Stefano, my friend,

Which frame do you think is the preferred frame?

With kind regards

Dear Sofia,

the TDE tells you that there is a body which moves more while another moves less in absolute sense. In the same way in a circular motion it is determined in absolute sense who is turning around.

All you can do is to select a local preferred frame of reference which can be considered inertial to a good approximation, that will be the one which moves less according to the results of the TDE.

Your lab is attached to an inertial reference frame (an abstract entity defined to proceed undisturbed at constant speed) till a certain extent which depends on how large is the resultant of the external (external "disturbances") and internal interactions (experiment itself) which determine its degree of non-inertiality.

Eventually you can get an Hierarchy of frames.

My dear Stefano,

You speak of other things than I speak. The preferred frame of which I speak (and Ilja too) is one single frame. It's not a frame we can choose, but a frame that the Nature fixed. Any frame in movement with this one is NOT a preferred frame. To understand what I say you have to be familiar with the so-called "Hardy's paradox". There is a very simple explanation of it in my

Article Hardy’s paradox made simple – what we infer from it?

This work shows that a conflict appears between the conclusions of two observers, each one traveling with an inertial frame, and the two frames being in relative movement with respect to one another.

Alternatively, but maybe less clear, you can see my posts in the thread

https://www.researchgate.net/post/QUANTUM_THEORY_VS_LORENTZ_COVARIANCE_Standard_relativistic_quantum_theory_seems_SELF-CONTRADICTORY_Any_idea_how_to_rescue_it2

But it is a lot to read.

With kind regards

Dear Sofia,

I can understand the conflict between QM/QFT, born with a preferred frame postulating a vacuum energy, and the implications of Special Relativity.

I would like to get rid of a myth about SR: Dirac did not harmonize SR with QM but harmonized QM with the high energy relation E2=E20 + (pc)2 (it can be also derived from SR some-how) which comes beautifully from relativistic momentum (Kaufmann experiments and gamma factor) and the work of a force, it is the extension of the conservation laws to high energies, it does not imply at all the SPACE-TIME of SR.

We have to understand where the two totally opposite views bring us :

SPECIAL RELATIVITY (LEYDEN lecture)

"Why must I in the theory distinguish the K system above all K' systems,

which are physically equivalent to it in all respects, by assuming that the ether is at rest relatively to the K system? For the theoretician such an asymmetry in the theoretical structure, with no corresponding asymmetry in the system of experience, is intolerable."

all the inertial systems are equal and I can make physics in all of them without any problem but such abstractions have to be used carefully.

LORENTZ LARMOR ELECTRODYNAMICS (LEYDEN lecture)

"As to the mechanical nature of the Lorentzian ether, it may be said of it, in a somewhat playful spirit, that immobility is the only mechanical property of which it has not been deprived by H. A. Lorentz. It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility. How this is to be understood will forthwith be expounded."

which tells us that there is one only preferred frame where the EM waves are supposed to run and the electromagnetic phenomena occur.

The Hierarchy of frames shown by the TDE, brings us to one only preferred frame eventually but it is not the one where we currently use for our experiments, it might match the CMBR.

This has for sure implications on the symmetries and the Hardy's paradox disappears, since part of Special Relativity which supports the relativity of simultaneity, the pain in the neck of Heisenberg, ceases to be valid.

Dear all,

I would like to point your attention to pages 76 and 77 of the famous book of JOHN BELL

Speakable and unspeakable in quantum mechanics

https://is.muni.cz/el/1441/podzim2017/FY2BP_TF1/um/Uceni_text_-_John_S._Bell_Speakable_and_Unspeakable_in_Quantum_Mechanics__First_Edition.pdf

in regards to the preferred frame of reference, to this paper:

"Mansouri-Sexl Test Theory: The Question of Equivalence between Special Relativity and Ether Theories "

http://www.ptep-online.com/2016/PP-44-17.PDF

there should be a mistake about its criticism on Mansouri, but the preferred frame concept remains.

Dear all,

The transverse Doppler in the case of blueshift cannot be derived from the LT, which are a group of transformation for which a redshift in one frame corresponds to a redshift in the other frame.

In other words the formula

a) f=f0 1/[(1 -β cos θ) γ] , the relativistic case for the "moving source", two dimensional, for θ=90 (TRANSVERSE condition) gives

f=f0 1/ γ TDE - redshift of the emitted frequency.

It is obtained with the LT.

----------------

The formula

b) f=f0 (1+β cos θ) γ, the relativistic case for the "moving emitter", two dimensional, for θ=90, gives

f=f0 γ TDE - blueshift of the emitted frequency.

It *cannot* be obtained using the LT.

-------------------

For θ=0 - the pure longitudinal case is relativistic as well

a) f=f0 [(1-β )γ]-1

b) f=f0 (1+β )γ

a) and b) are the same as c) f=f0 [(1+β)/(1-β)]1/2

In this case the motion is totally relative and the c) is a consequence of the LT.

---------------------

Hence IN-BETWEEN two inertial reference frames a TRANSVERSAL blueshift can never occur ...but at the same all experiments performed have a redshift and blueshift.

The blueshift occurs *also* for absorbers in a lab moving at constant speed (straight line), also while attached to inertial frames, it means that

1) either an object, even moving at constant speed in the lab, cannot be considered as being attached to an IRF (in that case it is automatic that the lab is the preferred frame)

2) or it is the concept of being "attached" to an IRF which deserves some more attention...

Comparison of New and Old Thermodynamics

1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.

2. New thermodynamics pursues universality, two theoretical cornerstones:

2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.

2.2. Hydrostatic equilibrium: applicable to gases and liquids.

3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.

3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.

4. See Appendix Pictures and Documents for details.

Dear all,

The transverse Doppler is the same in both directions according to LT (a group of transformations between IRFs) for which a redshift in one frame corresponds to a redshift in the other frame, same in the case of a blueshift.

a) f=f0 1/[(1-β cosθ) γ] , "moving source", two dimensional case,

for θ=90o it is f=f0 1/ γ Transverse DE - redshift of the emitted frequency.

From LT t'=γ(t-vx/c2) for x=0 it is t'=t/γ , by applying the inverse transformation it is t=t'/y

b) f=f0 (1+β cosθ) γ, "moving emitter", two dimensional case,

for θ=90o, f=f0 γ Transverse DE - blueshift of the emitted frequency.

From LT t'=γ(t-vx/c2) for x=0 it is t'=tγ by applying the inverse it is t=t'γ

-----------------------

The two formulas above do not match at all for θ0, so that it becomes compulsory to state which one of the systems is in motion.

At the same time it becomes contradictory to perform an inverse transformation and get the same result if an asymmetry a) or b) was previously postulated.

The two above become the same thing only when θ=0 which is the pure longitudinal case

a) f=f0 [(1-β)γ]-1

b) f=f0 (1+β)γ

a) and b) are the same as c) f=f0 [(1+β)/(1-β)]1/2

Only in this case it does not make sense to distinguish who is in motion and who is not.

The prediction of LT is redshift in both directions or blueshift in both directions also for the TRANSVERSE shift as if it were a LONGITUDINAL ONE, at variance with the experiments which never give the same shift in both directions.

The main point is that the INVERSE in the LT is not in agreement with the Physical evidence unless γ=1, which is the totally symmetric case.

The longitudinal RDE clearly prevents any possibilty to distinguish (as it occurs in acoustics), the motion of the source and the motion of the emitter... giving a unified well known and tested formula for the one dimensional frequency shift. (1-v)γ = 1/[(1-v)γ]

The transversal is natively bidimensional,

moving observer : (1-v*cos θ)γ and

moving source : 1/[(1-v*cos θ)γ] for θ different from 0.

for θ=90o

moving observer : γ

moving source: 1/γ

already tells us that for bidimensional cases there are different results, verified in labs, depending who is the one moving or the one stationary.

The second law of thermodynamics is incorrect. See figure below for details.

Dear all,

it does not matter that the emitter or the absorbers are *not inertial* inside the lab, like it is the case of blue-shift in ROTOR experiments. What matters is that photons are observed the same also in a Momentarily co-moving inertial frame (MCIF) , since the behaviour of oscillators do not depend on the intensity of accelerations since perfect oscillators are not supposed to be affected by acceleration according to the clock HP which has been experimentally verified.

Without reading through all the many referenced papers, let me ask, is the centrifuge measurement made with a single clock in the lab?

If so, then it should get a blueshift.

The Einstein results are only obtained when using a 2-on-1 clock measurement. Two or more reference frame synchronized clocks measure one moving clock.

