Stefano Quattrini "the point is that such phenomenon has never been tested experimentally and it comes from an interpretation of the LT."

The point is that these results are simple consequences of the equations for relativistic mechanics and electrodynamics, which has been extensively tested and verified and experimentally in many similar situations. It is true that these predictions have not be tested experimentally, and that it may be difficult to do so. However, if these predictions are to be avoided (why should they?), some already well tested equations have to be changed. Which seems extremely difficult to do, without running into conflict with already verified results.

The most important point is that you cannot construct a different mathematical theory for each physical phenomenon, just because you dislike some results.

Dear Eric, Eric Lord ,

ok

I don't find the shift in the instantaneous frame of A, but I calculate only the approaching speed in that frame which is easier, which is the same as the speed in the other frame since the speed is relative and the distance H is certainly maintained.

the velocity of light is invariant in any inertial frame of reference, c-v is another way to express the fact that in reaching a target , if an object is already endowed with speed v in the rest frame of emission, light will take more time to reach it in comparison of the condition where both were at rest.

I just apply the formula of the Doppler effect by considering what is the speed of the object in the instantaneous frame of the emitter, which for the sake of relative motion does not change.

this is quite irrelevant...and it is very consistent at low speeds where addition of velocities is a very good approximation.

Chapter Uniform acceleration - excerpt from Tensors relativity & cosmology

Dear Eric,

I've seen your derivation which goes to the relativistic Doppler effect between emitter and observer, which nobody denies here. I apply it at the first order, at higher orders does not mean much due to the fact that the variation of speed , Delta v, as I explained is so tiny, that it stays in classical physics.

Time of atomic clocks cannot be as Minkowski describes. Relative time does not have anything to do with Linear Doppler but it is instead relevant to Transverse Doppler as several experiment show.

In any case I still haven't found a satisfactory counter proof or failure of my simple derivation.

Here is the latest version with an additional explanation, where only the emitter is accelerated at the same time when the beam is shot as referred to a stationary IRF.

Preprint THE DOPPLER EFFECT IN ACCELERATED MOTION, RELATION AT HIGHER ORDERS

Dear all,

Lorentz, Poincare and Einstein mistakenly excluded the scale factor from the formulas of transformation. This is the worst blunder in physics for more a century. The time to correct it has come. Let`s do it and all the picture at once will clear up.

Dear Eric, Eric Lord

so following your script, what is the formula which represents the higher order of (1+gH/c2) which you propose?

Dear Stefano ~

The Doppler shift formula for uniform acceleration, derived in my (1976) book according to Special Relativity, is an an exact closed expression. So I can't see the necessity for (or the validity of) a non-relativistic analysis to find "higher order terms". As you know, my opinion is that that approach is invalid anyway because (a) the Newtonian/Galilean definition of acceleration d2x/dt2 is incorrect and because (b) in Galilean relativity the constant speed of light is not the same constant in different inertial frames and is even time-varying for accelerated observers! (You claim that this makes no difference, but it does make a crucial difference if you are seeking "higher order terms"!)

I've been attempting, as an exercise, to employ your method to find the exact closed form for fB/fA under the assumption that Galilean relativity is valid. I'm finding it quite tricky; if I complete the calculation I will let you know. (Unfortunately I no longer have the patience for this kind of thing that I had when younger!).

In particular, fA should be defined as the (presumed constant) frequency of emission relative to the instantaneous rest frames (IRF) of the emitter and fB should, similarly, be measured in the IRFs of the receiver. According to Galilean relativity the Doppler shift expressed in terms of frequency will be different from the Doppler shift expressed in terms of wavelength (because the speed of light is not the same for emitter and receiver, and those speeds are not even constants!

Dear Eric, Eric Lord

Eric:

please follow my reasoning:

Your derivation brings to

Fobserved/Femitted = sqrt [(1-v/c)/(1+v/c)],

the exact formula of the Relativistic Doppler effect of 1905 . It can be written also in the form Fobserved/Femitted = (1+v/c)/sqrt(1-v2/c2)

where (1+v/c) was found by Christian Doppler, the classic Doppler effect for approaching observers while the term 1/sqrt(1-v2/c2) is Einstein's contribution.

Now in our problem, as we all know, v is very well approximated by

v=gH/c, such that Fobserved/Femitted = (1+gH/c2) the classic result in which Special relativity is not needed, considering that in extreme conditions v=gH/c is of the order of some meters per second.

On the other hand that value v=gH/c is based on the fact that the light-time to cross the distance between absorber and emitter is H/c, which is what occurs only if source and observers are at rest.

I am sure you agree on the fact that the observer , since it is in accelerated motion, has to meet the beam before that elapsed time H/c, so it will meet the beam at a speed vf which is not v=gH/c but a bit less (if the beam is emitted in the opposite direction to the acceleration).

Eric:

what is measured by the accelerated observer is the proper acceleration g, as if every time the observer departs from a stationary motion.

The effect needs to be treated relativistic-ally only if the quantity v=gH/c, which is a good approximation of the speed of the observer in the reference of the absorber, becomes sufficiently close to c.

The coordinate acceleration cannot be relevant, except in reference to the MCIF of the emission, otherwise from within I could spot the absolute speed of the object by knowing the redshift. But again v=gH/c. And in any possible case since the quantities at stake are only gH and c, where g is the proper acceleration, even at higher order in your derivation, everything has to be a function of such quantities.

Eric:

(1+v/c) is accurate to a very high precision in experiments and speaks clear: at low speeds v/c

Dear Stefano ~

Yes, I follow your reasoning, but it troubles me for various reasons:

Ignoring relativistic (ie, SR) effects seems unwarranted as an approach to finding “higher order” effects due to uniform acceleration because SR effects would contribute to those higher order terms.

In particular:

(a) the concept of “uniform acceleration” g in SR is not given by dx/dt constant;

(b) by taking c to be constant, and the same constant in the instantaneous rest frame (IRF) of the emitter and in the IRF of the receiver, while employing a “non-relativistic” approach, you are using a hybrid method that is logically inconsistent;

(c) Saying that the quantity v = gH/c is a “good approximation” does not convince me if you are aiming to find “higher order terms”.

This is the basis of your argument, if I’ve understood it correctly:

The trajectories of A and B are given respectively by xA + ½gt2 and xB + ½gt2 where xA − xB = H, a constant. The Doppler shift for light is assumed to depend only on the relative velocity between the emission event (at time t0) and the absorption event (time t1).

