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.

 

[Hurkyl]

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.

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

 

[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?
Or would that lead to contradictions?

Michel

 

[nakurusil]

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]

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,

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

 

[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?
Or would that lead to contradictions?

Michel

Please have a look at my answer to Pervect below.

 

[pervect]

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.

 

[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.

 

[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.
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]

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:
https://www.physicsforums.com/showthread.php?t=117439
https://www.physicsforums.com/showthread.php?t=113915

 

[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:
https://www.physicsforums.com/showthread.php?t=117439
https://www.physicsforums.com/showthread.php?t=113915[/QUOTE]

 

[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.
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

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).

 

[robphy]

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.

 

[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:
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).

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)?

 

[robphy]

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

 

[nakurusil]

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

Arbitrary angle, please. No Lorentz transforms, please.

 

[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.

 

[robphy]

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

Arbitrary angle, please. No Lorentz transforms, please.

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.

 

[robphy]

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

 

[bernhard.rothenstein]

doppler

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).

As I see you are not able to give up your aggressive style. Should ridiculous be used in a scientific discussion? I have tried to help you and as I see you put questions concerning theirs content without consulting them. That is the style Latins named stante pede answer. I would avoid such a style. If you read Zhang you will see that the way in which he derives the Doppler formula, with arbitrary incidence angles, shows clearly that it holds only when it relates infinitesimal periods dt=F(theta',V/c)dt' i.e. very high frequencies. The Doppler formula obtained by using phase invariance and LT leads to the same formula but with finite periods. IMHO that is the consequence of the fact that the LT is applied in that case to a single point of the electromagnetic wave assuming that the observer could receive two successive wave crests remaining located at the same point in space. That is what some physicists call locality assumption in the period measurement by moving observers. In the case of the theta case, between the reception of two successive wave crests the angle can change whereas in the case of an accelerating observer it is his speed that changes between them.
IMHO the theta Doppler formula you find in the literature holds only in the case of very high frequencies!
Please avoid stante pede answers i.e. without consulting Zhang's paper.
Could you convince me that "Einstein formula is fully general, there are no special cases, applies for all angles,frequencies and relative speeds between source and observer." of course in a scientific language.
But we are very far from my initial question: Is clock synchronization compulsory?

 

[bernhard.rothenstein]

doppler and his relatives

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.

Interesting point of view. Do you think that performing a given experiment in a given inertial frame we could obtain results which are conflicting with Newton and Galileo. Say the relationship between the proper mass and the relativistic mass (accept please that concept). We obtain some experimental results which can be plotted (m/m(0) as a function of u/c) looking for a function which reproduces best the experimental results. Extrapolation of the experimental results shows that they are best expressed by m=m(0)/((1-uu/cc)^1/2. (1) Consider three inertial reference frame I,I' and I(0). I(0) is the rest frame of the particle that moves with speed u relative to I with velocity u' relative to I, I' moving with V relative to I. Apply (1) from I and I'. Eliminate m(0) between the eqaution you obtain and express its right side as a function of u' only via the addition law of relativistic velocities obtaining the transformation equations for momentum and mass. Of course the same approach can be used in the case of many other relativistic effects. Do you think that such an approach presents some pedagogical advantages? IMHO the addition law of relativistic velocities can be derived without using the LT.

 

[nakurusil]

As I see you are not able to give up your aggressive style. Should ridiculous be used in a scientific discussion? I have tried to help you and as I see you put questions concerning theirs content without consulting them. That is the style Latins named stante pede answer. I would avoid such a style. If you read Zhang you will see that the way in which he derives the Doppler formula, with arbitrary incidence angles, shows clearly that it holds only when it relates infinitesimal periods dt=F(theta',V/c)dt' i.e. very high frequencies. The Doppler formula obtained by using phase invariance and LT leads to the same formula but with finite periods.

Unfortunately this is not true: the Einstein derivation applies to ANY frequency. I do not know what gave you the idea about "finite periods" (you probably mean "discrete" periods) but either way, it is not true.

IMHO the theta Doppler formula you find in the literature holds only in the case of very high frequencies!

Whatever gave you this idea?

Could you convince me that "Einstein formula is fully general, there are no special cases, applies for all angles,frequencies and relative speeds between source and observer." of course in a scientific language.

Sure, read the original Einstein paper, I gave you the link about 3 times, maybe it is time that you read the paper.

But we are very far from my initial question: Is clock synchronization compulsory?

Yes. For the 4-th time. Read Einstein's paper.

 

[nakurusil]

The formula that accounts for the Doppler Effect relates two proper time intervals measured by the observers of the two reference frames respectively

Not really, it relates the observed frequency to the source frequency. See here:

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#For_motion_in_an_arbitrary_direction

and can be derived using initialized clocks theirs synchronization being not compulsory.

Not really, the derivation uses the Lorentz transforms. The Lorentz transforms have been derived assuming the Einstein clock synchronisation prior to the derivation of the Doppler effect. Both derivations happen in this particular sequence in the same paper. Here is the link to it :

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[nakurusil]

IMHO the addition law of relativistic velocities can be derived without using the LT.

Don't think so, check this out:

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


First sentence, from the top:

"A velocity addition formula appears in the special theory of relativity as a consequence of the Lorentz transformations"

For good reason: it is derived by simple chain differentiation of the Lorentz formulas. The very same way Einstein did it more than 100 years ago:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

See paragraph 5. This paper contains a wealth of information, should set all your misconceptions straight, once you bite the bullet and read it.

 

[bernhard.rothenstein]

Doppler

Not really, it relates the observed frequency to the source frequency
frequency=1/period




Not really, the derivation uses the Lorentz transforms. The Lorentz transforms have been derived assuming the Einstein clock synchronisation prior to the derivation of the Doppler effect. Both derivations happen in this particular sequence in the same paper. Here is the link to it :

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Do you think that the order in which formulas which account for a relativistic effect has relevance as long as Einsten's postulates are respected Sending people to Einstein for whom I have a profound respect makes the Forum useless as well as the work of those who try to present his theory with human face and more palatable

 

[bernhard.rothenstein]

doppler

Unfortunately this is not true: the Einstein derivation applies to ANY frequency. I do not know what gave you the idea about "finite periods" (you probably mean "discrete" periods) but either way, it is not true.




Whatever gave you this idea?



Sure, read the original Einstein paper, I gave you the link about 3 times, maybe it is time that you read the paper.

Please do not send me to Einstein because I respect his theory and know backward since youth. I also respect those who give simple derivations in accordance with Einstein's postulates. They are a good exercise before to read ALBERT my teacher. Even if I know that you do not read the references I give you, please have a look at
R.Neutze, William Moreau, "Frequency measurement by uniformly accelerating observers," Phys.Letters A 179 (1993) 389-390
W.Moreau, "Nonlocality in frequency measurement of uniformly accelerating observers," Am.J.Phys. 60, 561 (1992)
I think that we have nonlocality in the case f=F(theta,V/c)f' as well because between the reception of two successive wave crests theta and the radial component of the relative velocity change. So using in that case the concept of instantaneous velocity at the moment when the observer receives a wave crest, we obtain results that hold only in the case of very small periods. As far as I know in a Doppler Effect we have to compare the period at which the source emits two successive wave crests measured in its rest frame and the period at which the same wave crets are received by the moving observer measured in its rest frame. Both are proper periods.

Not motivated, short no and yes answers are not usefull nor for me but neither for the participants on the Forum. Had you a look at Zhang? I could send you a copy of the pages of interest as an attachment if you give an address. I think it is worth for you to follow the piece of advise gave to you Robphy #33.

 

[nakurusil]

Please do not send me to Einstein because I respect his theory and know backward since youth.

Then read his general derivation: it has nothing to do with any "crests", it has none of the restrictions that you are claiming, it is very straightforward.

I think that we have nonlocality in the case f=F(theta,V/c)f' as well because between the reception of two successive wave crests theta and the radial component of the relative velocity change. So using in that case the concept of instantaneous velocity at the moment when the observer receives a wave crest, we obtain results that hold only in the case of very small periods.

This is too bad. Because the formula derived by Einstein and agreed upon by everybody holds for ANY frequency. So the thing with "holds only for very small periods" sounds like you are misunderstanding some derivation or you stumbled on a bad one and you are holding it to being correct.

As far as I know in a Doppler Effect we have to compare the period at which the source emits two successive wave crests measured in its rest frame and the period at which the same wave crets are received by the moving observer measured in its rest frame. Both are proper periods.

As long as you do a proper derivation, yes. If you come up with a derivation that "holds only for very small periods", it is all bogus.

Had you a look at Zhang? I could send you a copy of the pages of interest as an attachment if you give an address.

Zhang is a very experienced physicist, is is unlikely that he made such a mistake. Did you consider the possibility that you are misinterpreting his writings? Why don't you scan the relevant page, turn it into a JPEG and attach it to the next post so we can all have a look at what you think is a "Doppler formula that holds only for very small periods"

 

[bernhard.rothenstein]

how correct is the "general" Doppler shift formula?

Zhang is a very experienced physicist, is is unlikely that he made such a mistake. Did you consider the possibility that you are misinterpreting his writings? Why don't you scan the relevant page, turn it into a JPEG and attach it to the next post so we can all have a look at what you think is a "Doppler formula that holds only for very small periods

As you suggested I present Zhang's derivation.
Consider a source of light located at the origin O of the I frame and a clock C located at that point. When C reads t(e) S emits a light signal along a direction that makes an angle w with the positive direction of the OX axis. At a time t(r) the light signal generates the event E(x=rcosw,y=rsinw,t(r)) and we have
t(r)=t(e)+r/c (1)
Differentiating (1) we obtain
dt(r)=dt(e)+dr/c (2)
which holds for each value of t(e) even for t(e)=0. Taking into account that by definition dr/dt(r)=Vcosw (3) represents the instantaneous radial component of an observer of the I' frame (2) leads to
dt(e)/dt(r)=1-(V/c)cosw (3)
(equation 2.10.17) in Zhang's derivation.) In (3) dt(e) represents a proper time interval whereas dt(r) represents a coordinate time interval. Taking into account the time dilation formula
dt'(r)=dt(r)/g(V) (4)
dt'(r) representing a proper time interval (3) becomes
dt(e)/dt'(r)=g(V)[1-(V/c)cosw. (5)
Arrived at that point Zhang considers that in the infinitezimal time dt(e) the source emits dn wave crests which are all received by the observer and defines the correspnding frequencies
dn/dt(e)=f(e) (5)
dn/dt(r)=f''(r) (6)
obtaining the final result
f'(r)=f(e)[1-(V/c)cosw]/g(V) (7)
equation (2.10.22) in Zhangs derivation.

I add to all that my own comments.
1. Equation (7) is the same as that derived from phase invariance and Lorentz transformations.
2.It holds only in the case of very small periods the velocity defined by (3)representing an instantaneous velocity.
3.The derivation involves the concept of wave crest which is not mentioned in the derivation to which you send me obstinately.
4.In the case of both derivations (7) holds only in the case of the first pair of received wave crests because for the second pair the angle w changes.
5.Considering the inverse transformation of (7) in which appears the angle w' and eliminating between them f(e) and f'(r) we obtain the formula which accounts for the aberration of light effect which IMHO uses initialized and not synchronized clocks.
6.Because dn=1 is a realistic value we see that the involved frequencies are infinite and so the associated photons would burn all they find in their way.
7.Leading to the same results the two derivations have the same physics behind them.
For more conformity please have a look at the original version of Zhang.

Please take a "time out" before an instantaneous answer and give punctual answers, inserted in my text taking into account that you consider that the Author is a serious one.
I would highly appreciate Albert's oppinion, but that is not possible, taking into account that he was open minded.

 

[nakurusil]

Thank you for taking the effort to post Zhang's solution.

Zhang is a very experienced physicist, is is unlikely that he made such a mistake. Did you consider the possibility that you are misinterpreting his writings? Why don't you scan the relevant page, turn it into a JPEG and attach it to the next post so we can all have a look at what you think is a "Doppler formula that holds only for very small periods

As you suggested I present Zhang's derivation.
Consider a source of light located at the origin O of the I frame and a clock C located at that point. When C reads t(e) S emits a light signal along a direction that makes an angle w with the positive direction of the OX axis. At a time t(r) the light signal generates the event E(x=rcosw,y=rsinw,t(r)) and we have
t(r)=t(e)+r/c (1)
Differentiating (1) we obtain
dt(r)=dt(e)+dr/c (2)
which holds for each value of t(e) even for t(e)=0. Taking into account that by definition dr/dt(r)=Vcosw (3) represents the instantaneous radial component of an observer of the I' frame (2) leads to
dt(e)/dt(r)=1-(V/c)cosw (3)
(equation 2.10.17) in Zhang's derivation.) In (3) dt(e) represents a proper time interval whereas dt(r) represents a coordinate time interval.

So far , so good.

Taking into account the time dilation formula
dt'(r)=dt(r)/g(V) (4)

The time dilation formula (4) is a DIRECT consequence of the Lorentz transform for time. So, Zhang's derivation is a consequence of the Lorentz transforms. I hope you realize that you just proved my point.



Now, to some secondary issues:

dt'(r) representing a proper time interval (3) becomes
dt(e)/dt'(r)=g(V)[1-(V/c)cosw. (5)
Arrived at that point Zhang considers that in the infinitezimal time dt(e) the source emits dn wave crests which are all received by the observer and defines the correspnding frequencies
dn/dt(e)=f(e) (5)
dn/dt(r)=f''(r) (6)
obtaining the final result
f'(r)=f(e)[1-(V/c)cosw]/g(V) (7)
equation (2.10.22) in Zhangs derivation.

So what gave you the idea that the formula applies only to very high frequencies? As an aside, how high do these frequencies have to be?

.
2.It holds only in the case of very small periods the velocity defined by (3)representing an instantaneous velocity.

Because he used differentiation?

3.The derivation involves the concept of wave crest which is not mentioned in the derivation to which you send me obstinately.

Yes, Einstein's standard derivation doesn't need any of the "crests". So?

4.In the case of both derivations (7) holds only in the case of the first pair of received wave crests because for the second pair the angle w changes.

This would be very bad, if your statement were true, Zhang's derivation would be invalid. So, either Zhang's derivation is worthless or you didn't understand it. Without a picture it is hard to tell but I am willing to bet, based on your other misunderstandings , that you didn't understand this one either.

5.Considering the inverse transformation of (7) in which appears the angle w' and eliminating between them f(e) and f'(r) we obtain the formula which accounts for the aberration of light effect which IMHO uses initialized and not synchronized clocks.

Just another misunderstanding: (7) has been obtained using the Lorentz transforms in expression (4). The derivation of the Lorentz transforms is based on Einstein's clock synchronisation.

6.Because dn=1 is a realistic value we see that the involved frequencies are infinite and so the associated photons would burn all they find in their way.

This is incomprehensible. Can you try again?
Ahh, I think I know what you are trying to say: do you really think that Zhang's formula doesn't apply for dn infinitely small? That there may be some magical lower bound to dn? dn is an infinitesimal quantity, therefore it is infinitely small.

 

[bernhard.rothenstein]

doppler again

Thank you for taking the effort to post Zhang's solution.



So far , so good.



The time dilation formula (4) is a DIRECT consequence of the Lorentz transform for time. So, Zhang's derivation is a consequence of the Lorentz transforms. I hope you realize that you just proved my point.

In our discussion it is not important that he uses the LT. What he shows is that the Doppler formula holds only at very small periods!

I told you for many times that many authors derive the time dilation formula without using the LT. They also derive the addition law without using them. The addition law of velocities leads directly to the LT. In your usual way to answer you told me that all that is trash and the journals which publish them have no scientific value. So that point is closed!



Now, to some secondary issues:



So what gave you the idea that the formula applies only to very high frequencies? As an aside, how high do these frequencies have to be?

I do not speak in terms of frequency but in terms of periods. The periods should be small enough in order to ensure that the velocity in the Doppler formula is an instantaneous one. That is the case in the classic derivation as well where the frequency in the phase is an instantaneous one and so not measurable.




Because he used differentiation?
Of course and because the involved periods in the Doppler shift formula are infinitezimal dt(e) and dt(r) and so theirs inverses are infinite.



Yes, Einstein's standard derivation doesn't need any of the "crests". So?

Without crests there is no Doppler Effect! Einstein's standard derivation applies the LT to a single point of the space through which the wave propagates considering that there the observer could receive two successive crests, making the very small period assumption.



This would be very bad, if your statement were true, Zhang's derivation would be invalid. So, either Zhang's derivation is worthless or you didn't understand it. Without a picture it is hard to tell but I am willing to bet, based on your other misunderstandings , that you didn't understand this one either.
Zhang does not present any picture. Sapienti sat! The aggressive style prevent me to answer because I could say that based on your misunderstandings... We are in the field of relativity.







Just another misunderstanding: (7) has been obtained using the Lorentz transforms in expression (4). The derivation of the Lorentz transforms is based on Einstein's clock synchronisation.
Here our oppinions diverge and so I do not insist. Please do not send me to the Classic because I could send you to modernists




This is incomprehensible. Can you try again?
Ahh, I think I know what you are trying to say: do you really think that Zhang's formula doesn't apply for dn infinitely small? That there may be some magical lower bound to dn? dn is an infinitesimal quantity, therefore it is infinitely small.