The notated times when the clocks pass are elements of physical reality, and must be in agreement among all observers. Therefore a 1-on-2 clock measurement obtains a blueshift, and this is perfectly consistent with the LT, because the LT is derived only from the 2 on 1 measurement (as a thought experiment).

The centrifuge seems to be 1 on 1. I haven't thought about that. But it seems likely it is equivalent to 1 on 2.

The de Broglie frequency may be considered to be a clock. The de Broglie wave in the rest frame of the particle has infinite wavelength, indicating Einstein convention synchronization of the de Broglie oscillator at all points in space.

To a moving observer, the de Broglie wave is dis-synchronized giving a finite wavelength. The moving observer crosses clocks defined by the wave phase which are progressively advanced - like flying East across time zones - and thus measures a higher de Broglie frequency when moving past a particle.

See:

• http://mc1soft.com/papers/2014-LeadingClocksLag.pdf figures 5 and 6

• Article Common Pedagogical Issues with De Broglie Waves: Moving Doub...

  section 2 - origin of the de Broglie wavelength (de Broglie's thesis was not translated into English for a long time - between WWI and WWII the Germans were prejudiced against French research)

Dear Robert,

the detector in Kunding experiments is set in circular motion.

The result of the centrifuge are obtained also with a double application of LT, there is no problem.

What I tried to point you out is something quite different.

>

I know but this is not directly relevant to the transversal shift issue which I'm pointing out.

Caro Stefano,

First, I would like to qualitatively discuss the differences between the classical transverse Doppler (interactions free) and the frequency shift in rotor experiments. The former has been verified without any problem, resulting always redshift (time dilation).

The other one involves two phenomena: usual time dilation and frequency-shift (caused by interaction). Let us pay attention to frequency-shift during interaction.

The rotor experiments involve the centrifugal force (inertial force), whose action is like the gravitational frequency-shift. If the gamma emitter is at the origin, the gamma photon travels in the direction of the force, resulting blue shifted. If the emitter is at radio R (rotating) we obtain redshift. Rotor experiments are not symmetrical.

Do you agree?

Regards

Caro Hugo,

remember the clock HP Hugo, centrifugal acceleration or any kind of acceleration does not affect clocks direclty.

The redshift experiments were performed all in linear motion since it was comfortable to do and they did them in order to comply with the theory. The point is that the electron moves in the lab and it is not viceversa: the lab is a box, the center of mass of the lab is always still, does not change, while the point mass of the emitting electrons was accelerated.

SR does not imply that in between two inertial systems there is always a redshift, but implies that there is symmetry.

Have a look to the little movie.....

Caro Stefano,

1) What is HP? I'm sorry, Stefano, I do not know what you're talking about.

2) I have convincing arguments to say that interaction affects time (to discuss later).

Clock Hypothesys. it is what has been verified in experiments with muons for variation of their half life time..

Caro (and lazy) Stefano, why don't you write Hypothesis instead HP? Remember that I am too old to understand your "millennial" mode.

The clock hypothesis still is an assumption. There are experiments that confirm it, and experiments that contradicts it. Besides, the SR theory explains the gravitational shift effect, whose consequence is that during the interaction (photon-field) the temporal evolution (frequency of photons) changes. I agree with that and I think that it can clarify the transverse Doppler in rotating systems.

Caro Hugo,

which experiments contradicts it?? or rather show that acceleration is the responsible of time dilation??

Caro Stefano,

In your initial question you refer to several articles that contradict the clock HP.

If possible, it is VERY important to read this subject from Fock's book (The Theory of Space Time and Gravitation), chapter 14 (pp 41) and sections 61, 62 (pp 229/237).

If you do not have access to the book, I will try to send you the topics (scanned).

Caro Hugo,

"In your initial question you refer to several articles that contradict the clock HP. "

I don't see it...

"If possible, it is VERY important to read this subject from Fock's book (The Theory of Space Time and Gravitation), chapter 14 (pp 41) and sections 61, 62 (pp 229/237)."

I have the book...I will check the pages you refer to..

Caro Hugo,

I looked at those pages, and I've already read it in the past..they deal with equivalence principle and the twin effect.

There is nothing in particular against the clock Hypothesys no experiment is reported...

The muon ring experiment is in total agreement with that HP in any case, and actually it is not anymore an HP but a fact....

Caro Stefano, just an example:

“…the equation for proper time given in section 14

t = ∫ √(1- v2/c2) dt

Is valid only in an inertial frame of reference, but not in an accelerated one.”

--------------------------------------------------------------- Fock (page 234)

We must conclude that the detected frequency shift in rotor experiments, will not match the theoretical results obtained by usual LT (time dilation).

Caro Hugo,

yes, because it is a consequence of the Lorentz Transformations which are defined in inertial frames of references. If you follow this path acritically you will have to get rid of accelerations in SR and give up with accelerators, but as you know it is not the case.

In order to avoid to throw away the water with the baby:

a) consider that light does not care about accelerated frames or not, the emission and absorption processes can be considered events (due to their infinitesimal duration) hence at constant speed. The concept of the Momentarily co-moving inertial frame is not an extravagant option offered by Rindler...

b) the values obtained in the muon ring experiment is exactly given by the gamma factor, this confirms that such formula t = ∫ √(1- v2/c2) dt and it is valid for radial* acceleration. If you use that formula you should obtain the same values of Fock who wanted, for the sake of precision, to use the other, since it was not yet experimentally demonstrated that it works also in RADIAL acceleration.

c) series of experiments with radially accelerated muons have been performed with different radii at same squared speed, obtaining same half-life time, this certainly confirm the clock HP:

Given a radial acceleration ar the frequency of a clock fc is not fc(ar)

The argument of Fock is not incorrect but the way he obtains the TD in the clock paradox can be obtained also otherwise...

I think you are missing especially is the fact that in a Rotor you have to perform two LT at different speeds and obtain

dt'=dt''[√(1- v'2/c2)/ √(1- v''2/c2)]

Caro Stefano,

I agree with you. The muon ring experiment seems to be conclusive.

This article is interesting.

https://arxiv.org/pdf/1508.02339.pdf

The subject we are discussing about is very complex, mainly because of difficulties of required experiments.

Caro Hugo,

exactly: The lifetime of muons turning in the ring is equal to the lifetime of the same muons travelling in a straight line.

What determines the time dilation is the "potential energy", nothing else...

there is a particular type of "equivalence" between centrifuge and gravitation, nothing to do with the equivalence principle though, which by the way should be valid only as WEP...

Стефано Кваттрини

Предлагаю посмотреть WAVE NATURE OF THE TRANSVERSE DOPPLER EFFECT AND THE “RED” AND “BLUE” FREQUENCY SHIFT ANOMALY IN AN ELECTROMAGNETIC WAVE FROM A MOVING RADIATION SOURCE Kuklin A.V., Kuklin V.A. TECHNICAL PHYSICS. THE RUSSIAN JOURNAL OF APPLIED PHYSICS . 2019. Vol.64. №1.Pp.111-115

С уважением

Владимир Куклин

Владимир Куклин

do you have description of experiments performed?

Dear Stefano,

russian scientists have a whole history for this.

Addendum: availability of the Russian original version:

Article Wave Nature of the Transverse Doppler Effect and the “Red” a...

Thanks for this interesting paper, Vladimir.

Is the English version also somehow available?

Best, Joachim Domsta

Стефано Кваттрини , Иоахим Домста,

Все наиболее известные экспериментальные данные до скоростей 0,05 С использованы из ссылочных материалов данной статьи.

Русская версия в свободном доступе. Английскую версию издательство или редакция журнала судя по их письмам в свободный доступ ограничили.

С уважением

Владимир Куклин

Владимир Куклин,

Thanks. With regards, Joachim

PS: The English translation by my browser of the last sentence:

"The English version of the publishing house or the editorial board of the magazine, judging by their letters, was freely available."

I think there is an error. Shouldn't it be at the end:

". . . , the free access has been restricted."

or something like this? (just checking my Russian:) JoaD

Иоахим Домста,

Да Вы правы: -свободный доступ английской версии закрыт. Чья это инициатива издательства или редакции не могу,

С уважением

Владимир Куклин

Stefano Quattrini

Sir, I would like to understand it in simple words, and what is the conclusion.? So that I could devise something......thankyou !

Vladimir,

You have a right to send this copy to RG.

Dear Dinesh Kumar Maurya

the conclusion is that Lorentz Invariance is only a very particular case not a general one.

Stefano Quattrini

Sir, make a summery of your findings and don't tell me exact values otherwise it will be a case theft, although I don't want it, what was the problem with Lorentz Logic, I just comprehend it like this

1) there is no problem in longitudinal Doppler effect ok only data will be not matching.

