1) the "apparent" reciprocal delay present in the LT disappears

2) the twin effect is immediately derived and consistent, while the LT require some passages which are of doubtful application due to what should occur in non inertial motion.

3) according to the LT if a body sees a red-shift by transversely emitted radiation, the other body moving inertially has to see a red-shift as well of the transversely emitted radiation. This has the consequence that the same radiation bouncing back and forth several times, from parallel moving IRFs would lose its energy in either frames of reference till it disappears.

According to the TT instead there is blue-shift if the radiation absorbed is emitted by the body who sees the red-shift. This is in agreement with the conservation of energy, since the frequency is reinstated in a loop.

3) the simultaneity is no more relative but absolute, although the moving clocks have a different period than the stationary ones. In accelerated motion two clocks set in sync and equally accelerated are not in sync after the end of the acceleration phase as a prediction of the Lorentz Transformations. They remain in sync with the TT, so that same history of motion correspond to same final setup of the clocks proceeding at same final speed.

4) at variance with the LT, their use in circular motion is possible due to the infinite speed of signals, where the Einstein sync procedure cannot be applied...

above all there is not anymore the Lorentz Invariance which causes all the above and is consequence of having admitted/postulated the constancy of speed of light everywhere and necessarily used that constant speed as a base for any sync method.

In this video is shown what would come out with the TT transformations

.https://youtu.be/asC2NYOCD50

at variance with the LT which would predict a redshift of the radiation for the rectilinear motion which would cause a discontinuity of behaviour.

Dear Stefano, I assume the main motivation for inventing the TT transformations was to introduce faster than light signals as you have stated. However, Lorentz invariance in SR has been very well tested in particle physics in particular. But then, what can explain the superluminal properties of entanglement within a Lorentzian spacetime? One answer to that quandary is presented in arXiv:1909.03845 [gr-qc] where it is shown that information can be transmitted superluminally by the Lie derivative of the metric \Psi_ab along a regular vector to its antisymmetric partner K_ab. This follows from the fact that the Lie derivative is invariant under the Diff(M) group of which the Lorentz group is a subgroup. The larger group is not limited by the speed of light which is the restriction in Lorentz transformations.

Dear Gary,

>

not necessarily. They natively get rid of the Invariance by assuming a local preferred frame, they are COVARIANT with a variable speed of light.

In addition we cannot find other transformation for superluminals, we should have only one type.

The Ginzburg's search of superlumnial sync stops at the light-spot which is a tecnique where only the phase is used, not actual signals..

not in the way it should be tested.

you give an additional reason for adoption of different transformations...

Stefano, what do you mean by "not in the way it should be tested" referring to Lorentz invariance in particle physics?

No, I did not "give an additional reason for adoption of different transformations..." but simply stated that larger group Diff(M) is not limited by the speed of light which is the restriction in Lorentz transformations. The Lie derivative is a solution to the superluminal quandary as stated. There is no need to abandon Lorentz invariance and it is most likely foolish to do so based on experimental evidence (that you are apparently rejecting).

Dear Gary,

yes..

locally it is simply impossible to appreciate variation of the speed of light with the experiments so far performed.

I don't reject LI thoroughly, I simply say that it is a particular case due to the choice of the transformations adopted which define a group. There are actual issues which are not easy to grasp...

The issue solved with the re-normalization are basically due to the systematic adoption of Lorentz Invariance...

What is left untouched, according to my opinion, is the invariance of the rest mass in electrodynamics with the overlytested mass energy equivalence..

Preprint FROM THE RELATIVISTIC MOMENTUM TO THE MASS ENERGY-EQUIVALENC...

which experimental evidence is strictly devoted to the LI or the constancy of the speed of light one-way, which is impossible to demonstrate unless in the problem of equally accelerated clocks which has never been performed.

Here a more specific paper on the superiority of the TT

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

Superluminal Velocities in the Synchronized Space-Time Sergey Yu. Medvedev Department of Physics, Uzhgorod National University

Again this one

https://medcraveonline.com/PAIJ/testing-einsteinrsquos-second-postulate-with-an-experiment-of-the-sagnac-type.html

this is the interesting dissertation of Selleri... where it is clear that the

inertial transformations are more powerful and general than Lorentz

http://blog.hasslberger.com/docs/Selleri_Weak_Relativity.pdf

As written in the following paper there is no other choice that the speed of light is variable with gravitation as initially thought by Einstein and strongly supported by Abraham and Levi Civita.

Preprint SHAPIRO TIME-DELAY, Curved 4D space-time or Variable speed of light

It gives the Tangherlini Transformations a remarkable added value.

Dear Sofia,

use appropriately means that he found the right thing but then he did not use it as he should have to. The proper time is indeed experimentally verified.

Minkowski lost the opportunity to overcome the Lorentz Transformations. LT sets unnecessary constraints to reality. They mix something strictly related to the proper time (gamma factor), irrespective of sync procedures or signal exchange, to what is strictly related to light transmission and clock synchronization...

The LT can be expressed also in the following from

(1) t'=gamma-1t -vx'/c2

and

x'=gamma(x-vt)

the term vx'/c2 is strictly related to the sync procedure adopted.

in accelerators the term vx'/c2 , which is a time, gets negligible due to the fact that x'/c is very small since c goes across that in negligible time (with v/c is always lower than the unity), hence it is t'=gamma-1t, easy to find from the proper time definition.

So the LT work in accelerators due to this fact and to the fact that all is referred to center of mass, which ensures the respect of symmetries which physically are yet another particular case.

When the time x'/c cannot be considered small the LT introduce errors and especially in the case of low speeds, gamma=1, you have

t'= t -vx'/c2

which is not a Galilean transformation t'=t. It gives results only if there is an exchange of signals, otherwise there is no way to make one clock in a relation like that with another one.

By displacing clocks in a suitable large volume relevant to the same IRF0, all in sych thanks to the Einstein Synch proc, vx'/c2 goes to 0, since the desynch with the closest clock , same as with any other in IRF0, is negligible.

hence you have

t'=gamma-1t

and

x'=gamma(x-vt)

which are the Tangherlini-Selleri-Marinov transformations where the simultaneity is absolute and light speed is not anymore and invariant.

The term vx'/c2 represents the failure of the simultaneity at a distance which affects the Lorentz Transformations. LT in this regard are just a particular case, due to a constraint which affects important degrees of freedom necessary for the unification of the interactions. That term has to be implemented on purpose, it is avoided in the more general Tangerlini transformations which complies with all the experiments so far performed in electrodynamics but throws in the bin the relativity of simultaneity for good.

I invite you to have a look at this paper Article A twin paradox for 'clever' students

which describes quite well the LT at low speeds and what happens, although it arrives to conclusions in disagreement with the evidence he shows. in other words he is trying to invoke a "time-dilation" even if there is no gamma around...which is like having understood nothing about the actual Phyiscs..

he is not able to understand the difference between a desynchronization due to application of EM waves (RELATIVITY OF SIMULTANEITY) and desynchronization due to time/dilation (RELATIVITY OF TIME) which is independent of EM waves. But actually this is quite usual...

