# Is clock synchronization compulsory

1. Feb 8, 2007

### bernhard.rothenstein

Working with clocks we have to perform an initialization (to ensure that when the origins of the involved inertial reference frames are located at the same point in space theirs clocks read t=t'=0) and a synchronization of the clocks of the same inertial reference frame ensuring that they display the same running time. The synchronization is performed following a procedure proposed by Einstein. The formula that accounts for the Doppler Effect relates two proper time intervals measured by the observers of the two reference frames respectively and can be derived using initialized clocks theirs synchronization being not compulsory. My question is: Could we derive the fundamental eqautions of special relativity without to synchronize the clocks of the same inertial reference frame? My oppinion is yes. Your oppinion is highly appreciated in the spirit of
sine ira et studio

2. Feb 8, 2007

### nakurusil

The answer is "no". The Lorentz transforms are a direct consequence of the clock synchronization, see paragraph 3 here. I think you asked the same question before.

3. Feb 9, 2007

### Hurkyl

Staff Emeritus
It depends on what you really mean by that question.

Coordinates are not necessary to talk about (the geometry of) SR -- it can be presented entirely synthetically in a manner similar to Euclidean geometry.

But in any coordinate chart that is noninertial, the form of the equations will be different.

4. Feb 9, 2007

### bernhard.rothenstein

clock synchronization compulsory?

sine ira et studio

5. Feb 9, 2007

### bernhard.rothenstein

clock synchronization compulsory?

Thanks. My humble point of view is that the Doppler Effect formula relating two proper time intervals involves only initialized clocks and not synchronized ones. Once derived, the Doppler shift formula leads to the addition law of relativistic speeds, which at its turn leads to the Lorentz transformations.
sine ira et studio

6. Feb 9, 2007

### lalbatros

Should that not be as simple as any -general- coordinate transformation?

The transformation to a rotating frame, where clocks cannot be synchronised, is well known.
But is it in any way different from any relabelling of the coordinates (eventually within two different inertial frames)?

Would it be possible to "synchronize" clocks with sound waves?
By synchronizing, I mean defining the time coordinates.
How would the transformation look like?

Michel

7. Feb 9, 2007

### nakurusil

The motivation is quite clear, the "classics" is Einstein himself. Do you understand his derivation?

8. Feb 9, 2007

### pervect

Staff Emeritus
If you intend to derive doppler shift, the standard approach is going to write the doppler shfit as a function of velocity.

The velocity you measure is going to depend on how you synchronize the clocks. So the answer is going to depend on how you synchronize the clocks.

The only option I'm aware of is to replace velocities with a geometric concept like rapidities. If you do this, then you can find the doppler shift geometrically, because the rapidity is also a geometric measurement that doesn't depend on the coordinate system (i.e. the choice of the clock synchronization).

The problem is that velocityis not a geometric measurement.

Without replacing the concept of velocity, I don't believe there is any way to eliminate the issue of clock synchronization.

I don't know if anyone has written a paper about the velocity-less "rapidity" approach to relativity, however.

9. Feb 9, 2007

### lalbatros

pervect,

I think one should be able to derive the doppler shift in any coordinate system, even in SR.
But of course, in the end result the "velocity" will pop up, of course.
And this velocity will bring us back to a certain definition of time, which is more suitable and simple, but not necessary.

I would be more comfortable if I could formalize what I said ...

Michel

10. Feb 9, 2007

### bernhard.rothenstein

clock synchronization compulsory?

The velocity you measure is going to depend on how you synchronize the clocks. So the answer is going to depend on how you synchronize the clocks.

Thanks Pervect.
Borders and language differences make that results obtained by physicists at one place of the Globe are not known by others working at other parts of it.
Paul Kard (1914-1985, Tartu State University Estonia) was one
of the pioneers of simple approaches to special relativity. A very small part of his contributions were popularized by Karlov [1].
He considers an experiment which involves two rods of different proper lengths in relative motion, takes into account the invariance of the speed of light and without mentioning clocks or theirs synchronization, deriving finally the the formula that accounts for the length contraction. A supplementary experiment in which clock synchronization is not involved leads to the formula that accounts for the time dilation. It is shown that the proper lengths of the two rods are related by the Doppler formula and the addtion law of relativistic velocities is also derived. He stops at this point his derivations in a "Lorentz free special relativity".
Considering an experiment in which two tardyons collide sticky and imposing mass and momentum conservation he derives the formula which accounts for m=g(V)m(0). A supplemental experiment in which one of the tardyons is replaced by a photon leads to the addition law of relativistic velocities. In both cases clock synchronization is not mentioned. The addition law of relativistic velocities leads without supplementary assumptions to the Lorentz transformations.
I have followed Kard's derivations with my humble knowledge, without finding flows. The work of Kard is concentrated in a short brochure in Russian. I could send essential parts of it to those who are interested, with the request to let me know their oppinion. Your oppinion is of special intertest for me.
As far as I know such approaches could be found in the American literature as well. Of course all derivations are in best accordance with Einstein offering a simpler access. Our discussion can involve only the content of the paper I quote each oppinion being highly appreciated.
[1] Leo Karlov, "Paul Kard and Lorentz-free special relativity," Phys.Educ. 24 165 (1989)

11. Feb 9, 2007

### bernhard.rothenstein

clock synchronization compulsory?