2) all the problem are with transverse Doppler effect (which in fact very small in extent) you can not see it as you are proceeding under relativity.

3) whenever we measure whatever way it does not matter how we perform the experiment, measure contributions comes from longitudinal Doppler effect!.

just correct me in this concern, if I am saying something else. , thank you !

Dinesh Kumar Maurya

you wrote >>1) there is no problem in longitudinal Doppler effect ok only data will be not matching >>

1) longitudinal Doppler works as expected, no problem with that. LDE is one-dimensional and reciprocal, it is indeed impossible to distinguish who is approaching to whom (departing from whom), it does not make sense. It is well known that v/v0 = (1+beta)gamma = ((1-beta)gamma)-1 by using the direct Lorentz transformation or the inverse the same is obtained.

There is reciprocity of behavior, symmetry..

2) there are issues with the TDE instead. Lorentz invariance predicts that also for TDE there is a reciprocity, a symmetry such that two inertial observers will see the atom radiation emitted from the other redshifted in the same way....

this cannot be reproduced in labs and is at variance with the clock HP which has been experimentally verified.

not at all, although it is almost always the largest contribution.

Stefano Quattrini

ok, now I understand the problem is with TDE that it is not reciprocal (one sided, asymmetric)......hoping soon.

>>not at all, although it is almost always the largest contribution.

(clarify.....perhaps again missed it???)

thank you for telling the experimental truth.

Dear all,

for the problems of LT there is an alternative...

https://www.researchgate.net/post/The_Tangherlini_Transformations_do_not_have_the_incoherence_of_Lorentz_Transformations_why_arent_they_used_instead

Dear Stefano Quattrini ,

you are stating (not for the first time, which means it is your honest opinion) that

"Lorentz invariance predicts that also for TDE there is a reciprocity, a symmetry such that two inertial observers will see the atom radiation emitted from the other redshifted in the same way.... "

After my and your discussion within the thread "What Einstein do..." I became convinced, that the source of the alleged contradiction related to the TDE is the implicit assumption, that the following beams coincide:

1. the beam tranversly reaching the detector(=absorber) when the detector in in motion and the emitter is at rest

2. the beam emitted transversally leaving the emitter when the detector is at rest and the emitter in motion.

As a matter of fact, they do not coincide, which can be obtained *) by the Lorentz transformations.

Best regards, Joachim

*) here was"equally by the Galileo Galilei as well as" - now deleted, sorry. A more precise setting of the last sentence in preparation. JoaD

Dear Joachim,

thanks again for your investigation which is quite valuable because you used the postulate of the constancy of the speed of light and drew the results, although I cannot understand how you consider the equivalence of the IRFs which is integral part in SR.

Galilei, whom you mentioned, applied the principle of relativity of motion of IRFs.

how do you determine in SR that the detector is in motion?

Every inertial observer is the same in SR. From the point of view of the observer, which is what counts in SR, the thing that tells him that he is moving and not the other objects at rest in other IRFs, is the fact that he is non-inertial (he detects also an acceleration).

In my problem I've chosen to involve only inertial observers. How would you justify in SR in such case that it is the observer to be in motion?

this is the case when the red-shift has been detected in the experiments and it matches also with the circular motion where there is red-shift as well for the observer always at rest. Being in the rest-frame of the detector I can say that the emitter is in motion.

never said that they match, the main point is that your analysis is based on instant of emission and instant of detection which is correct on that side and the fact that both the emitter and detector are point like objects.

Regarding the emission since we are considering a EM wave the source has to be considered "pointlike", regarding the detection It is preferable to choose a surface where the beam is shot vertically every-time, the difference between the time of detection and the time of emission is just t=h/c where h is the distance of the parallel platforms.

In SR as in Galilean mechanics unless non-inertial motion is involved, you are not authorized to say that you are moving, if you are at rest on a IRF.

And even non-inertial motion does not solve the problem, Stefano...

We must realize, that motion is not relative to frame, but body.

Dear Stefano, thanks for your response which - however - misses the point of my statement. According to my statements the BEAMS do not coincide, and you have read my claim as saying that the EMITTER and DETECTOR coincide. Please reread my last answer.

However, much more important for me is your opinion about my explanation of the continuous (non-rapid) change of the ratio of frequencies for the moving emitter - first along a straight line and after reaching the closed distance from the detector - beginning the circular motion.

Dear Joachim,

I don't know where you deduce that fact that I said that the beams coincide. They actually don't.

In addition the pointlike observer is a non necessary assumption, because you can imagine that each platform is an "extended observer".

I would be very grateful if you could attach your script again and add the case of the observer at rest, so that Eugene and others can see it, because it is a very good starting point for this discussion which can be enriched with images.

The key point here is to put at work the PURE relative motion as I said.

In your derivation you have a third observer at rest who measures the speeds, since you put vE=0 or vD =0.

The pure relative motion of the two IRFs in Deep space travelling in parallel directions at distance H, can be estimated by exposing

radars to esteem the speed. In that situation the average speed of light of back and forth is c, as per experiments, hence that configuration should be considered solid.

In the frame of IRF1 the other goes at speed v, in the frame of IRF2 the other goes at speed v or -v according to which system of coordinates we choose.

In that case IRF1 sees an emitter going at speed v in its own rest-frame and emitting normally to its direction of motion hence the freq-shift should be as per experiments for moving emitter 1/gamma.

I wait a feedback from this

Dear Stefano, I think that you can express your opinion about the following description of the case moving emitter implied by the assumption vD=0:

fierst part of Part D.

In the case of emitter moving along a straight line parallel to the x axis at distance h with velocity vE till instant t=0 , the detector perceives the Doppler blue shift decreasing continuously till some instant between 0 and h from the value γE*(1+vE) (as t→ -oo) to 1, and afterwords to the instant h still continuously decreasing (perceiving red shift) to the value 1/γE .

I cannot explain it in simpler formulas, until it is clear that the beam emitted at t=0 arrives at the detector at t=h

PS. The last picture says nothing to me, sorry. JoaD

Dear Stefano,

Let us agree at least wrt to the fact that any orthochronous LT maps any positive light-cone onto another positive light-cone and any negative light-cone onto negative light-cone. Therefore the emitter becomes again an emitter and the detector becomes a detector in new coordinates. Moreover, the ratio of frequences fD/fE for the beam joining an event of emission on the emitter world-line with an event of detection on the detector world-line remains unchanged after the change of coordinates according to any orthochronus LT. Which means, that the equivalence principle is not broken with respect to the Doppler effect.

Your claim:

It is impossible to find a pure gamma blueshift in a lab for emitters in motion!!!!

is invalid unconditionally, since, as you agreed many times, the effect depends on the angle of emission.

The blue shift would be perceived with ratio equal gamma for the beam which is measured at the instant when the emitter position is “over the head of the detector”.

The red shift would be perceived with ratio equal 1/gamma for the beam which is emitted at the emitter position is “over the head of the detector”.

Best, Joachim

Дорогие коллеги

Стефано Кваттрини

Йоахим Домста

Мне кажется, что Вы увлеклись обсуждением результатов математической операции линейного векторного преобразования Лоренца. При этом забываете, что причиной поперечного эффекта Доплера является не эта математика, а физика распространения электромагнитной волны.

Я уже предлагал Вам посмотреть статью, где мы собрали все упомянутые Вами работы по экспериментальному измерению поперечного эффекта Доплера и более поздние данные ( Победоносцев Л.А ) при скоростях до ветта=0,05. Даже при таких скоростях видно нарушение инвариантности. Кстати Айвс, ОН; Стилуэлл, и Мандельберг, Хирш I .; Виттен, Луи измеряли Доплеровский сдвиг, в отличии от Победоносцева Л.А , при угла близких к продольному Доплеру.

С уважением

Владимир Куклин

DOI: 10.21883/JTF.2019.01.46975.135-18 (Журнал ЖТФ)

DOI: 10.1134/S1063784219010195 (Scopus.com)

Dear Joachim,

>

The Longitudinal Doppler prevails while the angle between emitter and detector increases, never said the opposite. But this is not the point since what I've been looking for is always the situation where the beams are emitted normal to the direction of motion, which is the case of the "pure transversal".

better to find an agreement on the terms, I would better speak about the equivalence of inertial frames (the Equivalence principle is usually used for the gravitational and accelerated mass).

Sorry for the misinterpretation, but for pure gamma blue-shift I meant the one which is originated by the motion at right angles.

the blue-shift is detected as gamma for a moving detector

receiving the beam normally to its direction of motion

while the red-shift is detected as 1/gamma from a static emitter, emitted normally to its direction of motion, this is certainly true at least for circular motion.