Dear all,

Being t'= t *gamma-1 -vx'/c2 an equivalent form to LT of the transformation of time,

a) the first term is independent on exchanged radiation, as experiments confirm, while

b) the second term vx'/c2 vanishes in absence of light beams, and even then there is also another step to take, in order to make it real. It is a legacy of the sync procedure adopted just a retardation of signals in reaching a moving target.

That term v/c*x'/c is in any case virtually 0 in accelerators since x'/c accounts for extremely short times usually far below the elapsed times involved in the dynamics.

As a matter of fact in accelerators t'=gamma-1t hence a much more general transformation is used which is actually the absolute transformation of Tangherlini, in which the simultaneity is an invariant and LT are just a very particular case.

By using the equivalent form of LT and by considering γ = 1/√(1 - β2), β = v/c

LT: t'= γ-1t - vx'/c2;______x'= γ(x-vt).

TT: t'= γ-1t;_____________ x'= γ(x-vt).

GT: t'= t;________________x'= x-vt.

1) The approximation to classical Physics is given by |v|/c> 1 due to high speeds and x'/c TT: t'= γ-1t ; x'= γ(x-vt)

Lorentz transformations and TT at high speeds and very short distances in the primed frame are the same.

____________________________________________________________________

3) for γ->1 and t >> vx'/c2 (very short distances in the primed frame such that that x'/c is not detectable by laboratory instruments)

d) LT: t'= γ-1t - vx'/c2; x'= γ(x-vt). --> GT: t'= t ; x'= x-vt

Lorentz transformation reduce to Galilean only for low speeds and very short distances in the primed frame which is not at all general.

CONCLUSION

Tangherlini T. have the non trivial advantage over LT that, whenever the speeds are sufficiently low such that γ->1 , they reduce to the transformations of classical mechanics.

In accelerators they can be used in replacement to LT.

Dear all,

this paper talks about the advantages in ED to use TT instead of LT

Preprint Field-free electrodynamics

Article Implications of an Absolute Simultaneity Theory for Cosmolog...

Dear all,

just to clarify a bit about a non-acceptable result of SR using LT in the calculation of the twin effect:

Regarding the first picture with the clocks it is a simplification of LAAS proposed configuration:

The moving clock on the billiard is initially set in sync with the clock at rest with billiard, hence was in sync with all the clocks. The time dilation is intended as the difference (desync) between the moving clock and any of the clock at rest when crossed at 0 distance. Such configuration of time dilation is the correct one and is the one predicted by the Tangherlini Transformations.

Considering LAAS conclusion of his paper

LAAS considers the twins A and B initially at rest in IRF0 then the trip of B is:

a) twin B accelerates with g acceleration to speed v in one direction,

b) B coasts away from A

Laas:" A will age less rapidly than B from B's viewpoint"

c) B decelerates at -g, till stops in IRF0:

Laas:" B's clock will run at a much slower rate than A's clock"

"it is precisely during this deceleration period that A becomes older than B"

d) B accelerates again in the opposite direction

e) B coasts

d) B decelerates and stops besides A (B comes back from the trip).

As a matter of fact there is a specific situation, the deceleration where the aging is supposed to be much faster, that represents a huge flaw in the prediction power of SR. That absurd variation should be found as well in the problem I illustrated describing the bouncing ball The bouncing event of the ball but nothing occurs during that bouncing.

The prediction relevant to when B is coasting: "A will age less rapidly than B from B's viewpoint" is even a worse bogus of SR.

Yet another support for the Tangherlini Trasnformations

Article Why the Sagnac effect favors absolute over relative simultaneity

A test to discriminate between validity of transformations:

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

Here is a script which provides an explanation in terms of conservation laws of the time dilation of atomic clocks.

Preprint On the frequency shifts of oscillators in electrodynamics an...

Both transformations are artificially produced by mere mathematics . Both have absolutely NOTHING to do with the Reality of the Physicalistic world around us ,,,,,,,,,,,,,,,

LT itself is only suited for relativity , non-Machist relativity in the peculiar manner Prof Einstein wanted it to be. . . . ..

Stefano Quattrini I have a question in regards to TT rather than LT:

There seems to be something odd here: The LT have both x' and t' equal to γ times some expression involving x and t. but the TT equations have x equal to γ times an expression involving x and t' equal to 1/γ times an expression involving t. Doesn't this mean that in the TT there would be length contraction and time contraction (rather than Dilation).

How can the TT be claimed to predict the same results as the LT in regards to Time Dilation and Length Contraction (in so far as all the current experimental evidence is concerned)?

Declan Traill ,

it is enough to write the Lorentz Transformations in the equivalent form:

t'= t/γ - vx'/c2

x' = γ(x-vt)

TT is also obtainable when vx'/c2 is sufficiently small, due basically to x'/c negligible, that occurs for sure in accelerators..

t'= t/γ

x' = γ(x-vt)

Time dilation can be considered in the following equivalent ways:

moving clock ticks less

clock-rate of the moving clock is lower,

period of the moving clock gets longer.

t'=t/γ it means that t'

Stefano,

Ok, thanks - I see…

Stefano Quattrini I now know why I got confused. In your introductory text for this topic, you said "(LT) x’=γ(x-vt) ; t’= γ(t-vx/c2) "

Now you are saying:

t'= t/γ - vx'/c2

x' = γ(x-vt)

See how t' has changed?

Declan Traill ,

I was missing your post ..

which is the LT written in the Einstein's form

>

are the LT written in Lorentz' form.

They are equivalent, you can see by applying some algebra.

Oh! I didn’t see the prime ‘ on the x in the t’ equation!!!

To Stefano Quattrini

Dear Stefano, I hope I've got now more time to continue our interesting talks on the Tangherlini Transformation defined by the equalities (if discussing the case of (1+1) space-time):

x'= gamma (x-vt) . . . . (TT1)

t'= t/gamma . . . . . . . . (TT2)

Beside your contributions at least thos within RG, I found some references adjoint to the post with

"Fifty Years of the Tangherlini Transformations - an Alternative Version of Special Relativity", May 2009, by Dmitri Rabounski and Gregory Malykin, available at

https://www.researchgate.net/publication/253103416

It would be interesting if we could return to compare the two alternatives given by TT and LT with the the third option: the piecewise linear mappings of the world as seen by an observers reading only the positions of emission and instants of detecting the light continuously sent from the observed objects. If I remember well, these were (for some subregions) given by the equalities

x'= alpha (x - vt)

t' = t/alpha

where alpha = exp(theta), with theta = inv_tanh(v/c) (rapidity)

Unfortunately, I cannot find my post on this. I would be very grateful if you have a possibility remind me this note(s).

What distinguishes TT from LT is the preserving the simultanety and preserving of the two way speed of light (which I got to know from you:-) though not forming a group of mappings (implying the need of considering the preferred IRF).

In turn, the linear extension of the third transformations (over the whole Minkowski space) preserve simultaneity too and form a group of mappings, which makes them convenient for passing with calculations between more than two IRFs. However they do not preseve the speed of light (which is not strange since for such mappings the light is used as the messanger reporting the positions only.

