As a consequence of the discussion started during Bologna's May 1999 meeting (see points 1 and 2 in this same page concerning the Foundations of Physics), about the validity of some common objections coming from the critics of SR, I had a long exchange of mails with George Galeczki, the organizer of the 1997 Cologne meeting (see point 9 in this same page), and author, with Peter Marquardt, of the book: "Requiem für die Spezielle Relativität". I give thereafter an example of this discussion (I tried to "simplify" things the most possible, and even to avoid mistakes which were made from both sides during the debate, and were then recognized and corrected), which could be useful, I believe, in order to understand where problems are in the anti-relativistic field, and the necessity to push criticism rather further…

1 - All started with this mail:

Subject: Re: Back to Wesley

Date: Wed, 8 Sep 1999 19:58:26 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Caro Umberto,

I send you as attachment the text of an article I wrote as a by product of a

discussion with a relativist from the Albert Einstein Institute in Potsdam.

Il tuo, George

2 - This was my answer:

Very dear George,

thank you for your paper. I hope to make useful work for you in pointing out that all the part which refers to the paper by Shaozhi and Xiangqun in "Apeiron" seems to me quite SENSELESS, and that you would perhaps do better throwing it out.

According to these authors, you say that in a Lorentz transformation (LT) [I suppose that you are meaning here a "special" LT of the simple kind:

x' = (x-vt)gamma, y' = y, z' = z, t' = (t-vx/c²)gamma,

or of the even simpler kind:

x' = (x-vt)gamma, t' = (t-vx/c²)gamma,

in the 2-dimensional Minkowski's space-time]:

"the reciprocal x' = 0, t' = 0 implies x = 0 ; t = 0 only if both (x - vt) = 0 and (t-vx/c^2) = 0 , i.e. v = c".

Well, may I ask you to explicitate the meaning of that "i.e.", namely "idem est"?!

I hope that IT DOES NOT go like the following "argument":

a) x - vt = 0 implies v = x/t

b) (t-vx/c^2) = 0 implies t = vx/c^2

c) and then v = x/(vx/c^2) = c^2(x/vx) = c^2/v

d) which implies in its turn v^2 = c^2 ,

e) and then v = c (if v is greater than 0) .

This argument appears as one of those "contradictions" which Wesley would like and believe possible, but which show only that some people does not understand mathematics (just to say the least) at all. The plain truth is that, if x' = 0 and t' = 0, then univocally x = 0 , t = 0, if one adds the condition that the Lorentz transformation is invertible (which is true if, and only if, v is different from c), as simple linear algebra "proves".

This is enough to show that your "idem est" is wrong, since there are cases in which x-vt = 0 and (t-vx/c^2) = 0, but v is different from c.

This shows also where is the obvious mistake in the previous deduction: you cannot write x/t, unless you suppose IN ADVANCE to know that t is different from 0, otherwise you are writing 0/0 (for this kind of mistakes one is thrown out from the first year of an university degree in any scientific faculty - as a matter of fact, dividing by zero gives indeed a lot of contradictions in mathematics!).

Of course, the previous argument could be read in a different way, the only one not criticizable: let us SUPPOSE that the linear system x-vt = 0 and (t-vx/c^2) = 0 DOES HAVE solutions different from (0,0) (and then v in particular must be different from zero), namely auto-solutions, as one says in mathematics. Then, as everybody knows, the determinant of the matrix of the system, which coincides with the expression:

(gamma)^-2 = 1-v^2/c^2, must be equal to 0, namely, v^2/c^2 must be equal to one, and this happens indeed if, and only if, v = c. This could be the only one "truth" that two authors you quote could have correctly "claimed". In other words, they could have proved that the LT we are dealing with is not invertible if, and only if, v = c, thanks for this childish information!

Of course, the previous one is one of the reasons because, in relativity, one takes v less than c (but one could as well take v greater than c, but not v equal to c)!

I would be curious to know whether you have a different "argument" from the previous one in order to show that FALSE implication, I repeat it:

"(x - vt) = 0 and (t-vx/c^2) = 0 idem est v = c "

Fortunately, in the paper you add that this point has gone almost unnoticed, the contrary would have been very painful indeed.

I am sorry to say that this is another example of that very bad anti-relativistic criticism (in this case really unbelievable - COULD YOU PLEASE SEND TO ME A COPY OF THE PAPER YOU QUOTE?!), which discredits ALL our field of research to the eyes of academic colleagues, which then feel in some sense justified in not paying any more attention to ALL our papers and to ALL our arguments. I say it once more, this is the only one reason for my recent activity in pointing out at MISUNDERSTANDINGS (and not because I have, at last, seen the "light" of the "relativistic religion", as Wesley thinks!).

I am very curious what will be your reply, but, please, from now on, why don't you leave apart in your papers this kind of very low-level arguments?!

Best wishes from yours most sincerely

Umberto

P.S. 1 - I REPEAT that if I will persuade myself to be wrong in some part of my criticism to the anti-relativistic criticism I shall give up forever this kind of research...

3 - The previous mail unfortunately required a short addendum from my side.

Carissimo George,

excuse me if I bother you once again, but this Sunday morning I have re-read FOR THE FIRST TIME the mail I have written yesterday to you very hastily [...] I would like to underline explicitely that the determinant:

(gamma)^-2 = 1-v^2/c^2 was of course just the determinant of the matrix of the linear system, and NOT of the matrix of the LT we are studying, which, as everybody knows, is equal to one (gamma^2 times gamma^-2 = 1). Thus, when I sayed:

"(but one could as well take v greater than c, but not v equal to c)!"

I sayed something which was rather STUPID, since it deals only with that secondary unimportant linear system, and not with the LT in its globality, for which it is NECESSARY of course to take definitively v less than c. If v was greater than c, what has been said about the linear system would indeed remain true, but one could have not introduced the LT, with its factor gamma, which necessarily requires v less than c!

At last, would you consent to me two more words regarding ETHICS?

The argument I am actually discussing is very simple, and with no connections at all with other sectors of our personal physical and philosophical beliefs. Thus, it should not be so difficult to acknowledge where is the TRUTH, and to EXPLICITELY AGREE one with the other about this COMMON truth.