Dear Stefano,

about the ratio of the DE for the perpendicualr directions we were both long time ago in agreement.

Let me recall again, that my contribution is aimed to expalin your doubt that due to some necessary symmetry allegedly implied by properties of the LT , the red shift with 1/gamma would appear suddenly after a blue shift with ratio gamma just because of changing the rectilinear motiion into the circular. My question about this is:

QUESTION: Do you accept that the description of the phenomenon within circumstances ddetermined in part D explaines sufficiently well, that according to SR modelled via Minkowski space-time there is no sudden change of the ratio in the Doppler Effect?

A plain answer YES would be the best:-) If NO, then just please tell at least one place of the explanation which is not acceptable.

Best, Joachim

PS. For your convenience my explanation named D. is repeated below without changes (boldfacing is important to stress the continuity of the changes!):

Part D.

In the case of emitter moving:

- first along a straight line parallel to the x axis at distance h with velocity vE till istant 0

- and next along a circle with center at the origin of radius h, sending signals to the centrally posed detector,

the detector perceives first: Doppler blue shift decreasing continuously till some instant between 0 and h from the value γE*(1+vE) (in the limit of t→ -oo) to 1, and afterwords till the instant h still continuously decreasing (perceiving red shift) to the value 1/γE . And from this instant beginning, the red shift becomes constant with the ratio 1/γE.

Dear Vladimir Kuklin,

Thanks for your comment, which I would appreciate even more, if I can get a better undertanding of what is presented in your paper in relation to the current discussion. My aim was and is to explain the alleged contradiction of the formulas with SR within Minkowski model of the space-time, which was annouced by Stefano Quattrini within other thread *).

1.

As a matter of fact your formula (7.VK) is in exact coincidence with the one I am giving within my notes *) as formula (7.JoaD) (YES!) under the condition that vD=0, AND by neglecting γE ). This means that

- there are two ways of obtaining the well known formula ***): the one leading to (7.JoaD) via pulses sent from the emitter to the detector and to (7.VK) via EM waves emitted isotropically;

- (7.VK) is not relativistic since it does not depend on the proper time relation to the time of the IRF.

- (7.JoaD) is a little bit more general than (7.VK) since takes into account also the speed of the detector.

2.

My reading stopped at (8.VK) temporarily. One of the discouraging reasons is the following contradiction of the content of two claims: - on page 138 you have written:

где Rt ' =0 = r — радиус вектор точки наблюдения в момент начала движения заряда e0,

- and on the next page 139 directly below formula (7) you have written

В начальный момент времени t′ = r/c

3.

Let me stress additionally **) , that if the pure transvesal effect is to be considered, then it is not at the instant r/c (please comment this particualar objection separately, if possible, since I am not quite convinced about its (of the doubt!) correctness).

Best regards, Joachim Domsta

-------------------------------------------------------

*) https://www.researchgate.net/post/What_does_Einstein_do_in_the_Electrodynamical_Part_of_his_1905_SRT_paper

**)I am sorry that I am commenting before I have read the next parts of your paper; but this is my way of reading till the first inconsistency:)

***) recalled by Stefano Quattrini as follows: "The Doppler effect for detector at rest fd/fs mov.s =1/{[(1+v/c cos θ)] γ}"

(though one should neglect the relativistic effect, represented by the presence of γ if the coincidence with (7.VK) is to be obtained)

Dear Joachim,

yes,

a) a system at first in circular motion, naturally goes in inertial motion, no more subject of external forces (also the way around).

b) In rotors (at right angles) it is experimentally verified that the rotating observer sees a blue-shift of the frequency emitted: γ(v) where v is the speed of the observer in the IRF of the emitter.

c) According to LT, when in inertial motion, any system detects incoming radiation, at right angles with the velocity of the IRF of the emitter, red-shifted, 1/γ(v') where v is the speed of the emitter in the IRF of the observer (Einstein 1905 Doppler of moving emitter).

Conclusion: a sudden change of the frequency detected at right angles, from a certain γ>1 to a 1/γ'

Dear Stefano, don't you see that answering yes in the fist part and next displayin the contradicting pseudoexplanations cannot satisfy my expectation about the scientific discussion.

Moreover, don't you see that requiring

SQ: let's stay only in the case of right angles

you are falsifying the sequence of events, that before the angle is 90o it is OBVIOUSLY changinging continuously from 0 which means that before we have blue shift continuously decreasing to no effect which turns into the red shift?

The problem is at WHICH instants the changes become crucial, which I have listed in statement D.

Joachim

Dear Joachim,

>

I understand what is the reason of the point of disagreement:

you use an observer point-like always at the same position, it is obvious that with such configuration the angle changes.

I instead imagine to be on a long platform, same IRF1 but different positions inside such IRF1, to have the possibility while at rest in IRF1 to detect the emission at right angles from the other platform, as in the figure.

it seems crucial for you, for sure your result comes out obvious by using an additional variable which instead is fixed.

To make it very simple, what would see the moving observer at speed v in IRF0 when it is in position C1, when it detects the radiation incoming from C?

Dear Владимир Куклин ,

according to what you said in Russian, you affirm that you noticed that even with not so high speed with beta=.05, a violation of the Invariance occured, do you confirm?

"Witten, Louis measured the displacement of the Doppler, at variance with L. Pobedonostsev, at an angle close to the Longitudinal Doppler. "

Has it been well translated from your paper?

This is not what I'm interested in, because we all know that the RDE longituinal perfectly embodies the invariance.

Dear Stefano,

As you realize, this not the problem with detector at rest. But if you need my answer, here we are: fD/fE=gammaD which agrees with the presented formulas for vE=0. Interesting what you need it for?

Dear Jochim,

>

which one?

In the one I presented the detector is not at rest, but can we say according to relativity of motion that one of the two systems is at rest when you have two IRFs?

I repeat, referring to the previous figure, to make it very simple:

what would see the moving observer at speed v in IRF0 when it is in position C1, when it detects the radiation incoming from C?

According to your derivation the ratio it should be gammaD, and no discontinuity should occur then since previously it was gammaD as per experiments.

Am I right about what you want to affirm?

Now being your answer that, hence no paradox, the system should in-fact behave in the way it is depicted in my figure, since in that case the continuity of behaviour is complied.

Now it is the time to clarify if the LT really predicts that behaviour since such behaviour has nothing to do with the reciprocity/symmetry due to the relativity of motion of IRFs in general.

I repeat again: can we say according to relativity of motion that one of the two systems is at rest when you have two IRFs.

I ask a quite provocative question...

What is the discriminant for the body at C1, not accelerated, to understand that it is

at rest in a IRF2 and instead is the IRF1 to be in motion?

Дорогие коллеги

Стефано Кваттрини

Йоахим Домста

Безусловно, что рассматривая только longituinal RDE можно увидеть его соответствие Лоренц-преобразованию. И это очевидно, поскольку его классический вид одноосный. Как показали эксперименты Л. Победоносцева (угол 77о) даже при низких скоростях близких к бета = 0.05 использование гамма фактора Лоренца не позволяет получить адекватное значение красного и синего смещения частоты для углов отличных от 0о и 180о . А Айвс, ОН;Стилуэлл, измеряли Доплеровский сдвиг частоты при угле 7о , Мандельберг, Хирш И.; Виттен, Луи измеряли при углах 0о и 180о. Отсюда и подтверждение инвариантности по экспериментам последних.

Здесь возникает крамольный вопрос, что же это за теория когда продольный Доплер инвариантен, а поперечный нет?!

На мой взгляд, главное противоречие возникает поскольку Лоренц-преобразования и концепция Минковского ограничиваются плоским волновым фронтом исследуемой электромагнитной волны.

Поэтому и формулы (7.VK) и (7.JoaD) совпадают только для угла 0о и 180о .

С наилучшими пожеланиями.

С уважением

Владимир Куклин

Dear Stefano Quattrini and Vladimir Kuklin,

Before I made a detiled answer, let me sent a 1 page explanation why the transversal DE differs for Detector and the Emitter at rest, depending on the LT.

Best, regards, Joachim Domsta

PS. (7.VK) и (7.JoaD) совпадают для all angles between 0о и 180о (not counting the gamma factor).

Dear Владимир Куклин ,

I would say that the main contradiction arises because the LT within the Minkowski space-time although trying to give an answer to the full relativistic motion, do account for results in pure relative motion which cannot exist at all.

PROBLEM: For example imagine two parallel travelling platforms A and B getting close somewhere in deep space with attached IRFA and IRFB, whose reciprocal speed if measured with a radar method as v0, (is the only possible so far), like in the figure I attached and the bodies are known to approach or depart. The longitudinal RDE works perfectly and does not need anything else other than pure relative moving bodies.

On the contrary the pure transverse, whose value is determined with the use of the LT as 1/gamma(v0) in the case of radiation incoming from A to B, by following exactly the reasoning of Einstein 1905, has to be considered carefully.

v0 in fact, if referred to a third observer, could be 0 for A and v0 for B, or for A about 1/2 v0 and about -1/2v0 for B (or whatever makes up something close to v0 as the sum of the values).

In such cases by applying also the formulas of Joachim, totally different results for the different configurations would be obtained, meaning that the original Physical PROBLEM does not have one solution, it is undetermined or ILL POSED, while a result from two real platforms in deep space would give an actual measured value which does not depend only on their reciprocal speed for sure.

One degree of freedom is missing in the LT.

The transformations were originally conceived by Lorentz (then modified by Poincarè) in a preferred frame (which he himself thought the absolute one as the Aether). What is in fact known from the RADAR is just a difference of speeds v0 , if we perform the experiment in our lab we implicitly associate the Preferred frame to the LAB where we perform the experiments and know what platforms is at rest in the lab or not or what is their actual speed in the LAB.

Without the implicit assumption of the preferred frame of the LAB, where we actually make experiments, in the case of the Transverse Doppler, the problem is simply "a-priori" *not determined*.

The local preferred frame of the lab plays the role of a boundary condition, determining clearly, like in the case of the circular motion, what is moving and what is at rest. To conclude, In a pure relative motion case the result is undetermined for the pure transverse doppler, so that the relative motion in general loses its meaning for good.

In other words it is quite evident that the Lorentz-Invariance is a concept valid for the one dimensional problems where there is symmetry but it is untenable for problems which have more than one dimension like the transverse Doppler which is INTRINSICALLY ASYMMETRIC.

Four-Vectors (4-Vectors) & Lorentz I n v a r i a n t s of Special Relativity: A Study of Elegant Physics The Ultimate Four-Vector & Lorentz Invariant Reference

The Four-Vectors (4-Vectors) and Lorentz I n v a r i a n ts of Special Relativistic (SR) theory are fundamental entities that accurately, precisely, and beautifully describe the physical properties of the world around us. While it is known that SR is not the "deepest" theory, it is valid for the majority of the known universe. It is believed to apply to all forms of interaction, including that of fundamental particles and quantum effects, with the only exception being that of large-scale gravitational phenomena, where s p a c e t i m e itself is significantly curved, for which General Relativity (GR) is required. The SR 4-vector notation is one of the most powerful tools in understanding the physics of the universe, as it simplifies a great many of the physical relations.

SQ: In other words it is quite evident that the Lorentz-Invariance is a concept valid for the one dimensional problems where there is symmetry but it is untenable for problems which have more than one dimension like the transverse Doppler which is INTRINSICALLY ASYMMETRIC.

Let me guess that you are expecting the symmetry in the following form:

The following two ratios for the transversal DE must be equal

The ratio of fD/fE when the detector is at rest and source moves inertially on a line NOT containing the detector with velocity v

and

the ratio fD/fE when the emitter iis at rest and the detector moves inertially on the line NOT containing the emitter with velocity v

If this is your basis, then it is unjustified.

First -

despite your claims - the Lorentz transformation explains the substantial difference in rigorous calculations, see my last display specially for you written with great attention to be as precise and complete as possible

https://www.researchgate.net/profile/Joachim_Domsta/post/According_to_performed_experiments_can_the_transverse_Doppler_in_inertial_motion_comply_with_the_Lorentz_Invariance/attachment/5da25bd9cfe4a777d4e5c8af/AS%3A813317593509888%401570921433127/download/DopplerTransv.jpg

Also my former calculationsa re rigorously performed according to the rules of SR with correct use of the Lorentz transformation. Your statement: the Lorentz-Invariance is a concept valid for the one dimensional problems is entirely off any reasioning; the pictures not supported with calculations (deriving formulas) cannot be accepted as a proof, since the passage from one to the other does not take into account that the instants of emission and absorbtion in any IRF are not the same, unless the paths intersect. Moreover, you are forgetting, that the Lorentz boosts DO NOT PRESERVE ANGLES in the space parts. (among Lorentz transformations only rotations of the space part (without any modification of the time axis) preserves the angles. Therefore my last attachment is devoted to rigorous transformation of the end-events of the beam which is normal to the trajectory of the detector into the endevents of the beam in coordinates when the detector becomes at rest. it is shown in the bottom that the new section of the beam is NOT normal wrt the trajectory of the emitter.

Next -

in the first case the object being at rest is WAITING for the signals,

while

in the second case the object at rest is SENDING the signals,

These are the indications of discrepancy of the two cases you have asked couple of times. Hence the circumstances are not the same which invalidate your reason to state breaking of some symmetry which is not justified.

Independent of what you mean about my trials, they were made honestly, with greatest possible accuracy, repeated many times from different aspects, and I am now closing my discussion related to the pseudo-paradox.

Best regards, Joachim Domsta

JD:

For the 10th time, can you state in pure relative motion at constant speed, who moves and who is at rest?

You have already put asymmetry in the problem, you configured yourself in those sentences as a third observer who judges who moves and who is at rest.

Please stay in one of the platforms and check what happens, the LT are relations presented and born as relation between TWO IRFs, not three.

A general way of working from the transformations relying only on the relative motion (RADAR) but this seems to be impossible.

What is the result of the two generic platforms for which only the relative speed is known, one emitting on the other one?

According to Einstein is always a red-shift.

this means that, according to LT, if A and B are emitters going at constant speed in IRFA and IRFB, emitting at right angles with the direction of the velocity of the other platform (which is possible), the beams *will not be* normal to the platform they are departing from.

The LT models the behaviour of light as drops of rain which do not fall straight on a moving body, but they compose the relative motion, this is what is called relativistic aberration...

This implies that the difference of velocities of the two systems, in any case, translates in a longitudinal component of the Doppler.

There would be no way to get rid of it between moving platforms.

In circular motion, whatever the speed of the observer and the position of the emitter at rest, the result is always gamma, there is no aberration, it is experimentally verified also.

In the other cases of motion which is not circular the result is quite different from the pure gamma.

Again, this would imply a non trivial discontinuity of behaviour of the perceived light in passing naturally from circular to rectilinear motion which Physically cannot be present.

Dear Stefano,

Part I. of October 13

unfortunately your speach is inconsistent and not sufficiently precise. The BASIC two, though not the only issues are the following:

1.

first you are saying that only relative motion counts, and then you are distinguishing the case like this:

SQ: whatever the speed of the observer and the position of the emitter at rest,

At rest with respect to the third party? or with respect to the detector?

2.

Which beams are you taking into account, at which position are then the platforms?

Part II. of October 13

When talking about my way of derivation - it is consistent with the following understanding which you opposed so strongly:

the Minkowski world is a space-time which admitts different IRF-s. In each IRF the events possess their coordinates, which when passing to another IRF we need to recalculate by a siutable Lorentz transformation. Your platforms each has its own equations of motion which depend on the IRF. In some sytem of coordinates (=IRF) the platfom may be at rest and wrt to another system it can move (then with a constant vector velocity). EACH light beam connecting your platforms joins a particular event of emission on the world line of the emitter with the event on the world line of the detector. THE IRF IS NOT AN OBSERVER! IT IS JUST A BOOKKEEPER KEPT FOR CALCULATING THE MUTUAL RELATIONS BETWEEN EVENTS ASCRIBED TO OBJECTS. THE OBJECTS OF THE DOPPLER EFFECT ARE MOVING POINTS MOVING SUBLUMINALLY AND LIGHT-BEAMS LYING ON LIGHT CONES. THESE ARE CHARACTERIZED BY EQUATIONS OF MOTION WHICH CAN BE CONSIDERED IN ARVITRARY IRF AFTER SUITABLE CHANGE OF VARIAVLES ACCORDING TO A LT, e.g for calculating the coordinates of emission and detection of a beam in the space-time.

The LT invariance means that for a given PARTICULAR beam the ratio of frequences is independent of the coordinates wrt which it is calculated. The following inference is false in general: if a beam and a stright line in the space-time after projection onto the space part in one IRF are perpendicular, then this remains true after changing the IRF, as I showe in my last attachment.

Part III. of October 13

Sorry, but if your understandig is still different than the above, and if your explanations remain restricted to pictures without complete data related to all objects involved into the phenomenon, then my further participation seems aimless.