12. Feb 9, 2007

### pervect

Staff Emeritus
You can certainly derive a formula for any given coordinate system. However the details of the formula will be dependent on the coordinate system used, because the definition of velocity depends on the coordinate system used.

The doppler shift is a coordinate independent quantity, that doesn't for example depend on clock synchronization conventions, but the velocity does.

13. Feb 9, 2007

### bernhard.rothenstein

The doppler shift is a coordinate independent quantity, that doesn't for example depend on clock synchronization conventions, but the velocity does.

Thanks. Very important confirmation for me! Doppler shift is at the basis of the derivation of the Lorentz transformations via the radar detection procedure, expressed in I as a function of the readings of a single clock located at its origin O and in I' as a function of the readings of a single clock located at its origins O' when the radar signals are emitted and received back after reflection on the detected event. Doing so we should initialize the two clocks mentioned above avoiding clock synchronization at all. With the Lorentz transformations in our hands we can derive the addition law of relativistic velocities in the particular case when in each of the involved inertial reference frames proper lengths and coordinate time intervals are measured but also in other variants: proper length and proper time interval and probably in many other ways.
Did Einstein mention that approach to the Lorentz transformations?
Please confirm if I am right in the interpretation of your help concerning in an other thread.

14. Feb 9, 2007

### nakurusil

Actually, it is exactly the other way around, the relativistic Doppler effect is derived from the Lorentz transforms and the invariance of $$\Phi$$.
See the "classics", chapter 7, here

15. Feb 9, 2007

### MeJennifer

You completely mix up theory and experiment here.

Doppler effects are phenomena of nature. By a set of experiments we can conclude that the Lorentz transforms are in accordance with experiment, as is the case with the theory of relativity.

Last edited: Feb 9, 2007
16. Feb 9, 2007

### bernhard.rothenstein

clock synchronization compulsory?

Thanks. But as far as I know, Doppler Effect can be derived without using the phase invariance and the Lorentz transformations. I think it is the most derived Effect. As far as the "classic", 100 years of special relativity have brought many simple approaches, that make teaching of it a pleasure without violating the two postulates. Using them or not, as far as they are correct, is a question of taste. Sending allways to the "classic", for whom I have full respect, reminds me the Alexandria Library.

17. Feb 10, 2007

### nakurusil

This is interesting, can you quote a reliable source? Preferably a book ? Please do not quote some weird paper from Apeiron or one that has been collecting dust in arxiv. I would really like to see how such a thing can be done.

18. Feb 10, 2007

### nakurusil

On many subjects, the "classic" (i.e. A.E.) is still the best. Even after 100 years.

19. Feb 10, 2007

### bernhard.rothenstein

dopller effect and clock synchronization

Why do you always detect some wrong doing in my presence on the Forum? It is hard to me to find out where good relativity starts from your point of view. I propose some "non-classic sources".
1.Yuan Zhong Zhang, "Special relativity and its experimental foundations,"
(World Scientific, London 1996) pp. 41-45.
After presenting the "classic" derivation of the Doppler shift formula starting with phase invariance and LT he presents a derivation which involves special relativity only via time dilation.:rofl:
2.N.David Mermin, "It's about time," (Understanding Einstein's Relativity)
Princeton University Press, Princeton 2005pp/74-75
The Author derives the Doppler shift formula without using phase invariance and the Lorentz transformations showing that it leads dirfectly to addition law of relativistic velocities.
3.Hans C.Ohanian, "Special Relativity:A Modern Introduction (Physics Curriculum&Instructions 2001)pp.88-91
The Author derives the Doppler shift formula using a classical space-time diagrams following the intersection between the world line of the moving receiver and the successive wave crests emitted by a stationary source involving special relativity only via time dilation.
I think that the sources mentioned above are not weird papers or dust collected on arXiv. If it would be so, I regret the money I spent to procure them. I wonder that you do not know them!
As an old physicist I advise you to avoid such instant answers of "no" which could disappoint a beginner but not an old fox.

Audiemur et altera pars

20. Feb 10, 2007

### robphy

In the k-calculus (popularized by Hermann Bondi), using Einstein's postulates, the equation for the Doppler Effect is emphasized first. k turns out to be the Doppler factor. It is then used to obtain the standard Lorentz Transformations in rectangular coordinates. (Note that Doppler naturally arises when the Lorentz Transformation is written in light-cone coordinates [the natural eigenbasis of the Lorentz Transformations].)

See:
Bondi https://www.amazon.com/Relativity-Common-Sense-Herman-Bondi/dp/0486240215
Ellis-Williams https://www.amazon.com/Flat-Curved-Space-Times-George-Ellis/dp/0198511698
D'Inverno https://www.amazon.com/Introducing-Einsteins-Relativity-Ray-dInverno/dp/0198596863
Ludvigsen https://www.amazon.com/General-Relativity-Geometric-Malcolm-Ludvigsen/dp/0521630193

my related posts on Bondi at PF: