# Is clock synchronization compulsory

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 equations 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

nakurusil
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 equations 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.

Staff Emeritus
Gold Member
Could we derive the fundamental equations 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.

bernhard.rothenstein
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.
sine ira et studio

bernhard.rothenstein
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

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

nakurusil
sine ira et studio

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

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.

lalbatros
pervect,

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

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)

bernhard.rothenstein
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

Staff Emeritus
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

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.

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.

nakurusil
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

MeJennifer
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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bernhard.rothenstein
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.

nakurusil
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.

nakurusil
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.

bernhard.rothenstein
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

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

my related posts on Bondi at PF:

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nakurusil
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

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

my related posts on Bondi at PF:

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nakurusil
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?

bernhard.rothenstein
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.

nakurusil
The first Author I quote does. I think the formula he obtains holds only in the case of very high frequencies

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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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 D'Inverno https://www.amazon.com/dp/0198596863/?tag=pfamazon01-20 Ludvigsen https://www.amazon.com/dp/0521630193/?tag=pfamazon01-20 my related posts on Bondi at PF: https://www.physicsforums.com/showthread.php?t=117439 https://www.physicsforums.com/showthread.php?t=113915 I don't have time to look through all of their references, but I'd be surprised if these books didn't list this Bondi book as the primary reference for the k-calculus. As suggested by others in this thread, the motivation and presentation of various ideas in relativity often improves over time. So, you might find (say) d'Inverno's treatment (in a small part of a more technical book on Relativity) better than the Bondi book (on Relativity for the general public). Since you haven't seen the book, let me summarize the strength of the k-calculus approach. It uses a very physically-motivated radar-method to derive many of the important ideas of special relativity. The factor k is featured more prominently over other factors (e.g., beta [velocity] and gamma ) because it has direct interpretation as the doppler factor and has much nicer mathematical (and transformation) properties. The underlying reason is that the k-factors are eigenvalues of the Lorentz Transformation (with eigenvectors along the lightlike directions). By a coordinate transformation, you get the standard Lorentz Transformation in rectangular form. Last edited by a moderator: nakurusil 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
D'Inverno https://www.amazon.com/dp/0198596863/?tag=pfamazon01-20
Ludvigsen https://www.amazon.com/dp/0521630193/?tag=pfamazon01-20

my related posts on Bondi at PF:

I don't have time to look through all of their references, but I'd be surprised if these books didn't list this Bondi book as the primary reference for the k-calculus. As suggested by others in this thread, the motivation and presentation of various ideas in relativity often improves over time. So, you might find (say) d'Inverno's treatment (in a small part of a more technical book on Relativity) better than the Bondi book (on Relativity for the general public).

Since you haven't seen the book, let me summarize the strength of the k-calculus approach. It uses a very physically-motivated radar-method to derive many of the important ideas of special relativity. The factor k is featured more prominently over other factors (e.g., beta [velocity] and gamma ) because it has direct interpretation as the doppler factor and has much nicer mathematical (and transformation) properties. The underlying reason is that the k-factors are eigenvalues of the Lorentz Transformation (with eigenvectors along the lightlike directions).

Thank you, I'll check them out. I think we are getting on a tangent here, the subject was (and still is): are there valid derivations of the relativistic Doppler effect (the most general form) that do not use the Lorentz transforms?
From your answers I would be tempted to check D'Iverno, he is a respected author.

Out of curiosity, how would you do such a derivation using k-vectors? Can you write down the math (if it is not too involved)?

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Thank you, I'll check them out. I think we are getting on a tangent here, the subject was (and still is): are there valid derivations of the relativistic Doppler effect (the most general form) that do not use the Lorentz transforms?
From your answers I would be tempted to check D'Iverno, he is a respected author.

Out of curiosity, how would you do such a derivation using k-vectors? Can you write down the math (if it is not too involved)?

My post directly answers the question with: Yes, the k-calculus... although the transverse Doppler effect will take a little more work.
If you read my PF posts quoted above, you'll see that k is Doppler Factor. I'd rather not repeat it all here again (but I would put it in my PF-blog if it supported LaTeX).

lalbatros
The copernician revolution was to recognize that taking the sun as center is simpler.
Similarly, in special relativity, clocks synchronisation make things look simpler, but it is not really a revolution, nor is it a need. It just makes things simpler. And it is always possible to transform the formulas from general coordinates to a more simple view.
General Relativity encourages us to think independently of the coordinate system. The Doppler shift can be calculated for any metric and the impact of the coordinate system can be analysed easily in general terms. Transforming to locally Minkowski frames gives us the familiar expression for the Doppler shift, but the general expression from GR should be the reference, isn't it?

Michel

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nakurusil
My post directly answers the question with: Yes, the k-calculus... although the transverse Doppler effect will take a little more work.

nakurusil
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.

Since you simply didn't understand the issue, I will spell it out for you: derive the relativistic Doppler effect formula without using the Lorentz transforms. Please try using math, not prose.

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robphy said:
My post directly answers the question with: Yes, the k-calculus... although the transverse Doppler effect will take a little more work.

The longitudinal Doppler effect is the usual Doppler Effect.
The transverse Doppler effect is essentially Time Dilation.
For a complete k-calculus proof covering both cases, it's on my to-do list.
Since I've never seen it actually written out, I might write it up into a paper first.

I'm not sure why the 1+1 (Longitudinal) case [which is easily handled by the k-calculus without invoking a Lorentz Transformation] is insufficient for you.

Although the 2+1 and 3+1 cases are important, the longitudinal case is more fundamental. The 2+1 and 3+1 cases are obtained by extension [which would be easier with a Lorentz Transformation.. but could be accomplished without it with more work]. I can write down a pure 4-vector calculation to handle both the transverse and longitudinal cases without ever explicitly using the Lorentz Transformations. So, I'm not sure what you are after.

(It might be worth noting that A.A. Robb practically reconstructed [with much effort] all of the structure of Minkowski space [including obtaining the Lorentz Transformation] starting from a primitive order relation [the causal relation: "after"]. I mentioned this in this earlier thread https://www.physicsforums.com/showthread.php?t=149780 which you may recall.)

On another note, isn't this line of discussion actually tangent (or diverging away from) to the OP's original question?

nakurusil
The longitudinal Doppler effect is the usual Doppler Effect.
The transverse Doppler effect is essentially Time Dilation.
For a complete k-calculus proof covering both cases, it's on my to-do list.
Since I've never seen it actually written out, I might write it up into a paper first.

Not longitudinal+transverse. Arbitrary angle, please. Like Einstein's.

I'm not sure why the 1+1 (Longitudinal) case [which is easily handled by the k-calculus without invoking a Lorentz Transformation] is insufficient for you.

Because it is the most general formula that is interesting, not particular cases.

Although the 2+1 and 3+1 cases are important, the longitudinal case is more fundamental. The 2+1 and 3+1 cases are obtained by extension [which would be easier with a Lorentz Transformation.. but could be accomplished without it with more work]. I can write down a pure 4-vector calculation to handle both the transverse and longitudinal cases without ever explicitly using the Lorentz Transformations. So, I'm not sure what you are after.

Obviously, to see if you can derive the general case of the relativistic Doppler effect without making use of the Lorentz transforms.

On another note, isn't this line of discussion actually tangent (or diverging away from) to the OP's original question?

Not really, I challenged one of Bernhard's early claims (post #13), that such a derivation was possible. Somehow, it would make the realtivistic Doppler effect a more fundamental effect than the Lorentz transforms. I am having a very hard time believing it, especially in the context of Einstein't cleraly relying on the Lorentz transforms in the derivation of the relativistic Doppler effect.
I also challenged Bernhard's original post, which indicates that he believes that the Lorentz transforms can be derived without using the Einstein clock synchro, though the statement is refuted by Einstein's explicit use of the clock synchronisation in his derivation of the Lorentz transforms. So, I have two challenges against Bernhard's claims and they are interrelated.

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Somehow, it would make the realtivistic Doppler effect a more fundamental effect than the Lorentz transforms. I am having a very hard time believing it, especially in the context of Einstein't cleraly relying on the Lorentz transforms in the derivation of the relativistic Doppler effect.

So, at this stage, it may be best to study (say) the references I provided and see what is going on.
Until then...

nakurusil
So, at this stage, it may be best to study (say) the references I provided and see what is going on.
Until then...

I'll check D'Iverno (do you have a page number?) and I'll wait for your k-vector proof. At least, you might be getting a nice paper out of this discussion

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bernhard.rothenstein
doppler