The decisive step was taken by Lorentz, who in 1898 received a general form of transformations - containing a scale factor that acted on all coordinates (spatial and temporal). This factor reflected the overall change in scales when moving from one inertial reference frame to another. However, then Lorentz, Poincaré and Einstein came to the conclusion that it must be equated to 1, that is, this factor was excluded from the formulas.

According to my hypothesis, they made a fatal mistake here - the scale factor MUST NOT be equal to one, and its physical meaning is to reflect the Doppler effect, which is responsible for the overall change in scales. Read more in my article `Memoir on the Theory of Relativity and Unified Field Theory` (2000):

https://vixra.org/abs/1802.0136

Dr. Boutayeb, Thank you for asking this question, because it is most important. I had not realized until I read your six points above that Voigt was reacting to the Michelson-Morley experiment, but the date 1887 does of course coincide. At the moment I am going to avoid commenting on the issue of whether the Voigt versions are better, or the Einstein versions are better. The important thing in the meantime is to be aware that the speed of light seems to be a constant, and that this fact is tied up with the longitudinal Doppler effect in the light carrying medium.

Where it gets particularly interesting though is, that this principle is not to be confused with the related topic of Fitzgerald contraction of the Michelson interferometer. The latter idea may well have been a historical source of much confusion.

Dr. Verkhovsky, I have no doubt that it's all about the Doppler effect in light, but I don't see what you are gaining by making the scale factor not equal to one. The maths that Einstein used seems to be correct. The problem with Einstein's version simply seems to be his physical interpretation and the fact that he didn't use 4-vectors.

But at the moment, I'm interested in what was going on in the 1890s with Lorentz and Larmor, in that Lorentz in particular seems to having been working on a dual purpose, and the two purposes may not have been compatible. One of these purposes seems to have been to make Maxwell's equations have a common format under coordinate frame transformation. The other purpose was more kinematical about matter contracting due to motion through the aether. It may well turn out that the latter occurs up to a point, but is not accurately predicted by the Lorentz transformations, which are in fact only about the Doppler effect in light.

And of course the ultimate point may be that in all waves where mutual motion between source and receiver occurs, that it's the frequency that changes and not the mutual wave speed.

The significance of Voigt seems to be that his method was actually closer to Einstein's method.

To Frederick David Tombe

You wrote: `I don't see what you are gaining by making the scale factor not equal to one. The maths that Einstein used seems to be correct`.

I can`t agree with you. The Lorentz Transform lies in the basis of all theoretical physics, so any its change will lead, we can say, to a new physics: the dependence of distances, masses, charges on the speed of relative motion will become different.

More than 100 years ago, it was discovered that Maxwell's equations allow for a conformal group of transformations, and it would be logical that this group is the basis of all physics. By throwing out the scale factor, the founding fathers of SRT unreasonably narrowed the group of transformations from conformal to linear orthogonal. There were unsuccessful attempts to introduce conformal symmetry -- see overview: https://www.arxiv-vanity.com/papers/0808.2730/

And only with an introduction of the lost scaling factor in the formula of transformation, it is possible to do. All this will have very important consequences, I tried to show them -- see my article: The True Geometry of Nature (Hypothesis)

https://vixra.org/abs/1804.0311

As for V. Voigt, there is an article about his work:

Article Voigt transformations in retrospect: missed opportunities? O...

Frederick David Tombe

Thank you very much for your comment.

About length contraction:

Lorentz and Fitzgerald explained the null result of MM experiment with the length contraction. Voigt had a different idea: he wanted to explained MM experiment with a new formulation of the Doppler effect. Voigt didn’t like Lorentz's idea to use an additional hypothesis that cannot be demonstrated experimentally.

About Doppler effect:

As we all know, the Doppler effect is only a change of the frequency of the signal due to a motion relative to the medium of the source or/and of the observer. In classical view of the Doppler effect, there is no space time transformation in the sense of special relativity. Voigt was in that context of classical Doppler effect: he didn’t consider x’, y’, z’ and t’ as real changes in space and time of bodies. They were only auxiliary variables for his calculation of the Doppler effect.

About c=constant:

Please note that Voigt’s paper is also for acoustic wave. Do you think that c=constant is true for acoustic wave?

Of course, the speed of propagation does not depend on the speed of the source but speed is always relative to the observer. There is no reason to make the speed of light a constant if all the speeds in nature (like speed of sound) are relative to the observer.

My view on Voigt’s work:

The phase of a wave can be written k.x+c.t where k is the wave number. k=w/c.

w is the frequency, c is speed of light (or speed of sound), x and t and space and time variables.

If the source is moving, c does not change in the phase of the wave: c’=c. Then only the frequency change. Voigt considered the more complex scenario where the direction of motion of the object has an angle with the direction of light.

Dr. Verkhosky, Could it maybe be then, that the scale factor of one applies exclusively to EM radiation, but that we have to change it for kinematical situations?

Lev Verkhovsky

The factor that you added uses the relativistic Doppler effect. The relativistic Doppler effect was calculated by using the unmodified Lorentz transformation.

At this point, I am not an advocate of using space-time transformation either Voigt transformation, Lorentz transformation or a modification of these transformations.

Also, I am not an advocate of the relativistic Doppler effect.

I consider that Voitg's work was misunderstood: only a change of frequency of the signal is the result of a Doppler effect, either for acoustic wave or for electromagnetic wave.

To Halim Boutayeb

>>>The factor that you added uses the relativistic Doppler effect. The relativistic Doppler effect was calculated by using the unmodified Lorentz transformation.

I don't see anything wrong with this fact. Einstein obtained the formula for the Doppler effect from the "truncated" Lorentz transform. The Doppler effect is of fundamental importance -- it changes the scale, so after the unmodified Lorentz transform, you need to do a second -- Doppler`s transformation. But in reality, they both work always together, so they need to be combined into one.

I have not delved deeply into Voigt's work; I refer to him in historical terms as a forerunner.

Frederick David Tombe: "Could it maybe be then, that the scale factor of one applies exclusively to EM radiation, but that we have to change it for kinematical situations?"

I believe that we should consider real physical scales, not solid rulers and abstract clocks, but the characteristics of light signals (wavelength and oscillation period). They are affected by the Doppler effect, so it will have a universal value (for all kinematics).

Dr. Boutayeb,

Yes, I agree with you that there is no time dilation as per Einstein's understanding. Only frequency change. And it's only in connection with EM radiation that I can make any definite sense out of the Lorentz transformations.

Voigt and Einstein therefore differed significantly in this regard. But it does seem that Voigt and Einstein had something in common that made them both differ from Lorentz. They both began their argument on the premises that the speed of light is a constant.

@Frederick David Tombe

c=constant is implicit with Voigt and also in Lorentz. It is explicit with Einstein, who uses it as an hypothesis and proves it afterward from his formulas. By imposing the wave equation to keep its firm, we have implicitly c=constant, then it is clear that the result will also give c=constant.

Both Voigt and Lorentz used the wave equation and imposed that it should keep its form. Voigt and Lorentz used the same method. The only difference is the multiplication by the factor gamma to x', y', z' and t'. With Voigt y' and z' are function of v with the factor of the inverse of gamma. Thus the gamma factor exists already with Voigt. We can say that Voigt invented the Lorentz transformation and the gamma factor. With Lorentz, y' and z' are not function of v, the factor disappear after multiplication with gamma. This multiplication was done afterwards. We can say that Voigt and Lorentz derived the transformation by using the same method.

Einstein uses c=constant to derive the same transformation than Lorentz without using the wave equation. His method based on signal synchronisation is at origin of many debates and it is not repeated in books about relativity. Now they use Minkowski equation to prove LT. However, Minkowski equation is derived from LT. It would be much more clear in these books to repeat Voigt's method and to do the multiplication with the gamma factor.

Another difference of Einstein with Voight/Lorentz is that Einstein considers that t' is true clock time and x' is a space characteristic (not independent variable) for physical moving object. For Voigt x', y', z', and t' are auxilarly variables to derive his Doppler effect. For Lorentz they are also auxilarly variables used to derive different problems in optics and the convective form of Maxwell equations.

I consider that Voigt's work can be corrected in order to remove the confusions introduced by special relativity. If instead of changing the independent variable x, y, z, t we change the characteristics of the wave (propagation constant, frequency) by using modern wave theory, the problems introduced by the space-time transformations disappear.

Dr. Boutayeb, Let me just clarify something about Lorentz. Was Lorentz working on the premises that the Michelson-Morley result was (1) due to the arm of the interferometer contracting, or (2) the speed of light being constant, or (3) both?

In my opinion, it can't be both, but I think that Lorentz maybe thought it was both.

Lorentz didn't use his transformation for the purpose of predicting MM experiment. He explained MM experiment with length contraction only, before his invention of local time (and thus Lorentz transformation). With his local time wich is exactly t' of Voigt (without gamma factor) he derived the formula for Fizeau's experiment with water. The Kaufmann experiment with particles and developing a convective form of Maxwell's equations make him use and develop his LT.

Concerning the year 1887 for MM experiment. Michelson, following Maxwell's idea, made his first experiment in 1881. He repeated the experiment with Morley in 1887. Scientists started to debate about the experiment in 1881-1882, this is why Michelson repeated the experiment with another person in 1887.

@Lev Verkhovsky

You start with LT and multiply it with a factor. However the main problem is how do you derive LT in the first place. This derivation should be included in your paper.

Voigt's method for the derivation of his LT was to consider that the wave equation (either it is for acoustic wave or electromagnetic wave) should keep its form. If we search in internet we can find convective wave equations. There is no physical reason for the wave equation to keep its form. There is a classical wave equation with an observer at rest and there is a convective wave equation.

To Halim Boutayeb

>>>You start with LT and multiply it with a factor. However the main problem is how do you derive LT in the first place. This derivation should be included in your paper.

I don't see the need for that. The purpose of my work was to point out an error in the generally accepted Lorentz transformations and how it should be corrected. I also tried to deduce some consequences from the new (corrected) type of transformations.

Thanks to you and to Frederick David for questions.

Dr. Boutayeb, Yes, Lorentz came up with the contraction idea and only after that did the idea of a local time arise, and this idea may have originated from Larmor. But when Lorentz had his transformations completed, wasn't it the length contraction aspect which he was depending on in order to explain Michelson-Morley, rather than the idea that the speed of light was constant, as per Voigt and Einstein?

Dr. Verkhovsky, In the article below, the analysis that runs from equation (18) through to equation (33), which is largely textbook based, would suggest that no correction is needed for the Lorentz transformations,

Article The Lorentz Aether Theory

They are being used in connection with four-vectors, and only for fields. In my opinion, it's the only context in which they can be used accurately.

Frederick David, if all the arguments I have given in my article have not convinced you of the need to correct the Lorentz transformations, it is difficult for me to add something new to them. I can't say anything about your work, because I don't know enough about electrodynamics.

It is interesting that you have an article “The Double Helix Theory of the Magnetic Field” , and I have an article about the structure of the DNA molecule: `DNA: the Double Helix or the Ribbon Helix?` https://vixra.org/abs/1803.0104

@Frederick David Tombe

Your question is very interesting and I will try to investigate it in more details.

I will tell what I remember now.

First Lorentz postulated the length contraction to explain Michelson experiment.

When he derived the equation for Fizeau experiment with water by using Voigt's local time, he derived a formula that would also explain MM if the index of the medium is equal to one. It seems that two different explanation exist in Lorentz work. This need to be confirmed.

@Lev Verkhovsky

Thank you very much for your comments and for your responses. I have found interesting that you derived Gerber's potential.

Best regards

By the way, in PHYSICS TODAY (March) the article `The fall and rise of the Doppler effect` by Prof. David Nolte

https://physicstoday.scitation.org/doi/10.1063/PT.3.4429

Very interesting paper.

However I don't agree with the author: Voigt did predict the transverse Doppler effect with his analysis, although he don't talk about it explicitly.

Please see Fig. 3 of the paper referenced above:

https://physicstoday.scitation.org/doi/10.1063/PT.3.4429

In the parameters for x' coordinate if we replace t with x/c we can recognize the longitudinal Doppler effect factor (1-v/c).

If we look in y' and z' coordinates we recognize the transverse Doppler effect term, which is often called quadratic Doppler effect sqrt(1-(v/c)^2).

In conclusion, Voigt predicted the transverse Doppler effect. For completion of his work we just need to make a difference between moving observer and moving source. The factors are inverses of each other for the two cases.

To make Voigt's work more in agreement with modern wave theory approach, instead of parameters x', y' and z' we should have kx', ky' and kz' which are the components of the propagation constant in 3D space. The parameter t' of Voigt should also be understood with the inverse of the frequency.

We can then replace the space-time transformation with frequency-time transformation (Fourier) to develop convective form of Maxwell's equations. Frequency-time transformation is very well understood and applied daily by engineers and students. Space-time transformations such as LT have no physical basis.

In 1910, the British Bateman and Cunningham showed that Maxwell's equations are invariant under a conformal transformation, which includes tension-contraction, as well as inversion. If we use modified Lorentz transformations (with a scale factor reflecting the Doppler effect), then we get exactly the conformal transformation.

Question: what is the physical meaning of inversion?

(I have a guess, but my weak knowledge does not allow me to substantiate it.)

Dr. Boutayeb, That's the point that I'm leading to. Lorentz was trying to solve different problems all at once but it eventually narrowed down to the Lorentz transformations that Einstein used.

Voigt and Einstein however were of the view that the speed of light was a constant and that was central to their equations.

Voigt however wasn't treating the time variable in the sense of time as we normally measure it. In Voigt's case it was more like the inverse of frequency, in which case it was only referring to the frequency of the light, and hence the Doppler shift. I would subscribe to that perspective and not to Einstein's time dilation perspective.

But meanwhile we still have to discuss what Lorentz's and Larmor's physical interpretations were.

Two of Bateman's papers are available here:

The Conformal Transformations of a Space of Four Dimensions and their Applications to Geometrical Optics:

https://en.wikisource.org/wiki/The_Conformal_Transformations_of_a_Space_of_Four_Dimensions_and_their_Applications_to_Geometrical_Optics

The Transformation of the Electrodynamical Equations:

https://zenodo.org/record/1433552#.XzAnWShKg2w

Larmor's paper On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media (1897):

https://en.wikisource.org/wiki/Dynamical_Theory_of_the_Electric_and_Luminiferous_Medium_III

Frederick David Tombe

In one of your paper, you present an original interpretation of E=mc^2 in the sense of classical mechanics. You make a parallel with Newton-Laplace equation

c=sqrt(K/rho)

where c is speed of propagation, K is the resistance of an elastic body to deformation by an applied force and rho is the density. E is then equivalent to K and m is equivalent to rho. You show that this was shown in Maxwell’s paper.

In a certain sense you replace the electron or other particle with a perturbation of the medium of propagation.

Can you please elaborate more this idea and show how the gamma factor can come into the picture (I am thinking about particle accelerator where a relativistic mass gamma*m is used)?

In the meantime, I will continue my research on Larmor and Lorentz.

Halim Boutayeb, I'll say you my guess: Inversion connects the leading and lagging potential.

Dr. Boutayeb, First of all, is this the paper that you are talking about? Presentation Radiation Pressure and E = mc²

The gamma factor may not be relevant in this analysis.

@ Frederick David Tombe

Yes, I think this is the paper. From my understanding, E=mc^2 is incomplete without the relativistic mass, i.e. gamma should be present. This is how relativists and many non-relativists (for example Petr Beckmann) explain inertia and kinetic energy. The relativistic mass is also used in particle accelerators.

Since we are talking about LT and the gamma factor, I thought about your formula. I thought that maybe your approach can replace the concept of an increasing mass with velocity.

the relativistic mass/ velocity-dependent mass is used here in the framework of what it is called "Kaufmann mechanics", by the non-relativist J.P. Wesley:

https://www.jamespaulwesley.org/Document_Files/Weber_Electrodynamics_Part_III_Mechanics_Gravitation_JP-Wesley.pdf

Relativists use E=mc^2 as a result of LT. Some non-relativists use also E=mc^2, but for them this is the result of the velocity-dependent mass where gamma factor is present.

If another interpretation of E=mc^2 is found, based on classical mechanics, the gamma factor may also come into the picture, in order to explain physics of particle accelerators.

Thomson and Heaviside were the first to come with the idea of the increasing electromagnetic mass by using the analogy with moving solid in fluid. However in fluid, this is only an apparent increase of mass not a real increase of mass:

https://books.google.com/books?id=e9wEntQmA0IC&pg=PA121&lpg=PA121&dq=heaviside+moving+charge&source=bl&ots=f3lQruqKUt&sig=ACfU3U0xzjw-1iRDe4jputkZcJM7t7Q0tQ&hl=fr&sa=X&ved=2ahUKEwjB6uOIouDgAhWp7IMKHR6iB9UQ6AEwBnoECAIQAQ#v=onepage&q=heaviside%20moving%20charge&f=false

"The quantity on the right-hand side of Eq. (1) that multiplies the acceleration is commonly called the added mass. This name is used because the term involving the acceleration is usually moved to the other side of the equation so that the total quantity multiplying the acceleration is m+CMmair.":

https://pdfs.semanticscholar.org/354f/7a7c77be63fcfa7742252eff1a017f8ed164.pdf

Dr. Boutayeb,

The analysis in that paper was based on the assumption that mass is conserved. That of course doesn't mean that mass is actually conserved, but in the context of the issues involved in that analysis I was working on the basis that electrons and positrons in the background electron-positron sea have an average fixed value for their mass. The issue of mass increasing with velocity only becomes of significance when bodies are moving through the electron-positron sea. So it's a different topic.

Dr. Boutayeb, Putting it more simply, the gamma factor and mass increase would be a convective effect relating to motion through the aether, whereas the issues raised in the paper in question relate to the steady state in a wave at a fixed point in space. Hence in the particular context, the gamma factor is not relevant.

Dr. Boutayeb, In this paper here by Dr. C.A. Zapffe, we can see between pages 40 and 68, three different derivations of E = mc2. In the third case, Einstein himself showed that the LT are irrelevant.

The issue of mass increase with velocity is a convective issue, not related to E = mc2.

https://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2696

By the way, I met both Dr. Wesley and Dr. Zapffe in the 1980s and I've stayed at both of their houses in West Germany and the USA respectively.

I wonder what cosmology will look like with a new type of transformation (with a Doppler multiplier). I can't cover the whole picture, just the individual effects. Hubble's law: the further away an object is, the faster it moves away -- the greater the redshift. But the greater the redshift, the greater the length scale, which means that the distance itself is SMALLER. And then the force of attraction is GREATER.

Dr. Verkhovsky, The red shift is certainly mysterious, but I think we're a long way away from getting any reliable explanations for it. Generally speaking, cosmology is a highly speculative topic.

Dr. Boutayeb, Would I be correct in saying that Voigt never concerned himself with mass increase with velocity? Wasn't he only interested in the Doppler effect in light waves.

You are right, Voigt was never concerned about mass increase with velocity, as far as I know. His paper of 1887 was only about wave theory (sound or electromagnetic wave) and Doppler effect. Kaufmann made his important experiment discussing increase of mass in 1901, and Abraham proposed the first theoretical model for this mass increase in 1902. Although, Lord Kelvin and Heaviside predicted an apparent increase of mass for a moving charge earlier.

I am personally, in the present time, trying to find a different approach where the mass is not increasing. The concept is still in early stage, it is based on Voigt, Klinaku, with some ideas from Ritz. I consider Voigt's 1887 paper the most important paper for both relativists and those who would like to find an alternative to LT and special relativity.

https://www.researchgate.net/publication/331320142_Michelson-Morley_experiment_general_Doppler%27s_principle_Maxwell%27s_equations_particle_accelerators_and_Mossbauer_experiment

Frederick David Tombe

You wrote: `The red shift is certainly mysterious, but I think we're a long way away from getting any reliable explanations for it. Generally speaking, cosmology is a highly speculative topic.`

Reliable explanations can only be found on solid grounds. But for over a hundred years, the main foundation -- Lorentz transformation -- has been of the wrong type. In particular, with corrected transformation formulas, the dependence of mass on speed will be completely different.

(Please don't call me Doctor, I'm not a doctor.)

Hi Lev, In the restricted case of EM waves and fields, I believe that the Lorentz transformation is correct when done in four-vectors. My concern is the manner in which it has been extrapolated into kinematics. I'm not at all convinced that mass increases or that length contracts exactly as predicted by the Lorentz transformations. And I certainly don't believe in Einstein's time dilation in any context. I believe that the time variable should be read as the inverse of the frequency of the waves.

Dr. Boutayeb, There might be mass increase with velocity, but I doubt that it will be directly tied to the Lorentz transformations. In all of my theoretical works involving kinetic energy, I presume from the outset that mass is fixed although I don't necessarily believe that it is fixed. It's possible that as we continue to apply energy to a moving body, that some of it might go into increasing the internal pressure (mass/potential energy) within the body rather than increasing its external speed. But I have no formulas for this.

Hi Frederick David,

I think the transformation should work in both kinematics and Maxwell's equations. My statement is quite specific: initially, the conversion contained a scale multiplier, which was mistakenly discarded. It must be returned.

After that, we need to solve difficult issues of interpretation of the corrected type of transformations.

For the scale factor, see

https://www.mathpages.com/home/kmath733/kmath733.htm

https://www.mathpages.com/home/kmath759/kmath759.htm

Hi Lev, I agree that there is a strong possibility that the transformations might work in kinematics for a scale multiplier that is not unity. But as regards matters relating to the Doppler effect in EM waves and fields, I think it should be unity.

Hi Frederick David,

I advice you to pay attention to articles by Beitman and Cunningham (see above in this thread). I think they are of fundamental importance for the issue in question.

Hi Lev, Could you please supply the Beitman and Cunningham link again along with the page number and section number of the relevant part.

To Frederick David Tombe

Halim Boutayeb added a reply August 9

Two of Bateman's papers are available here: The Conformal Transformations of a Space of Four Dimensions and their Applications to Geometrical Optics: https://en.wikisource.org/wiki/The_Conformal_Transformations_of_a_Space_of_Four_Dimensions_and_their_Applications_to_Geometrical_Optics The Transformation of the Electrodynamical Equations: https://zenodo.org/record/1433552#.XzAnWShKg2w

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

I can't give precise instructions, because I haven't delved into these works myself (I'm not an expert on Maxwell's equations). For me, the important conclusion is that they allow a broader transformation group (conformal) than the Lorentz transformation group (in its current form). I assume (but do not strictly show) that introducing a Doppler multiplier will result in a conformal group.

Let me recall the words of P. Dirac: It appears as one of the fundamental principles of Nature that the equations expressing basic laws should be invariant under the widest possible group of transformations (Proc. R. Soc. Lond., A 333, 403-418, 1973).

Hi Lev, Thank you. I'll take a look.

Hi Lev, OK, I've had a look at Beitman and Cunningham and I found it to contain far too many equations, and complex equations at that. Early on I gathered that the author was merely introducing the Lorenz gauge (sometimes known as the Lorentz condition) but after that there seemed to be an endless amount of mathematics, and so I lost the train of what he was trying to say. I would have needed somebody to point out the significance of each line in the mathematical manipulations.

In my own article, I believe I have satisfactorily made the only relevant point of the Lorenz gauge between equations (18) and (33), and I can't see what extra Beitman and Cunningham are adding to the argument.

In the case of equations (18) to (33) here, these are largely textbook based,

Article The Lorentz Aether Theory

Hi Frederick David,

110 years ago, the British Bateman (not Beitman -- this was my mistake) and Cunningham obtained a very important result, which is still not comprehended (and is poorly known even in Great Britain).

I think now you understand the essence of my hypothesis, and its connection with their result. But this question turned out to be difficult even for you -- a specialist in electrodynamics. I'm sure the picture will clear up soon for you .

Thanks for your interest and efforts, I wish you success.

Lev, Can you show me in the Bateman paper where he introduces the scale multiplier.

Dr. Boutayeb, Regarding where you said,

Dear Frederick,

I think you should mention Woldemar Voigt in your paper. Lorentz recognized many times Voigt's paper "On Doppler's Principle" (1887).

I wanted to, but I couldn't fit it into the chronology. Although Voigt was the first to deal with the Doppler shift in light, his approach was quite different to that of Lorentz and Larmor, and I believe that Lorentz wasn't aware of Voigt until about 1908.

I'm not even a fan of Lorentz. Strictly speaking, I support Einstein's versions of the Lorentz transformations, but in four-vector format, and in conjunction with waves and fields only, and in conjunction with Maxwell's sea of molecular vortices. Lorentz was too 'ad hoc' for me. I much preferred Larmor's approach.

Frederick David,

I advise you to look at:

Cunningham, Ebenezer (1910). "The principle of Relativity in Electrodynamics and an Extension Thereof" . Proceedings of the London Mathematical Society. 8: 77–98. (I have no link);

Useful link: https://arxiv.org/pdf/hep-th/9701064.pdf

Dear @Frederick David Tombe

There is an important question regarding LT: how is it derived? This question is often forgotten and a huge number of papers deals with how to use LT and/or what are the consequences of LT.

It is very clear how Voigt derived LT. I think that Lorentz knew about Voigt's method because they knew each other and they use to write to each other letters.

How Lorentz derived LT? It is clear that he used Voigt's method and later he made the multiplication with the gamma factor.

How Einstein derived LT? His 1905 method is not repeated anymore. Later he proposed another method based on the division per zero. Now, in relativity books they simply use Minkowski equation to derive LT. However, Minkowski equation was derived from LT. They should show how it was deprived by Voigt.

Are they many methods to derive LT? I don't think so. It is clear that LT is an invention by Voigt and only his method can give LT.

Because Voigt invented LT, we can understand the real meaning of LT with his paper. LT is a mistake because we can repeat Voigt's work without adding additional time variable and we can deal with Doppler principle without changing the time of our clock. Voigt certainly didn't do it purposely, special relativity is not his fault. There is no need for either LT or special relativity in science.

Dr. Boutayeb, I certainly don't agree with Einstein's interpretation since it involves time dilation. I consider the time variables simply to refer to the reciprocal of the wave frequency.

But as regards the Voigt transformations, can they be put into four-vector format in order to produce the important results at equations (26) and (33) here,

Article The Lorentz Aether Theory

Dear Frederick David Tombe ,

Your paper starts from the premise that LT is correct and you show that you obtained correct results with them. However, in my point of view, if you can obtain the same results without LT it would be even better.

First, there is no physical reason for transforming the space and time variables. You agreed with me that it is the frequency of the wave that is changing, not time. But you still use a transformation of space and time and the frequency variable is not present in your work.

Secondly, obtaining good results with a method does not mean that the method is correct. In my point of view, the method would be correct if there is a physical meaning for it. In order to obtain the physical meaning for LT, for me, it is more important to show how LT is derived rather than to show how it can be used.

As you know, Voigt used the wave equation (which works for both: sound and electromagnetic wave) to derive LT. Combining Maxwell's equations for a TEM wave give a wave equation, since this was a target for Maxwell (because he was inspired by the 1856 Weber-Kohlrausch experiment) as you have shown in your papers. These two facts show already the link between LT and electric and magnetic field components of Maxwell's equations. It will not be a surprise that LT can give good results for some specific problems. If you can obtain the same results without LT it is better because you will not use unnecessary space-time transformation concept.

Best regards,

Halim

In Wesley`s 1986 paper:

https://link.springer.com/content/pdf/10.1007/BF00735382.pdf

"Voigt thereby obtained the relations that are today inappropriately called the Lorentz transformation. Voigt represented his Doppler effect mathematically in terms of space and time variables, whereas the Doppler effect can involve the propagation constant and frequency only. Voigt's unfortunate mathematical representation of his Doppler effect in terms of space and time apparently led Lorentz and others to naively conclude that space and time themselves might actually change in a moving system"

Dear Halim,

I arrived finally to the full understanding about the inadequacy of the Lorentz transformations. There is a very sound logic behind LT which involves an obvious equivalence of IRFs from which also inevitably descends an invariant speed of signals, if finite. It is evident that the postulates which seem so obvious, bring to unphysical consequences in the way they are used.

An IRF is an entity which is stationary from minus infinity to plus infinity in time and extended indefinitely in space, endowed with clocks all in synch.

IRF0 and IRF1 ,definite the same, have a relative speed v gives naturally birth to a symmetry. Since no difference can be found, if there is a limited speed of signals, then it has to be the same for all of them, so as a matter of fact LT/SR is based only on one postulate as GT.

Such configuration of multi space and times is not usable as such, if used otherwise then implies different things.

a) there is no physical object which is attached to an IRF forever, but it belongs to one with an approximation and for a limited period of time.

b) inertiality which is operatively defined as absence of accelerations can be obtained as a limit from a circular motion with 0 acceleration and diverging radius at constant speed. This configuration does not make the rotational system and stationary one symmetric. In this case, as experimentally verified, the relation between the times is just determined by the t'= gamma-1 t . For two generic IRFs the relation is determined by t= gamma-1t - vx/c2 . The vx/c2 term cannot exist since it does not come out in such experiments.

This means that if one system is considered inertial, another system, although not affected by forces, hence inertial, cannot be the same as the first.

Dear Stefano,

It has been a long time. I hope you are well and safe.

I do not agree with the relation between time which you said is verified experimentally.

I prefer Lorentz's first view concerning this formula as a mathematical local time not a physical time. A mathematical artifice which imposes a constant speed for any reference plane.

I think that the true physical effect is only a Doppler effect which acts on frequency not time.

Please see this interview of Paul Dirac, especially his point of view of Einstein's time which should not be the true time:

https://youtu.be/Et8-gg6XNDY

Best regards

Dear Halim,

regarding the relativity of time I have to disagree, since in the muon ring experiment where no EM waves were exchanged, the muon decay slowed down exaclty by the factor gamma.

As a matter of fact a further confirmation of the untentability of the term vx/c2 can be found here

Preprint ABOUT SLOW TRANSPORT OF CLOCKS AND SIMULTANEITY

Dear Stefano,

In your linked paper above, you are still referring to old relativistic transformations, such as Voigt's and Lorentz's; previously you have also referenced Tangherlini's transformations.

Certainly the question proposed by Halim Boutayef is about Lorentz transformation(s), but I consider that there should be at least some reference to new alternatives, such as my proposed relativistic transformations, which were published here, at Researchgate, about two (2) year ago.

My transformations suggest very different equations in Physics, such as a new EM forces equation, which is purported to replace the so-called "Lorentz forces" equation, or a new form for the EM invariants, as well as a more compact derivations of Maxwell's equations.

Below please find the links to two of my papers. (Sorry, cannot find how to insert hyperreferences):

“…Now, in relativity books they simply use Minkowski equation to derive LT….”

- that is correct about relativity books; however this derivation from the condition of conservation of the quadratic form s2= (x2+y2+z2–t2) was found by Poincaré [here he uses c=1] see “Sur la dynamique de l’ electron” submitted 25 of July 1905; printed 1906, what formally relates to the 4D space[time] with the metrics (X,Y,Z, it). Minkowski simply used this result.

However Poincaré well understood, of course, that real [factually] Matter’s spacetime is the real [mathematically] 4D Euclidian space[time], and so the derivation above was for Poincaré only an interesting mathematical result.

However in 1908 Minkowski postulated, that real [factually] Matter’s spacetime is just the 4D [further and till now in the standard SR “Minkowski space”] spacetime with strange the metrics above, i.e. that real [factually] dimension “time” is imaginary [mathematically] one, in spite of that was rather strange.

“…. However, Minkowski equation was derived from LT. …..”

- that isn’t, in certain sense, rigorously correct. The equation and the conservation condition for the quadratic form s2 above is purely mathematical fact, whereas the Lorentz transformations link physical parameters of material bodies as they are measured in moving relatively inertial reference frames. So, though formally the constancy of s2 indeed, of course – see above, “follows” form the transformations , that are principally different things, physics isn’t mathematics.

That

“…I prefer Lorentz's first view concerning this formula as a mathematical local time not a physical time. A mathematical artifice which imposes a constant speed for any reference plane….”

- is correct. The “local time” and “local space” in Lorentz-Poincaré interpretation indeed were only some ad hoc variables, using of which enables to obtain correct physical results; that is quite usual way at developing every theory; and all theories, including all recent ones, eventually are based on some transcendent ad hoc assumptions.

That is another thing, that Minkowski postulated that the [global infinite] space and time in Minkowski space compose real [factually] Matter’s spacetime, the letters “x” and “t” are coordinates just whole space points, what was/[and is in official physics till now] fundamentally wrong,

- and so further discovered, correspondingly, a lot of strange [further and till now in the standard SR “fundamental relativistic properties of Matter’s spacetime and fundamental relativistic effects”] fundamentally non-existent properties of Matter’s spacetime – “space contraction”, “time dilation”, and physical effects – that just the “contracted space” really contracts lengths of moving real bodies, that just the “dilated time” really slows real moving clocks, etc.

“……I think that the true physical effect is only a Doppler effect which acts on frequency not time.…..”

- that isn’t correct. Any humans’ terms/notions, which they use at description of some objectively existent, including material, objects/events/processes, by no means act on these objects/events/processes. In this case, say, if some moving light source radiates photons ahead along its motion in space, that the physical momentum of the source acts, which sums up with momentums of photons, that are radiated at atoms’ transitions in the source, and so radiated photons have energy/frequency larger comparing with the atoms are at rest in the space.

What are Lorentz transformations, when they are valid completely, and when non-completely, how it is possible to measure absolute velocity in the 3D space of the Matter’s fundamentally absolute, fundamentally flat, and fundamentally Euclidian, [5]4D spacetime with metrics (cτ,X,Y,Z,ct),

- all that is practically completely clarified in the Shevchenko-Tokarevsky’s informational physical model, for first reading see https://www.researchgate.net/publication/342600304_The_informational_physical_model_some_fundamental_problems_in_physics DOI: 10.13140/RG.2.2.12325.73445/2;

Including to derive the Lorentz transformations and most of basic fast mechanics equation it is enough to know Pythagoras theorem; and to know what is “Matter”, “Space”, “Time”, “Energy”, also, of course, these – and many other fundamental things are scientifically defined in the paper above .

In this Lorentz transformation concrete case see paper “Measurement of the absolute speed is possible?”

https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible DOI 10.5281/zenodo.48709,

- where on first 6 pages the transformations, etc., are derived; the whole paper describes how the absolute velocity can be measured.

Cheers

We don't have information as "Absolute". We do , however , have Absolutes from which we may arrive at information. Things other than (and against) this postulate only lead to weirdly bizarre entities such as dark matter , dark energy , wormholes , uncoordinated shift of horizons , etc , etc . . . ..

It is not exactly clear how much acrobatics to be done would be allowable when you wanna obtain certain results as negating the negation of those things that are nowadays ordinaries of modern physics : things like LT and Minkowskian 4_D.

Seems pupils and students ought to totally avoid classical notions in physics !!

While some of the same classic ideas are exploited to give birth to AND to promulgate the so-called modern physics.

The true question to ask is : how is it that fundamentals in the base of physics show no signs of veering and swinging in the course of the past half-century ??

- that is some on first glance a questionable claim, which really is fundamentally wrong in both points.

Firstly – to say about “Absolute” it is necessary before to define – what is “Absolute”? As a rule in concrete case of some system of objects, including, say, the system of objects “Matter”, this notion is applied to utmost fundamental and common for all elements In the system. Really, as that is rigorously proven in the Shevchenko-Tokarevsky’s “The Information as Absolute” conception https://www.researchgate.net/publication/260930711_the_Information_as_Absolute DOI 10.5281/zenodo.268904,

- there exists only one [and some phenomena, objects, etc., that directly relates to this phenomenon] utmost common for everything phenomenon “Information” – everything “is made” only as some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. Including Matter is a huge for human, however infinitesimal comparing with the Set, element of the Set.

Again – that is rigorously proven, see linked paper above. It is useful in this case to read the SS post March 28 in the thread https://www.researchgate.net/post/What_is_the_difference_between_cell-based_consciousness_and_brain-based_consciousness[though to read whole SS posts series from March 5 that relates to what is “cognition” is useful as well]

At that humans principally cannot have some other Absolutes from which we may arrive at information, since humans at birth know practically nothing about their environment; and all – firstly new – information obtain only experimentally. All humans’ knowledge is empirical, whereas any experiment principally proves nothing, and so cannot be an “Absolute”.

From that there is only two exclusions – mathematics, which is purely a product of the fundamentally non-material informational system “human’s consciousness”, and the SS&VT conception above, which is based, of course – see above, on experiments ,where some information as a data is observed – what all humans constantly do, however in this case it is enough to make one experiment to derive the proof above.

In all other cases the consciousness can obtain, and analyze, only always – really fundamentally at least partially transcendent/uncertain/irrational information; and so, if some points in some science are stated as some “Absolutes”, and these “Absolutes” are used as some postulates in some theory, in many cases these postulates really turn out to be some postulated illusions; including most of the postulates in the SR/GR, besides the Galileo-Poincaré relativity principle, are illusions – and the using of the principle in these theories is an essential illusion as well.

Just because the absolutization of this principle up to really mystic omnipotence resulted in postulating in the theories of the really only convenient mathematical tool “Minkowski space” in the SR [further pseudo Riemannian space in the GR] as the real Matter’s spacetime, in discovering of “relativistic properties and effects”, including indeed

“…weirdly bizarre entities such as dark matter , dark energy , wormholes , uncoordinated shift of horizons , etc , etc…..”

- whereas these things rigorously follow from, in this case the GR, postulates.

Really the relativity principle isn’t omnipotent, the inertial reference frames aren’t absolutely completely equivalent and legitimate, correspondingly the Lorentz transformations aren’t completely valid is some cases, Matter’s spacetime is absolute, etc.

More see the SS posts above and links in the posts.

Cheers

Sergey Shevchenko

Hi !

You say ;

" some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. "

Agreed !

However , the relata comprising the PATTERNS you are talking about are , as you yourself suggest , mere Patterns . .. . . You are sort of objectifying them , , , , , , , This is a sin in physics . . . .

This is not dissimilar to those mathematicians who regard their topics of discussions as TRUE OBJECTS . . . . .Some of my mathematician friends talk (and write) that way !!

You go on to say :

" From that there is only two exclusions – mathematics, which is purely a product of the fundamentally non-material informational system “human’s consciousness”, and the SS&VT conception above, which is based, of course – see above, on experiments ,where some information as a data is observed – what all humans constantly do, however in this case it is enough to make one experiment to derive the proof above. "

I just don't know whether you have deep-studied writings of Kurt Godel or not . . . . . . . . .

You say :

" In all other cases the consciousness can obtain, and analyze, only always – really fundamentally at least partially transcendent/uncertain/irrational information; and so, if some points in some science are stated as some “Absolutes”, and these “Absolutes” are used as some postulates in some theory, in many cases these postulates really turn out to be some postulated illusions; including most of the postulates in the SR/GR, besides the Galileo-Poincaré relativity principle, are illusions – and the using of the principle in these theories is an essential illusion as well. "

You are typing theses sentences of YOURS out of MY keyboard . . . .You are absolutely a True Brave Non-conventionalist Scientist . . . . .

Best of Regards

REZA

Reza Sanaye

Hi!

And a few notes to your last post. First of all – what is written in the SS posts – and linked papers, of course, isn’t trivial; and to understand what is written is necessary to read that attentively enough and to think; whereas you seem to be in a hurry. So, say, that

“…[SS quote] " some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. " [end quote]

Agreed !

However , the relata comprising the PATTERNS you are talking about are , as you yourself suggest , mere Patterns . .. . You are sort of objectifying them , , , , , , , This is a sin in physics . .”

- looks as some such example. Again, in the “The Information as Absolute” conception [the link see SS post above] it is rigorously proven that everything “is made” only as some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. Including the informational system of the patterns/sub-systems “Matter” is a huge for human, however infinitesimal comparing with the Set, element of the Set; and the human’s consciousness is an element of the Set,

- and really the informational systems “humans”, including physicists, decode some informational links, etc., between informational patterns/sub-systems in Matter, just – and only because of – that both systems are made from only one stuff “Information”.

“…[SS quote] From that there is only two exclusions – mathematics, which is purely a product of the fundamentally non-material informational system “human’s consciousness”, and the SS&VT conception above, which is based, of course – see above, on experiments ,where some information as a data is observed – what all humans constantly do, however in this case it is enough to make one experiment to derive the proof above. "[end quote]

I just don't know whether you have deep-studied writings of Kurt Godel or not . …..”

- your comment in italic above looks as rather questionable one. Kurt Gödel writings very indirectly relate to the notion “proof” in mathematics, he proved that every complex enough mathematical theory , which is based on a set of concrete axioms, is incomplete, i.e. there exist some mathematical propositions, which are true in the theory, but their truth cannot be proven in the theory. However, besides this rather exotic cases, all in mathematics is some theorems, which have the proofs, i.e. it is proven that the theorems’ propositions are logically consistent with the axioms.

Again – some proofs are principally impossible in Nature sciences, since humans obtain any information about objects/events/processes in Matter only empirically, whereas any experimental outcome – again in fundamental contrast to the “The Information as Absolute” conception – doesn’t prove anything.

Starting from the obligatory step in any proof – the “proof of existence” – from any experiment, where some, say, object was observed, by no means follows existence of this object next time moment; and even the human’s assumption, that this object exists now, can be an illusory at all.

In mathematics, which is purely the product of the fundamentally non-material informational system “human’s consciousness”, the proof of existence is usually quite simple – a mathematician simply writes “Let A is…”, “Let B is…”, etc., and A and B become to be existent.

In the conception it is rigorously proven – see last SS comment to the conception in https://www.researchgate.net/publication/260930711_the_Information_as_Absolute/comments and the section Property I5 in the paper] that any informational pattern/system logically cannot be non-existent, and so exists – as an element of the absolutely fundamental and absolutely infinite “Information” Set always; i.e. the Set exists fundamentally having no Beginning and no End; where everything had happened always, and is happening always, absolutely infinite “numbers” of times in accordance with unique scenarios, etc.

The absolutely fundamental phenomenon “Information” is very complex and paradoxical phenomenon…

See also the last SS post in https://www.researchgate.net/post/Time-as-fourth-dimension-is-there-any-experimental-evidence

Cheers

Dear Sergey Shevchenko

"- that is correct about relativity books; however this derivation from the condition of conservation of the quadratic form s2= (x2+y2+z2–t2) was found by Poincaré [here he uses c=1] see “Sur la dynamique de l’ electron” submitted 25 of July 1905; printed 1906, what formally relates to the 4D space[time] with the metrics (X,Y,Z, it). Minkowski simply used this result."

the quadratic form s2= (x2+y2+z2–t2) has no experimental background and has no physical meaning. Voigt invented LT by mistake, Lorentz used LT for his electrodynamics, Poincare liked Lorentz work. The quadratic form s2= (x2+y2+z2–t2) and LT are both mistakes with the same origin (Voigt).

"However Poincaré well understood, of course, that real [factually] Matter’s spacetime is the real [mathematically] 4D Euclidian space[time], and so the derivation above was for Poincaré only an interesting mathematical result.

However in 1908 Minkowski postulated, that real [factually] Matter’s spacetime is just the 4D [further and till now in the standard SR “Minkowski space”] spacetime with strange the metrics above, i.e. that real [factually] dimension “time” is imaginary [mathematically] one, in spite of that was rather strange."

Math alone is not physics. If LT is only a mathematical tool with a change of variable, it should be abandoned from physics.

"that isn’t, in certain sense, rigorously correct. The equation and the conservation condition for the quadratic form s2 above is purely mathematical fact, whereas the Lorentz transformations link physical parameters of material bodies as they are measured in moving relatively inertial reference frames. So, though formally the constancy of s2 indeed, of course – see above, “follows” form the transformations , that are principally different things, physics isn’t mathematics."

Again, as you said this is purely math (a change of variable). LT has no experimental background. Please read Lorentz work: it is a change of variables. Lorentz introduced LT parameters as auxiliary variables with no any physical meaning.

"is correct. The “local time” and “local space” in Lorentz-Poincaré interpretation indeed were only some ad hoc variables, using of which enables to obtain correct physical results; that is quite usual way at developing every theory; and all theories, including all recent ones, eventually are based on some transcendent ad hoc assumptions."

Usual way to do physics (before relativity) is to define precisely the parameters. If the variable t' of LT is not real time (as I support), but only a mathematical tool (auxiliary variables), LT should be abandoned because it gives confusion in physics and make researchers wasting their time with it.

Your text is very long, sorry if I can not respond to all.

In point of fact , LT can occur only on those topologies that had already the Plane-bifurcation Event. If and when that has not taken place , you may primordially arrive at change(s) without any time. In the type of independent breathers, nonlinear classical reinforcement solutions are present. These solutions are located in space over and above time (usually exponentially). The casings on the part of locally Euclidean lattices may well show symmetry for translations. Discrete breathers are not restricted to the dimensions of intended topologies. These vary from 'generic' bifurcations of 'dissipative' vector fields without form until they have a dimension threshold that expands with a bifurcation co-dimension. The expression would obviously go invariant under diffeomorphic transformations of any other parameter. Briefly, dynamism is ( the development of) the Topos-gage as counting dimensions. We have 2n + 2-dimensional phase space of the parameterized system. One limitation limits orbits to a 2n+ 1-dimensional hypersurface; we are left , thence , with a 2-n dimensional orbit in complete harmony to the dimension of original system phase space after labeling the gage orbits with points in the physical phase space. No LT can possibly occur , either.

Dear Stefano,

The muon decay is not a convincing proof for me. There are other explanations that do not involve time dilation in the literature.

Statistically someone who smoke cigarettes a lot has more chance to get cancer and to die prematurely. This does not mean that time has been contracted for him. In the same way, the analysis of muon lifetime cannot be used to prove that time is modified. Only a direct experimental proof of time dilation should be used, otherwise this concept should be discarded from physics.

@halim

Another mystery the interval put in a special format s^2=x^2+...-c^2t^2 is only invariant, rest other forms e.g.

S^2=t^2(v^2-c^2) is not ???, What is your opinion on it??

Interval would have meaning only if it could be derived properly.

Furthermore what is ds^2??

Thanks