I hope that you will acknowledge that I am right, or will try to show to me that I am wrong; we cannot go on maintaining our OPINIONS, even when there are showed OBJECTIVELY WRONG. The beatiful side of mathematics is that there exists in it an objective truth, and the truth, even of this "minor kind", is always beatiful, don't you agree?!

I always hope also, after some months, that you will agree explicitely with me that your argument about aberration was well founded, but ineffective in the aim of showing that aberration cannot be explained by relativity. Remember, you said that the relativistic aberration should depend, according to relativity, from the relative velocity earth-star, and this is correct, but I replied that we do not know this relative velocity, and that in practice aberration is seen just as a difference of TWO aberrations in different times, and this wipes out the part depending from the star, leaving only the earth's revolution velocity taken TWICE!

[I shall dedicate the whole point 3 of this same page to this question of the usual relativistic explanation of astronomical aberration, which as a matter of fact had interesting sviluppi; in the following correspondence the question will be touched every now and then]

Once again, this is an OBJECTIVE TRUTH, and we should never consent that pride or other personal feelings would prevail over truth...

Sempre ciao, e scusa,

il tuo UB

P.S. I have written this mail before reading your reply, and I quite agree with you that this was a minor point in your article! This was just the reason why I suggested to you to drop the whole argument. My criticism was not addressed to YOUR paper, but to the paper of these two chinese physicists!! To give an opinion about the rest of the paper would not be actually so easy to me, since I am still suffering of various health afflictions, and the paper is not so simple for me to be grasped in its essential message...

MAY I ADD THAT WE SHOULD NOT CONSENT THAT OUR PAPERS COULD BE ATTACKED BY ORTHODOX PHYSICISTS, EVEN IN MINOR POINTS?!

4 - The following four mails are: Galeczki's reply quoted in the previous P.S., two new replies to my comments in points, and a further comment about aberration.

4-1 Subject: Re: Back to Wesley

Date: Sat, 11 Sep 1999 22:14:06 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

I added the Xu reference in the last moment , but it is really not of vital necessity to the article. I would, probably, drop it.

Typically, you attacked a minor point in an article whose main message is that THERE IS NO KINEMATICALLY INDUCED "TIME DILATION". If SRT were notself-contradictory, it could have explained Doppler effect, an effectconnected with LIGHT PROPAGATION, a phenomenon EXTERNAL to emitting atoms, or to moving clocks. This, however, has nothing to do with the INTERNALRATE OF A CLOCK, which is outside the competence of a theory concerning STRUCTURELESS, POINT-PARTICLES. This is much more important than the Xu-argument, since by nullifying "time dilation", it kills with one stroke the "twin paradox" and other stupid"physical consequences" of SRT. So, come back, please, to physics and give your opinion about the rest of the article.

Ciao, George

4-2 Subject: Re: Back to physics

Date: Sun, 12 Sep 1999 12:01:01 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

I´m always grateful for technical advices that could improve the presentation of an article. As a matter of fact, the Xu & Xu argument has no direct connection with the rest of my manuscript and is , as you eagerly pointed out, untenable.I have no difficulties in giving to somebody right. I usually send preprints to colleagues and take into consideration their remarks an criticism. I am in friendly relationship with both Paul Wesley and you and it would be a pitty if we would not be able to be direct and open among us and ready to accept criticism. Paul accepted several times criticism from me. Sometimes he makes in letters incorrect mathematical statements, but I found no essential mathematical errors in his books. On the other hand, I do found physical errors in your writings, but this is not the theme of this message.

I have to draw your attention on the fact, that what I wrote about a work being "almost unnoticed", referred to Ishiwata´s communication, rather than to the paper of the Xu´s. What Ishiwata pointed out was that:

"The invariance of the interval is one of the hypotheses in the SRT. Mathematically speaking, it is a perfectly consistent generalization. (from LIGHT to MATTER, G.G.) However, it has not been realized that the hypothesis is physically incompatible with the concept of 4-dimensional continuum, except when the interval vanishes; that is, except when the Lorentz transformation is applied to the light. A thorough examination of this limitation in the applicability of the Lorentz transformation discloses a crucial fact that, should the limitation be overlooked and the Lorentz transformation be applied to others than the light as in SRT, there no longer exists non-0 relative velocity ´v´ that satisfies Einstein´s symmetry requirement, k(v) = k(-v), in 4-dimensional space. Once these facts are fully understood, it cannot be denied that the special relativity is physically inconsistent and various experimental results, which have been considered to prove the correctness of the theory, have nothing to do with. For, there is absolutely no relationship between the relative velocity the experimentalists consider in practical measurements and the relative velocity in the SRT, the existence of which has just been denied."

I gave you the full quotation in order to spare the time and the cost of the ordinary mail. I shall send you per fax. a paper presented on a prestigeous conference on ´relativistic thermodynamics´, in which Ishiwata´s argument played a central rôle. The conference proceedings include the discussions after each presentation and nobody questioned Ishiwata´s argument.

After all this information, I repeat that the main content of my preprint is

the non-existence of "time dilation".

Ciao,

il tuo George

4-3 - Subject: Re: A last short comment...

Date: Sun, 12 Sep 1999 12:13:14 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

I fully agree with you that we should not provide to the orthodoxy reasons and pretextes to attack us and to cut letter exchanges. In this respect, critical and constructive criticism from friends are invaluable. Till now I never supplied such reasons to the orthodoxy in my writings.

George

4-4 - Subject: Re: Remark on stellar aberration

Date: Sun, 12 Sep 1999 13:45:15 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

allow me just one remark conserning your "relativistic explanation" of stellar aberration. In your effort to show that SRT can explain stellar aberration, you (who wrote the very good paper with Mamone Capria) confused - once more - the principle of relative motion (PRM)) with the principle of relativity (PR). Besides, what allows you to use the Galileian velocity addition law, once you rejected them in favor of the Lorentzian kinematics? As I already mentioned, in my contribution to the Proceedings of the 1-st Perugia Conference (1989) I discussed just this point, namely the use of Galileian kinematics WITHIN a system and that of Lorentzian kinematics BETWEEN relatively moving systems. (Pure schizofrenia).

Take care of yourself,

George

5 - Here it is my first answer to this Ishiwata's "argument", including some remarks about aberration.

Very dear George,

would you forgive me if I confess to you that even Ishiwata´s argument seems to me quite ununderstandable (and very likely incorrect)?!