Best regards, Joachim Domsta

SQ In such cases by applying also the formulas of Joachim, totally different results for the different configurations would be obtained

Not true, they are only different from those expected by Stefano, who declares that the fD/fE ratio must be the same for circumstances which are different and only sound like they were the same.

Basic error: the LT does not preserves angles between straight lines after their projection from the space-time onto the space part, since the result of the projectio - EVIDENTLY - depends on the IRF used for the partition into the pure space and pure time subspaces, unles the LT is the rotation of the space part (i.e. without varying the time axis).

Dear Joachim,

you forgot to specify circular motion, this is important and is experimentally verified. In that case it is clear who is in motion, since

the moving body feels acceleration (this is re-known). For sure in a pure Kinematical analysis this does not come out, this just to make clearer the limitations of the kinematical analysis.

I agree and never said that!!! What is possible to do, implicit in the drawings I presented, is to have platforms to which IRFs are attached and to place observers all over the platform, this is the usage in Physics.

of which under the relativistic picture they move or are at rest according to the view point.

Let's try to find the solution of the "symmetric platform problem" step by step instead of saying phrases to the air.

a) With the RADAR (experimentally proven) method, the reciprocal normalized speed beta=v/c between the platform A and B

to which IRFa and IRFb are attached is detected.

b) by defining a positive direction of the speed (from left to right), if Platform A sees Platform B moving from left to right, then B goes at speed beta while A goes for B at speed -beta.

d) let's apply your derivation in Eq.(7JoaD) to this case: first it is γD= γE due to the previous assumption.

By trivial algebra it is: fD/fE =1 (1)

Which is what it should be expected in a symmetrical problem, one sees the other like the other sees one.

e) Now A is at rest in a LAB, this means that A and B continue to measure beta with their radar, but vA=0 and VB= v , the result have to be the same...but now B is in motion in the lab, by considering the emitter at rest as in your (9JoaD) :

vE=0, fD/fE = γD(1- beta2 tD/(tD-tE)) which

for tD=0,

fD/fE = γD (2)

the results shoud be exaclty the same if only "relative motion" counts, but as you can see:

Either your derivation is ok for A and B in "true relative motion" Espression (1) or it is valid for a motion with a preferred frame as in the equation (2). Since in the II case there is experimental verification, the (1) has to be rejected as a general result.

The invariance as you can see is gone, the final result of what is going to be detected, depends on the chosen "status" : the fact to be able to establish previously what is in motion and what is not (DYNAMICS beyond a pure kinematic view of the transformations)

Two generic platforms do not exist in nature, they physically come from somewhere and the result is one but not pre-determinable only with the relative speed.

The result of fD/fE =1 is a trivial case when two trains have opposite speed in the embankment of the station (PREFERRED FRAME) or the emission from opposite sides of a rotor (Experimentally verified). Hence for the transverse Doppler, the symmetry occurs only in a trivial case, hence the symmetry does not exist.

Yes, It is as I said it in my previous post, always according to the LT based on the constancy of the speed of light.

This, I also said, brings inevitably to the discontinuity of behaviour.

ARE YOU AWARE THAT YOU ARE IMPLICITLY USING THE CONCEPT OF WHO IS IN MOTION AND WHO IS NOT BY SETTING YOURSELF AS A THIRD OBSERVER? if not the matter gets serious..

SQ: let's apply your derivation in Eq.(7JoaD) to this case: first it is γD= γE due to the previous assumption.

you are not applying the derivation but wrongly applying the formula derived correctly;,

In that case please, apply it correctly to "pure relative motion"!!!

I REPEAT:

Please stay in one of the platforms and check what happens, the LT are relations presented and born as relation between TWO IRFs, not three. It should be a natural way of working by relying only on the relative motion (RADAR) but this seems to be impossible.

Remembering that the result should be the same for both parts due to the group of transformations and should be either RED-SHIFT or which is more credible, the problem is UNDETERMINED.

Dear Stefano,

There is nothing like the pure relative motion which considers simumultaneously the speed of a wrtr b = v and tthe speed of b wrt a = -v. At least I no not know the corresponding equations of motion.

I REPEAT: Iam using according to ANY irf the motion of all objects. The definition of transversisy is IRF dependent as my maanuscript shows. I do not know any

Best Joachim

Dear Joachim,

The RADAR which is longitudinal Doppler, whose behaviour also LT predict very well is "pure relative motion" , a relation between two inertial frames only, full stop. In that case it does not make sense to talk about at rest or in motion and the result you get by putting one at rest and the other in motion is the same as considering the way around or both moving, the only thing which counts is the relative speed. Both of the IRFs see the same thing, a RED-SHIFT or a BLUE-SHIFT according to their reciprocal speed a perfect implementation of the symmetry.

The transverse Doppler in the same situation is not independent on the actual status of motion of the bodies at stake. It is a generalisation of what occurs for circular motion where it is clear that the rotor moves more than the axle in absolute sense (try to average the square speed in a period of rotation and you see that from any IRF the averaged squared speed of the axle is always lower than the averaged squared speed of the rotor in a period of rotation).

So the nature of the two is totally different. There cannot be symmetry for the transverse since it cannot be defined by the sole relative speed of the two IRFs as you had the chance to notice.

If platform A sees a Red-shift of incoming radiation from platform B at right angles, B has to see a BLUE-SHIFT of the radiation incoming from A at right angles.

CONCLUSION

The group of transformations hold good for the longitudinal Doppler, do not hold good anymore for the transverse. In a pure relativistic/symmetric scenario where the Galilean Transformations hold good for simple mechanics relative motion , for the same scenario the LT with transverse shifts, either cannot be defined by the sole relative speed or they predict by the symmetry a red-shift in both ways, which would be impossible to reproduced in a lab since it produces discontinuities of behaviour.

The derivation proposed by Joachim holds good according to the performed experiments but it is based on a third observer, it relies on additional information: what is at rest and what is in motion at constant speed, which is at variance with the equivalence of frames of reference, in agreement with a "local preferred frame".

JoaD's derivation seems not to be able to provide an answer about the case of a pure relative motion and is right, since such problem is an ill-posed problem.

Best

SQ: The derivation proposed by Joachim holds good according to the performed experiments Thank you! SQ: JoaD's derivation seems not to be able to provide an answer about the case of a pure relative motion . . . . Right, the reason is that there is NO such notion like "the case of pure relative motion".

SQ"... since such a problem is an ill--posed problem . . . "

Which problem? The problem I have correctly explained within my two manusripts is well posed.

JoaD

Dear Joachim,

>

in principle there should not be, but you have to admit a local preferred frame of reference and get rid of symmetry and in-variance as well, then.

The pure relative motion is just a relation between two inertial frames and it is what transformations are all about... Galilean transformation implement in their scope of work that "regime". Galilean transformations do not need a local or global preferred frame of reference to work but they can also cope with that, it does not make any difference, the results are the same (in their low speed scope of work and infinite speed of signals).

Lorentz Transformations can only in the one dimensional case and have even higher relativity implementation than GT...

But since their inverse does not work in the case of the pure Transverse doppler which is natively bi dimensional, in inertial motion, they simply have to be replaced.

That is why the Tangherlini Transformations are way better than Lorentz'

SQ: The pure relative motion is just a relation between two inertial frames and it is what transformations are all about...

Let me repeat, that I do not know the definition of "pure relative motion".

JoaD

Dear Joachim,

it is relative motion without any other reference either than the reference frames which are in relation. The one which Einstein always used : "take two Inertial frames of reference" (from nothing...). For him was enough this arrangement with the constancy of the speed of light to derive the LT in 1905 and the relativistic Longitudinal Doppler, unifying the moving emitter and the moving source.

It was enough to find the relativistic Doppler effect in two dimension for the moving source which is just the classic divided by gamma....

but not enough to find the one for the moving observer....because by definition would not make sense between inertial frames of reference (this you don't seem to grasp) .. for that there has to be the requirement of non-inertiality or the implicit assumption of something which moves and something else is stationary (which is what occurs always in circular motion)

RESQ

Dear Vladimir Kuklin [the letter below is attached in the doc format for better exposed sub- and super-indices]

Here is the kindly requested proof of the first part of my assertion [now in a simplified form]:

ASSERTION. Formula (7.VK) of paper [VPPED] is in exact coincidence with the one I am giving within my notes [ETDD] as formula (7.JoaD) under the condition that vD=0, AND by neglecting γE .

It follows, also that the two coincide (the first again up to the factor γ) with the well known formula {suggested for this forum by @Stefano Quattrini}, derived e.g. in J.D. Jackson's book [CE] as formula (11.38) on page 364.

THE EXPLANATION.

