I would assume that the clock in water, unless you maintain some perfect symmetry where everything cancels itself out, experiences more gravity, and time dilatation is stronger under heavier gravitational fields:

https://www.snexplores.org/article/a-new-clock-shows-how-gravity-warps-time-even-over-tiny-distances

No, one clock A just below the surface of water so that pressure and gravitation are negligible..

The “speed of light“, that parameter of relativity, in water is actually still c. The apparent slower speed of light results from the polarization of the electric charge of the material under the applied electric field of the incident light. This isn’t the propagation of a single EM field from some distant source alone (which does propagate at c). Instead you get the superposition of the applied field PLUS a new additional field from each electric bond in the material that oscillates as a dipole in response to the applied field adding its own EM field to the mix. The charge in the material cannot respond instantly to the applied field so there is a phase delay in the polarization. The superposition of the applied field plus the polarization field (together called the displacement field or D in Maxwell’s equations) has a phase velocity < c due to the finite response time of the material’s charge. This means that the phase velocity is < c even though each and every component field of that superposition is traveling at c.

If c were truly different and reduced to c/n, then nothing could travel through water faster than c/n. However particles do travel through water at > c/n as can be seen by the Cherenkov radiation this produces.

Mike Albert ,

the principal thing to agree is the final effect which cannot be different than the twin effect in vacuum, in case there are doubts about it I can explain you why.

But how would you apply the Lorentz Transformations in such case?

with c in gamma and cwater everywhere else?

Such configuration does not make sense with EMwaves...

Again, the water does not affect the value of c or any relativistic phenomena such as the twin effect. c is still c, time dilation, length contraction, mass increase, etc are all still dictated by the same c whether in water or out. As I described, the effective slowing of light in water is NOT due to a change in the value of c, but rather due to the addition of more EM sources (dipole radiators) and the superposition of all the fields.

Mike Albert ,

this has been understood, I've also written in the manifest of this thread.

so you want to mean that you would apply Lorentz Transformations always in vacuum...

Dear all,

it is quite clear that the Lorentz Factor is only dependent on the characteristic speed of light in vacuum related to the magnetic and electric constants.

What about the Lorentz Transformations then?

They are not applicable in media for obvious reasons...

Dear @Stefano Quattrini

A scalar wave driven by the equation

psi(x,t) = f(x-wt)

under the LT coresponding to relative velocity v of the new IRF' become a function given as follows

psi'(x',t') = f(x'-w't')

where w'=(w-v)/(1- vw/c^2).

Similar, though much more complex formulas are obtainable for ARBITRARY function psi depending on the space-time coordinates (x,t). Formally it can be written as follows

psi'(x',t') = psi(L^{-1}(x,t))

where L^{-1} denoted the invercargill Lorenzo transformation of coordinates (x,t) to the primed coordinates (x',t').

In particular, if in the IRF the waves are transported isotropic then their speed in the moving IRF' their velocity is nonisotropic.

PS. A SRT derivation of the Fizeau effect can be found in many places, e.g. at

https://en.m.wikipedia.org/wiki/Fizeau_experiment#Derivation_in_special_relativity

Dear Joachim Domsta ,

the Fizeau effect has nothing to do with "time dilation" aka twin effect. It is the effect of dragging of light through water, partially summing up the speed of water.

Dear Stefano you say

Which should be closed by adding

" ... to the speed of light equal to c/n, according to the composition formula of velocities"

According to this the Fizrau effect is well approximated by the SRT. In particular it may be seen as consistent with the claim that the time delay in moving medium is governed by gamma factor determined by c (not c/n).

Dear Joachim Domsta ,

Maxwell equations governing the propagation of light in water contain the speed of light in vacuo or the speed of light in water?

Dear @Stefano Quattrini

To the best of my knowledge it is the speed of light in water.

Dear Joachim Domsta ,

I totally agree... so if one derives the Lorentz transformations, the same as Lorentz did from Maxwell equations, it is expected to have a gamma with the Speed of light in water...

Dear @Stefano Quattrini

Your conclusion would be correct if the wave equation should remain unchanged after this transformation. However the Fizeau experiment disproves this conjecture: the speed of light in moving water is not equal the speed in water at rest.

Dear Joachim Domsta ,

yes, relative speed between the source and the water further modifies the speed of light in stationary water, according to Fizeau experiment. Only out and back average SOL is constant in water. Such average is equal to the SOL measured when the source/observer is stationary with water.

Nevertheless the SOL in moving water is always less than SOL in vacuum....

So the gamma factor cannot in any case be the same as the one in vacuum .