Best regards,

Joachim

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Stefano Quattrini added a reply

2 minutes ago

Dear Joachim Domsta ,

>

Yes. You can find it also in the head of the thread. Also the link to the thesis of Tangherlini in which these transformations were conceived is there

http://zelmanov.ptep-online.com/papers/zj-2009-04.pdf

yes I remember that you did something like that once.. I have to find it again... but as I remember you did it for Lorentz not for TT.

>

this I don't remember...

Tangherlini, the US physicist, suggested an original procedure of synchronizations of clocks at two distant inertial frames, which totally differs from Einstein's method . Einstein's method uses light signals, while Tangherlini's method uses faster-than-light signals, e.g. phase light spots produced by a rotating laser . According to Einstein's special theory of relativity, laws of nature must be valid in all inertial frames which are connected by Lorentz transformation. This transformation is a linear transformation, where the scalar product defined in the four-dimensional Minkowski space remains invariant and satisfies the group properties. HERE COMES THE CORE OF THE CONUNDRUM . It is shown, despite the aforementioned circumstance and also despite the fact that the Tangherlini transformations differ from the Lorentz transformations (in particular, the Tangherlini transformations allow the velocity of light to be anisotropic in a moving inertial frame of reference), the Tangherlini transformations provide adequate explanations to all known well-verified experimental tests of the Special Theory of Relativity.

The anisotropic neighborhood also has the manifolds thereof coming together without impinging upon their own locally valid "Laws" as well . Several possible applications of the Tangherlini transformations could give an explanation to the effects, already predicted by physicists but not yet registered. In particular, once the effects have been experimentally observed (a possible violation of the Lorentz-invariance may be involved), the effects might be more properly described with use of the formalism of the Tangherlini transformations. During the last seven decades, physicists have discussed kinematic theories which are claimed as alternatives to the Special Theory of Relativity, or are based on transformations of the spatial coordinates and time from one inertial frame into another one which differ from the Lorentz transformations ,too .

Dear Stefano Quattrini

Thanks for your response. Now I am trying to verify more rigorously what I expected, that the two way light velocity remains c after TT. Unfortunately I have met some problem with this proof, thus I need to read the papers you have referred to much more carefully.

Regards, Joachim.

PS. Due to my troubles with internet I expect to be back not earlier than tomorrow evening. JoaD

Joachim Domsta I have that proof that the two-way speed of light is c despite there being anisotropy (c-v and c+v light travel times in the moving frame:

See Section 2 The Vacuum Mode Interferometer in my paper here:

https://www.scirp.org/journal/paperinformation.aspx?paperid=115944

Declan Traill

Thanks for the interesting considerations. Possibly they are somehow related to TT. In any case it seems important to do research on models of transformations ensuring invariance of the 2-way speed of light. My analysis of your paper need some time I get to "translate" it to my way of structuring the content.

Regards,

Joachim Domsta

Declan Traill

Consider two charges q and -q, which are in the same place for t ≤ 0 and are also in the same place for t ≥ ∆t.

but move against each other in the interval 0 < t < ∆t, separating at time 0 at location r0 and coming together again at location r1 at time ∆t. A field which propagates from these two charges at the speed of light and at the location r only

for times t different from zero, for which t > |r - r0|/c and t < ∆t + |r - r1|/c are valid and independent of the inertial frame in which we live(inertial frame in which we are located). (Great Problematik is that we have to necessarily assume that the charges do not move with superluminal velocity).

If we choose in particular ∆t infinitesimal, then the light flash comes at the

time t = |r - r0|/c, so it moves with the speed of light itself . Since the transformation is not compatible with the

laws of Newtonian mechanics and it is not compatible with the Maxwellian - equations.

(the light must propagate in a moving inertial system with a velocity depending on the direction).

THEN : the question arises which of the three possibilities is fulfilled in nature:

(i) there is an excellent inertial system for electrodynamics, for which the Maxwellian equations only hold (Ether hypothesis).

(ii) modify the Newton's mechanics,

(iii) Maxwell's equations have to be modified.

REZA

Reza Sanaye As the two-way speed of light is still c, despite the anisotropy in the moving frame, Maxwell's equations will still be seen by the moving observer to be observed. For an external observer, Maxwell's equations are also still seen to be observed, but the shape/frequency of the EM waves being observed will be different. This difference is the de Broglie waves we observe of moving matter.

Declan Traill ,

The homogeneous Maxwell equations, the ones which lead directly to the wave equation, are invariant under Lorentz Transformations, for sure. This has been demonstrated long ago by Lorentz and Einstein and I checked it myself, meaning that in such case the fields E and B are covariant under LT.

The weak point remains in the transformation of the charge density in the inhomogeneous equations.

I exchanged several mails with Vladimir Onoochin and I pointed out a possible mistake in a crucial point of a script he was publishing. He found then, with the help of another guy, the correct solution and finalized the paper belowPreprint COMPARISON OF EINSTEIN'S AND LORENTZ'S APPROACHES TO PROVING...

He did not know TT but apparently he found them initially in a wrong way (I told him that he indeed derived the inertial transformations) finally he found TT or inertial transformatons as the ones preserving the Invariance of the non homogeneous Maxwell equations.

Dear Joachim Domsta ,

it should be clear that the application of the equivalence of the inertial frames to Einstein's train embankment experiment is quite questionable.

Preprint Einstein train-embankment thought experiment revisited

there are two compelling facts described in paragraph 5 which should be more than sufficient to show that there cannot be any equivalence in such experiment.... not even approximated at the first order in v/c.

homogeneous Maxwell equations , elected to be true representative of wave equations , still have to deal with spatial anisotropy that even they themselves are prone to give rise to . Bifurcations and multi-furcations on the route would most naturally lead to come of the invariancies observable on topologies with non-smooth routes . More than 6 decades ago , it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support surface electromagnetic waves, which now play crucial roles in plasmonics, metamaterials, and nano-photonics. Here we show that surface Maxwell waves at interfaces between homogeneous isotropic media described by real permittivities and permeabilities have a topological origin explained by the bulk-boundary correspondence.

Stefano Quattrini

Dear Stefano,

Before I may have any answer to your question on chapter 5, I need to understand your conclusion of the thought experiment your have inferred in chapters 1–3.

After thorough analysis I doubt about  your convinction that the lights signals starting at A and B are simultaneous for both observers M  and M’.  Please note that setting equal indications of all clocks does not make all the events E(A), E(B, E(A’)  and E(B’) simultaneous in both  IRF and IRF’.

As a basis of my doubt I would like to mention that (at least within SRT) synchronization remains valid only  for comoving clocks. Of course it is not the same as simultaneity, though these two families of features (simultaneity  and  presence of synchronization) stay in some correlation, I think.

Regards,

Joachim Domsta

Dear Joachim Domsta ,

It is crystal clear to me that light will not strike at once in M' but will strike at once in M. I never stated that Einstein, in affirming that fact was wrong.

"Einstein thought experiment involved two beams of light, emitted at once from two different positions A and B, belonging to an embankment. An observer M sits on the mid-point between A and B, detecting at once the light emitted by A and B. A moving observer M’ overlapping with M, when the light is emitted from A and B, detects the light from A and from B, not at once. That is a natural consequence of retardation of light in reaching a moving target."

The above is my description of the train embankment thought experiment (TBTE), the effect illustrated by Einstein is a physical effect, the same found in rotational motion as the Sagnac effect.

Light crossing a shorter path (approaching M'), will arrive first to the target. In TBTE the same result can be obtained even with bullets .

In Sagnac effect this fact is even more compelling and it is not possible to use bullets.

Sagnac effect also demonstrated the independence of the speed of light on the source which I assumed was true in the following part of the paper.

NEVERTHELESS Einstein's experiment is not sufficient at all in demonstrating anything about simultaneity because the emission of light occurs only in the stationary frame hence it does not involve relations between experiments occurring in different frames, which are necessary to state something.

Simultaneity is based on equal indications of clocks at once, otherwise, it would not be even measurable. The point is, is it possible to set in sync clocks that way?

It is not possible in the case of equivalent inertial frames, but as I said in point 5 at least in the TBTE there is no room for an equivalence hence simultaneity can be certainly absolute.

If the equivalence of inertial frames is fulfilled as I mentioned, pairs of clocks in sync will desynchronize twin pairs of clocks in motion.

In the TBTE, as written in point 5, these frames cannot be equivalent, the embankment is a preferred frame and the simultaneity can be transferred to the train from the embankment.

Dear Stefano Quattrini

I think that within SRT this alleged inequivalence is solved by the followng argumentation: the embankment is distinguished by the author of the experiment, who has performed synchronization of A and B in the rf of embankment (and in the sequel A with A' and B with B'). The results will be the same (mutatis mutandis) if the sychronization of A' and B' is performed within the rf of the train (and in the sequel A with A' and B with B'). The light beams will reach M' instantly and in different instants they will reach the observer M.

Regards, Joachim Domsta

Dear Joachim Domsta ,

Dear Stefano Quattrini

It depends on the definition of equivalence; it was never defined rigorously within many threads of RG known to me; and I am not so clever to guess it :-(

Of course it cannot be a proof of ROS since this is just a thought experiment. However by accepting SRT (which is born with SOR), the weak equivalence mentioned by me may be seen as explained. For understanding your opinion I need more details of the definition you use.

Regards, Joachim

Dear Joachim Domsta ,

it is easier to define the non-Equivalence of inertial frames: given two frames with the same experimental setup (in my description in both systems there are two clocks, set at the same distance, able to trigger emission of waves towards an observer set at the center of them) , following the same procedures (on overlapping with the corresponding clock both emit photons), if the outcome of one experiment differs, the frames are not equivalent.

Yes, but also for the fact that the simple TETE (train-embankment...) does not prove anything at all. That is why there are two alternatives:

ABSOLUTE and Relative of simultaneity.

Ros is the impossibilty to use pairs of clocks in sync to synchronize twin pairs of clocks in relative motion.

That is not what the TETE showed and Sagnac too which is more complete.

I certainly miss that, I do not remember when you mentioned.

Dear Stefano Quattrini

The weak equivalence here is meant by me the property implied by SRT:

If we apply the synchronization wihin IRF and send simultaneously two signals from A and B toward the center, then they arrive at M at the same instant and in different instants to M'

which under switching the system indicates the same relation:

If we apply the synchronization wihin IRF' and send simultaneously two signals from A and B toward the center, then they arrive at M' at the same instant and in different instants to M.

Obviously I realize that this is not pure sense equivalence unless finished by much more rigorous formulation. However I thought wrongly that you tried to suggest lack of the second property of this scenario.

Thank you for your question.

Joachim

Dear Joachim Domsta ,

yes, to my understanding your suggested configurations are fully supported by Sagnac's, with the interferometer rotating with the source or at rest with the axis of rotation. In both cases the interferometer will not receive the pulses simultaneously and the delay is exactly the one registered in the non-rotational configuration (only a matter of path length).

Nevertheless, the frames in the Sagnac effect cannot be equivalent, otherwise, all frames should be equivalent, regardless if they are inertial or not. So the effect you describe cannot rely on the equivalence of inertial frames.

The Sagnac effect is not a proof of Relativity of simultaneity either, but only a proof of the independence of the speed of light on the speed of the source.

I consider your proposal a verification of the reciprocity of the behavior of light emitted in a condition of relative speed, which, by the way, involves the longitudinal Doppler effect which testifies a longitudinal motion relative to a source. M' in TBTE detects a Doppler effect same as M in your reciprocal configuration.

Dear all,

here is a paper

"Optical data implies a null simultaneity test theory parameter in rotating frames Edward" T. Kipreos∗ and Riju S. Balachandran†

testifying the supremacy of TT over LT.

https://arxiv.org/pdf/2106.09537.pdf

Comparison between TT and Standard Lorentz Transformations:

Conclusion:

• The Tangherlini transformations offer a valuable alternative perspective for analyzing relativistic phenomena, providing clear and consistent explanations for various scenarios.
• Their assumption of an absolute frame of reference simplifies the analysis and avoids certain paradoxes and ambiguities associated with the standard Lorentz transformations under Einstein's interpretation.
• While the standard Lorentz transformations have been extensively tested and confirmed in a wide range of experiments, the Tangherlini transformations highlight the ongoing discussion and exploration of the foundational principles of relativity.

In summary, the Tangherlini transformations provide a consistent and straightforward framework for understanding various relativistic phenomena, offering clear explanations and avoiding certain conceptual challenges associated with the standard Lorentz transformations under Einstein's interpretation of special relativity.

Article The Sagnac effect and the role of simultaneity in relativity theory

Why one at all should bother about anything that is non-physical (not satisfying the “material objectivity”) that is different from ondulatory (for sound) or (re-)emissionic (for light/EM-waves), no matter that form-invariance/“covariance“ (or, ”equivalence of frames”) may not preserved?!

Anyway, the question should be what is the meaning of the latter(s) - that the solution of the wave equation in particular inertial frame provides the correct rropagation) and/or providing correct evaluation in another inertial referent frame (which apparently cannot be fulfilled with either of the two).

On the other hand, the very wave equation may not be the ‘full-fledged’ model for the EM waves propagation, since longitudinal waves (as primary mechnism underlying the the appearance and propagation of transverse waves), that is non-zero valued divergences of electric and/or magnetic inductions are not accounted for…

Slobodan Nedic ,

in a medium the frames cannot be equivalent, I guess you know that... there is a preferred frame...

Stefano Quattrini I do know, of course - so, under (wrong, though) assumption that the light/EM-waves propagate undulatory (in the Aether as sound in the air) only Voigt’s transformations should be used.

Lorentz field transformations or Tangherlini coordinate transformations

Slobodan Nedic not wrong! I have proven it to be true. See my paper here outlining the experiment that proves it: Preprint Detection of light speed anisotropy and Aether wind speed us...

