) between such two clocks by means of clock transport will be just the same as with light signals, independent of the speed with which you move your clocks.

8. Jun 20, 2015

### PAllen

If you are talking about expansion, you can't ignore gravity. The theory in which such expansion is modeled (general relativity) is a theory of gravitation, and the phenomenon doesn't arise without such a theory.
No, it is more. Even if expansion amount is measured to be isotropic, it does not follow that its affect on clocks is isotropic. Assuming this is necessary to your thought experiment, and immediately robs it of informational content for a one way light measurement. Without assuming this, you have to re-synchronize independently and ... you know where that leads. It might help you to know that all of SR can derived from the following assumptions, as an alternative to what Einstein used:

- isotropy
- homogeneity
- principle of relativity (no experiment can detect a class of motions we define as inertial)
- (these alone imply, by a long derivation, that there is an invariant speed, which may be infinite). Then, assumption of finite invariant speed leads uniquely to
conventionally formulated SR (with isotropy, by assumption).

These lead to SR as formulated with Einstein clock synch. To rule out 'conspiratorial anisotropy', you need ensure that you don't assume isotropy for any of the physics relevant to your experiment.

9. Jun 20, 2015

### rede96

Thanks very much for the reply, but I just really don't get this. Sorry! I am struggling to understand what any other frame has to do with my measurement. The clocks are in my frame, they are just one meter apart, I can see the seconds pass on each one and can see they tick over at the same time. So there must only be a very small difference in the clock's synchronisation.

What happens after that point I can see may lead to problems, but all measurements could be taken in my FOR. I make it so the clocks send a signal at the same time (by their clocks) and being in the middle, I measure the difference in time between receiving the two signals. I agree that might not tell me much about the one way speed of light, as there are many other factors to consider as have been pointed out. But I would have thought that if the difference in times between the signals I am receiving from Clock A and Clock B is great compared to the small error in clock synchronisation at the start, then I know the error isn't down to clock synchronisation. (Assuming the clocks remained in sync.)

Ok, thanks. I didn't mean ignore it terms of the thought experiment, I just mean I would assume no effects to start with to make understanding the other elements of the problem less complicated. So do appreciate that I can't ignore gravity.

Yes I think so. My natural reaction would be to send signals to the clocks as they moved apart to make sure they stayed in sync. But if I understand what you are saying then this would just be setting what I would measure as the one way speed of light.

10. Jun 21, 2015

### harrylin

It is much harder to explain the fact that perspective matters than it is to simply show this to be true by means of that other perspective!

First of al, if you move the clocks at the same speed relative to you away from each other over the same distance, then they may not be perfectly on time but they will be perfectly synchronized relative to each other in your rest frame; they are perfectly "in tune" with each other according to you.

Now, the clocks are in all frames; so, look at the same situation from another frame's perspective.

---------------<-C2 - you - C1->------------ v--->

According to the system S', you -as well as the clocks before you start to transport them- are moving at 0.99c to the right. When you transport them, clock C1 is moved in forward direction relative to you so that its speed v1 is more than your speed, and clock C2 is moved backward relative to you so its speed v2 is less than your speed. Consequently, according to S' the clocks are now not ticking at the same rate and will therefore be out of tune with each other after you transported them.

If you plug numbers in the time dilation equation (gamma factor) you find that the effect of that difference is considerable because you subtract nearly c squared from c squared.

In fact this is just one way to verify that the Lorentz transformations really work: according to the relativity principle we are not able to perform an "absolute" synchronization.

11. Jun 21, 2015

### Staff: Mentor

For simplicity, rather than have them 1 m apart, have them right next to each other, immediately adjacent. You can reduce this error or difference to 0 simply by reducing the distance to 0.

I have noticed that you use this terminology a lot, so I thought that I would mention it. Objects are not "in a FOR". Measurements are not "in a FOR". Observers are not "in a FOR". Events are not "in a FOR". All of those things are in every FOR. A FOR is not a physical thing which you can be in or out of or which you can move between.

The only thing that can be considered to be "in a FOR" is an analysis. You choose a FOR and then you do your analysis "in that FOR". It is simply a mathematical description of the physics. But you can choose any FOR to do your analysis and in that second FOR you will still analyze all of the same objects, measurements, observers, events, etc. "in that new FOR".

This is the problem. The standard name for the experiment that you are describing is called "slow clock transport". Assuming that slow clock transport maintains synchronization is equivalent to Einstein clock synchronization.

12. Jun 21, 2015

### rede96

Ah ok. I think I am referring to my frame of reference as a short way of saying anything that is at rest wrt to me. So when the clocks are together they are in my FOR, I am really just being lazy and not saying the clocks are at rest with respect to me. But point well received thanks.