Dear @Stefano Quattrini

The relativistic composition formula for velocities gives result consistent with the experiment as it it is explained in the wiki source referred to in my post #9 on p. 1.

- - - - - - - - -

PS. The average for different one way SOLs will be given by me later. The formula for speeds close to c looks differently if compared to the Galileo formula, which is the so called harmonic average:

2/c_av = 1/c1 + 1/c2

[as I mentioned once in the past; I do not remember in which thread :-( ]

Dear Joachim Domsta ,

yes, never said the opposite.

Nevertheless if one wants to derive LT from Maxwell equations in water, the SOL cannot be the same as in vacuum.

Right. So why should we do this despite the experiment contradicts invariance of the speed of light in water?

Dear Joachim Domsta ,

if LT are derivable from Maxwell equations in general, not only in vacuum, also the gamma factor must refer to a lower speed of light.

Since the gamma factor (TWIN EFFECT) can only refer to the characteristic SOL in vacuum, Lorentz Transformations in Einstein's form

t'=gamma(t-vx/c2)

x'=gamma(x-vt)

cannot be derived from Maxwell equations in water.

Thus: what is the question?

Dear Joachim Domsta ,

the question is the following:

Lorentz Transformations in Einstein's form cannot be derived from Maxwell equations in water.

Lorentz Transformations in an generalized Lorentzian form

x'=gamma(x-vt) ; t'=gamma-1 t - vx'/K2

where K is a variable instead of constant c

can be derived also from Maxwell equations in water?

Dear @Stefano Quattrini

Dear Joachim Domsta ,

In a medium like water from the Maxwell equations, Lorentz Transformations, can be derived, in the following from

x'=gamma(x-vt) ; t'=gamma-1 t - vx'/K2

where K=K(v)

Dear @Stefano Quattrini

Your LT is not THE LT. Reasons:

THE LT transforms motions with speed c into motion with the same velocity.

Your LT does NOT fulfil the above DEFINING condition unless K(v) = c and gamma(v) = 1/sqrt{1- (v/c)^2}. . . q.e.d.

K(v) is not the constant c then your LT does not preserve the c value for the speed of light in vacuum.

Dear Joachim Domsta ,

that is for sure....x'=gamma(x-vt) ; t'=gamma-1 t - vx'/K2

nevertheless these should work in the dielectric (DE-IONIZED WATER)

and can be derived by Maxwell equations in a dielectric

gamma is always gamma(v) = 1/sqrt{1- (v/c)^2}, it is determined experimentally in the twin effect irrespective of the medium..

Yes basically K(v) represents the violation of the Lorentz Invariance which Lorentz himself supported since the beginning having conceived his transformations with a preferred frame where only there the SOL was c.

It is very interesting the following paper

"Reconciliation of the Rosen and Laue theories of special relativity in a linear dielectric medium"

https://arxiv.org/pdf/1904.05438.pdf

"In a 1952 American Journal of Physics article, Rosen [3] considered an arbitrarily large, but finite, macroscopic Maxwellian dielectric such that an observer in the interior of the dielectric has no access to the vacuum i) microscopically, because the continuum limit precludes an interstitial vacuum, and ii) macroscopically, because the boundary of the dielectric is too far away from the interior for light to travel within the duration of an experiment.

Because the vacuum is inaccessible, there is no way to determine the speed or direction of the dielectric medium with respect to the Laboratory Frame of Reference. Consequently, there is no way to apply the Einstein relativistic velocity sum rule. Then the speed of light in a Maxwellian dielectric w is independent of the motion of the source or material. The index-dependent material Lorentz factor"

So I was in good company not to take for granted that the gamma factor is irrespective of the speed of propagation in the medium...

Also Finn Ravndal seems to make the same assumption of attributing to gamma a lower SOL...

"Effective electromagnetic theory for dielectric media"

https://arxiv.org/pdf/0804.4013v3.pdf

I thimk that the relativistic questions

are mostly discussed in vacum

Dear Stefano Quattrini

JoaD: "Your LT is not THE LT."

SQ:

Ok. Thanks.

SQ:

No, only THE LT (with K=c) works in dielectrics since the SRT composition formula for velocities is well verified by the Fizeau experiments (comp. my post #8 on p.1 and the wiki article referred to in my post #9 on p.1).

= == = = = =

With respect to your kindly shared considerations - I am not interested in alternative theories unless they lead to formulas fitting the reality with better approximation.

Best regards,

Joachim

Dear Joachim Domsta ,

that Fizeau formula is verified in experiments does not mean that SR works in dielectrics... in such case infact Einstein-LT should be changed with a different speed of light, as Finn Ravndal suggests, which is not possible because the gamma factor is irrespective of the medium!!!!