Declan Traill Thank you bery much for your article with the - by all means - effecticve experiment, which still might not be the proper one to distinguish/resovle on the mechanism of light/EM-waves in the ’empty’-space/aether. The experiment being reminisent of the Sagnac-effect/laser-gyroscope, as far as I know, the second postulate cannot explain them (Dr. Cynthia Whitney), and (re-)emission theory can (Dr. Dowdye), but I don’t know how it would be about the undulatory mechanism of propagation !?

Slobodan Nedic ,

Sagnac effect, can be reduced to travel-time of a wave packet in regards to a moving target. It is very well explained by Lorentz-Larmor electrodynamics which at the end of the day relies on the Lorentz field transformations and Absolute Lorentz coordinate transformations (Tangherlini). In LLE light is measured isotropic (or more isotropic) only in the stationary frame of the lab, and not measured the same for relative moving bodies inside the LAB.

Stefano Quattrini , The Tangherlini transformations are just the transverse Doppler effect. They are equivalent to the Lorentz transformations for the case of x = vt. If however, we use x = ct in the Lorentz transformations, we have the return-path longitudinal Doppler effect for light.

Frederick David Tombe ,

yes, nevertheless has so far the same prediction power as SR, without any paradox.

Lorentz field transformations can account for Doppler since they admit a preferred frame.

Lorentz coordinate Transformations cannot because they infringe conservation laws and it is evident in the Doppler Radar

Stefano Quattrini , The truth is, that the Lorentz transformations are never coordinate frame transformations. They are either Doppler effect or they apply to the change of the electrostatic field surrounding a charged body into a magnetic field as it accelerates through the EM wave-carrying medium, towards the speed of light.

The paradox is only one of the absurdities associated with abandoning the aether and treating the LT as coordinate frame transformations. The other absurdity is time dilation itself, even without the paradox. Lorentz's local time was the answer, had he only identified it with the angular frequency of the tiny rotating entities that make up the EM wave carrying medium.

Frederick David Tombe ,

LT, in Einstein's interpretation are coordinate transformations, but they are not correct. Einstein's interpretation of LT is not Physically correct for several reasons one of which is that the RDE, if derived in the condition of the equivalence of inertial frames, infringes the conservation laws.

LT cannot be coordinate transformations because in Lorentz Interpretation which is correct, t' is not a coordinate time. They are field transformation FT so basically LT are a version of the LFT.

Time is instead a coordinate time in Tangherlini transformations which are correct as coordinate transformations. For light waves in any cases the LFT must be used which agree with TT in case light is not used, because the retardation term is not present.

Preprint Einstein train-embankment thought experiment revisited

Preprint Length contraction as a necessary consequence of the two-way...

Stefano Quattrini You might be interested in my animated modeling of different scenarios, including the one you have illustrated:

https://www.energyfieldtheory.com/copy-of-about

And the 3rd animation on this page:

https://www.energyfieldtheory.com/demos

Incidentally, you can download theinteractive PC demo apps for all of this modeling at the top of this demos page too!

It is called InterferometerTiming.exe

a paradox in the application of the Lorentz transformations

Preprint CONSERVATION LAWS and the Doppler effect through the Doppler RADAR

Stefano Quattrini It's seems OK to apply the Tangherlini/Selleri transformations to atomic clocks in the GPS. They are of course simply the LT in the special case of x = vt.

But as regards the LT of fields, in order to bring a vxB out of E, we need to use the more general LT where x remains unspecified.

Frederick David Tombe ,

sure but

a) the time of LT is not the actual time but a fictitious one except in some special cases where TT and LT match

a) use Lorentz Field Transformations not LT

b) even if you use LFT the result is approximate due to the following problem

Preprint CONSERVATION LAWS and the Doppler effect through the Doppler RADAR

Stefano Quattrini When I referred to the LT, I was referring to the Lorentz field transformations. There is only one physical rest frame and so I was not considering the concept of inertial frames of reference in relative motion. And time, in those field transformation equations refers to the frequency of the tiny vortices that make up the EM wave-carrying medium.

Article The Lorentz Aether Theory

It does not refer to the astronomical time that we use to measure the passing of the day.

Frederick David Tombe ,

the four-vector notation with energy and momentum for example does exclude the presence of a physical rest frame.

Stefano Quattrini I don't see how the four-vector analysis excludes a physical rest frame. I have gone through the 4D space-time analysis here at section VI, and then followed up with a physical interpretation at section VII,

Article The Lorentz Aether Theory

Frederick David Tombe ,

Stefano Quattrini There only is one frame of reference in the analysis which I provided. It's the frame of reference fixed in the physical EM wave-carrying medium.

A short comparison between the results of TT and LT

TWIN EFFECT

a) From experiments Twin-clocks show different counting when rejoined after separation.

(LT) The "clock-rates" are the same according to SR (all clocks have the same "rate") it is only the trajectory in SpaceTime to make the difference. It Shows that LT is just a tool of calculation in this case.

(TT)In TT all clocks moving in the isotropic frame, change their clock-rate in reason of their kinetic-energy per unit of rest energy (ECIF, GPS) as referred to that frame.

DIRECTION OF LIGHT

b) no experiment available so far

Einstein light clock by applying LT predict tilted light trajectory in the moving system, if observed from the stationary system.

Let's consider two sources A and B at rest which emits waves in the same direction, and they hit the same target.

if B is brought in another position and accelerated to a speed v perpendicularly to the trajectory of the light, if A and B emit again from the same position.

"A" will hit the target in the lab while B will miss the target. The distance where Bwave hits the target is a function of v.

Equivalence of inertial frames implies a composition of the SOL sideways with the "velocity" of the frame.

In TT, the light goes straight in an isotropic frame like ECIF. In a lab on the surface of earth, it is approximately isotropic, no artifact of sideways is foreseen. Any moving system in the preferred frame will "see it tilted".

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

SAGNAC effect and desynchronization

c) Waves emitted simultaneously by a moving emitter/observer in a close loop are detected non simultaneouly.

A and B are set in sync from a central synchronization procedure or from the isotropic frame, testing their synchronization by exchanging light, the return time is not H/c but H/c-vH/c2 or H/c+vH/c2, as a first approximation.

LT interprets that as time keepers having an offset so they are "unsynchronized" having been synchronized when at rest.

By using Eisntein sync procedure in a sequence of equally separated clocks by H, along the circle of length L, the the final result with LT about Sagnac is a desynchronization of the last with the first clock vL/c2 .

That is the "accumulated failure" or TIME GAP involving the Einstein synchronization procedure used in motion.

It simply shows that the use of LT in this realm of circular motion is not appropriate as also Einstein et al used to say.

it is explained straightforwardly with TT without resorting to unnecessary synchronization procedures. It is enough to apply time dilation for the moving observer.

TT interpretation is simple: light increases or decreases its retardation in connecting A and B which move in a frame which has been requested to be isotropic. Since it did not cover the same distance H but a bit more H+ H*v/c or a bit less H-H*v/c considering the frame where the axis of rotation is at rest approximately isotropic.

In TT the offset has nothing to do with a "desynchronization" (as the one occurring in the twin effect) , it is just an apparent effect due to the use of light signal in non-isotropic frames to establish simultaneity (moving frame is not isotropic if there is a frame where it is isotropic like ECIF).