First he says that: "The invariance of the interval is one of the hypotheses in the SRT ... However, it has not been realized that the hypothesis is physically incompatible with the concept of 4-dimensional continuum, except when the interval vanishes; that is, except when the Lorentz transformation is applied to the light".

The space time-interval is an invariant in Minkowski space-time in all case, not only if it is equal to 0. It defines the so called "causality relationships", which have in my opinion a precise understandable meaning. The problem is perhaps to understand well what is this "meaning", which of course cannot be connected to the spatial velocity of some trip from one spatial point to the other. It seems to me that many people have not realized some of the most important features of relativity, for instance that only a 4-velocity has an absolute meaning, and not a 3-velocity!! It is even obvious that that interval has to be connected with the only one physical invariant of the theory, namely the light's speed, what is bad in it? I really do not see how this can be an issue against relativity. At the end, quite on the contrary, I would say that a LT does NEVER "apply to light", since v<c is a strict requirement of the theory.

Then he goes on saying that: "A thorough examination of this limitation in the applicability of the Lorentz transformation discloses a crucial fact that, should the limitation be overlooked and the Lorentz transformation be applied to others than the light as in SRT, there no longer exists non-0 relative velocity ´v´ that satisfies Einstein´s symmetry requirement, k(v) = k(-v), in 4-dimensional space".

I do not believe that this is true, I would like to see a rigorous proof, but this makes come to my mind the only one real mistake which I have found in my paper "Most common misunderstandings..." (nobody has blamed me for this point, but it was a real bad mistake). In the preliminary version of the paper, in the section dedicated to the twins paradox, I have written:

"which shows for instance that, if v is the speed of alpha wrt omega in the point-event e1, then -v is no longer the speed of omega wrt alpha. As a matter of fact, the first is equal to square root of (1-1/g^2L^2), the second to -gL times square root of (1-1/g^2L^2)".

Well, this was an unfortunate computational mistake: quite on the contrary, the two velocities are exactly equal the one to the opposite of the other, which shows that the quoted "Einstein's symmetry requirement" holds not only for any pair of inertial observers, but in some case even for non-inertial ones (to say the truth, I have not gone in enough depth and generality into this question, but I should have recognized at once that I had made a mistake).

By the way, you claim that I make "physical errors": of course this is quite possible, the only unforgivable mistakes are logical and mathematical, which are sciences "a priori". Physics is a posteriori science, and everything can be changed in any moment, due to more experimental information. Let me give you an example. In this moment, I believe that the Earth's "absolute velocity" is zero, or very near to it. This would be a physical mistake if it was 10 Km/sec, or 300 Km/sec, but it would be even worst if this velocity was for example not a constant, or not definable at all (as Einstein proposes). In any case, a "physical" mistake, which in I would consider forgivable. What is not forgivable is to say in some occasion that this velocity is 10 Km/sec, in another one that it is 300 Km/sec, or to make assertions which sometimes would imply the first value, sometimes the second. In other words, the real "sin" is against logic, coherence, attention to the reasons of the opponents, and no more. I always confine my analysis only to the logical conceptual framework of physical theories, and not to their possible experimental truth, which I assume just as an hypothesis, always ready to leave this assumption in favour of another...

I can add to this opinion that everybody can make mistakes, and that everybody can be forgiven for these, that in any case, when one believes to have found something astonishing, something which should cause a "minor revolution", as Post says of his paper about Michelson and Sagnac, something which would prove that all people were wrong just in force of plain logic, and not of more information, well, in this case one should be much more cautious, ask to competent colleagues whether his argument is right or not, etc.. In the contrary case it is not surprising that he would be harshly blamed, if he has made some mistake (and when this happens, this is what I define AUTO-ILLUSION, it would be better not to have them in the field of the serious anti-relativistic criticism).

Coming back to your argument, then Ishiwata says: "Once these facts are fully understood, it cannot be denied that the special relativity is physically inconsistent and various experimental results, which have been considered to prove the correctness of the theory, have nothing to do with. For, there is absolutely no relationship between the relative velocity the experimentalists consider in practical measurements and the relative velocity in the SRT, the existence of which has just been denied".

The first part of this sentence seems to me perhaps true, but hazardous, since it does rely on the previous very likely wrong considerations. The second part seems to me quite good, and I always will thank you very much for having made me understood that what physicists measure in practice does not strictly correspond to the relativistic requirements.

At last, you say: "a paper presented on a prestigeous conference on ´relativistic thermodynamics´, in which Ishiwata´s argument played a central rôle. The conference proceedings include the discussions after each presentation and nobody questioned Ishiwata´s argument".

As I have written to Monti, SILENCE is not a good argument in favour of anything, I would have not said myself anything against this argument during the conference, for many reasons (one needs time to think, one does not like to see other people confused, and so on...), but I am very dubious that the conference was a real high-level academical conference, could you confirm to me that? And could you tell me in what journal Ishiwata's argument has been published? Or which physicists have written positive comments in its favour? I repeat you once again, that I mean nothing, it is not me that you have to convince, but much more eminent colleagues...

A few more comments before conclusion.

You wrote in your last mail about aberration: "In your effort to show that SRT can explain stellar aberration"

...But I am not making any effort!, I am not exposing my personal opinions! I just studied this argument, and I sincerely found correct the relativistic answer, the one which you can easily find written in all textbooks. The hypothesis that all people is wrong at such a simple level is very unbelievable...

Then you add: "you (who wrote the very good paper with Mamone Capria) confused - once more - the principle of relative motion (PRM)) with the principle of relativity (PR)". Well, this could perhaps be true, SR is indeed a bad counter-intuitive theory, and I often make mistakes in its interpretation, WHEN I DO THINGS BY MYSELF. These mistakes are much less likely when I follow well known paths. I hope you will agree that there is a great diference between original research, in which one goes on as a blind-man, and can make lot of errors, and the simple popularization of very well settled arguments. But please, show me where I have made this confusion, I do not believe that this is true (PRM concerns interactions between moving bodies, I have not treated "forces").

At last, you say: "Besides, what allows you to use the Galileian velocity addition law, once you rejected them in favor of the Lorentzian kinematics? As I already mentioned, in my contribution to the Proceedings of the 1-st Perugia Conference (1989) I discussed just this point, namely the use of Galileian kinematics WITHIN a system and that of Lorentzian kinematics BETWEEN relatively moving systems. (Pure schizofrenia)".