Dear @Stefano Quattrini

Do you object correctness of the content of the wiki article at the address given in #9 on p.1?

Dear @Stefano Quattrini

Your doubts witness that in your structure of notions principles of the space time depend on the state of the matter, which requires experimental confirmation. Up today there is NO experiment which confirms such suggestions. It is not enough to say

Moreover I want to point at unappropriateness of suggesting difference between the following allegedly different transformations:

LLT: x'=gamma(x-vt); t'=(1/gamma) t - x'v/c^2

ELT: x'=gamma(x-vt); t'=gamma(t - xv/c^2)

SINCE THEY ARE EQUIVALENT.

The only possible difference may be the physical meaning of the variables and parameters. But then still the two transformations remain equivalent. For elementary example please accept that in the Ohm law I=U/R equivalent to U=RI the role of voltage U and may be seen once as the cause of flowing the curren, and in Ianother circumstances as the effect of flowing the cirrent I. BUT THE RELATIONS AFTER THE INTERPRETATION IS FIXED REMAIN EQUIVALENT.

PS. More straight formulation: Writing U= RI we do not STATE that the source is of current type nor of voltage type.

PS2. IMHO the Minkowsku space-time deals as a background for describing phenomena, and is not influenced by them. Changing IRF we change the coordinates in order to describe the physical phenomena perhaps in a more convenient equations. But the phenomena remain unchanged. In particular by freezing water we do NOT expect any change to the Lorentz transformations or we are resigning of SRT. Of course all said above is not to be meant as a proof of validity of SRT but an advice which experiments should be performed for correct drawing of the limits of SRT. For me it is unacceptable to state simply that LT should be changed with a different speed of light.

Dear Joachim Domsta ,

Dear @Stefano Quattrini

1. ... And I didn't say that you say they are not mathematically equivalent. But you always say (and have even repeated in last post) that the pairs of equations are NOT physically equivalent. And only this is strongly opposed by me as follows:

if the term  x'v/c^2 is the Lorentz' in one pair of the transformation equations, then it has THE SAME meaning in the other pair of transformation equations. I cannot give more simple explanation than the already TWICE presented analogy to the electric resistor (now for the third time):

A. If I is the current of the source supplying the resistor in the equation U=RI, then it is the also the current of the source supplying the resistor in the equation I = U/R.

B. If U is the voltage of the source supplying the resistor in the equation U=RI, then it is also the voltage of the source supplying the resistor in the equation I = U/R.

= = = = = = = = = =

2. I think the subject of your concern is the following principle of SRT:

《In any circumstances (including all possible continuous or discontinuous, homogeneous or inhomogeneous media) there is (=exists) a limit value of possible speeds of motions which is the same in any chosen inertial reference frame. 》[much more consistently used in a rigorous way for derivations of LT, e.g. by Jacek Szarski]

The doubts presented in your posts are caused by replacing the notion of "limit value of possible speeds of motions" by the widely (though wrongly) named "speed of light". The truth is that the nature exposes this limit speed ONLY as the speed of massless particles in vacuum.

3. I wonder if the appeared need of repeating my former explanations isn't a sign to close the two above issues without further argumentation, at least from my side.

Best regards,

Joachim Domsta

Dear Joachim Domsta ,

words of Finn Ravndal

https://arxiv.org/pdf/0804.4013.pdf

"Light in a dielectric medium moves slower than in vacuum. The corresponding electromagnetic field equations are then no longer invariant under ordinary Lorentz transformations"

"This brings to the fore again the old problem related to how the principle of relativity is combined with the Maxwell field equations in a continuous medium."

Dear @Stefano Quattrini

Why are you repeating the quotations? I have replied them in my posts already.

To the the first segment my answer is briefly as follows: yes the equation in new coordinates is such that the speed of em is anisotropic according to the relativistic composition formula (given already within my FIRST post #8 on p. 1.)

Summary of my comments to the the second quoted segment is contained in the appropriately formulated postulate [frankl: in a non professional though sufficiently complete way] within double angle braces in my LAST post #35 (i.e. #5 on p. 4).

I cannot reply anything more without multiple repetitions, which I want to omit as quite useless.

Best regards, Joachim Domsta

Changing independent variables in differential equations is a standard math procedure. In the simplest example of ODE

dy(x)/dx = f(x)

the passage to new variable X= g(x), leads to the following equivalent ODE for the new unknown function defined by

Y(X) := y( g^{-1} (X) ):

dY(X)/dX = f( g^{-1} (X) )/ U(X)

where

U(X) := dg(x)/dx with x=g^{-1}(X).

For PDE like the wave equations the procedure uses suitably the rules of multidimensional analysis. Practical algorythms are widely accessible in textbooks on mathematical methods in physics.

Presenting here derivation of them would be too much space consuming. Anyway, to the best of my knowledge the result for the wave equation in the moving system of coordinates becomes a hyperbolic PDE which in general case uses substantially all partial derivatives of the second order. In the 2D case (of one spatial and one temporal variables x' and t') these are the partial derivatives

f_{x'x'}, f_{x't'} and f_{t't'}.

Usage of the mixed derivatives is responsible for anisotropy of the speed of the waves in the moving medium. In the (1+1)D case this corresponds to different values of the speed in the opposite directions. The result of application of the LT is presented in post #8 on p.1.

PS. Changes of the independent variables in differential equations for 4-tensor or 4-spinor fields requires simultaneous transformation in the space of values.

Just one simple example: The 4-vector field a(x,t) after LT changing the (x,t) variables into new coordinates (X,T) by Lorentz matrix M as follows

(X,T) = M•(x,t)

is changed into the following vector field

A(X,T) = M•[ a( M^{-1}•(X,T) ) ].

For obtaining the transformed PDE this modification of the field should be accompanied by suitable changes of the differential operators, in accordance to the rules of multidimensional analysis.

The aim of the enclosed note is to present main steps leading to the transformed equation for waves moving with velocity w under LT with velocity v in the (1+1)D case. As a side effect the velocities of the forward and backward waves are obtained (confirming validity of the composition formula).

Dear Joachim Domsta ,

in this paper of Michael E. Crenshaw

https://arxiv.org/pdf/1904.05438.pdf

describes Rosen's viewpoint about the modified Lorentz Factor:

"Then, in the limit of continuum electrodynamics, the macroscopic Lorentz factor in an arbitrarily large simple linear dielectric is given by Eq. (21).

Now, the speed of light cd will be different in different dielectrics and we are considering only simple linear dielectric materials in which the speed of light is inversely proportional to some constant n. For each linear isotropic homogeneous dielectric with index ni , there is a different material Lorentz factor"

Do you agree that Rosen's viewpoint is wrong?

Dear @Stefano Quattrini

Thank you for the (repeated) request about my opinion on the Rosen considerations. Please treat the following as my last reply about it:

In SRT the Lorentz transformation is based on the principle formulated in point 2. of my post #5 on p.4. Roughly: the SRT is based on the invariance of some isotropic speed c when passing to another moving reference frame [this c is exposed by the nature as the speed of massless particles in vacuum]. Consistency of this postulate with reality is stated by MM wrt light speed. Also the Laue interpretation of the Fizeau experiment via SRT composition formula proves consistency of the SRT with reality.

On the other hand the observed speed c_d of light in dielectrics DEPENDS on the velocity of the medium and on its direction. Thus independence of this value c_d of the speed of the medium can be used at most as a basis of some New Relativity Theory, then obviously inconsistent with the real events.

Dear Joachim Domsta ,

this is clear.

this is not clear. IN any case to my understanding Rosen's proposal is wrong because if one uses that gamma factor in a dielectric (deionized water) does not get the correct twin effect.

Dear @Stefano Quattrini

My sentence "Thus..." is a logical consequence of the first one starting with "On the other hand ..." and the basis of LT which is the existence of a limit value of possible speed of motions which is isotropic and unchangable after passing to another moving IRF.

Sorry, but your disagreement means we talk about different transformations.

Dear Stefano, what is your definition of LT?

Dear Joachim,

Do not answer with questions please. Which gamma factor would you use for the twin effect in water, the one proposed by Rosen? Because as you notice in the paper it derives that as being the time dilation factor.

Dear @Stefano Quattrini

Sorry, but my answer is already given in my posts till #4 on this current page 5. The post #5 starts new question, though closely related to your question. Please be so kind and answer if you want or refuse.

BTW, I am continuing to neglect the Rosen way as obviously not consistent with SRT and additionally ended with a formula inconsistent with observed Fizeau effect.

PS. My answer to the last question is given in #1 p.2. Just to make it clear that I do NOT answer by question, here is the copy:

JoaD: "the Fizrau effect is well approximated by the SRT. In particular it may be seen as consistent with the claim that the time delay in moving medium is governed by gamma factor determined by c (not c/n)."

Dear @Stefano Quattrini

Is this what you expected?