LIGHT-TIME VARIATION

d) if on the LASER-GYRO, the interferometer goes close to the speed of light, light must take a much longer time than H/c to reach it. In opposite direction light should take much less time than H/c, hence the result is totally ASYMMETRIC.

The offset between clocks in Sagnac is correctly predicted at the first order as vH/c2 (used also as the Sagnac correction in GPS) and it is symmetrical to a good approximation at low speeds.

(LT) For LT the offset, between moving clocks, previously set in sync is predicted as +-gamma*vH/c2 , remains symmetrical...

(TT) From calculations involving Sagnac effect (in agreement with TT), the offset must be instead +/-sqrt[(1+v/c)/(1-v/c)]*vH/c2 which is asymmetrical as expected.

ACCELERATED CLOCKS and resynchronization

e) the other bizarre consequence of offset of equally accelerated clocks a consequence of Relativity of simultaneity, does not occur according to TT.

Using light beams it is detected an offset, same as Sagnac offset, but it is just as an apparent desynchronization because the rocket departed from an isotropic frame and it moves now in a non-isotropic one.

LENGTH CONTRACTION

f) Length contraction is symmetrical for SR, although to allow the out and back speed of light as c in a moving frame it is necessary that length contraction besides being REAL must be also NON-SYMMETRICAL.

Preprint Length contraction as a necessary consequence of the two-way...

Although in Relativity, for two moving spaceships, it asserts that each spaceship's clock is running slower than the other - simultaneously - as is seen on the Minkowski diagrams using intercepts of lines of simultaneity with the other spaceship's ct axis. I have proven this to be false using the LT, and find as you have said here that t' = t'' (i.e. the rates of time on both spaceships are the same). This proves the Minkowski diagram interpretation as wrong. I have a paper that fully explains this and how to correct it, here:

https://ccsenet.org/journal/index.php/apr/article/view/0/46861

Actually if you use light you can find such an offset, because in general the moving body in the isotropic frame will not find the light speed being isotropic...no matter if it moves or not in circular motion, it just moves in the isotropic frame.

Lorentz Field transformations are valid although one must consider that inside them there is also the contribution of the probe which is responsible of a residual magnetic effect in non-stationary electricity.

Yes, and my experimental work proves that light is moving isotropically in a preferred frame and anisotropically in the Earth’s moving frame.

basically the Sagnac correction, required after Einstein's synchronization between GPS base stations, displaced east-west at distance H, already proves that.. to have global sync one must override Einstein's sync which fails for moving objects of vH/c2

That is basically in line with Tangherlini...

Although relativists will never admit that it is a falsification of SR basically a falsification of the initial sentences of Einstein 1905

light-time to connect A to B = light-time to connect B to A...

That can be obtained only tricking the clocks with Einstein synchronization procedure.

Yes, but they don't accept that and have invented an SR explanation. I don't see how they can with my experimental results.

A signal originating in some other frame

May take some time to arrive at my frame

Depending on distance is contemplated

In lorenz, i consider

yes, but this is just a light time delay.

Einstein forces A to B equal B to A everywhere, it is a very strong constraint which is disconfirmed by experience.

Thatz why there is an inverse transformation

But you may be talking about frequency

And Doppler, thats different.

Dear all,

Consider the LT in the Larmor and Lorentz original form (mathematically equivalent to Einstein and Poincare')

x'=γ(x-vt)

t'=γ-1t - vx'/c2

the term vx'/c2 is a time with different interpretations

Einstein-Poincare' : part of the coordinate time of the moving system, resynchronization term

Larmor-Lorentz: light-time variation to cross x in comparison to x/c at rest in the isotropic frame, does not have anything to do with the "real time"

From the result of Sagnac calculations, the difference between the light-time at rest (time for light to cover the distance when the interferometer is at rest) and the light-time in motion, as measured by a stationary observer is

DT= (vx/c2 )/(1-v/c) where x can be the whole path or a short part of it.

It is measured between two points as detected by the stationary observer, obtained without any use of the Larmor/ Lorentz Transforms.

For the moving observer the gamma is applied and

DT'= (vx/c2) sqrt[(1-v/c)/(1+v/c)]

this is the difference between two light times.

The term vx'/c2 = v(γ(x-vt))/c2 = γ*(vx/c2 -v2t/c2)

which for t=x/c

vx'/c2 = γ*(vx/c2 -x/c*v2/c2) = vx/c2γ(1-v/c) = (vx/c2) sqrt[(1-v/c)/(1+v/c)]

hence we can also write in this case

x'=γ(x-vt)

t'=γ-1t - (vx/c^2 ) sqrt[(1-v/c)/(1+v/c)]

the result is the same...so the right interpretation of the term vx'/c2 is a light-time to connect two positions.

So the Larmorian and also Lorentzian interpretation is clear and is the one which complies with Sagnac experimental evidence:

the difference of times to connect two points in motion with the difference to connect the same points when at rest in the preferred frame, is not the same at all and no synchronization is needed in principle if the frame where the motion occurs is isotropic.

Sagnac effect IN CLOSED LOOP provides always that result. It is a ROBUST apparatus which relies on the constancy of the out and back speed of light, irrespective of the isotropy of SOL in the frame of the axis of rotation.

It is based on the fact that in absence of gravitation the out and back SOL is c.

Stefano Quattrini

"Sagnac effect IN CLOSED LOOP provides always that result. It is a ROBUST apparatus which relies on the constancy of the out and back speed of light, irrespective of the isotropy of SOL in the frame of the axis of rotation.

It is based on the fact that in absence of gravitation the out and back SOL is c."

You don't seem to be aware that in modern Sagnac interferometers, glass fibers are used to guide the light. As a consequence, the speed of light is c/n (n being the refractive index) in the fiber rest frame, which is the rotating frame.

In the inertial frame, the speed of light is not c (because it is not moving in vacuum but a material), and it is different in the corotating and counterrotating directions. You can calculate the velocities from the velocities in the rotating frame via the Lorentz transformations or the relativistic velocity addition theorem (c+ = (c/n+v)/(1+vc/(n c2)), c- = (c/n-v)/(1-vc/(n c2)) and this gives the correct resut for the Sagnac effect.

The phase shift is actually independent of the actual speed of light, because the c in Sagnac's formula is the vacuum speed of light and that formula holds also for the glass fiber case. But to obtain the result in the inertial frame, where the fiber is moving, you have to use the correct, different velocities in the two directions. And since the velocity in a moving fiber is not known a priori, you have to calculate it from the velocity of the fiber and the velocity of light in a fiber at rest, which is known to be c/n, using the correct method of velocity addition.

K. Kassner

"You can calculate the velocities from the velocities in the rotating frame via the Lorentz transformations or the relativistic velocity addition theorem"

the relativistic velocity addition is what FIZEAU discovered with his experiment and that is valid also for Tangherlini Transformations.

Nothing new..

Stefano Quattrini

"the relativistic velocity addition is what FIZEAU discovered with his experiment"

Nonsense. You cannot discover a comprehensive theoretical law by experiment. You can at best confirm it for a particular case. Fizeau tried to determine the ether drag. He got a result that Einstein later showed to agree with his velocity addition theorem. But Fizeau did not develop a velocity addition formula himself. He would not have been able to, because his experiment did not provide data for general velocity addition.