The quantities of formulas of [VPPED] (which are based on the assumption that c=1), can be replaced by expressions dependent on quantities introduced in [VPPED] as follows:

h2=x2+y2; xE(tE) ≡ vE ⋅ tE = z - v ⋅ t' = r⋅cos(α) - v ⋅ t' ; vE = -v .

Moreover, since xD(tD) =0, according to (4) of [VPPED] we get

tD - tE ≡ √{ h2 + [xE(tE)]2} = √{ r2 - 2⋅r⋅cos(α)⋅v⋅t' + v2⋅t'2} .

Therefore the ratio of frequencies according to (7) in [VPPED] equals

fE(tE)/fD(tD) = γE ⋅ ( 1 + {v2⋅ t' - r⋅cos(α)⋅v}/√{ r2 - 2⋅r⋅cos(α)⋅v⋅t' + v2⋅t'2} )

which coincides with with (7) of [VPPED] (with absent factor γ ), if one accepts also c=1 and idntifies the ratios of our concern as follows: fE(tE)/fD(tD) = f'/ f ≡ λ / λ' .

[ETDD] by Joachim Domsta: Examples_Time_Delay_Doppler.pdf (contribution via Research Gate) wthin this thread.

[VPPED] by A.V. Kuklin and V.A. Kuklin: Волновая природа поперечного эффекта Доплера и аномалии ”красного“ и ”синего“ смещения частоты электромагнитной волны

движущегося источника излучения, Журнал технической физики, 2019, том 89, вып. 1,

DOI: 10.21883/JTF.2019.01.46975.135-18 (Журнал ЖТФ),

available at https://journals.ioffe.ru/articles/viewPDF/46975

[CE] by Jackson, J.D. (1999): Classical Electrodynamics. 3rd Edition, John Wiley & Sons, New York, available at https://ia601603.us.archive.org/7/items/ClassicalElectrodynamics/Jackson-ClassicalElectrodynamics.pdf

Dear All, this note is to show that the emitted beam

which is perpendicular to the trajectory of the emitter with respect the IRF of the detector at rest

is NOT perpendicular to the trajectory of the detector with respect to the IRF of the emitter at rest.

Best regards, Joachim Domsta

Dear Joachim,

thanks for the clarification

yes it is known that assuming a constant speed of light for every IRF there is such "asymmetry". The Trajectory of the beam is perpendicular to the moving observer so it is normal to both if they are parallel. In the other case it is not...

Basically (assuming c constant) the velocity of light does not compose as a vector in the direction of motion (remains c) but composes sideways with the motion of the IRF.

It has to be considered that:

a) in the case of circular motion the beams are at right angles both ways.

b) for IRFs it could be possible to discriminate who is at rest and who is in motion by simply measuring the angle of arrival of the beam. OR let's say you could discriminate between two IRFs who moves more and who moves less. This is the reason why SR states that only for non-inertial RFs it can be considered a moving observer, only in case of acceleration.

c) consider also that after being attached to the rotor, if the detector proceeds with constant speed along the tangent, a serious discontinuity due to the trajectory of beams is found right at the moment when the acceleration ceases.

Dear Stefano,

I have to get a rest of your mixing and jumping changes of claims. The phenomenon I have lately described has nothing to do with geometric theorem of parallel straight lines intersected by a normal line!

1. I am comparing the cases when the beam is normal to one trajectory while the second object is at rest and there is no talk about normality to the trajectory which is just one point! And I didn't refer to equality of the speed of light in each IRF

2. I have suspended considering the circular motion since you didn't agree till now that in the case of rectilinear motion, the two subcases

FIRST: of the detector at rest, detection from direction perpendicular to the trajectory of emitter

SECOND: of the emitter at rest, emission into the direction perpendicular to the trajectory of detector

ARE SUBSTANTIALLY DIFFERENT with respect to the ratio fD/fE.

Contrarily,

-- you are claiming an imagined WRONG interpretation of LT that they must give the same result referring unrigorously to LT despite a CLEAR AND CONCISE application of LT to the Doppler effect within my notes, jsut repeating in simpler - seemingly - way the KNOWN formulas!!!!!

-- for the first time in last answer you are suggesting WITHOUT REFERENCES existence of some experimental proof by using the following words:

SQ:" a serious discontinuity due to the trajectory of beams is found right at the moment when the acceleration ceases."

Nota bene, all the trajectories of beams are straight lines and a discontinuity of any must look very strangely. Who noted this, please?

Regards, Joachim

Dear Joachim,

>

I feel the same. You don't seem to understand what is written. Or at least you imagine something which is really wrong!!!

>

Doesn't have a relation to what I have been talking about in the previous post and in other posts. What you just wrote is a triviality with no sense!!

It is a discontinuity "due to" a jump in the directions of the trajectories of the beams predicted before and after the curvature change, not "of the" trajectories.

Due to the fact that in circular motion the trajectories are always perpendicular to the direction of the emitter according to SR.

It is not to be noted by somebody doing experiments, since such discontinuity in reality cannot be present, but it is what comes out of SR in passing from circular to rectilinear motion and vice versa.

Dear Stefano,

you stated: It is a discontinuity "due to" a jump in the directions of the trajectories of the beams predicted before and after the curvature change,

which - I agree - is realy different of what I have understood from your first assertion that

" serious discontinuity due to the trajectory of beams is found "

Anyway, I had right to misunderstand your intention.

But now, you are admitting realy strange behavior of the beams: The beams are emitted continuously - to the best of my understanding the emission of e.g electromagnetic waves - and those beams under discussion are joining the instantaneous position of the emitter with the detector. Hence the DIRECTION varies continuously as well. Where is the trap: "Can the trajectory of the emitter be not continuous?" or: "Can the distance between the emitter and the detector a discontinuous function of time?" I have no idea how could one derive the discontinuoty of the direction of the beams joining the event of emission and the event of detection by a detector at rest, unless the trajectory of the emitter possesses a jump!

Best, Joachim

PS. Anyway, you are still returning to the ciscular motion combined with the rectilinear without reaching agreement with respect to the pure rectilinear motions. And you are still a believer without any rational reference to mathematical calculations that the two subcases

FIRST: of the detector at rest, detection from direction perpendicular to the trajectory of emitter

SECOND: of the emitter at rest, emission into the direction perpendicular to the trajectory of detector

ARE SUBSTANTIALLY the same with respect to the ratio fD/fE. Aren't you?

Dear Stefano, fulfilling one of you requests, I am attaching my note completed now with the case of detector at rest (in section5) and a conclusion (in section 6).

Best, Joachim

PS. In the 9th and 10th linesfrom the bottom on page 3 the word detection should be replaces - obviously - by emission. Thanks, JoaD

Dear Joachim,

in the attachment you can find the considerations of mine about your script.

Once clarified, it is the possible to proceed further.

thank you

Stefano

Dear Stefano,

thank for your detailed comments. However I have noticed different understanding od you and me. My first severe doubts related to your kind answer concerns the notation and naming of the the particular events:

First,

SQ: Where E belongs to IRFE and D belongs to IRFD

No particular IRF-s of the emitter and the detector are distinguished by me. I can agree only with ONE reference frame and to call it according to your proposal IRF0. Without this we never come to mutual understanding. Perhaps the following additional argumentation will be heplful in undertanding the approach I use: switching to another IRF would require application of suitable LT, and this step is not necessary untill we introduce the proper time. Moreover, till eqn. (5 JoaD) the description of the DE is equally valid for both - relativistic as for non-relativistic cases.

Secondly,

SQ: The equation (5 JoaD), by non-considering the differentials . . .

. . . makes NO MATHEMATICAL SENSE. (5 JoaD) is derived directly from (4 JoaD) by application of standard differential calculus: If two wariables (here tD and tE) are bonded {deterministically, in a one-to-one way} by equation of the form, say:

G(tD, tE) = 0

then the implicitely defined function tE = h(tD) datisfies the following differential equation :

∂ G (tD, tE)/∂tD ∙ dtD + ∂ G (tD, tE)/∂tE ∙ dtE = 0, i.e. h’(tD) = - [∂G (tD, tE) /∂tD] / [∂G(tD, tE)/∂tE ]

which in our case with additional use of (4 JoaD) leads to (5 JoaD).

In our case G equals the "LHS minus RHS" of equation (4).

Therefore also the following remark is not applicable:

SQ: In addition, it is not clear what is dtD and dtE since the times are all referred to t and should be the same.

and consequently, the following concusion is wrong:

SQ: It is undisputable that dτD /dτE = γD-1 dt/γE-1dt

Untill we get consistency i this respect, we cannot follow further steps, since this are our languages which are different.

Best regards, Joachim

Dear Joachim,

>

yes, in fact it was the case to introduce them when the proper time was considered.