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

Here is the composition formula for subluminal velocities w, v :

w' = (w-v)/(1-wv/c^2) . . . . . (1)

PROPOSITION. If (1) is a consequence of the transformation of the following Lorentz form

x'=A(v)(x-vt) . . . t'=sqrt{1-(v/c)^2} t - B(v) x' . . . (2)

then

A=1/sqrt{1-(v/c)^2} . . . B=v/c^2 . . . (3)

- - - - - - - - - -

For proof it suffices to calculate x'/t' for x=wt and compare to formula (1).

Dear Joachim Domsta ,

Ok I see that there is agreement about Rosen's inconsistency with actual experimental evidences. What Michael E. Crenshaw described as a support to Rosen is not in agreement with Twin effect.

The idea to derive the LT from the Maxwell equations in a medium other than vacuum is nonsense. The relativity principle does not hold for the Maxwell equations in a medium, i.e., they change their form on a change of the velocity of a reference frame moving with respect to the medium. So the Maxwell equations in a medium have the form of the ordinary Maxwell equations, with the vacuum speed of light replaced by the medium speed of light, only in the frame with velocity zero with respect to the medium. In particular, even the two-way speed of light in the medium depends on the velocity of the reference frame with respect to the medium.

Another thing to be kept in mind is that the "Maxwell equations in a medium" that we are talking about here do not hold in any medium with constant dielectric coefficient and permeability for arbitrary frequencies. There is no non-vacuum medium, in which the speed of light would be the same at all frequencies. The speed of light approaches c for high frequencies in all media. So the Maxwell equations with constant speed of light in a medium are always a phenomenological approximation, strictly valid only for monochromatic light and in practice applicable only in a limited frequency range. They are not fundamental, whereas the vacuum Maxwell equations constitute fundamental classical laws of physics.

it means that some more general Transformations can do the job.

yes, vacuum is a very particular case...

Stefano Quattrini

"it means that some more general Transformations can do the job."

No, it does not.

You cannot derive the LT from Maxwell's equations alone. I mean, you can derive, in principle, all the coordinate transformations that leave Maxwell's equations invariant, and will find that the LT are among them (just as rotations, translations, time reflection). But "deriving" the LT from Maxwell's equations means assuming that Maxwell's equations do not change form when describing electromagnetic phenomena in a frame of reference moving at constant velocity with respect to the one in which they were assumed to hold originally. You then find that the new frame is related to the old one by a Lorentz transformation, not by a Galilean one. Now, that assumption (of form invariance) was not made before some experiments had shown that the alternative, namely that the equations describing electromagnetic phenomena in a moving frame had a different form from the original Maxwell equations (obtained from their original form via a Galilean transformation), was wrong. One experiment showing this was the Michelson-Morley experiment. The Galilean-transformed Maxwell equations predict the presence of an ether wind which that experiment would have detected if they were correct.

For the Maxwell equations in a medium nobody really ever expected invariance with respect to a change of the frame of reference, because the medium clearly defines a preferred frame. And there were experiments by Fizeau (in 1851) that had shown that there was some drag effect by a moving medium on the speed of light, so it was clear that Maxwell's equations in a medium could not be invariant under a change of velocity with respect to that medium.

Since you need the invariance of the equations with respect to the velocity of the "medium" in order to "derive" the transformations between the frames at different velocities, it is clear that you can do such a derivation only on the basis of the vacuum equations, because vacuum is the only "medium" for which the invariance holds.

K. Kassner ,

Dear @Stefano Quattrini

You have stated:

>

This inference is logically unacceptable. Indeed, Rosen's derivation is based on FALSE assumption that the light speed is independent of the velocity of the reference frame with respect to medium. To the contrary, it is TRUE that the speed of light in vacuum is independent of the velocity of the reference frame.

Dear Joachim Domsta ,

Dear @Stefano Quattrini

Lack of experimental confirmation of 1WSOL is not an argument to FALSIFY the derivation in vacuum. The more that there is NO experimental contradiction of this postulates.

Therefore using invalidity of Rosen's to argue against Einstein's is a severe abuse of logical rules of justification.

Stefano Quattrini

"if such a derivation is meaningless in a medium, in fact, it is meaningless also in vacuum which can be considered in principle a stationary medium in the lab frame with a different dielectric constant."

No. Here you are dead wrong. The idea that vacuum can be considered a stationary medium (which would define a preferred frame of reference with velocity zero -- that is the meaning of stationary) was prevalent before the failure of all experiments measuring the ether drift. But it has been shown to be incorrect. There is no way of determining the velocity of a frame of reference with respect to vacuum, so Newton's relativity principle prevails and vacuum cannot be assigned a velocity, hence vacuum cannot be claimed to be stationary, in principle. That's the whole crux of the difference between a medium (which is stationary in the frame where its atoms/molecules are at rest) and vacuum!