"and that is valid also for Tangherlini Transformations."

Wrong. The velocity addition theorem for the Tangherlini transformations (if the system S' is moving with velocity v w.r.t. S reads: u = u'/γ2+v, where u' is the velocity in S' and u in S (and we assume the three velocities to be coaligned, but the general formula can also be derived). This does not agree with Fizeau's results, by the way.

The crucial point of my post that you obviously have missed is that c/n is the velocity in glass, if the theoretical description is based on a Einstein synchronized time. Of course, all of classical mechanics and electrodynamics is formulated in terms of Einstein synchronized time. Classical experiments (and theories) are built on the premise that you can measure time in different places simply by transporting clocks that were synchronized in one place anywhere you need to keep time. In the prerelativistic era, i.e. without consideration of large-velocity phenomena, clock transport and slow clock transport were the same thing. And it is known that slow clock transport produces Einstein synchronization. (As does the specification that the one-way speed of light is isotropic.) All practical synchronization methods needed in experiments implemented Einstein synchronization (of course without knowing the term and definitely without realizing that synchronization of clocks essentially means defining time globally).

Anyway, Tangherlini coordinates produce an apparent anisotropy even for a completely isotropic system. They make the speed of light direction dependent, and not only the vacuum speed of light. The speed of light in glass is different in the forward and backward direction along the anisotropy axis of the Tangherlini coordinates. In fact, the speed of any wave phenomenon is no longer constant relative to the oscillating medium (equality along opposite directions holds in Einstein synchronization where you have the standard wave equation, but not in Tangherlini synchronization, which depends on an external direction leading to a coordinate anisotropy without physical anisotropy).

Stefano Quattrini "the difference of times to connect two points in motion with the difference to connect the same points when at rest in the preferred frame, is not the same at all and no synchronization is needed in principle if the frame where the motion occurs is isotropic."

If you assume the frame to be isotropic, including the speed of light, then it is Einstein synchronized. You have provided the synchronization yourself, because light signals can serve to define time at a distance. Of course, you can assume a frame to be isotropic and still have anisotropic speed of light, if you choose a different synchronization than Einstein's. Then you have chosen to describe an isotropic frame with anisotropic coordinates, which may not be skillful, but is not disallowed. It is perfectly legitimate to describe a spherically symmetric geometry in cylindrical coordinates. It is perfectly legitimate to use anisotropic Tangherlini coordinates to describe an inertial system (which is isotropic).

Please realize that in any setup where you have knowledge of signal velocities, you have already set the synchronization. (For you could in principle use the signals to transfer time readings between distant clocks and if their readings did not yield the time that went into the definition of your velocities, your velocities would not apply.)

K. Kassner ,

Stefano Quattrini "Go to read Tangherlini dissertation please, before announcing things in a so confident way as the Gospel."

I have done the calculation (which is better than reading a thesis), not declared something I simply believed, so what I said was correct, as I proved it mathematically.

But you don't seem to have read Tangherlini correctly. What he says is that you can get the Fizeau result from his, essentially by calculating a so-called slowness, but that is not the velocity in Tangherlini synchronization, it is the velocity in Einstein synchronization, calculated from the Tangherlini synchronization velocity (via the appropriate coordinate transformation).

Now that is of course possible. The two coordinate sets express the same physics in different coordinates. But the velocity in Tangherlini's synchronization is definitely different from the velocity in Einstein synchronization (except in the isotropically coordinized frame, the one you would probably call absolute) and does not equal the Fizeau result. (The Fizeau result can be recovered from it and Tangherlini shows how on the pages you mentioned.) And the description of the Sagnac effect with glass fibres, while definitely doable in Tangherlini synchronization, will be more involved than in Einstein synchronization. It is as simple as that.

K. Kassner ,

Your result

Stefano Quattrini So what? That is precisely what I said. The velocity addition theorem is different for the Tangherlini transformations than for the Lorentz transformations. (In fact, there are two velocity transformation formulas, one for a velocity in S' as seen by S and one for a velocity in S as seen by S'. The reason is that the velocities are not reciprocal in Tangherlini coordinates. If S' moves at velocity v in S, S moves at velocity -γ2 v in S'. Moreover, the whole discussion applies to S with Einstein synchronization and S' synchronized externally to have the same simultaneity relation as S. If both frames have Tangherlini coordinates [i.e. time coordinates that are not orthogonal to their spatial coordinates], then things become more complicated.)

Here is the derivation, which is pretty trivial: we have x' = γ(x-vt), t'=t/γ.

Then dx'/dt'=γ(dx-vdt)/(dt/γ) = γ2(dx/dt-v), which is precisely the result you presented me. Why? To signal agreement? I mean, this is the calculation I referred to when saying I don't need to read the thesis to obtain the velocity addition theorem.

The reason why the Sagnac effect with a glass fiber is more difficult (though not by much) to treat with Tangherlini coordinates is that you don't know the velocities of light in either frame to begin with. You first have to calculate them from the result known in an Einstein synchronized frame.

We know that in the rotating frame, where the fiber is at rest, the velocity of light will be ±c/n. That is a velocity in an Einstein synchronized frame, because it is due to the Maxwell equations and the time in those is Einstein synchronized.

You have then two options to calculate the Sagnac time difference. The simplest is to take the result known from the literature that a locally Einstein synchronized time coordinate (in the comoving frame) has a jump discontinuity along the rim of a rotating disk, just as the angular coordinate φ of polar coordinates. And just like that jump discontinuity has a universal value of 2π, the Einstein synchronized time coordinate jumps by a universal value (for given radius and rotation velocity) that is half the Sagnac time difference. So any two signals sent around the disk at equal opposite speeds will arrive with this time difference back at their origin, which nicely explains the Sagnac effect for all types of signals, be they sound, atoms, light in a glass fiber or light in vacuum. The only thing that is important is that the two opposite velocities are equal in magnitude. This general result is not as easily obtainable in other synchronizations.

Anyway, you don't have to argue with the time discontinuity, if you use the Lorentz transformations to transform the velocities ±c/n back to the inertial frame. Then you will get the velocities of light in the forward and backward directions and using those, you can correctly predict the Sagnac time difference.

Now if you wish to use Tangherlini transformations to calculate the effect, then one more step is needed, because you don't have any result for the velocities in either the inertial or the rotating frames to begin with. But you know the Einstein synchronization result ±c/n. And knowing the relationship between the Einstein time and the Tangherlini time in the local frame, you can calculate these velocities to be ±c/n/(1±v/cn)=±c/(n±v/c).

Again, you then have two options to calculate the Sagnac effect. The first is to stay in the rotating frame and use the two velocities obtained from the preceding step to calculate the round trip times. The time difference is the correct Sagnac time difference in that frame, as the locally Tangherlini synchronized time does not exhibit a jump discontinuity (which otherwise would have to be added to or subtracted from, the time difference obtained from the velocity-induced round trip times).