My answer is that I have never made use of "Galileian velocity addition law", could you please tell me explicitely where? Quite on the contrary, I have written that: "The starting point for understanding relativistic aberration is to carefully distinguish between speed (scalar velocity) and velocity (vectorial velocity)", and then that: "SR second postulate prescribes the light's speed to be independent from the motion of the source (in any inertial frame), but not the light's velocity, which in fact can depend from the velocity of the source".

Going on, I used Lorentz transformations in order to prove my assertions, and I concluded that: "This is the reason for relativistic aberration, since the light coming from the source will be received by the "moving observer" shifted under an angle theta such that tg(theta) = v/c.squareroot(1-beta^2) which is almost equal to beta, and that is (almost) all".

Where have you seen "Galileian velocity addition law"?! Even in the previous section, dedicated to the wrong Monti's assertions about Roemer observations, I wrote explicitely: "In the previous argument one makes not use at all of any composition of velocities", I repeat it, of ANY composition, neither galileian nor relativistic.

But do you really believe that to defeat relativity will be so easy, that relativity is so stupid or ineffective that it will be enough to win it with a few words, with a short observation?! I hope not, I still remember Marinov talking about the findings of his neighbour's child about Michelson-Morley, which he wrote even in a paper which was completely wrong...

Ciao, sempre un carissimo saluto, e comunque sempre FORZA...

il tuo UB

6 - This long debate took then other directions, including discussions on Sagnac effect, Ehrenfest paradox and so on. Some weeks later, I asked Galeczki to come back to Ishiwata:

"Please remember that I would always be very curious to know your comments to my long mail about Ishiwata's argument, and to have your answers to the many questions I have put there to you. In particular: I am very dubious that the conference you quote was a real high-level academical conference, could you confirm to me that? And could you tell me in what journal Ishiwata's argument has been published? Or which physicists have written positive comments in its favour?".

The following are two mails I received from Galeczki thereafter.

6-1 - Subject: Ishiwata; Ehrenfest and like

Date: Tue, 28 Sep 1999 10:16:43 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "Umberto Bartocci" <bartocci@dipmat.unipg.it>

Caro Umberto,

I cooperated from the beginning with you in the hope that we will be able to organize a concerted action against the SRT. Instead, to quote Millenium Twain, you are building a "tower of Babylon" with your "special relativistic explanations" of different effects and experiments. I begin also to detect the Hilbertian arrogance ("Physics is too difficult to be left to physicists!") of some mathematicians, ignorant in physics, but pretending to be able to solve during a coffee-break physical problems which have been discussed for decades by professionals.

After this preamble, I provide you the information you asked for:

1/ S. Ishiwata, "Inconsistency of Special Relativity", Bulletin of the American Physical Society, ser. 11, 13, 662, 1968, paper GJ2

2/ Ishiwata quoted by: M.Z v. Krzywoblocki "Thermodynamics in View of some Recent Developments in Relativity", in: "A Critical Review of Thermodynamics" (Mono Book Corp.,1970, E.B.Stuart, B.Gal-Or and A.J.Brainard editors, University of Pittsburgh, School of Engineering )pp. 145-160). "The concept of an invariant scalar (or any other quantity) is compatible with the fundamentals of the Einstein special relativity in the four-dimensional space-time when and only when it is equal to zero. This fact was emphasized by Ishiwata."

3/ About the "Ehrenfest paradox":

a) T.E.Phipps, Jr., "Do Metric Standards Contract?", Foundations of Physics, 10, 289-307, 1980

b) V. Cantoni, "Comments on "Do Metric Standards Contract?", Foundations of Physics, 10, 809-810, 1980

c) T.E.Phipps, Jr., "Do Metric Standards Contract? -A Reply to Cantoni", Foundations of Physics, 10, 811-817

d) D.G.Ashworth and R.C.Jennison, "Surveying in rotating systems" J.Phys. A: Math. Gen., 9, 35-43, 1976; "Surveying in rotating systems II: Triangulation radius", idem, p.1257-1260

e) K.McFarlane and N.C.McGill, "Light ray and particle paths on a rotating disc", idem, 11, 2191-2205, 1978

An attempt was made (Weinstein, Nature, vol.232, 548, 1971) to explain the retrograde curving of radial paths by "Thomas precession". This was clearely disproved in Phipps' "rigid" rotor experiment. (Lettere al Nuovo Cimento, vol.9, 467-470, 1974). Phipps published also an INTERNAL REPORT (TN 9752, November 1972) by the NAVAL ORDINANCE LABORATORY: "The Thomas aberration: a relativistic optical noneffect", in which this "SRT effect" was experimentally disproved.

I mentioned here just the pertinent works on the subject. I would not recommand you to read the literature and even less to try "to discover America" at the end of the second millenium....I provided you already several invulnerable physical arguments against SRT. Stop defending this contradiction ridden non-physical theory and let´s concentrate on the central task mentioned at the beginning of this message.

Ciao, il tuo George

6-2 - Subject: Re: Ishiwata; Ehrenfest and like

Date: Wed, 29 Sep 1999 18:08:17 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

1/ Your misunderstanding of the Sagnac-effect is really astonishing! Of course you are allowed to analyze what happens on the rotating platform FROM THE LABORATORY -in first approximation a reasonable inertial frame of reference (IFR). HOWEVER, YOU ARE NOT ALLOWED TO USE THE ROTATING PLATFORM AS A REFERENCE FRAME, SINCE IT IS NOT INERTIAL AND RECIPROCITY DOESN´T HOLD !! The "special" relativistic procedure to replace "locally, at every moment" the non-inertial frame by a "comoving IFR" is a FARCE - rather than physics. It lays also at the bottom of your controversy with Selleri.

In the same wain you could say that "an infinitesimal line element of a curve is linear", or that "every state of an IRREVERSIBLE Carnot-process is a REVERSIBLE, EQUILIBRIUM STATE". In a NON-RECIPROCAL theory, recognizing the existence of a PREFERRED FRAME OF REFERENCE , the situation could be different. Also, you can´not have at the rotating platform "locally" an isotropic velocity of light, but in average -around the whole circumference - c + v , or c - v !