>

yes, infact, that's why I was wondering...

ok, now it is clear what is behind your derivation !!! You applied the Dini's theorem..

although I would like to see better the steps in between if possible.

but dτD = γD-1dt and dτE = γE-1dt are derived directly from the definition of proper-times...

once you have defined the IRF0, everything gets referred to that. Unless you give a different meaning to dτD and dτE .

Dear Stefano,

"but dτD = γD-1dt and dτE = γE-1dt are derived directly from the definition of proper-times...

once you have defined the IRF0, everything gets referred to that. Unless you give a different meaning to dτD and dτE ."

Obviously, however even though the dtD and dtE are "measured" in the scale of IRF0 they are also bonded via (5), and therefore they do not cancel in the final formula for the ratio of frequences.

Wrt to the more detailed derivation of (5) from (4) I need more free time, sorry - another duties are calling me every day:-(

Best, Joachim

Dear Joachim,

ok

in any case it is not necessary to have that in order to continue in any case.

From the analisys I made emerge two facts:

a) your derivation starts from one IRF0, the lab frame, disseminated of synchronized clocks which implements the absolute simultaneity inside of it.

b) the generic relation of time between a moving clock in IRF0 with speed v0 and any stationary clock, occurs according to dτ =γ-1dt where t is the time of any of the stationary clock. In other words

t'=γ-1t and x'=γ(x-vt).

Dear Stefano,

SQ:"derivation starts from one IRF0, the lab frame, disseminated of synchronized clocks which implements the absolute simultaneity inside of it."

I mean that the usage of the word "absolute" is an overuse, since it suggests wrogly that the derivation is based on this obviously false assumption that such an absolute time is accepted.Not at all, instead I am using the time of THIS particular IRF0 just for reporting all events ina consistent system ofnumbers. And - consequently - the function describing the dependence of the ratio on time is valid only for THIS time-variable. More precisely of the variable tE which is ARBITRARY, and teh it determnines uniquely (determnstically) tD and - in next steps - R(tE):=fD(tD)/fE(tE). What is invariant - is the following: in any other IRF with say coordinates t',x'... for the event with coordinates (tE,xE(tE) ) the SAME event denoted in the corresponding coordinates by (t'E,xE'(tE') ) the detection will happen at the SAME point with the new coordinates (t'D,xD'(tD') ) with EXACTLY thesame ratio R'(tE') = R(tE). Thus, as you see correctly my approach (seemingly - common among a large group of theoretical physicists) that the event do not change when passing between IRF-s, only their coordinates vary.

Honestly, I am not entering your and the others' way ofpresenting anything with clocks, unless it is the issue of discussion. For DE there is no need more than just to accept (which might be disputable anyway, if one wants to change the model of reality) that for each moving object the intensity of varying the proper time (again - independent of the IRF) wrt to the time elapsing according to an arbitrary but fixed GIVEN IRF is detrmined by the gamma factor defined by the CURRENT speed of the object wrt to the GIVEN IRF. Changing IRF - according to the presented approach - the proper time elapsed between any two events does not change, only the coordinates of the events are changed. In that sense, there is also no physical time delay, but just the different run of different clocks.

Regards, Joachim

Dear Joachim,

.

You can call it how you want, common-time if local absolute time is inappropriate for you!!!

Dear Stefano,

Abbreviated response only:

When talking about verification wth reality you are probably right, but am not on the wave to receive all info about this. I was talking about the calculations which is based on a simpler set of basic assumptions.

thanks for your comments which perhaps sometimes will lead me to the same questions.

BTW: It seems to me, however, that for cheching the Doppler ratio experimentally we do not need clocks, but just exchange of FModulated signals carrying the info encoded by the emittent (like - thought not exactly the same as) watching emssion spectra of some atoms in some oscilating states (!? - just a guess)

Regards, Joachim

Dear Joachim,

The calculations are important in physics if the model they represent makes sense. The LT make sense only with a constant speed of light for example. They do not make sense in gravitation since C coordinate is not constant.

To check the Doppler we need oscillators (atoms which pass from one energy level to another in a cavity under a difference of potentials) which on one side they are primordial atomic clocks, on the other side they can be used as emitters of EM waves if set to emit in free space rather than in a cavity.

Dear Joachim,

back to the topic. I think by now we can agree that your original and effective derivation relies on the following:

1) 2d platform P always attached during the experience to IRF0 (no acceleration)

2) t time of a clock at rest in P which is the same all over the platform, guaranteed by all the clocks, in sych according to Einstein sync procedure.

3) Relation between times: time t and the generic t' of a moving clock with constant speed in IRF0, according to t'=γ -1t . where γ=γ(c,v) where c is constant and v is kept constant.

4) relation between lengths x'=γ(x-vt)

Dear Joachim,

did you eventually realize that your derivation relies on Tangherlini Transformations?

Dear Stefano,

thanks for the question, which I cannot answer positively due to lack of consistency of the Tangherlini Transformations with respect to the invariance of the Minkowski pseudo-metric. Indeed, if

t'=γ-1t and x'=γ(x-vt)

then

t'2 - x'2 \not-equal t2 - x2

even for points lying on the light-cone.

Dear Joachim,

isn't this

dt'= γ-1dt

nothing but the differential relations of the proper time?

of which t'= γ-1t is just a direct consequence being v constant

Dear Stefano,

1.

I have used the following symbols:

t x the coordinates of the first IRF

t' x' for the coordiantes of the second IRF

The relation betweem them if we want to express events in different system of coordinates is given by [t',x'] = [t,x] \circ Lo + [t'o,x'o] where L is necessarily an orthochronus Lorentz transformation, which is not equal any Tangherlini transformation, unless the relative speed of the IRF-s equals vo=0 (\equiv \gammao = 1)

2.

The proper time \tau(t) is a notion related to any SUBLUMINAL MOTION of a single point-particle. This scalar function is independent of the IRF and varies from point to point of the trajectory. For motion given by the world line [t, x(t)], at instant t (wrt the system of coordinates), the derivative

d tau(t)/dt =1/ \sqrt{1 - v(t)2} where v(t)= |dx(t)/dt|

and is constant only for motions with constant length of the vector of speed, including the case of the1+3 dimensional time-space.

Thus the derivative in general is not constant.

3.

The proper time (according to the convention I am supporting as an admissible model of the SRT) is the time showed by the clock traveling with the point particle, which could be literally called "inner clock of the object". This admitsalso, that two objects with clocks equally set at instant of meeting in one space point, after their travel ended at another instant at some - possibly other space point - might show different time elepsed between the meetings. However, one cannot - within this interpretation - compare the age of the objects in the meantine between the meetings, since our common uderstanding requires to state at which instant the ages are compared. On the other hand- as it is well known - no two different events of the Mnkowski time-space can be said "absolutely simultaneous" unless they conincide.

Dear Joachim,

>

NO, it is enough to read the Mansouri and sexl paper to understand it

http://ivanik3.narod.ru/Eather/MANSOURI/MANSOURI1.pdf

ok, but I don't see how this is relevant to the discussion

the argument is about inertial motion, I don't know why you involve any kind of acceleration here.

The proper time is tau, and is related in IRFs by tau=t*gamma

t'=t*gamma-1 is in a inertial frame of reference

yes..

>

yes unless the motion is symmetric, this is well known.

>

you can for sure if you have a very wide platform with clocks in sync.

With that you have a common time and you can decide to compare them at a common time. THe GPS also defines a common time with all the sats.

I tell you again, it is worth understanding better the meaning of the common time...that is a way to propagate the simultaniety on a 2D or 3D inertial Platform to which an IRF is attached.

If this is clear ok, otherwise it is not worth proceeding.

IN regards to the Tangherlini Transformations and their more generality.

http://www.ptep-online.com/2014/PP-38-04.PDF

Dear Stefano,

SQ:>> NO, it is enough to read the Mansouri and sexl paper to understand it > According to performed experiments, can the transverse Doppler in inertial motion comply with the Lorentz Invariance ?

Dear Joachim,

my NO, is about your "NECESSARILY" is about your affirmation that LT are inevitable and it is explained in Mansouri and Sexl that also the TT are valid hence not necessary.

http://ivanik3.narod.ru/Eather/MANSOURI/MANSOURI1.pdf

You made an affirmation, which has corroboration which I do not share, I said that in force also of well known papers your affirmation has no foundation!!!!

You applied the Tangherlini Transformations because you stated and you used the actual relation dt'=gamma-1dt for your calculations.

It is the same as t'=gamma-1dt for v constant, which is the case of RDE in inertial frame of refrerences.

You did not use t'=gamma(t-vx/c2)