That is also why Einstein did not claim, in his later expositions of relativity, to have disproved the existence of ether. Rather he said that the ether (if there is one) cannot be said to have a particular velocity. Which distinguishes it from ordinary materials. And which is the reason why there exists an ether theory (LET) that is empirically equivalent to special relativity. The ether of Lorentzian ether theory has the property, contrary to the ether in all the failed preceding ether theories, that its velocity cannot be ascertained experimentally. So it does not have a velocity in any physical sense (in particular not the velocity zero).

K. Kassner

the absence of the aether drift stated only that it is not possible to detect motion of earth from experiences inside a lab on Earth.

It is well known now that in ECIF light is isotropic since GPS relies on that, and MMX experiment does not falsify the presence of an hypermedium strongly related to the gravitational field of Earth.

take two clocks stationary in ECIF at distance H, where SOL is isotropic, set them in sync (such that the light time difference is H/c), tA-tB=0. Then let them depart, by checking their synchronization they will find a difference. Such difference is, according to Sagnac ta-tb= vH/c2 hence

v= c2(ta-tb )/H

that is the speed of the object in the local vacuum around earth.

it does not infact, it is much more complicated than the simplistic way you want to convey. It is the bodies who refer to the aether, not the way around...

so it is not meaningful to find the speed of aether, respect to what???

Lorentzian electrodynamics is based on a preferred frame to which locally a physical problem refers.

Lorentz found the transformations in this form

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

x'=gamma(x-vt)

although these are mathematically equivalent to Einstein and also physically if vx'/c2 is considered a coordinate time, hence the "offset of clocks", they are not physically equivalent in general. vx'/c2 is the term derived directly from Sagnac effect which has nothing to do with the "offset" of clocks which is just an "apparent"... but it is the light-time to connect two bodies which move in the frame where light is isotropic (ECIF for example).

Stefano Quattrini

"take two clocks stationary in ECIF at distance H, where SOL is isotropic, set them in sync (such that the light time difference is H/c), tA-tB=0. Then let them depart, by checking their synchronization they will find a difference. Such difference is, according to Sagnac ta-tb= vH/c2 hence

v= c2(ta-tb )/H"

So what?

That is the velocity with respec to ECIF, not "with respect to vacuum". Stationarity in the ECIF does not mean stationarity "with respect to vacuum". You don't seem to understand the meaning of the relativity principle. (And are you really claiming it to be wrong? Despite the fact that no experiment has ever shown a violation of it?)

"Lorentzian electrodynamics is based on a preferred frame to which locally a physical problem refers."

I was not disputing that. This is a metaphysical frame. What I said is that there is no way to experimentally determine the velocity with respect to vacuum (i.e. the ether frame). It is not a physical frame. It is philosophy. And even self-defeating philosophy, similar to solipsism. Claim something with properties that make it unprovable, and there you have a conspiracy theory... Occam's razor suggests to avoid this.

K. Kassner ,

there is a way to determine the velocity of a body in local vacuum around earth E-CIF or Sun S-CIF or interstellar CMBR, they are not the same for sure..

This does not mean that there is not an hypermedium.

Lorentz electrodynamics is not expected to work in general but as SR is limited by gravitation for example.

Take two clocks A,B in a rocket, set at distance H and bring them sufficiently far from earth ( farther than Lagrangian point 2), the velocity has the direction of head-tail.

a) turn off the engines

b) flip the rocket normal to the direction of its velocity

c) set A and B in sync.

d) flip again the rocket to its previous orientation (along its original direction).

1) according to Special relativity A and B will stay in synch since the rocket always went at constant speed so it was belonging to the same intertial frame all the time. The light-time to connect A and B should be always H/c

2) according to Lorentz Electrodynamics A and B will detect a variation of the light time which connect them. The difference detected is vH/c2 , that is due to the motion in the S-CIF. The rocket moved in SCIF where the SOL is isotropic, at variance with its own inertial frame where light is not isotropic.

Dear @Stefano Quattrini

I am really sorry witnessing your impertinent prapaganda about properties of light propagation velocity in some local IRFs as if it were a property of observations contradicting the SRT.

The most controversial claim reads as follows:

The truth is that:

- according to SRT, in ANY inertial reference frame the velocity of light is isotropic;

- no observations contradict this statement yet.

PS: Another substantial objections have been formulated in my post # 7 on p. 6.

Dear Joachim Domsta ,

that is not the "truth", it is the truth according to SR, because it is not experimentally verified. In the case it was experimentally shown, then it would be a truth.

->

Sagnac does it if it is interpreted in the right way...

On the other hand I explicitly said : according to Lorentz Electrodynamics, that is not the case that SOL is isotropic in every inertial frame but since there is a preferred frame, light is not isotropic in relative moving frames (ECIF is isotropic, relative moving systems sufficiently close to Earth are not)

Dear @Stefano Quattrini

The Lorentz ED is based on the independence of the equations of IRF. Therefore the statement

is invalid not only in SRT but also in the LED.

Dear Joachim Domsta ,

Lorentz ED assumes that there is a preferred frame where SOL is constant c and isotropic while in all other frames SOL is not isotropic. The equations are invariant under such transformations

t'=gamma-1 -vx'/c2

where vx/c2 is the light-time variation in the new frame to cover the length x in comparison to x/c which is the time taken by light to cover x in the preferred frame..

Dear @Stefano Quattrini

0. x or x'?

1. If the wave equation is independent of the IRF the speed of the waves is isotropic in any IRF

2. Unbelievible: does LTE realy leads to anisotropy of light speed in any IRF?

PS. Does it make sense to develop any theory like LED which stays in contradiction with experiments?

Dear Joachim Domsta ,

the experiment which can discriminate is the following..

Take two clocks A,B in a rocket, set at distance H and bring them sufficiently far from earth ( farther than Lagrangian point 2), the velocity has the direction of head-tail.

a) turn off the engines

b) flip the rocket normal to the direction of its velocity

c) set A and B in sync.

d) flip again the rocket to its previous orientation (along its original direction).

1) according to Special relativity A and B will stay in sync since the rocket always went at constant speed so it was belonging to the same intertial frame all the time. The light-time to connect A and B should be always H/c.

2) according to Lorentz Electrodynamics A and B will detect a variation of the light time which connect them. The difference detected is vH/c2 , that is due to the motion in the S-CIF. The rocket moved in SCIF where the SOL is isotropic, at variance with its own inertial frame where light is not isotropic.

In the second case if a value different from 0 is found as vH/c2 then a special kind of aether does exist "locally" in close relation with the gravitational field of the SUN.

I remind you that the term vx'/c2 was found intially by Larmor and Lorentz as the additional time to reach the detector of a body in motion. That was made to describe the behavoiur of light, considering that it has a propagation domain which is the preferred frame.

(some useless lines are deleted)

Dear @Stefano Quattrini

Your experiment is not determined in terms of some given IRF. In particular it is not presented how LED works in this circumstances. Moreover you used quite strange condition to be away from Earth.

And finally you are omitting the key point: If the equation of a wave is the same in each IRF then the velocities of the waves are also the same in each IRF (you have never denied or confirmed correctness of this conclusion; however you continue to repeat as a mantra that the equation after transformation is the same but the velocity is isotropic only in one prederred frame). This is what you are asked to explain before I will discuss these issues. Please note that there is no possibility to agree 'partly' with so deep inconsistency.

Best regards

Joachim Domsta

Dear Joachim Domsta ,

I did not say that the equation of a light wave is the same in every IRF that is what Einstein said and it is not in agreement with LE

Dear Stefano,

That's from your post #5 of this page:

'To be invariant' means in particular that the wave equations of em have the same form in (x',t') as in (t,x) coordinates. Doesn't it?

Dear Joachim Domsta ,

it is determined if one assumes that the rocket which goes in free space can be considered attached to an IRF. If not then SR is not even wrong, it is inapplicable.

The strange condition of away from earth is to avoid direct effects of gravitational field on the rates of clocks.

Dear @Stefano Quattrini

Please do not addrees any comment to me, before you reply to the question from post #1 p.8, in conjuction with my statements in #9 p.7.

Best regards,

Joachim Domsta

Dear Joachim Domsta ,

I address any comment I want, then if you do not want to answer, it is up to you.

Dear Stefano, our correspondence came to the dead end as follows:

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SQ, #1 p.7

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JoaD, #4 of p.7: "The Lorentz ED is based on the independence of the equations of IRF. Therefore the statement

is invalid not only in SRT but also in the LED."

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SQ, #5 of p.7:

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JoaD, #9 p.7: " If the equation of a wave is the same in each IRF then the velocities of the waves are also the same in each IRF (you have never denied or confirmed correctness of this conclusion; however you continue to repeat as a mantra that the equation after transformation is the same but the velocity is isotropic only in one prederred frame). This is what you are asked to explain before I will discuss these issues. Please note that there is no possibility to agree 'partly' with so deep inconsistency."