2/ Concerning your "explanation" of the "Ehrenfest paradox", it is neither original, nor correct. I quoted from the rich literature on this subject ONLY THE MOST RELEVANT AND IMPORTANT WORKS. To ignore them would be like trying to figure out whether square root of "-1" has a meaning

and to rediscover complex analysis..... The articles of Ashworth and McFarlane will show you the "correct, special relativistic" calculations of the light and particle paths on the rotating platform. The "effect" predicted in the ´Nature´- article by Weinstein was experimentally disproved by Phipps, as I wrote you at least three times. BOTH "EHRENFEST PARADOX" AND "THOMAS PRECESSION" ARE EXPERIMENTALLY NONEXISTENT, THEREFORE THE THEORY PREDICTING THEM IS WRONG !!

The problem with (some) mathematicians is not that they try to introduce more RIGOR, but when they try - for example- to "redefine an inertial frame of reference".....

All the best,

George

7 - These were my answers.

7-1 - Very dear George,

thank you very much for your mails, that now I shall try to read with great attention (I still owe you an answer about Dr Walton and the argument of the change of units!).

I hope that all our discussions will at last produce a good result, at least in the growing of understanding, and I really do not understand why you are afraid of a "tower of Babylon", or of the "Hilbertian arrogance". As far as the first is concerning, I believe that one MUST respect the point of view of the opponent theories, and I do not see why we wish to win our battle with "imperfect" arguments: for instance, Sagnac does not disprove relativity, why do not acknowledge that, and try to find other arguments against the principle of relativity?! (of course, I may be wrong, together with most of the "orthodox" thinkers, but why then you, Monti, etc. do not show clearly where are the mistakes we are doing? Of course, one should not say that SR does not concern non uniform motions!!). I agree with you that SR is a very bad theory, with devastating consequences in the general culture of our time, but for this very reason our victory should be irrefutable! As far as the second, it is obvious that mathematicians try to introduce some RIGOUR in logical arguments, this is not so bad, if not "excessive".

Moreover, things are not so really difficult that one cannot discuss them without knowing all what has been said in the PAST. For instance, about my arguments concerning Ehrenfest paradox, what is important is to ascertain whether they are correct or not, and not whether they are original or not. Past can help you, but each generation (each single individual!) cannot but rebuild again the whole knowledge, go again along all steps of all the discussions, this is an essential task for making the understanding of science not decrease. I send to you a beautiful quotation in Italian, hoping that you will be able all the same to catch its essence:

Federigo Enriques (Le matematiche nella storia e nella cultura, Ed. Zanichelli, Bologna, 1938):

"Per i valori dello spirito come per quelli materiali dell'economia, sussiste una legge di degradazione: non si può goderne pacificamente il possesso ereditario, se non si rinnovino ricreandoli nel proprio sforzo di intenderli e di superarli".

Sempre un carissimo ciao, e grazie,

il tuo UB

7-2 - Very dear George,

I owe you a lot of thanks for the attention dedicated to me in your last mails (particularly for the precious bibliographical references!), but mostly for the patience you have exhibited during this debate, born after Bologna's meeting...

Anyway, I am very sorry for not having being able to make me understand both from you and from Selleri, who seem to believe that I have made many superficial and wrong comments, when I am sure that this is not true. May I tell you that, quite on the contrary, just today I received a letter from Cavalleri in which he says, literally: "Many congratulations! You are at last mastering Special Relativity"?

What makes me more sad is that I was not able to go on with a plain technical discussion, argument after argument, all interconnected the one to the other, in order to at last arrive to some acceptable "truth". For instance, in one of my last mails, I tried to reply to some of your objections, as below, but I did not receive a SPECIFIC comment.

> Then you add: "you (who wrote the very good paper with Mamone Capria) confused - once more - the principle of relative motion (PRM)) with the principle of relativity (PR)". Well, this could perhaps be true, SR is indeed a bad counter-intuitive theory, and I often make mistakes in its interpretation, when I do things by myself ... But please, show me where I make this confusion, I do not believe that this is true.

> At last, you say: "Besides, what allows you to use the Galileian velocity addition law, once you rejected them in favor of the Lorentzian kinematics? As I already mentioned, in my contribution to the Proceedings of the 1-st Perugia Conference (1989) I discussed just this point, namely the use of Galileian kinematics WITHIN a system and that of Lorentzian kinematics BETWEEN relatively moving systems. (Pure schizofrenia)". My answer is that I have never made use of "Galileian velocity addition law", could you please tell me explicitely where? ... Where have you seen "Galileian velocity addition law" [in my argument]? Even in the previous section, dedicated to the wrong Monti's assertions about Roemer observations, I wrote explicitely: "in the previous argument one makes not use at all of any composition of velocities", I repeat it, of any composition, neither galileian nor relativistic".

Now I should have to comment to your last comments, but as I told you I am indeed rather depressed. Anyway I shall try to say something (but not concerning all your arguments - anyway, thanks for your final reply to my inquiry, I shall try to publish a "virtual book" with all the answers I have received, and since you have been a privileged interlocutor I shall send to you a preliminary copy, for advice).

a - I do not understand Mrs Walton.

b - I believe that Ishiwata's argument is foolish, as I wrote recently to Selleri in the mail written in Italian which I sent even to you, but perhaps it is different from which it seems, I am waiting to have the xerocopies of all his paper.

c- Your argument of "change of units" would require from my side to try to explain "foundations" of SR, which is a difficult task (I do not believe I would be able to write a good book on this argument, as I could do for instance with respect to a book concerning the foundations of geometry). When you put c = 1, you assume to measure space and time with the same system of units, namely you can measure distances with a clock. When you want to fix a length unit measure in your IFR, you fix a given one, say a rod, and then you extend it in all directions just by means of the formula 2L/c. In other words, as you well know, one sends a light's beam in many spatial directions, and say that the distances are equal if the times in which light comes back are equal, as measured by his own clock. If two different observers makes this procedure in two different IFR, does this mean that they are "changing units"?, I would say not, in any case I sincerely cannot believe that SR could be defeated by this kind of objections. And after all, one should first understand how one could compare any kind of units in different frames, one moving with respect to the other, in SR the units could be said to be the same since their procedural definition is the same.

d - You claim that I misunderstand Sagnac in an astonishng way, I sincerely believe that it is true the converse. In SR you have c-v and c+v as average velocities with respectt to a single observer, and c as istantaneous velocities with respect to the clocks of any other observer placed in the border of the platform, this is simple mathematics, how can you and Selleri do no agree with that?! I even do not see any trouble in "understanding" that, since they are measures made with different, and not synchronized, clocks!

You say that I am allowed to analyze the effect "FROM THE LABORATORY (in first approximation etc.)", and I wish to say: first, that you must realize that in this kind of arguments one discusses Gedanken-experiments (as I said to Selleri, Sagnac could not even have made his experiment, but all this discussion could have been made all the same! - namely, the fact if the terrestrial laboratory is more or less inertial DOES NOT MATTER AT ALL); second, that computations from the given IFR are quite enough in SR in order to foresee what should happen to the "imaginary observer" in the platform. Computations of proper time are in this case very easy, how can you not accept that?! If the two events, coming back of the two light's beams, are not simultaneous in the given IFR (as far as that, ANY IFR in SR, we take the one in which the centre of the platform is still just by sake of simplicity, but it is not necessary - in this argument, of course from the point of view of SR, there is no any privileged reference frame at all!), they cannot be simultaneous even for the observer in the platform, that is really all, the remainder is just mathematical computations in order to know the quantitative side of the effect.

e - About my "explanation" of Ehrenfest paradox, I have sent it to you just because it seemed to me, from a previous your communication, that you were possibly interested in it. May I tell you that "neither original, nor correct" are assertions in some sense contradictories? If what I have written is not original, namely it has been written already by some other physicist, and in this case very likely an "orthodox" one, then very likely what I have written IS correct (these things are just exercises in a SR course, cannot be matter of more advanced research), and I would be happy. If it is not correct, it is very likely that nobody has ever written it!

About the ignorance of previous works on this, or other, argument, I can agree with you, and as a matter of fact I was curious to compare my analysis (possibly wrong in points that you did not comment!) with that of other people, but only AFTER having thought by myself. But I hope you will agree that it is just an opinion, and that there exist eminent "schools" which suggest quite the contrary. When I was studying number theory and algebraic geometry in Cambridge, U.K., my professors always recommended us to face any problem WITHOUT knowing anything about the previous attempts to solve it!

I wish to conclude that I find it very funny that I, considered a strong Hilbert's opponent in the field of philosophy of mathematics, now I have to defend him from your critics! Yes, mathematicians could really show to physicists how to DEFINE the concepts they are manipulating, for instance to define space and time and their possible coordinatizations, otherwise one gets in a MESS and it is difficult to get out from it (I believe that most of this discussion with you and with other physicists show the necessity of a common language, and of rigorous definitions...)

Ciao, sempre un carissimo saluto, and let us hope that, our polemics notwithstanding, relativity will be defeated (what is your opinion about Theocharis's news?)

il tuo UB

P.S. With his letter, Cavalleri has sent to me a paper by his own about Ehrenfest paradox (which I did not read until now), published in Il Nuovo Cimento, 1968; are you interested in receiving it from me by ordinary mail?, I would be happy to send it to you...

8 - Then it came another "argument" (8-1) against SR, to which this section is principally devoted; it did concern relativistic dynamics and was in some sense connected to the previous Ishiwata's idea. One will find later in this point 8: some of my answers, but not only; most of Galeczki's replies, even to other people involved in this debate (which I include in order to possibly understand better his point of view); moreover the introduction and the "proof" of what I call "theorem T".

8-1 - Subject: Re: "The shortest argument against STR

Date: Fri, 1 Oct 1999 20:21:21 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

My dear truth searchers,

Prof. Umberto Bartocci has challenged me to find the shortest irrefutable

argument against the "special" relativity. Here it is:

THE INVARIANT : c^2t^2 - x^2 = c^2t´^2 - x´^2 = INV.

IS INCOMPATIBLE WITH ANY EQUATION OF MOTION: x = f(t) ,

(c^2t^2 -f(t)^2 =/= INV.) with the exception of x = ct , therefore INV. = 0 .

There was, anyway, NO INVARIANCE in "special" relativity, ONLY COVARIANCE (Maxwell´s equations, which scramble the electric and magnetic fields, are Lorentz-COVARIANT). The homogenous SCALAR wave equation is INVARIANT under Galilei transformations while the inhomogeneous VECTOR wave equation is COVARIANT.

Please state in concise form your opinion.

Best regards,

George Galeczki

8-2 - Von: Franco Selleri <Franco.Selleri@ba.infn.it>

Datum: Samstag, 2. Oktober 1999 08:37

Betreff: Re: "The shortest argument against STR

An: George Galeczki <nc-galeczge@netcologne.de>

Cc: umberto bartocci <bartocci@dipmat.unipg.it>

Dear George,

Thank you for all the messages you sent me. There are things on which we agree, e.g. Sagnac. However your last search for truth below is wrong. An equation of motion does not have to be invariant, simply because the velocity of an object is different relative to different inertial systems: light is an exception. The invariance is preserved if you introduce in your invariant below the right equation of motion, different for different inertial system, and the invariant is different from zero.

Searching for truth does not mean believing the first argument coming to our mind. We should be more self critical.

Franco

8-3 - Subject: Re: "The shortest argument against STR

Date: Sat, 2 Oct 1999 12:13:14 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: Franco.Selleri@ba.infn.it, bartocci@dipmat.unipg.it

Dear Franco,

do you believe c^2t^2 - f(t)^2 were an invariant under Lorentz

transformations ??

Actually, my argument points out Einstein´s confusion between the Eulerian coordinates (x ; y ; z ; t) and the Lagrangean x(t), y(t), z(t) ones. I didn´t claim that the law of motion x = f(t) has to be invariant; my claim is that c^2t^2 - f(t)^2 is not invariant.

Think it over again.

Best regards,

George

8-4 - Very dear George,

thank you for your mails and for your fax. Unfortunately, all printed pages were unreadable, only a few lines were good, so I cannot take advantage of the information you wished to send to me.

As far as Cavalleri is concerning, may I tell you that I am happy because his compliments mean that I understand SR, which DOES NOT MEAN that I agree with SR, or that I like SR! I hope as you that SR will be soon defeated, and perhaps it will even happen by hands of people who do not understand the theory (do not wish to understand it!), but let me say that I find it very unlikely. Just for giving you a further example, Selleri has just sent to me a paper in which he quotes Wallace, in a point in which Wallace states that the value of the speed of light, in our solar system, "does not coincide with c, as foreseen by General Relativity", as if in GR an invariance principle for the speed of light would hold in a general coordinate system!

Moreover, I have to say, with all respect and friendship, that even your recent argument does not show a good understanding of SR, but first let me ask you: why my sincere research (I really asked for HELP, I did not intend to "challenge" anybody!) for the BEST argument against SR has become a research for the SHORTEST argument?!

Well, having say that, I try to explain why your argument is clearly wrong (and please let me remark that one could say that this is just simple mathematics, in some sense no physics at all). When you take the invariant x^2-c^2t^2, this value, either zero or not, can be seen as a sort of "distance" between the two "events" (0,0) and (x,t), and this is indeed a general invariant of Minkowski space-time M; namely, if you take any other (not necessarily "inertial"!) reference frame system, in which (0,0) becomes (a,b), and (x,t) becomes (c,d), when you compute (in the right way!) that "distance" between (a,b) and (c,d) you get the same value as before. When you consider only Lorentz transformations, namely homogeneous (orientation-preserving) isometries of M, (0,0) remains (0,0), and (x,t) becomes (x',t'), and, as everybody knows, x^2-c^2t^2 is exactly equal to x'^2-c^2t'^2, under the well known substitution:

x' = (x - vt)h , t' = (t - vx/c^2)h

(let me indicate with h the well known appropriated factor).

Now you say: let us take x = f(t), then f(t)^2 - c^2t^2 cannot be an invariant, unless f(t) = ct , case invariant = 0. This is of course NOT CORRECT, since, when you take the event (f(t),t), you get indeed an invariant exactly as before, which means that, if the event (f(t),t) becomes the event (x',t') in the new IFR, then f(t)^2 - c^2t^2 is again exactly equal to x'^2-c^2t'^2, and the fact that this is zero or not does not matter.

Going a bit further with the analysis, in your observation there is indeed some interesting point to remark, but one must put things rather differently. First of all, a general "equation of motion" in SR is NOT of the kind you say: x = f(t), this is just a special case. This is another example of what I mean by being not willing to understand exactly SR. You cannot use in SR space and time as the classical "old" concepts, as Minkowski said very clearly since 1907, in his celebrated address to the Gottingen Mathematical Society! In M there are TWO coordinates, x and t, which, according to relativistic physics, should be considered "of the same nature"; this means that an "equation of motion" must be one of the kind:

x = x(u), t = t(u), with the additional requirements: first, that the 2-velocity (x'(u),t'(u)) has a negative ds^2 [*], namely, that x'(u)^2-c^2t'(u)^2 < 0; second, that this "curve" is future-pointing. Having thus precisely DEFINED what a motion is in SR, please remark that the first of the aforesaid additional conditions implies that t'(u) can never vanish, which means, in force of the well known implicit function theorem, that one can write (first LOCALLY, but then GLOBALLY, since we are in the case of 1 variable) write the inverse of the function t = t(u) as u = u(t) and then express x as x = x(u) = x(u(t)) = some function of t, x = f(t), which was your starting point. Well, one can say that these are just pedantic mathematical sophistications, with no "physical meaning", but this argument becomes interesting just in connection with your statement! The interesting question to ask is (and I think that this is the fundamental point hidden under your argument; I must even say that in my personal experience many people have not understood it): if one takes an equation of motion of the kind x = f(t) - and one is indeed free to consider only this particular case, as I have said before - how can one write the new equation of motion in the new coordinate system, connected to (x,t) by the Lorentz equations: x' = (x - vt)h , t' = (t - vx/c^2)h ? As one can immediately see, one gets: x' = (f(t) - vt)h , t' = (t - vf(t)/c^2)h , which is exactly an equation of motion of the general kind I said before, and we must now express it globally as x' = f(t') . As a matter of fact, when you compute dt'/dt, you get (1 - vf'(t)/c^2)h, which shows that this derivative is always different from zero, AS IT MUST BE, if and only if the product of the two "velocities" v and f'(t) is different from c^2, which is indeed one of the requirements of SR (the absolute values of v and f'(t) cannot exceed c)! Since this product is different from zero, you can write the inverse function of t' = (t - vf(t)/c^2)h, let it be t = g(t') , and you get at last:

x' = [f(g(t')) - vg(t')]h = some function of t' = k(t') .

Well, I hope that you will agree that the value k(t')^2 - c^2t'^2 is EXACTLY EQUAL to the value f(t)^2 - c^2t^2 which you started with, and only this correct interpretation implies that f(t)^2 - c^2t^2 is indeed an INVARIANT, in all cases. In conclusion, your question to Selleri: "do you believe that f(t)^2 - c^2t^2 were an invariant under Lorentz tranformation??" has a definitive POSITIVE answer, when correctly interpreted according to relativistic set-up!!

Let me comment once again that one cannot work on contemporary physics, and even worst on criticism to contemporary physics (which is a much more difficult task!), without including some sophistications like these (but in other modern theories the involved "mathematical language" is much more complicated than the previous one...).

I hope that you will appreciate my sincere effort of "explanation", and please believe that all I am doing is aimed in the direction of our common wish, to see relativity disproved, and the restoration of "classical" space-time categories in science,

best wishes from yours most sincerely

Umberto

* [see the correction made in point 8-9]

8-5 - Subject: Re: "The shortest argument against STR

Date: Thu, 7 Oct 1999 08:03:59 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "Umberto Bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

as I once told you, you are pushing your rôle as "advocatus diavoli" ad absurdum.....Fanatical supporters of SRT are highly inventive and introduce all the time new definitions, postulates, a.s.o. For example, the indifference of ´moving clocks´ to accelerations has to be stated as a third postulate of SRT.

In your reply to my shortest (and GOOD, even if, possibly, not THE BEST) argument against SRT, you claim that: "According to relativistic physics.....an equation of motion has to be one of the kind x = x(u); t = t(u)". May I ask you whether it is a new postulate?

Where have you picked it up? Can you give me an example where x, t, d/dx, d/dt play a ´symmetrical rôle´in an ´equation of motion?