Instead, one can, as in the Einstein case, transform the velocities back to the

inertial frame. Now you do not transform the velocities ±c/n, using the Lorentz transformations but the velocities ±c/(n±v/c), using the Tangherlini transformations. Since you are transforming back to an Einstein synchronized frame, you will of course obtain the same velocities in the inertial frame as in the calculation without the Tangherlini transformations (the calculation with Tangherlini is slightly more complicated than the Einstein one). And then you will get the correct Sagnac time difference in the Einstein synchronized frame.

Logical inference leading to the general form of linear transformation of coordinates conserving the property '2WSOL=c' in the {1+1}D space-time goes as follows:

One starts with the following general form of transformation passing from reference frame with isotropic SOL=c to coordinates of a reference frame moving with velocity v

x'=A(x-vt) . . . t'=Cx + Dt . . . .  (*)

Then one gets for the speeds c+ and c- the following expressions

c+ = A(c·t-v·t)/(C·c·t+D·t) = A·(c-v)/(C·c+D)

c- = -A(-c·t-v·t)/(-C·c·t+D·t) = A·(c+v)/(-C·c+D)

It follows that the 2WSOL c' is given by

1/c' = 0.5·(1/c+ +1/c- )

. . . = [(C·c+D)·(c+v)+ (-C·c+D)·(c-v)]/[2·A·(c²-v²)].

Standard transformations lead us to the following expression

c' = A·(c² - v²)/[c·(D+C·v)].

The condition “2WSOL=c” is now equivalent to "c’=c", which is equivalent to

A /γ²= D+C·β·c . . . . . . . (2WSOL=c).

I. IF  A=γ ,  THEN  D+C·v=1/γ

. . . I.1. If aditionally C=0, then D=1/γ

. . . I.2. If instead of C=0 aditionally D=A , then C=[ √{1-β²} - 1/√{1-β²} ]/v = - γ·β / c

II. IF the primed time coordinate t' shouls equal t/γ whenever x'=0, THEN C·β·c + D must equal 1/γ. Jointly with (2WSOL=c) it implies that A=γ.

Summary. Among linear transformations of the form of (*) satisfying "2WSOL=c" the following holds

. . . "A= γ" and "t'=t/γ whenever x'=0"  are equivalent

. . . LT is uniquely determined by "A=γ AND D=A"

. . .TT is uniquely determined by "A=γ AND D=1/γ"

In particular there are no more degrees of freedom in chosing TT than for LT.

Briefly: the condition "the primed time coordinate t' shouls equal t/γ for all x' " is limiting in the same degree as the "1WSOL=c".

Domsta always forgets synchronization, which in TT is automatic while LT need Einstein synchronization which is an additional condition.

considering

t'= gamma-1 t - vx'/c2

the presence of the term vx'/c2 as a coordinate time which is related to Einstein synchronization which is an additional condition.

If instead vx'/c2 is considered just a light-time variation due to speed in the preferred frame, such resynchronization does not occur.

t'= gamma-1 t is Tangherlini does not need any synchronization.

and my Opponent neglects to define what in His vocabulary means that a transformation is more or less limited than the other. I keep stressing that both transformations are uniquely determined by the relative velocity of the primed irf with respect to the original one.

If one talks about possible applications, then the LT have obviously more possibilities since they are applicable to ANY irf while TT can be applied only to the preferred frame and requires to perform some EXPERIMENTAL VERIFICATION whether the irf of considerations satisfies "1WSOL=c".

In particular, if we do not know the speed of our lab wrt the preferred irf then our experiments cannot be translated into terms of the preferred frame and they will have low scientific value.

Conclusion. TTransformation are more limited in applications than LTransformation. The more that there is no reliable method of verification the property "1WSOL=c"

and my Opponent ignores that the synchronization technique of LT implies that

a) two clocks must be at rest

b) two clocks cannot be part of a non inertial frame to be synchronized

successfully

Besides that the Einstein Train Embankment Thought experiment can be performed with sound at rest with the embankment, prefectly explain with absolute simultaneity...

To set in sync the sound sources at a distance, one can use light, which is much faster. The only condition is that the wagon is open, is just a moving observer which does not drag air with it.

What emerges is that the blasts will reach simultaneouly the stationary observer on the embankment and non simultaneously the moving observer, same as what occurs with light.

Pity that here we have a stationary medium.

Stefano Quattrini What I said is

1. my Opponent neglects to define what in His vocabulary means that a transformation is more or less limited than the other.

2. I keep stressing that both transformations are uniquely determined by the relative velocity of the primed irf with respect to the original one.

3. If one talks about possible applications, then the LT have obviously more possibilities since they are applicable to ANY irf while TT can be applied only to the preferred frame and requires to perform some EXPERIMENTAL VERIFICATION whether the irf of considerations satisfies "1WSOL=c".

4. In particular, if we do not know the speed of our lab with respec to the preferred irf then our experiments cannot be translated into terms of the preferred frame and they will have low scientific value.

5. Conclusion. TTransformation are more limited in applications than LTransformation. The more that there is no reliable method of verification the property "1WSOL=c"

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Your last post does not respond to any of these points, but you present it as if it was an answer to my last post. Additionaly you WRONGLY suggest that I have been tellng somewhere something incorrect about .

Do you or did you see wherever in my current post or in any other former posts any statement about properties of any procedure of synchronisation? Isn't it once more a 'smart' lie about my allegedly wrong contributions? Think about this honestly, please.

Joachim Domsta

affirms

and he affirms

I simply tell you that the transformations are uniquely determined if one is able to apply also the synchronization procedures which he always neglects.

I've told him for the 10th time but the stubborness is paramount.

Besides that he does not consider that the Train and Embankment thought experiment is a trivial example of non simultaneous arrival of waves, verified also in acoustics. The advantage is such that one can use light to set in sync the sources of sound implementing a sort of hyper-sonic (instead of superluminal) synchronization.

Simultaneous emission of sound waves implies non simultaneous absorption of them by a moving observer set in the middle when the emission occurs.

This kind of synchronization becomes absolute for sound, same as Tangherlini, hence the effect depends on absolute simultaneity not relative.

New lie: . How Stefano can know what I have ever considered in my life? Again a personal invective! When will this come to the happy end?

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

All I have vclaimed about is that

-- in the SRTheory the speed of light is independent of the IRF, and

-- that according to rigorous considerations this implies that some events simultaneous in an IRF1 may be not simultaneous in another IRF2.

The appropriate (equivalent to KNOWN) proofs of this inference has been presented by me couple of times within RGate, and no error of them or those given in books has been ever reported by anybody. The thought experiments presented by my Opponebt do not fulfill requirements imposed upon rigorous proof therefore are of no scientific value if they lead to contradiction with the known mathematical proofs.

it is not a thought experiment it is a trivial consequence of material waves which Joachim Domsta wants to ignore, otherwise the castle in the air he is defending will blow up miserably..

Stefano please do not care of what I want. It's better to answer with the use of arguments. In particular, answer to the question: what is the difference between :the rigorous inference from assumptions" and "the inference by saying 'it is a trivial consequence' of the assumptions"

is absolute simultaneity in agreement with the results of observation?