I quote Zhang " We now assume that the n-th and the (n+dn)-th crests are received at the point O (i.e. at the same point in space,locality assumption, my remark). If I remember well from analysis very small means that during it nothing changes!
As I have mentioned in the previous thread the Doppler formula and its inverse contain the angles w and w'. Handling them we obtain the aberration of light effect which is not associated with clock synchrnization involving only initialization. How do you explain that?
Consider a scenarion in which the observer moves with constant velocity parallel to the OX axis at y=constant, the source being located at the origin. IMHO the period he measures is continuosly changing a fact not allways mentioned in the literature. Not taking into account the nonlocality at high periods we make errors!




I have tried to present Zhang's derivation with my comments. It leads to the same formula as phase invariance and LT do. How do you explain that fact? I think that it is the result of the fact that the derivation you like, obscures some interesting pecualiarities of the Doppler Effect. I know some modernits who consider that the use of the LT obscures the physics behind the studied effects. Discussing with me please avoid a personal address without to put in question my ability to understand the stuff we discuss. I could suppose the same thing about you. We are in relativity! I will no longer answer your comments if you do not give up that unpolite and offending style, a fact I have mentioned for so many times.

I invite people on the Forum to participate to the discussion. The stuff is interesting and all of us have to learn from it!

 

[nakurusil]

The time dilation formula (4) is a DIRECT consequence of the Lorentz transform for time. So, Zhang's derivation is a consequence of the Lorentz transforms. I hope you realize that you just proved my point.

In our discussion it is not important that he uses the LT. What he shows is that the Doppler formula holds only at very small periods!

Of course this is not true, you are misinterpreting his work.

I told you for many times that many authors derive the time dilation formula without using the LT.

1. So, the one that you claimed not to be using LT (Zhang's) turned out to...be using LT. Try another paper, please, you failed on this attempt.

They also derive the addition law without using them.

2. Please provide one from a reputable source after you prove your first point. You haven't done it yet. (see point 1)

I do not speak in terms of frequency but in terms of periods. The periods should be small enough in order to ensure that the velocity in the Doppler formula is an instantaneous one. That is the case in the classic derivation as well where the frequency in the phase is an instantaneous one and so not measurable.

3. Why makes you persist in this nonsense? It is clearly non-physical.

Of course and because the involved periods in the Doppler shift formula are infinitezimal dt(e) and dt(r) and so theirs inverses are infinite.

4. You realize that this is wrong, why do you cling to it?

Without crests there is no Doppler Effect! Einstein's standard derivation applies the LT to a single point of the space through which the wave propagates considering that there the observer could receive two successive crests, making the very small period assumption.

5. There is no very small period assumption anywhere in the description of the relativistic Doppler effect. There isn't any in the Zhang description, it is all based on your misinterpretation of his derivation.

 

[MeJennifer]

I will no longer answer your comments if you do not give up that unpolite and offending style, a fact I have mentioned for so many times.

I invite people on the Forum to participate to the discussion. The stuff is interesting and all of us have to learn from it!

Thanks Bernard.

By the way, I already lost my appetite in having any discussion with nakurusil due to his attitude here on PF.

 

[bernhard.rothenstein]

clock synchronization

Thanks Bernard.

By the way, I already lost my appetite in having any discussion with nakurusil due to his attitude here on PF.

Please stay here. Probably together with others we will convince him to do not mix scientific discussions wih offending people.

 

[bernhard.rothenstein]

Clock Synchronization

I postpone my answer until others will express their oppinion concerning the stuff under discussion.
If you think that you can convince me and as I see others in a dictatorial style (You told me that the Forum is not mine. Because we are relativists I could say that it does not belong to you.) simply stating that I do not understand things which are obvious and without giving any prove then you are in error.

 

[wisp]

Bernard

I doubt I’ll convince you, as you are an old fox set in your relativistic ways. But your posts are interesting and warrant courteous reply.

In response to whether you can derive the relativistic Doppler equation without using Lorentz Transformations, and without need of Einstein’s clock synchronization.
The answer is yes.
See equation set 9.6 and 9.7
http://uk.geocities.com/kevinharkess/wisp_ch_9/wisp_ch_9.html

The general Doppler equation (9.6) includes arbitrary angles for both source and observer with respect to ether. Clocks are initialized at origin t’= t=0, and thereafter do not need synchronizing.
The equation set produces a match for the relativity’s velocity addition formulae only if the observer and source angles are zero.

The equation set (9.7) matches relativity’s Doppler equation for an arbitrary angle when the observer’s speed through the ether is zero.

Regardless of whether you support ether concept, it’s fascinating that the derived general Doppler equation can mirror relativity this way.