# Is clock synchronization compulsory

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

## Answers and Replies

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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
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.

Hurkyl
Staff Emeritus
Gold Member
Could we derive the fundamental eqautions of special relativity without to synchronize the clocks of the same inertial reference frame?
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.

clock synchronization compulsory?

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.
I asked again because I have not received so far a satisfactory answer. Could you motivate your "no' answer without quoting the "classics" in the spirit of
sine ira et studio

clock synchronization compulsory?

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.
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

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

I asked again because I have not received so far a satisfactory answer. Could you motivate your "no' answer without quoting the "classics" in the spirit of
sine ira et studio
The motivation is quite clear, the "classics" is Einstein himself. Do you understand his derivation?

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.

pervect,

I don't understand your remark:

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.
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

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)

clock synchronization compulsory?

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
Please have a look at my answer to Pervect below.

pervect
Staff Emeritus
pervect,

I don't understand your remark:

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
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.

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.

Doppler shift is at the basis of the derivation of the Lorentz transformations via the radar detection procedure, .
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

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
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.

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clock synchronization compulsory?

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
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.

Thanks. But as far as I know, Doppler Effect can be derived without using the phase invariance and the Lorentz transformations.
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.

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

dopller effect and clock synchronization

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.
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

robphy
Homework Helper
Gold Member
bernhard.rothenstein said:
Thanks. But as far as I know, Doppler Effect can be derived without using the phase invariance and the Lorentz transformations.
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.
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/dp/0486240215/?tag=pfamazon01-20&tag=pfamazon01-20
Ellis-Williams https://www.amazon.com/dp/0198511698/?tag=pfamazon01-20&tag=pfamazon01-20
D'Inverno https://www.amazon.com/dp/0198596863/?tag=pfamazon01-20&tag=pfamazon01-20
Ludvigsen https://www.amazon.com/dp/0521630193/?tag=pfamazon01-20&tag=pfamazon01-20

my related posts on Bondi at PF:

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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/dp/0486240215/?tag=pfamazon01-20&tag=pfamazon01-20
This book has a terrible review, it is characterized as a "con-job". I will try the other references, D'Iverno sounds reasonable.

Ellis-Williams https://www.amazon.com/dp/0198511698/?tag=pfamazon01-20&tag=pfamazon01-20
D'Inverno https://www.amazon.com/dp/0198596863/?tag=pfamazon01-20&tag=pfamazon01-20
Ludvigsen https://www.amazon.com/dp/0521630193/?tag=pfamazon01-20&tag=pfamazon01-20

my related posts on Bondi at PF:

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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
Thank you, I'll check them out. They all seem to get the formulas of time dilation WITHOUT using the Lorentz transforms, right? Wonder how they do that....

And they all get the general relativistic Doppler effect (not some particular case), i.e. the one for arbitrary angle $$\theta$$, right? Exactly as in the Einstein paper, including the transverse Doppler effect, right?

clock synchronization compulsory?

Thank you, I'll check them out. They all seem to get the formulas of time dilation WITHOUT using the Lorentz transforms, right? Wonder how they do that....

And they all get the general relativistic Doppler effect (not some particular case), i.e. the one for arbitrary angle $$\theta$$, right? Exactly as in the Einstein paper, including the transverse Doppler effect, right?
The first Author I quote does. I think the formula he obtains holds only in the case of very high frequencies because he does not take into account the so called non-locality in the period measurement in the case of oblique incidence or accelerating source and observer. I presented my point of view on arxiv a place you scorn. Many other Authors even those who derive it using phase invariance and LT avoid to mention that peculiarity of the Doppler Effect.

The first Author I quote does. I think the formula he obtains holds only in the case of very high frequencies
1. Aren't you contradicting yourself?
2. this is ridiculous, the Doppler effect applies at all frequencies, are you saying that Zhang came up with somehockey derivation that applies only at high frequencies?
3. One more time, any of the papers you quote produces the relativistic Doppler effect as general as Einstein's derivation? Einstein formula is fully general, there are no special cases, applies for all angles,frequencies and relative speeds between source and observer (as long as v<c).

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robphy
Homework Helper
Gold Member
This book has a terrible review, it is characterized as a "con-job". I will try the other references, D'Iverno sounds reasonable.
Most pop-books aren't well received. For \$10, it's not bad for what it is trying to do. Bondi's lectures on the k-calculus (as part of review articles in general relativity) that appear in conference proceedings have more meat to them. (Bondi also had a series of lectures on the BBC that try to make relativity more accessible to the general public.)

Bondi's book pre-dates all of these other more-technical books that I listed (which appears to have been incorrectly quoted in your last post).

Ellis-Williams https://www.amazon.com/dp/0198511698/?tag=pfamazon01-20&tag=pfamazon01-20
D'Inverno https://www.amazon.com/dp/0198596863/?tag=pfamazon01-20&tag=pfamazon01-20
Ludvigsen https://www.amazon.com/dp/0521630193/?tag=pfamazon01-20&tag=pfamazon01-20

my related posts on Bondi at PF: