# Clock synchronization problem

1. Jul 16, 2007

### bernhard.rothenstein

Consider the clocks C(0)(x=0,y=0) ticking and clock C(x,y=0) stopped and fixed to read t=x/c. Source S(0,0) emits a light signal towards clock C. Arriving at its location the light signal starts clock C and we say that C(0) and C(x,0) are synchronized a la Einstein.
Is there something wrong in the statement above?

2. Jul 16, 2007

### neutrino

Well, you didn't explicitly state than the C(0) reads t=0 when signal was emitted. I wouldn't call that wrong, but just an omission.

3. Jul 16, 2007

### bernhard.rothenstein

clcok synchronization

Thanks. It is an omission!

4. Jul 16, 2007

### richard.coppack

T= 0

If we could sit on a photon and travel at the speed of light. Would a clock that we were carrying stop completely? I have always wondered. RC

5. Jul 16, 2007

### pervect

Staff Emeritus
The short answer to the question is that you can't sit on a photon.

To avoid hijacking this thread, I'd suggest that you find one of the other threads where this has been discussed, for instance google finds (physics forum "sitting on a photon")

6. Jul 16, 2007

### alvaros

Yes and "a la Newton" I think.

7. Jul 17, 2007

### bernhard.rothenstein

clock synchronization

'If wrong, please tell me why

8. Jul 19, 2007

### alvaros

If both clocks are at rest, as I understood, you can use light or sound to synchronize them. Newton would agree. You are right.

When one is moving respect to the other .. ask the experts.

9. Jul 19, 2007

### Voltage

I'm not quite sure if this is relevant and I'm something of an Einstein fan so I don't like to say this sort of thing: I read somewhere that there was some kind of inherent problem with Einstein's clock synchronization. There was some kind of presumption that the light takes the same time to travel both ways between the clocks. But don't quote me on this. It was about GPS and might not have been trustworthy. (I find it hard to tell what I can trust). Perhaps one of the experts can advise.

10. Jul 19, 2007

### pervect

Staff Emeritus
There are other reasonable reasons for using Einstein's clock synchronization. Google finds, for instance http://adsabs.harvard.edu/abs/1988AmJPh..56..811B, but if you look at the literature (including the reference list for this paper) you'll probably find that there are still some people and papers who make a rather "big deal" about clock synchronization in the literature. This has the general effect of confusing some people new to relativity, while not actually accomplishing much.

Here's my simplified "take" on the situation.

Consider taking a plane trip from New York to LA, nonstop. Ignoring take-off and landing time, you leave at 7 am, you arrive at 9 am, a two hour flight by the clock. However, by your watch, it takes you 5 hours to fly the 2000 mile distance.

On the return flight, when you leave at 7 am, you arrive at 4 pm, an 8 hour flight. But it still takes 5 hours by your watch. (I've idealized the numbers a bit, to make the example simpler).

Given that the distance is 2000 miles, is it reasonable to say that your velocity flying east from LA to NY is 2000/2 = 1000 mph, while your velocity flying from NY to LA is 2000/8 = 250 mph?

The answer, I hope, is clear - it is not "reasonable", though I suppose I should add that a sufficiently perverse and determined person can reformulate physics to work with this definition of "velocity". The point is that using this approach of allowing arbitrary clock synchronization, some reformulation of physics is needed, that this idea does not match the common, intuitive idea of what a velocity is.

For a more specific example of why physics has to be reformulated to use this defintion, consider using these "velocities" in the standard equation momentum = mass * velocity. If you do so, you will incorrectly conclude that the plane flying east has much more momentum that the plane flying west. This is testable by a rather expensive, dramatic, and unrealistic experiment of crashing one plane into another, and noting where the pieces fall. It the momenta of the two planes are equal, the pieces should be symmetrically distributed over the location of the impact - if the eastward plane has over twice the momentum of the westward plane, the pieces should fall with a large eastward bias.

What you conclude is that the cocks at LA and NY are not properly synchronized, because of "time-zones", and that (in this simplified example) the velocity of the planes flying eastward and westward are the same, i.e. 2000 mi in 5 hours, or 400 mph.

How can we make this observation more formal? We can say that, at low velocities, we expect that when clocks are properly synchronized, velocity (the distance divided by the difference in times on the lab clocks) will be equal to celerity (the distance divided by the time on a clock you carry with you). See http://arxiv.org/abs/physics/0608040 for a definition of celerity and velocity (and thanks to robphy for finding this reference).

If we use any other scheme for synchronizing our clocks other than the standard one, we will notice the same effect that our airplane traveller does - that our velocity is not equal to our celerity even at low velocities. (Unfortunately, though, at low velocities, the experimental difference is small).

There is another way of putting this that is more readily tested in that it doesn't involve comparing almost equal numbers - rather than stating that velocity is equal to celerity at low speeds, one insists that the ratio of velocity to celerity not depend on direction. This is in some respects the more usual approach, it is one way of approaching what people mean when they say that space-time is isotropic, i.e. doesn't have any preferred directions.

Note that we cannot directly measure the "celerity" of light, because we cannot make a clock go at the speed of light. But by using slower-than-light signals, we can come up with a means of synchronizing distant clocks that is "fair" by imposing either the requirement that celerity be equal to velocity at low velocities, or that in general the ratio of celerity to velocity must not depend on the direction in which one travels (though it can depend on the velocity).

Furthermore, we can find (and test) that this means of synchronizing clocks yields the same clock synchrnoziation as the much-simpler-to-implement method of Einstein of using light signals.

Last edited: Jul 19, 2007
11. Jul 20, 2007

### bernhard.rothenstein

clock synchronization

I am affraid Newton would not agree because from his point of view time is absolute!
Regards

12. Jul 20, 2007

### Voltage

Thanks pervect. I've printed the arxiv article and will read it offline. The Brehme link was to an abstract, but it's a good lead, thanks. The article I was referring to is a little unreliable, judging from some of his other stuff which doesn't fit with even my mental model. So I won't raise it here. It did however talk about a 14ns GPS adjustment to the radio-defined "time now" in San Francisco and New York, which seemed quite reasonable.

Can you advise if the wikipedia articles below can be trusted? They look good, but I do have some trouble telling the difference between good science and bad.

http://en.wikipedia.org/wiki/Global_Positioning_System

http://en.wikipedia.org/wiki/Sagnac_effect

Sorry bernard, this is relevant, I'll try to explain why later. But now work calls. Must go.

13. Jul 20, 2007

### yogi

As I read this, it is a one way sync. Einstein's method depends upon the over and back readings. The two clocks will not be synchronized a la Einstein

Last edited: Jul 20, 2007
14. Jul 20, 2007

### bernhard.rothenstein

clock synchronization

Thanks. Do you mean that c(+) is different from c(-)? Is there some experimental evidence for that?

15. Jul 20, 2007

### pervect

Staff Emeritus
I don't see anything obviously wrong with the Wikipedia article (the version I looked at was

http://en.wikipedia.org/w/index.php?title=Sagnac_effect&oldid=141039015

If you want reliable technical details for the sagnac effect, I'd suggest http://relativity.livingreviews.org/Articles/lrr-2003-1/ [Broken] section 2 (though it may be a bit too technical).

You can also try the last version of the Wikipedia that Chris Hillman contributed to:

http://en.wikipedia.org/w/index.php?title=Sagnac_effect&oldid=53804564
(that's not nearly as authoratative as a peer reviewed reference, but it's probably slightly more reliable than a pot-luck version of Wikipedia, which is sometimes very good and sometimes not-so-good.)

What's basically going on here is that it is impossible to synchronize all clocks in a rotating frame according to the Einstein convention, see for example another paper http://arxiv.org/abs/gr-qc/9805089. (This gets a bit technical in spots as well.). One relevant non-technical exceprt:

If you start synchronizing clocks pairwise using the Einstein convention, going clockwise, when you work your way around the globe the ending clock won't be Einstein synchronized with the starting clock - the Einstein synchronization process is not transitive in rotating frames when you have a complete loop.

What this basically means is that GPS time, and also TAI time, are not "fair" or isotropic synchronization schemes as I described in my previous post. Thus if you measure the speed of a plane going east-west, and going west-east, and you use GPS methods to synchronize the clocks you won't get the "true" velocity (the one that gives the momentum as a function of velocity independent of direction). For planes, the errors are very slight - at large velocities, though, the differences can become important.

If you do a thorough literature search, you will undoubtedly find that there is some confusion in the literature, i.e. not everyone agrees with Tartaglia's position. In some (but not all cases) the issue is just semantics, where people use "velocity" to be any rate of a distance coordinate with respect to a time coordinate, regardless of the physical significance (or lack of the same) of this number, i.e. they don't require that momentum be derivable solely from velocity, but allow momentum to depend on both velocity and direction. That's one of the reasons I said

Last edited by a moderator: May 3, 2017
16. Jul 21, 2007

### yogi

No - no evidence - but much has been written on this. What Einstein needed in 1905 was a transform that would produce a null for MMx type experiments - he could have simply postulated that the over and back velocity is always constant in our universe - but instead he went further and employed a method of synchronization that embraced the idea that the one way velocity would always be measured as constant - but by the same token, he viewed it not possible to measure the one way velocity since you have an interdependence between time and distance. Einstein synchronization abrogates this quandry, and it is consistent with the experimental results even if it ultimately turns out that the two "one way" speeds are in fact unequal

17. Jul 21, 2007

### bernhard.rothenstein

clock synchronization

18. Jul 21, 2007

### yogi

Your assumption will recover the LT when you eliminate the uncertainty in the distance measurement....then the clocks will be synchronized a la Einstein.

19. Jul 21, 2007

### country boy

It may be worth noting that the "over and back" convention is a special case of requiring that the speed of light is independent of path. One observer (stationary) may see the light following the same path in both directions, but another (moving) observer will see the two paths as different. In special relativity, the speed is always the same.