That relative velocity is v(t1) − v(t0) = g(t1 - t0).

The light travels from xA + ½gt02 to xB + ½gt12.

That is, it has travelled a distance H − S in time t1 − t0, where S = ½g(t12 − t02).

The speed of light is then c = (H − S)/(t1 − t0).

Note that your expression S = ½g (t1 − t0)2 is not correct.

“What matters is the instantaneous speed of the absorber when the detection occurs, in the inertial frame of reference of the emission (source) where the speed of light is constant c”

I don’t agree. What matters are the frequency of emission in the IRF of the emitting event and the frequency of absorption in the IRF of the absorption event. Those two IRFs are related by a Lorentz transformation.

I’m sorry Stefano, I had no wish to get into an argument with you about this problem! It’s just that when I get a ”Researchgate notification” I feel under an obligation to convey my opinion. I cannot say I’m convinced when I am not... (-;

Dear Eric,

>

No argument Eric, you manifest your doubts I manifest mine.

We have to resort to first principles as much as possible to check what is real or what is not. Otherwise where is the funny part?

What I invite you is to give just one chance to the game: that what you are sure to know may contain a flaw.

sure in fact it is not correct, mainly because you are making c additive which is not, but in fact I did not write that and I already explained you why. In any case continue reading.

what matters first of all is what has been experimentally verified.

The Linear Doppler effect has been verified to high accuracy with spectroscopy

(1+v/c)/sqrt(1-v2/c2) and there we have to start, where v is the speed of the detector in frame of the stationary source in the Lab.

So what matters is to determine v.

Do you agree so far?

In order to go on with the discussion I made my script more exaustive

Preprint THE DOPPLER EFFECT IN ACCELERATED MOTION, RELATION AT HIGHER ORDERS

I invite you to have a look at page 2: where the simpler configuration in the second part of the page is presented.

The original formula presented by Domsta for the problem of doppler in accelerated motion in the other thread https://www.researchgate.net/post/What_is_the_actual_physical_meaning_of_the_Lorentz_Transformations

is this

(1) Fd/Fe = 1+ gH/c2[sqrt(1+(g*tE/c)2 )- g*tE/c]

this is instead his formula for rigid acceleration

which is quite similar to mine but still has that unphysical tE which is not a surprise.

The formula obtained by me fd/fe= √(1+2gH/c2) is not the most general for sure, but is certainly more accurate than fd/fe = (1+gH/c2).

I will propose later the one which Stephen Boughn who is a known relativist , correctly found.

For transverse and gravitational redshift the proper times are the correct way to express the shift and these are relevant only to effects at higher orders in v2/c2.

The Longitudinal Doppler effect is native 1+v/c, and does not have that order of magnitude (v/c)2 .

There has been no experiment with equally accelerated clocks performed , it is quite likely that an experiment performed will show no relation with proper times mainly due to the reason given above.

Dear all,

just the necessary hints on how to compute the Doppler in accelerated motion in relativistic dynamics, already calculated in classical dynamics as

fd/fe= √(1+2gH/c2) ≈ (1+gH/c2) .

1) ΔS = c2/g √(1+(gΔt/c)2) - c2/g ≈ 1/2gΔt2 for Δv

Dear Eric, Eric Lord

I spoke with Prof. Boughn about the problem, he provided me the following answer not far from mine but it is directly relativistic:

1) ΔS = c2/g √(1+(gΔt/c)2) - c2/g (≈ 1/2gΔt2 for Δv

Dear Stefano ~

If A and B have the same constant Newtonian acceleration g their trajectories are respectively x = xA + ½gt2 and x = xB + ½gt2, where xA − xB = H, a constant. If light is emitted from A at time t0 and received by B at time t1 then the light has travelled a distance (xA + ½gt02) − (xB + ½gt12) = H − ½g(t12 - t02) = H − S in time t1 − t0. Then, assuming the speed of light c to be a constant, I get

½g(t12 − t02) + c(t1 − t0) − H = 0.

By denoting (t1 − t0) by Δt you've been misled into treating this equation as a quadratic in Δt, which it clearly is not. Δt2 is ambiguous: Δ(t2) ≠ (Δt)2.

For reasons I’ve already tried to convey, any attempt to find higher order terms in the non-relativistic expression fB/fA ~ (1 + gH/c2) for the Doppler shift due to uniform acceleration using only non-relativistic arguments is inevitably going to be logically inconsistent.

The required Doppler shift can be investigated by applying the principles of SR, as I showed in the pages I recently uploaded. Note first that Newtonian acceleration g and relativistic acceleration K are not the same; they are related by a factor that is second order in the time varying velocity: K = γ3g, γ = 1/√(1 − (dx/cdt)2). Note further (and more importantly) that the constant relativistic acceleration KA of emitter A and the constant acceleration KB of receiver B cannot be equal because that is inconsistent with the requirement of constant distance H. The non-relativistic approximation fB/fA ~ (1 + gH/c2) corresponds to H “sufficiently small” so that KB/KA ~ 1. The exact expression is fB/fA = KB/KA which, as I’ve shown, can be obtained from the standard relativistic Doppler shift formula fB/fA = √ [(c + vA)/(c − vB)]. I’d like to be able to express KB/KA in terms of H to compare with the expression you’ve given; I've tried but I can’t see how to do it and don't want to struggle with it any more!

Dear Eric,

please pay attention to what I wrote

we all agree with this.

yes infact I propose the relativsitic relation as suggested by Boughn

ΔS = c2/g √(1+(gΔt/c)2) - c2/g

yes I know, and I propose the following, also suggested by Boughn which is the accurate relation for the problem

Δv = gΔt/√(1+(gΔt/c)2)

and this

cΔt = H - ΔS.

You can find the solution...

Joachim Domsta

please express yourself better.

Joachim Domsta

Not at all. But I can see, this time at least for sure, that you don't feel like surrendering to the fact that you are dead wrong!!!

Just provide a more accurate evaluation of the approximated time H/c, used in the well known shift (1+gH/c2), necessary for light to go from emitter to absorber in accelerated motion. By now you should have found it after all your calculations.

Despite my lack of access to my files, let me remind Stefano what I have done in order to explain the incorrecteness of the assuption that the IDR in His models is substantially emission-instant independent. The calculations are performed for both modeles: with the constant Newtonian acceleration and with constant proper accelerarion keepeing constant the space coordinate in one IRF, which becomes then the distinguished one. Also the dependence is substatial in both fashions - with relativistic or classical way of counting the relative velocities an instants of emission and detection related by the ray performing the source and the absorber. I hope that anyone who would like to listen Mr Stefano Quattrini about how deeply wrog I am, will have simple opportunity to verify His Holy Words. These are the links to the scripts (ALL FROM HIS THREAD "what is the actual .." , thus Mr Stefano Quattrini had obviosly access to them without any trouble): https://www.researchgate.net/profile/Joachim_Domsta/post/What_is_the_actual_physical_meaning_of_the_Lorentz_Transformations/attachment/5ee3003632fcf50001922951/AS%3A901455007465472%401591935030156/download/DopplerAccelerated5.pdf https://www.researchgate.net/profile/Joachim_Domsta/post/What_is_the_actual_physical_meaning_of_the_Lorentz_Transformations/attachment/5ee3d11032fcf50001924865/AS%3A901679260131334%401591988496517/download/DopplerAccelerated4.pdf https://www.researchgate.net/profile/Joachim_Domsta/post/What_is_the_actual_physical_meaning_of_the_Lorentz_Transformations/attachment/5ee085ec3ffef50001f738be/AS%3A900771008770048%401591771952575/download/DopplerAccelerated2.pdf

Thank you for your attention,

Joachim Domsta

I have to say that a lot of work has been done by Joachim Domsta in the attempt to find a solution for the problem of frequency shift in accelerated motion.

Unfortunately the only way seen by Domsta to provide a solution to such problem is with proper times of emitter and observer.

The formula of Doppler tested since 1843, when Christian Doppler found the effect for binary stars, as the shift fa/fe=1+v/c as the Longitudinal Doppler effect where v is the relative speed between earth and one of the binary star, is a pure classical effect. It was later on transferred to work successfully into material media and the 1/(1-v/vm) was found for the moving source where vm is the speed of transmission of the medium. Later it was extended to arbitrary angles.

That formula, one of the most tested and demonstrated valid in Physics. is totally ignored by Domsta in the solution of the problem. Although he reported that it has been derived as a consequence.

Despite of the fact that fa/fe=1+v/c certainly depends on the proper frequency of the source fe, like the one of the sound for example, it cannot depend on the proper frequency of the observer since in classical mechanics this feature does not exist, although the effect is present.

As stated several times, that formula, despite different derivation relying on waves, is also, according to the derivation of Erwin Schrodinger (1922), Enrico Fermi (1932) , Leon Brillouin (1970), Redzic(1988), Giuliani (2005), obtained from the conservation laws , due to momentum transfer of the observer to the absorbed photon.

Such momentum transfer has nothing to do with the proper times of the observer, the observer detects an amplification or diminishing of light due to the fact that its atoms undergo a scattering process where the linear momentum transfer of the radiation is larger than the one at rest so that an additional energy in the frame of the atom is absorbed compared to what would occur at rest.

Relativistic effects involving "proper times" are present only at orders equal or higher than v2/c2 , not certainly related to linear momenta transfer.

As a conclusion all the attempts to use proper times to find effects related to longitudinal Doppler effect in this full form, including also the effect to the first order in v/c ( not only the transverse Doppler) , are doomed to fail due to fundamental conceptual Physical mistakes.

I actually did not check, if there are other conceptual errors in Domsta's scripts, which brings the values, of the frequency shift of radiation inside a rocket in accelerated motion, to depend on the coordinate time of the emitter or observer referred to an external IRF.

Dear all,

in the attachment you can find the derivation with the additional relevant results of

Preprint THE DOPPLER EFFECT IN ACCELERATED MOTION, RELATION AT HIGHER ORDERS

the generalized version for high speeds (relativisitc dynamics) as suggested by Prof. Stephen Boughn following similar principles of my classical derivation.

SQ (20 hours ago):

>>yes infact I propose the relativsitic relation as suggested by Boughn

ΔS = c2/g √(1+(gΔt/c)2) - c2/g (1*)

yes I know, and I propose the following, also suggested by Boughn which is the accurate relation for the problem

Δv = gΔt/√(1+(gΔt/c)2) (2*)

and this

cΔt = H - ΔS. (3*) Unfortunately the only way seen by Domsta to provide a solution to such problem is with proper times of emitter and observer.

Trying to put a patch on your blunder again and crash into the wall of the Momentarily comoving inertial frame?

Don't you even dare to think that I followed your derivation!!!!!!!!!!!!!!!!!!!!!

Yes you used certainly the Relativistic formulas nobody never denied, are written on all books, but you did not use the fatidic 1+v/c which makes a lot of difference my dear and you did not find the delta time.

Prof. Boughn suggested me to go relativistic with the same formulas I applied classically following the same reasoning as my original paper (since the end of May). He is a known relativist with lot of papers on SR published in famous journals, he found the delta time and the final shift, and said that it was unexpected for him that my classical solution was right up to the second order.

Regardless of your "applied formulas" you arrived to an inacceptable result of dependence of time of emitter and detector!!! And you still sadly say that it is more general!!! That is the crash of all Physics.. you pretend to teach SR to somebody, are you serious???

There was a simple misprint (should be and is tE=0), which made you blind wrt the real content and intention: you have got an opportunity again to catch JoaD on obvious error. Wow!

In fact, relativistic formulas 6.1 and 6.2 follow from the non-relativistic formula (5) by suitable multiplication by the ratio of gamma factors.

SQ: >>Yes you used certainly the Relativistic formulas nobody never denied

don't worry, your derivation has much more errors.

Do not even compare my derivation with yours which arrives at a total disaster and meaningless result.

infact you wrote a lot of nonsensical expressions

>

at last!!!! After crashing into the wall. You finally understood that your blunders are not needed because there are people who is able to provide help to solve the problems correctly!!!!!!!!!!!!!!!!! It was checked also by myself and it is written in my script that my classical derivation was correct to the second order.

SQ" your derivation has much more errors. "

at least one please!

the result of your derivation is the biggest error ever!!!

phi! let it be, not your problem!