Yes I was aware of the issues of slow clock transportation. Which is why in my thought experiment I set them 1 meters apart to start, as I wanted cosmological expansion to separate them. That way they wouldn't be travelling through space-time, which would mean no time dialation effects.

But as has been pointed out I was still assuming the situation was isotropic. Which apparently I can't do.

13. Jun 21, 2015

### rede96

Sorry, I seemed to have quoted you above by accident :)

I am not sure I get what you mean. Lets say have the clocks together at rest wrt me. And after I synchronise them, each one fires a light pulse to objects that are the same distance away from each clock (1 fires left, the other to the right) the objects reflect the light back and the clocks measure the time elapsed. I assume the clocks would measure the same duration for each light pulse.

My 'speed' is zero relative to clocks. So it doesn't make any sense to me to say I am moving at 0.99 c in any direction. If I move one clock to the left by 1 meter taking 1 minute and the other clock to the right by 1 meter taking 1 minute. When I look at the clocks I see they are still in sync.

If I was to now send the same pulses to the two respect objects from each clock, when I measure the round trip for light I still get the same time elapsed for both clocks. (Not the one way speed of light I know)

So the clocks have moved apart but are still in sync to me. And any measurements I do with these clocks where the tests are identically symmetrical, I will get the same time elapsed on both.

So why do I need to worry about what speed I am moving relative to someone else?

14. Jun 21, 2015

### PAllen

It is worth clarifying this point. Expansion of space is a quite useful image, up to a point, but it is not in contrast to 'motion in spacetime'. Each free fall world line 'going with the hubble flow' has a path in space time. When the distance between them grows, it is relative motion through space time as much as any other case (of course, it is coordinate dependent how the distance grows - to define distance you need choice of simultaneity surface to measure it along). There is no mathematical or theoretical difference between this and the growth in separation between two other arbitrary world lines. Note that relative motion of distant objects is inherently ambiguous in general relativity due to space-time curvature, but one plausible choice of convention for relative motion distant galaxies gives exactly the speed implied by their observed Doppler effect [ for others, despite being above OP's head, the convention is to parallel transport 4-velocity over null geodesic light travels on]. [edit: Note, that if you take this one choice among infinitely many alternatives for relative velocity, you conclude that the Doppler has the same breakdown between non-relatavistic Doppler and time dilation as a local object displaying the same Doppler. Thus, the whole idea that using cosmological expansion sidesteps time dilation is wrong. The situation is worse than SR in there no unique definitions of the quantities you hope to avoid.]

Last edited: Jun 21, 2015
15. Jun 21, 2015

### Staff: Mentor

You really should stick with SR before jumping into GR. In GR not only do you have the same issues of simultaneity, but you also have the difficulty of defining the distance and relative velocity of distant clocks.

16. Jun 22, 2015

### harrylin

I cannot match your two statements here above. If you are aware of the issues of slow clock transportation then you know that the two clocks only stay in sync according to a single selected frame of observation (at least in standard SR, without cosmology).
Once more, that's the same argument as can be used with clock synchronization by means of light pulses, according to which synchronization would then be "absolute"; an egocentric approach to physics easily prevents one from understanding such things as relativity of simultaneity and slow clock transportation, which you say you understand.
It is impossible to see that they are in sync according to all reference systems. What you can see, is that if you assume that you are in rest, then as the light rays from each clock will take the same time, it follows that the clocks are still in sync. So one may say that they are in sync according to reference system S.
Those two things, one way speed of light and clock synchronization, are part of the same package....
Yes of course: you chose the system in which you are in rest; there is in general no need to do that. For example, for GPS a system was chosen in which everything is moving.
It's not about worrying; instead, it just prevents from obtaining the kinds of insight that helped Einstein to write several breakthrough papers.

Last edited: Jun 22, 2015
17. Jun 22, 2015

### Staff: Mentor

You certainly can assume isotropy, in fact, it is a common assumption. What you cannot do is to then claim that the resulting measurement experimentally confirms isotropy.

18. Jun 22, 2015

### rede96

Yes, I know I jump around a bit. I really wish I had more time to go into more depth on lots of topics. But I really appreciate the input. thanks.

So silly question, does than mean isotropy is relative?

19. Jun 22, 2015

### rede96

So just out of curiosity, how is it that distant galaxies can recede relative to us faster than c with out violating relativity?

20. Jun 22, 2015

### rootone

Because the galaxy is not moving THROUGH space at a speed exceeding C, it is space itself which is (relative to us) receeding at that rate, and the object is embedded in that space.
Relatively forbids the first scenario, the second it does not.