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SQ, #10 p.7: >

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JoaD, entire post #1 p.8: 《Dear Stefano,

That's from your post #5 of this page:

'To be invariant' means in particular that the wave equations of em have the same form in (x',t') as in (t,x) coordinates. Doesn't it?》

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JoaD, #3 p.8: "Please do not addrees any comment to me, before you reply to the question from post #1 p.8, in conjuction with my statements in #9 p.7."

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SQ, entire post #4 p.8: 《Dear Joachim Domsta

I address any comment I want, then if you do not want to answer, it is up to you.

Dear Joachim Domsta ,

no and in fact this is not true in general.

For acoustic waves also spherical, the speed of the wave emitted from a stationary source is not measured the same by a moving observer.

The last post by @Stefano Quattrini falsifies the basic role of wave equation, which is a rigorous description of ALL features of the wave, including its phase and group velocities.

The last post of Joachim Domsta , shows that he is very likely not aware that the speed of a wave in acoustics cannot be measured the same by a stationary observer and by a moving observer (provided that the sound itself is not used to measure the speed)...

Evidently my Esteemed Opponent didn't see the content of my first post in this thread (#8 on p.1):

JoaD: "A scalar wave driven by the equation

psi(x,t) = f(x-wt)

under the LT coresponding to relative velocity v of the new IRF' become a function given as follows

psi'(x',t') = f(x'-w't')

where w'=(w-v)/(1- vw/c^2)."

The good news is that it is never to late to realize the following meaning:

### if w is the speed of sound of the medium at rest, then w' is the speed of sound perceived from the IRF' moving in the same direction with velocity v ; whenever |w|, |v| < c. Obviously consequently we have also |w'| < c, as well. ###

PS. For another complementary context the Readers are kindly asked to look at post #9 on page 5:

https://www.researchgate.net/post/The_twin_effect_in_water_must_give_the_same_result_as_the_one_in_vacuum_what_about_the_derivation_of_LT_from_Maxwell_equations_in_such_case/5

Thank you for your attention,

Joachim Domsta

Evidently what has been written my Esteeemed Opponent has nothing to do with my objection which remains true..

JoaD, #7 p.8: The last post by @Stefano Quattrini falsifies the basic role of wave equation, which is a rigorous description of ALL features of the wave, including its phase and group velocities.

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SQ, #8 p.8:

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JoaD, #9 p.8: "[the formula] w'=(w-v)/(1- vw/c^2) .. [has].. the following meaning:

### if w is the speed of sound of the medium at rest, then w' is the speed of sound perceived from the IRF' moving in the same direction with velocity v ; whenever |w|, |v| < c. Obviously consequently we have also |w'| < c, as well. ###"

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SQ, #10 p.8:

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Conclusion: The problem is that Stefano Quattrini's only objection concerns things of which I am not aware and which cannot be the subject of scientific discussion. In particular there is no need to reply to such made up accusations.

Joachim Domsta

The opponent claims

"### if w is the speed of sound of the medium at rest, then w' is the speed of sound perceived from the IRF' moving in the same direction with velocity v ; whenever |w|, |v| < c. Obviously consequently we have also |w'| < c, as well. ###"

w'=(w-v)/(1- vw/c^2)"

So he seems to agree that for acoustic waves also spherical, the speed of the wave emitted from a stationary source is not measured the same by a moving observer.

I didn't agree with the sentence:

Sentences to agree /disagree:

a) Acoustic waves, emitted stationary in the medium are spherical.

b) the speed of acoustic waves, as measured by the stationary medium, represent the characteristic speed of the medium

c) the speed of acoustic waves emitted at rest in the medium, if measured by a moving observer in the medium at speed is w= u-v, to a first order approximation.

Maybe it is not on the subject of this discussion but according to one recent publication:

M. Consoli and A. Pluchino, Michelson-Morley Experiments: at the crossroads of Relativity, Cosmology and Quantum Physics. Int. J. Mod. Phys. A, Vol. 38, 2330017 (2023)

- open access -

the preferred frame (or the frame of stationary ether) can be detected not in the MM devices which light paths are filled by vacuum but by some medium. It seems water is a good medium to detect this frame.

Dear Vladimir Onoochin ,

thanks a lot for your very interesting suggestion :

"Michelson-Morley Experiments: at the crossroads of Relativity, Cosmology and Quantum Physics"

which I found in Arxiv as

https://arxiv.org/pdf/2402.12421.pdf

it has something in common with the paper I have been working on for some months at and I just published here in relation to the topic of this thread

Preprint Special Relativity and Lorentz Electrodynamics Is there a wa...