Preprint THE DOPPLER EFFECT IN ACCELERATED MOTION, RELATION AT HIGHER ORDERS

Dear Eric Lord ,

yes,

(1) v = gt/√(1+(gt/c)2) is a consequence of what you say (integration)

by applying for the displacement

S = c2/g √(1+(g/c)2) - c2/g and c t = H - S.

you can find t= H/c (1+gH/2c2)/(1+ gH/c2)

then plugging t into (1) it is v= gH/c (1+gH/2c2)/(1/2(gH/c2)2 +gH/c2+1)

and then using the relativistic Doppler

fd/fe=(1+v/c)*gamma = (1+gH/c2)

in other words the overall relativistic effects compensate for the effects of the difference between the light time H/c valid at rest and the one found in acceleration H/c (1+gH/2c2)/(1+ gH/c2).

Such difference is Dt = gH2/2c3 /(1+ gH/c2)

sufficient to keep the ratio always as (1+gH/c2)

Dear Stefano ~

With respect to an arbitrarily chosen (“stationary”) inertial frame it is possible for an observed emitter and receiver A and B to have the same velocity and the same constant acceleration K at every instant while remaining a constant distance apart, H.

The problem you are concerned with is the Doppler shift observed by an observer at B, in his instantaneous rest frame. That is quite a different problem, for which the two requirements (1) KA = KB and (2) H remains constant

are incompatible.

Moreover, you seem to have not taken note of my crucial remark that the formula

½g(t12 − t02) + c(t1 − t0) − H = 0.

(that follows readily from the fact that the light travels a distance H − S in time t1 − t0) is not a quadratic in (t1 − t0). Your analysis goes of the rails precisely at that point.

You say “I propose the relativistic relation as suggested by Boughn”. Have you considered the possibility that Boughn might be wrong? Have you checked the reasoning that led him to that relation? You shouldn't take and apply formulae lifted from others uncritically, without careful clarification. Your analysis of a basic problem like this one should stand on its own without the reader having to take the trouble to consult and assess extraneous material.

Dear Eric, Eric Lord

fist of all let's stress the fact that the point of agreement is for t=0.

Your crucial remark brings exactly to the destruction of a theory.

The consequence of what you say : you can find the relative speed by pure internal measurements which does not care about measuring a time with atomic clocks, but just with the help of a spectrometer.

I sit down in my spaceship in the rear with my spectrometer and I detect a variation of the received frequency from the oscillator at its head increasing with time, although the acceleration I measure with my accelerometer is always a constant g, engines at same regime.

UNTENABLE for a coherent physical theory, experiments in same exact conditions within an accelerated LAB may provide different outcomes.

The basic mistake by SQ:

two points moving wrt a fixed {1+1}-IRF0 with acceleration, though under the restriction that

(*) . . . . . x(t) - y(t) = const

form a rigid lab (with a seat for the observer :-).

The main reason is that the simultaneities with the same proper instant do not coincide; are even not parallel.

A rigorous calculation has been delivered Him in another thread. Roughly it is proven there that if the above condition (*) is fulfilled in two IRFs with a nonzero relative velocity, then the acceleration cannot be of constant non-zero sign.

For followers' convenience, I am attaching the note once more. Any comment is welcome.

Joachim Domsta

In replay to Domsta

Domsta's basic mistake is in thinking that what he is managing is the absolute truth and the postulates he uses cannot be discussed or do not need verification. His basic mistake is to think that Physics necessarily responds to certain rules of math so far postulated with no escape, regardless of the absurdity of physical behaviour in its results which jeopardize the coherence of Nature itself.

Regardless of that, he continues to propose calculations which are indeed necessary to understand that the underlying theory has some serious flaws as the vx'/c2 term in the Lorentz transformation, at the base of the relativity of simultaneity, which prevents it to reduce relativistic relation, in some cases, to Classical physics .

Stefano Quattrini "experiments in same exact conditions within an accelerated LAB may provide different outcomes"

But Stefano, the conditions were not exactly the same! Because you did not follow the advice of your scientific advisors (like certain presidents), you gave exactly the same acceleration to the front and end of your laboratory. As a result, the laboratory broke apart in thousands of pieces yesterday! How can you expect the results to be the same today -- after such a calamity?? :-D

This issue, to the best of by knowledge, was introduced by E. Dewan and M. Beran in 1959 (and therefore, in agreement with well established physics tradition, called "the Bell spaceship paradox"), and is by now well understood and quite well explained by those who may have understood it (and others). A good way to understand the problem physically, is to use Rindler coordinates (essentially the same as applied by Christian Möller long before, and seemingly by Friedrich Kottler much-much earlier, and ---all according to Wikipedia --- even by a person named Albert Einstein before him, more than 110 years ago).

I was about the mention a textbook by Eric Lord, where the issue is also discussed, when I got an extremely strong feeling of déjà vu! Could time be a cyclic coordinate??? At least on Research Gate?

Kåre Olaussen

yes length contraction which determines the B-S paradox, something which you cannot notice from within but you may notice from outside.

x'=gamma(x-vt)

Stefano Quattrini "something which you cannot notice from within"

It is the other way around: The prediction is that you cannot notice the effect from a fixed outside IRF, but those following the two spaceships will certainly observe that the rope between them breaks.

Kåre Olaussen

not Bell's interpretation...

Stefano Quattrini "not Bell's interpretation..."

Bell goes into considerable detail and calculations explaining why a length contraction must occur, when viewed from a fixed outside IRF, using the known (and extremely well tested) behaviour of electromagnetic forces. This leads to a breaking of the string (a physical event) in all coordinate systems. It is not a matter of a coordinate dependent interpretation, it is a physical prediction. Which is already an obvious consequence of Lorentz transformation laws. What John Bell does is not an interpretation, it is an additional physical explanation based on the Maxwell equations.

John Bell: "Violent acceleration could break the thread just because of its own inertia while velocities are still small. This is not the effect of interest here. With gentle acceleration the breakage occurs when a certain velocity is reached, a function of the degree to which the thread permits stretching beyond its natural length."

Kåre Olaussen

Einstein : "the question of whether the Lorentz contraction exists or does not exist in reality is misleading, because it does not exist "in reality" insofar as it does not exist for an observer moving with the object. However, it does exist "in reality" in the sense that it could be detected by physical means by a non-comoving observer"

Such thread breaking if exists is supported by the relativity of simultaneity, vx'/c2 since what would be different is the time between head and tail hence the force, it is the same mechanism which is supposed to make the offset in accelerated motion relalistic. At the end of the day is only a misinterpretation of the LT and how synchronisation works.

Stefano Quattrini "Such thread breaking if exists is supported by the relativity of simultaneity"

Yes, that is the direct (and simple) way to predict the phenomenon, with no physical length contractions.

What Bell shows through his calculations is that moving atoms, held together by electromagnetic forces, will necessarily "be" (look) Lorentz contracted in their direction of motion, when described from a fixed IRF. That is the pre-relativistic way to describe this phenomenon, quite instructive but extremely cumbersome.

Kåre Olaussen ,

the point is that such phenomenon has never been tested experimentally and it comes from an interpretation of the LT. We have to discuss again about that, although in 2017 we discussed already. I identified some really interesting elements..

Stefano Quattrini "the point is that such phenomenon has never been tested experimentally and it comes from an interpretation of the LT."

The point is that these results are simple consequences of the equations for relativistic mechanics and electrodynamics, which has been extensively tested and verified and experimentally in many similar situations. It is true that these predictions have not be tested experimentally, and that it may be difficult to do so. However, if these predictions are to be avoided (why should they?), some already well tested equations have to be changed. Which seems extremely difficult to do, without running into conflict with already verified results.

The most important point is that you cannot construct a different mathematical theory for each physical phenomenon, just because you dislike some results.

Kåre Olaussen

consequences which are absurd, but fare enough it is a matter of taste as I see...

>

Everything related to the relativity of time is well tested and sound and depends exclusively on the gamma factor.

The term vx'/c2 in the Lorentz Transformations

t'=gamma-1 + vx'/c2

had an interpretation that forced it to match with a sort of relativity of time. It is instead only the extent to which the Einstein Synch procedure fails for objects which are not at rest. It is just a measure of the failure of simultaneity between moving bodies once they have been set in synch.

It is the outcome of the Einstein SYnch procedure between accelerated objects, that is the synch that is lost in that way, that's all....

C. H. Wörner & R. Rojas: “An elementary approach to the gravitational Doppler shift”, Eur. J. Phys., 38, 015604 (5pp). doi: 10.1088/0143-0807/38/1/015604 (2016).

Pity that it infringes the EP after a while, due to the tE

In response to SQ: >> it infringes the EP after a while, due to the tE

Unfortunately it is not possible to discriminate between the two in any experiment one will see only the constant value. The variable value is either falsified or not falsifiable

Stefano Quattrini: >>Unfortunately it is not possible to discriminate between the two in any experiment

right about what?? In applying the math, never denied that!!!

This has to enter in your mind dear...

Never spoke about math errors always spoke about arbitrary application of postulates.

SQ: >>

right about what?? In applying the math, never denied that!!!

I am sorry for your lack of understanding.

Stefano Quattrini

SQ: >> I am sorry for your lack of understanding.

Which apology?

A man returns home late in the night after some meeting with friends. His wife wakes up and ask him: where is our money?

His answer: Which money?

Domsta,

so when I told you since the beginning that your formulas derived on june 4th and now corrected by Jonathan, brought to paradoxes I was right!!!!

If you knew the Physics you would have the humility to understand it before.

I arrived at the result of 1+gh/c2 in the case of accelerated rocket, before you understood that it was the right one it was the general case and you still purported your formulas which were wrong.

I see now the renewed version.

You did not have the Physical capability to understand how wrong was your initial formulas!!!!

which is what I derived with the only relativity of time as fd/fe= 1+gH/c2

SQ this morning to me:

>> You did not have the Physical capability to understand how wrong was your initial formulas!!!!

which is what I derived with the only relativity of time as fd/fe= 1+gH/c2

Your formulas were wrong Domsta.

Here all can find the derivation of the classical at higher orders, which is a good approximation of the time taken, but it is not a good approximation of the effect, which is instead well represented by the derivation with the relativistic relations.

Preprint THE DOPPLER EFFECT IN ACCELERATED MOTION, RELATION AT HIGHER ORDERS

SQ: Your formulas were wrong Domsta.

Which one?

Domsta,

june 4th

1) fD/fE =1+ gH/c2 *[sqrt(1+(gtE/c)2 )- gtE/c]

July 2nd

2) fD/fE =1+H/[sqrt(L2+t2E)+tE]

it takes a lot of imagination to make them the same, not to mention the vice to hide the c constant which does not help.

At least you should provide apologies for having declared "the gospel" and then retreated for another one....

At least in the 2nd July version there is the 1+gH/c2 (translated from your singular notation) at the bottom of your script which is the only right thing, although wrongly obtained from the ratio of proper times same as the formulas above. Good outcome, conceptual failure...

Stefano Quattrini

It appears you are referring to 6.1 and 6.2 of the png document that Joachim Domsta wrote. While I agree that, for me, at least, it "took a lot of imagination" to see that they were the same, they are demonstrably and provably the same.

To see why, refer to section 8 of the attached document.

Jonathan Doolin

2) fD/fE =1+H/[sqrt(L2+t2E)+tE]

maybe it is the case to set it up dimensionally...

tE is a time H is a length,

unless I take for granted that it is

1+H/[c*sqrt(L2+t2E)+c*tE]

what is written in 2) physically makes little sense...

Stefano Quattrini

>

>

That could be because you left out a quotient of c and changed the T to an L. It should read:

fD/fE=1+H/[c sqrt(T^2+t_E^2)+t_E]

Then factoring out a T, (Note that $T=c/g$) in this example, both emitter and detector have the same acceleration, g.

fD/fE=1+H/(c T[sqrt(1+(t_E/T)^2)+t_E/T])

Then let \phi=arcsinh(t_E/T) and you have

fD/fE=1+H/(c T[cosh(\phi)+\sinh(\phi)])

Recognizing the identity $\cosh(\phi)+\sinh(\phi)=e^\phi$, this becomes:

fD/fE=1+(H/cT) e^{-\phi}

The c hasn't disappeared, but when you replace T=c/g, this becomes

fD/fE=1+(gH/c^2) e^{-\phi}

fD/fE=1+(gH/c^2) (\cosh(\phi)-\sinh(\phi))

fD/fE=1+(gH/c^2) (\sqrt{1-(u_E)^2}-u_E)

Where u_E= t_E/T = g t_E/c

Jonathan Doolin

you forgot a c I think here, otherwise what comes out from the square root does not match dimesionally with t_E. In any case I did not change T with L, I simply copied from Domsta doc, where it is written what I started from.

In any case, I was discussing things in the current context. You took out the c, and changed the T to an L.

If you want to refer to another document, and change the current context, then post the whole document, and we can discuss that.

I've pointed this out before, but perhaps you didn't understand. Formulas that are derived under assumptions of one circumstance, are not necessarily identical to formulas that are derived under other circumstances.

I was referring to precise documents I cited there reporting what was written there exactly. Nothing more.

june 4th (6.2)

1) fD/fE =1+ gH/c2 *[sqrt(1+(gtE/c)2 )- gtE/c]

July 1st to be more precise, the case for XE=Y

2) fD/fE =1+H/[sqrt(L2+t2E)+tE]

they do not match even considering to replace L with c2/g,

And even considering the missing c at the denominator of 2) without which such equation is nonsensical in Physics

Joachim Domsta Stefano Quattrini

The first screenshot came from DopplerAccelerated2

The second came from DopplerAccelerated4

The issue is with the three clauses in the latter screenshot, in the sentence:

(A) "By repeating some former considerations of this case

(B) corresponding to the arbitrary value of c

(C) we arrive at ...

The sentence is ambiguous enough that it is easy to misinterpret it so that (B) is associated with (C)

However, I think, from the context of what Joachim actually did, he meant clause (B) to be associated with (A). Clause C was associated with DopplerAccelerated4.1 which set $c=1$

Clauses (B) and (A) refer to DopplerAccelerated2.pdf where $c$ was arbitrary.

At the end of the day what matters is that, with the use of proper times, for non rigid motion, the problem depends on tE.

This fact would imply that necessarily in a rocket two detectors at distance H would not measure the same proper acceleration. This is a direct consequence of having assumed that the relativity of simultaneity has real effects. Since such effect can be eliminated by a matrix of clocks stationary with the IRF of departure, it is obvious that it is only apparent.

>

That's true. Moreover, the solution that produces rigid motion is unique, and named "Rindler" motion. At $t=0$, the Rindler observer at $x=L$ from the horizon has acceleration $g=c^2/L$.

Correct. Their proper acceleration is $g=c^2/L$

Okay.

>

Here you have a counterfactual antecedent.

You cannot eliminate the differences in acceleration of the Rindler observers by invoking a matrix of stationary clocks at $t=0$.

Nor can you eliminate the differences in acceleration by saying "They were stationary ($v=0, g=0$) before $t0$".

Yes, actually it does not even exist.

The term vx'/c2 in LT , in accelerated motion, does represent exactly the de-sync which two clocks would undergo if they exchanged a light ray in the attempt to set in sync while having a relative speed v.

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

with these tranformations the Doppler is just (1+gH/c2), since it is obtained with the relativity of time, only which stems directly from the proper time of the observer.

I have found, in the attached (section 9), for a Rindler observer at L, observing another Rindler observer's light from L+H, will have a Constant Doppler Ratio of

CDR = IDR = f_D/f_E = (L+H)/L

Replacing L=c^2/g_L, this becomes

DR = f_D/f_E = 1+ H g_L/ c^2.

Thank you Jonathan Doolin for very precise proof that the IDR for a pair of concentric rindler motions is insependent of the instant of emission.

Best regards, Joachim Domsta

It is only math

Stefano Quattrini "This is a direct consequence of having assumed that the relativity of simultaneity has real effects. Since such effect can be eliminated by a matrix of clocks stationary with the IRF of departure, it is obvious that it is only apparent."

This cannot be decided by making arbitrary coordinate transformations alone. A rope connecting two equally accelerated objects does not care about how many clocks you have placed around in the universe.

One must also consider how the physical equations (describing f.i. materials) changes with coordinate systems. The standard relativistic transformations leave these equations the same. Other transformations leads to different equations, and predictions like length contraction of materials, as discussed by John Bell. You may use whatever coordinate systems you prefer, but some are more convenient for calculations than others. With correct calculations, the physical predictions comes out the same. Physics is coordinate invariant.

Kåre Olaussen

you are completely right in what you wrote, since I expressed myself very poorly.

The point is: such effect, although not so "secondary" for relativity, is not demonstrated to exist, although the application of the model used (LT) says that the effect has real consequences.

Such effect stems from the term vx/c2 in the LT, by a simple math on the time transform and space transform we get t'= γ -1 t - vx'/c2

by using in t (IRF0) a matrix of clocks in sync MX such that the primed IRF', has always one clock of MX at negligible distance, while moving relative to IRF0, that term disappears, what remains is simply t'= γ -1 t.

The term vx'/c2 represents the failure of the simultaneity at a distance, somebody else used already this description. It is the difference between the light time x'/c and the time x'/c +x'/c * v/c (or H/c + H/c*v/c) which a beam of light takes to reach a body going at speed v when set at distance x' from the origin.

So it is the way around, It is just a "coordinate effect" which cannot exist as a "real effect".

Stefano Quattrini

Kåre Olaussen

Joachim Domsta

In sections 9.3 attached, I first discuss how the instantaneous, L=0, \Delta \varphi, acceleration of the Lorentz Transformation, is mathematically identical with the g=c^2/L, \Delta \tau = g \Delta \varphi/c acceleration of a Rindler observer. In this section I refer to a gif image at http://www.spoonfedrelativity.com/pages/TemporalFacing.php In this animation there are not just Rindler observers, but are also time-like and space-like lines, which Lorentz transform over the course of the animation. The time-like lines represent paths of free-falling particles.

In section 9.4, I point out that real rockets accelerate from back to front, and it is molecular forces that communicate the force to the front of the rocket. I don't have any technical calculations, but I do state without proof that once the rocket reaches an equilibrium, if that rocket continues to accelerate at constant speed, then the particles should follow the path of Rindler observers.

In section 10, I have started to think about "the phase" of an emitted signal in some more detail. I'm not entirely sure where this train of thought will lead, but hopefully it will eventually provide better insight into some differences in the approaches to calculating the doppler effect.

Jonathan Doolin ,

in your pag. 45 General Case

I hope that such sentence brings to state that (1+gH/c2) is the general solution without dependence on tE so the frequency shift in accelerated motion is independent on time.

>

I don't agree. One could put the engines in the middle of the rocket like same as what occurs for sub orbital vehicles (like airplnes) which are being built, then what is the result?

so there is no more thread breaking??? In one case there is a force which "breaks the thread" between equally accelerated observers since it is supposed to increase, purported by most, and now since there is the structure of the rocket such "force" becomes constant.

Regarding the Lorentz Transformations:

have a look at the results of the elapsed time which at least, starting with 0 speed so far I did not see disagreement with Kare Olaussen about these:

• H/c for observers at rest with the emitter
• Δt = H/c (1+gH/2c2)/(1+ gH/c2) for observer in accelerated motion

and their difference - gH2/c3 / (1+gH/c2).

Being v/c = gH/c2 , that difference, at the first order is - gH2/c3 = v /c *H/c

which is vH/c2 .

That term corresponds physically to variation of the light-time in reaching a moving target going at speed v, in comparison to the time H/c which the same act would require if at rest.

It is just the calculation of the light-delay due to relative motion. Same as the desync occurring by attempting a sync procedure in relative motion instead of being at rest.

That explains the term of the Lorentz transformations vx/c2 which is just an estimation of the offset , between relative moving clocks, about same events due to the fact that the communication with EM-waves, implies a delay.

I have added another subsection for chapter 9, discussing a rocket placed in the middle of a vehicle.

Jonathan Doolin

Very interesting way to start of a new approach, very promissing for getting insight into the relativistic dynamics.

Q: Did you use fictitious or frictitious forces in the model (p.47)?

By the way the second makes for me more sense when the distance varies during the expacted equilibrium state of the motion. The first seems to be quite mysterious.

It is all ingrained in the non-metabolized difference between a time dilation which is a real and experimented fact (twin effect, gamma in muon ring experiment and Yves and Stillwell experiment) in electrodynamics and gravitation (hafele and keating, vessot and levine) and a retardation/anticipation of signals (vx'/c2) as a difference with the sync condition.

Both of them can provoke offsets between atomic clocks but the Physics behind is totally different. While the time dilation occurs independent on the transmission of signals, the retardation of signals do have effects (rather than desynch clocks) if and only if signals are transmitted. This tragic mistake which mixes apples (time dilation/proper times) with bananas (retardation of signals) is at the base of the belief that relativity of simultaneity is an effect having tangible outcomes, which by the way has never been verified in any experiment.

Joachim Domsta

There are four different lengths of concern... $L$ the distance from the Rindler Horizon to the location where the accelerating force is applied, $H$, the distance from the Rindler Horizon to the front or back end of the rocket, $\Delta x$, the length of an arbitrary segment of the rocket, and $d\Delta x$ the amount by which such a segment of rocket should be stretched or compressed by Newton's second Law.

With Newton's second Law, you can state, directly that $a = \Sigma F/m$. The reason I said "fictitious" is when you imagine the "accelerated frame of reference" it appears that the spring is stretched or compressed by gravity or other field-type force, when really, no field-force is present. In other words, the reality is there is acceleration being balanced by the force of the spring. The fiction is there is a field-force being balanced by the force of the spring.

I am currently considering Young's Law with Newton's second Law

$a=F/m= \frac{A Y}{m_{effective}} d\Delta x/\Delta x$

I am considering a beam of mass $m=\rho V = \rho A H$ which is compressed or stretched by its own weight, with $m_{effective}=\frac 1 2 \rho A H$

With these in mind, one can show:

$\rho a H = 2Y \frac{d\Delta x}{\Delta x}$

I expect if I go through section 9.5 again, being more careful with notation and keeping these three distances, $H, \Delta x, d\Delta x$ in mind, I should be able to combine this equation for further insights.

Joachim Domsta

>

In section 9.5, I have tried, with the current version, to keep the various distances as clearly distinguished as I could.

Thank you, Jonathan Doolin , but currently I am closing my SQ chapter. Hopefuly I become more available soon. Best, Joachim

BY assuming true the dependence on tE, of the frequency shift detected by the rear detector in a rocket,

• twin rockets A and B,
• departing parallel at the same time from a platform to which an IRF0 is attached
• having the same direction of motion,
• with A maintaining the acceleration g since departure
• having A and B different hystories of motion (for example B coasted and then accelerated strongly)
• reaching at the same time, with same proper accelerations g, the observer C at rest with IRF0.
• A and B communicate, at the same time, their values of the frequency shift to C, relevant to the detector sitting at the rear of each of them.

The values which C acquires are not the same (both differing from (1+gH/c2).

Their difference would depend exclusively on their history of motion to which tE has to be dependent.

The shifts would not depend according to the dependence on tE only on the instantaneous conditions of acceleration and length of the twins as measured by C at rest.

A difference can be detected realistically only if the twins counted the time elapsed with atomic clocks in sync at their departure (twin effect) showing a difference in the counting to C at the same time. That is not the case, the rear is endowed only with a trivial spectrometer to make an instantaneous measurement of an incoming frequency.

There cannot be any difference in the rockets as seen from the observer C.

So tE cannot have an influence on the frequency shift of equally accelerated observers.

As a matter of fact the choice of MCIF where the speed has to be assumed 0 for the calculation is the only viable choice. Hence (1+gH/c2) is the most general formula for such problem.

In my opinion the latest explanation by SQ has no real value as a scientific argumentation since it does not present the suitably complete system of the assumed equations, not talking about the lack of derivation of their solutions.

The problem is correctly explained.

Joachim Domsta

>

I agree, there are many ambiguities, and I think, one inconsistency.

(1) He starts with a self-inconsistent description

Rockets A and B are said to depart from the same platform, at the same time, maintain acceleration g, and reach C at the same time, which would require them to have the same history of motion. Yet he also says they have different histories of motion.

(2) He does not define if H is the height of either rocket.

(3) He does not give a clear definition of "relevant" in "the frequency shift relevant to the detector sitting at the rear of each of them."

(3) He has rocket A and B communicate their frequency shift to C, and claims these will be different from 1+gH/c^2 but does not give any rationale for the claim.

In section 9.4 of my growing "JDoolinDoppler" document, "I state without proof that once the rocket reaches an equilibrium, if that rocket continues to accelerate at constant speed, then the particles should follow the path of Rindler observers."

Rindler observers, in a rocket of height H under smooth acceleration should eventually reach a "Rindler Equilibrium" where the internal measurement of the frequency shift is measured to be higher by a factor of $1 + gH/c^2$ in the front of the rocket than it is in the back.

Once that ratio has been measured it is not going to change when it is communicated to the observer at C. But SQ claims that C receives communications of two different measurements from the two rockets.

• Does SQ mean that A and B do not measure the front/back frequency ratio to be $1+gH/c^2$?
• or does he mean something happens in the process of communication ... that somehow, C receives different information from A and B than the information sent by A and B?
• Or has SQ given H some other definition, so that $1+gH/c^2$ has nothing to do with the frequency ratio between top and bottom of the rocket accelerating at g?

pay attention !!! A and B have same acceleration at the beginning and at the end only. Only A maintains constant acceleration for the whole trip. So for sure they can have a different hystory of motion, only at the beginning and at the end they accelerate the same and are parallel. B as I said can for example coast for a while (no acceleration) and then will have a faster acceleration and then accelerate again at g.

>

yes, it is better to specify that the distance between observer and emitter (in each rocket) is H.

the frequency shift is detected by the rear detector, if you prefer.

I have rockets A and B communicating at once to C, since they arrive at once in that position. If the frequency shift which is communicated to C is not different from (1+gH/c2) then it means that it does not depend on tE (and I would agree). The rocket A was always accelerating at g, while B at a certain point was inertial (coasted) and then departed again with higher acceleration, diminished to g on reaching the speed and position of B.

If in both cases you mean that the result is always (1+gH/c2) I certainly agree with you, so no dependence on tE . On the contrary if A has one result as calculated with proper times then B has to have another result for sure, it is a paradox.

Stefano Quattrini

You have addressed my questions, and now I agree on this point

>

The Instantaneous Doppler Ratio (IDR) was independent of tE in the case of a rocket in Rindler Equilibrium. (JDoolinDoppler Chapter 9).

However, then you go on to say:

This would seem to be an attempt to argue against the claim of JDoolinDoppler Chapter 8: For observers arranged one in front of the other, with equal accelerations, the IDR is dependent on tE.

In the context of JDoolinDoppler Chapter 8, there is, in fact,

• only one time when the front rocket and the back rocket have distance $H$ between them (from their own points-of-view).
• There is also only one time when the front rocket and back rocket measure each other's relative velocity to be zero (from their own points-of-view).
• The equation for the IDR was similar to 1+gH/c^2, but with an extra factor like 1+(gH/c^2)(e^\varphi_D). The extra factor should indicate that the emitter and detector are approaching (blueshift) before t_E, and receding (redshift) after t_E. There is only one moment where the extra blueshift/redshift factor is one: (e^\varphi_D=1)

All of these are the same (unique) moment. and during that moment, you can pick out a (unique) choice of MCIF where both emitter and detector are stationary. However, under the circumstances of JDoolinDoppler Chapter 8, 1+gH/c^2(e^\varphi(t_E)) is a more general expression of the IDR than 1+gH/c^2.

Ok, I understood that you argue that in the accelerated rocket the value is always

(1+gH/c2) so in this case there is no paradox.

What is not clear though is the equilibrium which is reached. In other words the tail and head should have different proper accelerations and the structure of the rocket should cope with such finite difference at constant distance H.

Jonathan Doolin

So in principle your are giving credit to the fact that, although the frequency shift is independent on tE as seen by the observer inside the rocket, you have different proper accelerations inside the rocket providing always the same value of the frequency shift.

>

>

Yes, this is in equations (26) and (31) of JDoolinDoppler Chapter 2.

>

I would say, for completion, the coping question to be answered is to calculate the maximum forward and backward lengths, based on a material's ultimate tensile strength, density, and Young's modulus.

Mathematically, the question could be posed "At what point on the beam's length does the pre-acceleration position differ from the post-acceleration position by the amount necessary to overcome the ultimate tensile strength of the beam?"

Ok so there is general agreement that, in the case of the accelerated rocket, which is the case treated in my script since the beginning, described by somebody as "rigid motion" the frequency shift is always (1+gH/c2).

On the other hand, according to SR, the tail will have g acceleration while the head will have a different acceleration which from you script (31) should be

gE= g (1-gH/c2)

In such case the equivalence principle would fail , since also at the first order the head of the rocket does not have the same acceleration as the tail of the same order or magnitude as the frequency shift detected from D (1+gH/c2).

>

I would not, so much, say the equivalence principle fails, so much as it is misleading.

"The equivalence principle, (in relativity) is the principle that, in any small region of space-time, the effects of a gravitational field are indistinguishable from those of an appropriate acceleration of the frame of reference. "

In the region H

the indistinguishability of the two implies that in an experiment you focus on what occurs inside the elevator, otherwise it is certainly determined by looking outside if you are in a gravitational field or in accelerated rocket.

Let P be "indistinguishability of gravity and acceleration"

Let Q be "small region of space time"

Let R be "poor precision in devices measuring Newtons/kilogram or frequency shift"

I have stated (Q and R) implies P

You have P implies Q.

The logic is not equivalent.

I did not state that P implies Q, I stated that P implies that even in the small the accelerations of head and tail cannot match.

First you stated (P implies Q) otherwise (NOT Q implies NOT P).

Now you stating (P and Q) implies (NOT R).

The Equivalence Principle is: (Q and R) implies P.

In the scenarios of JDoolinDoppler Chapter 9, we have reached (NOT R) without any reference to the equivalence principle. This denies the antecedent of the equivalence principle, nothing is to be gained by attempting to apply it now. (except, perhaps the recognition that this thing shouldn't be called a principle.)

(NOT R) is "We DO have sufficient precision to measure a difference"

The idea by Jonathan Doolin to use dynamics for describing the rigidity of an accelerated "rocket" requires - I think - first to consider the simplest case of two massive points joint by a spring. Despite it seems to be easy, I have no rigorous proposal yet how to manage this case. Let me try, however, to formulate some doubts implied by the requirement that the info about the acceleration of one end-point is transferred to the second end with the speed of light. This would lead to delay which means that if the ends were at rest till t=0, and the rear/tail started to move at intsant zero due to a force pushing it, then the head will stay at rest untill the info reaches it. Hence - in no case this would be a rindler motion concentric with the one of the rear. Isn't this proper line of argumentation also for inapproprietenes of the explanation of the constant length by some forces in case of continuously distributed mass of the rocket between the head and the tail?

LT implies the variation of frequency fd/fe, for the Longitudinal Doppler, in reason of the term vx'/c2 which is a desync, the term which "mixes" space with time.

It represents the "failure of simultaneity" between moving objects originally found by Henri Poincare after defining the simultaneity at a distance for stationary objects (sync procedure same as Einstein) with light beams.

The Linear Doppler effect fd/fe=1+v/c for moving observer, in classical mechanics (CM), is a direct consequence of the conservation laws applied to the energy and momenta of the quanta of light (when v