21. Jun 22, 2015

### rede96

So even though it is not moving through space, from what I understood by this:
Is that time dilation still occurs for those distant galaxies relative to us?

22. Jun 22, 2015

### PAllen

Yes, time dilation occurs for distant galaxies compared to us, in the same sense as for a muon created in the upper atmosphere reaching the ground even though it 'should have decayed'. However, note that ime dilation is a coordinate dependent notion (unlike differential aging). This is true in both special and general relativity. Why is time dilation coordinate dependent? Because in standard coordinates in which the muon is at rest, time dilation is irrelevant, and the ground collides with the muon before decay due to length contraction instead (and it is earth clocks which are dilated in these coordinates, not the muon's 'decay rate clock'). Similarly, using one (among many, because there is no unique answer in GR) plausible interpretation of cosmological redshift, each galaxy considers a distant galaxy to have time dilation corresponding to the speed implied by the SR Doppler factor.

23. Jun 22, 2015

### PAllen

Because they don't. Popular literature and even some textbooks erroneously conflate a separation rate with a relative velocity. Consider special relativity first, as Dalespam has wisely advised. In a given inertial frame, if particle A is moving left at .9c, and particle B is moving right at .9c, the rate of growth of separation between them is 1.8c. However the relative velocity between them is about .9945c. The superluminal recession speeds given in cosmology are separation rates not relative velocities. In GR as well as SR, it is mathematically impossible for bodies with timelike world lines to have superliminal relative velocity. What is true in GR is that relative velocity of distant objects is ambiguous* but always < c. For that matter, separation rate is also ambiguous, there is a preferred coordinate system used in cosmology: one which manifests isotropy and homogeneity. The superluminal separation rates are computed in this coordinate system. However, GR says all coordinate systems have equal standing, and separation rates would be completely different in other coordinate systems. Thus this is 'conventional quantity' [ a very useful one - commonly used conventions are well motivated] but still a convention.

For contrast, the invariant observable, which has different manifestations in different coordinates, is the ratio of observed red shift to observed luminosity of objects believed to have known intrinsic luminosity.

*ambiguous: to compare vectors (like velocities) you nee to bring them together. The process for doing this in a way that preserves direction (in space-time, that is spacetime direction i.e. 4-velocity) is called parallel transport. In special relativity, this process is unique - it does not matter what path you use to bring the vectors together, you get the same result. Thus, for simplicity, we often say that you can compare distant vectors in special relativity. However, in general relativity, due to spacetime curvature,the result of parallel transport depends on the path chosen. In fact, such path dependence is the dentition of curvature. However, no matter what path you use for parallel transport, give two 4-velociteis that you transport to the same event, you always get a relative speed < c. Thus, in GR, relative speed is fundamentally ambiguous but always < c despite the ambiguity.

Last edited: Jun 22, 2015
24. Jun 22, 2015

### PAllen

No, it means that you can't assume, in any way, that physical behavior is isotropic if your goal is formally demonstrate isotropy. If you assume isotropy in your experimental design, and verify that it behaves as predicted, you have verified that the universe is compatible with the assumption of isotropy. You have not demonstrated that is 'really is' isotropic unless you rule out all forms anisotropy that can mimic isotropy (what I have called conspiratorial anisotropy). In the case of special relativity, it is a rigorously established result there is a class of anisotropic models that produce exactly the same observations as the normal model that assumes isotropy. I call these conspiratorial, because they are very special anisotropic models that ensure that e.g. the two way speed of light is always isotropic, while the one way speed is not.

I also think that this issue is peculiarly overblown in special relativity, because in the rest of physics compatible with the assumption of isotropy is taken to mean is isotropic as far as the practice of physics goes because we would be lunatic to over-complicate our theories by worrying about conspiratorial anisotropy. This whole issue is literally hardly ever asked in any other branch of physics.

25. Jun 22, 2015

### rede96

I don't disagree with anything there, and to be honest, although not in any great detail, I do understand the principle of separation versus velocity as well as adding relative velocities. So if for a moment we assume I do understand that, then the issue I am having understanding is elsewhere.

I think here is one of the areas that causes me confusion. For example, we might have different length meter sticks which we use to measure distance. Each one is perfectly fine to use as long as we recognise we are using different meter sticks and we stick to our chosen convention when doing measurements. However there is an absolute distance between objects we care to measure. Even if we label this distance differently. I see it as the same with relative velocities of distant object and separation rate.

So one of the things I was wondering about, is it possible to have an separation rate > c. If yes, then would principles like time dilation and length be relevant. As I see time dilation and length contraction to be effects of moving though space time. Separation in not 'movement' through space time.