- Let us examine a specific problem, that of the motion of a mass under the action of a CONSTANT FORCE, the same in both relatively moving inertial frames of reference (IFR´s):

d/dt[m°v(1 - v^2/c^2)^-0.5] = F ; F/m° = a° (1)

v(1 - v^2/c^2)^-0.5 = a°t + C* ; for v(0) = 0 ; C* = 0 (2)

v(t) = a°t [1 + a°t/c)^2]^-0.5 (3)

x(t) = c^2/a°.{[1 + (a°t/c)^2]^0.5 - 1} (4)

(x + c^2/a°)^2 - c^2t^2 = (c^2/a°)^2 ("hyperbolic motion") (5)

c^2t^2 - x^2 = 2{[1 + (a°t/c)^2]^0.5 - 1} (6)

- In the "primed system" (S´), moving with velocity V relative to (S),

the acceleration a° is the same. The solution x´(t´) will also be the same,

except that the initial velocity will be v´(0) = V, thus C* = V:

x´(t´) = (c^2/a°).{[1 + (a°t´/c + V/c)^2]^0.5 - 1} (7)

c^2t´^2 - x´ = 2.{[1 + (a°t´/c+ V/c)^2]^0.5 - 1} (8)

where t´= gamma.(t - Vx/c^2) ; gamma = (1 - V^2/c^2)^-0.5 (9) .

Look at (6) and (7) and tell me whether you are till convinced that

c^2t^2 - x^2 were an invariant??

Best regards,

George

8-6 - Subject: The best argument against SRT.

Date: Fri, 8 Oct 1999 10:48:04 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "Thomas E. Phipps, Jr." <tephipps@pdnt.com>

CC: "Umberto Bartocci" <bartocci@dipmat.unipg.it>,

Dear Tom,

in spite of your initial reflection that, perhaps it would be weiser to stay apart from this "cat fight", you are - till now - the only one who got involved in the shortest (and best) argument against SRT. Since our first contact back in 1987 - just after the publication of you "Heretical Verities: Mathematical themes in physical description", you have always been a perceptive, profound and honest discussion partner. At the present "stagnation" of the letter exchange with the "advocatus diaboli", I´m turning back to my original, short argument and shall try to present it in an understandable and convincing form.

The incompatibility between the invariant (ct)^2 - x^2 = INV. and any equation of motion x = f(t) =/= ct really reduces to the confusion between Eulerian (x, y, z, t) and Lagrangean [x(t), y(t), z(t)] coordinates. The clue is provided by the only original contribution of SRT to (pseudo)physics, namely the measurement of the position of a distant moving mass-point by out and back reflected electromagnetic (e.m.) signals, with postulated equal velocities in all directions and both senses: c(out)=c(back)=c.

This stringent prescription, instead of increasing the dimensionality of space by one - by adding a "time coordinate" - replaces length measurement by time measured with one clock at the origin of the coordinate system, thus reducing the dimensionality, so to say, to one. That the invariant INV. has to be zero, i.e. (ct)^2 - x^2 = INV. = 0 is both simple and profound. The position x is measured by assuming that x = ct in (S) and that x´= ct´ in (S´), i.e each reference frame has its "own time". The Newtonian equation of motion x = f(t), on the other hand, relies upon the Newtonian concept of universal, position and velocity independent time and/or absolute distant simultaneity. The difference between the Newtonian and the Poincaré-Einsteinian distant simultanity lays at the bottom of the incompatibility between x = ct and x = f(t). The confusion is compounded by the use of the same "t" to designate two different quantities, both called "time". "t" in x = ct is the moment of distant reflexion, defined as the arithmetic mean between the moment of emission and that of the reception of the e.m. signal, as indicated by a clock at the origin of the coordinate system. It is assumed that c(out) = c(back) and that the distant object is "momentarily at rest". As you see, semantics plays an important rôle in this tragicomedy. Moreover, to call x = ct "equation of motion of light" -in analogy with the equation of motion x = f(t) of a mass-point - means to strain the language and is, unfortunately, misleading. Note also the indiscriminate use ofe one- and two-way light velocities, the former being - by decree- non-measurable. In SRT x = ct has to be always a "RADAR distance".

Writing these lines I now fully realize what a Parmenidean "bloc Universe" means and why in his "Unended Quest" Sir Karl (Popper) called Einstein ´Parmenides´! I also understand the meaning of Einstein´s words "For us, scientists, times is just an illusion...", shortly before he passed away..... End of a long story.

Best regards,

George

P.S. Your plea for common sense, as expressed in "A Bartocci Derby Entry", could persuade - as you put it - a Budhist. Although agreeing with you (since I know you), I think that this introduces - unnecessarily - an element of subjectivity in the argumentation. Besides, "purists" like Mendel Sachs would say that "force" has no place in ("a properly understood") SRT and that ´equations of motion´ could be meaningfully discussed only in GRT.

8-7 - Subject: Summing-up

Date: Sun, 10 Oct 1999 16:04:08 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "Umberto Bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

I have finally found a "strict and rigorous mathemathical formulation" of my best and shortest refutation of SRT.

Let x(µ)^2 = (cT)^2 and dp(µ)/dT = F(µ) be the Minkowski INVARIANT and the COVARIANT form of Newton´s equation of motion, with x(µ), T and F(µ) staying for position 4-vector, proper time and 4-force, respectively. THE SOLUTION xµ = xµ(T) OF THE EQUATION OF MOTION CANNOT SATISFY THE MINKOWSKI INVARIANT SINCE IT CONTAINS THE NON-COVARIANT INITIAL CONDITIONS, TOO.

1/ My dear Umberto, looking back to the last ten days, I would like to express my grattitude for your stimulating, tought provoking and sometimes embarassing comments and statements. It doesn´t matter, actually, whether you are a convinced critic of SRT, or a believer in its logical/mathematical perfection. The end result confirms once more my positive experience with BRAIN STORMING, which I practice for years with my colleague Peter Marquardt.

2/ Newton´s equation of motion, for velocity independent masses and forces depending only on relative distances, is INVARIANT under the 3D Galilei transformations (GT): r´ = r + V.t ; t´ = t . Although invariance fails, unfortunately, for m(v) = g(v).v (g - the gamma-factor) and for more general forces, Newton´s equation of motion in the form dp/dt = F remains valid! The failure of GT means that there is always and everywhere a unique, global, preferred inertial reference frame, which can be approached by successive approximations. Mass increase with velocity is an absolute effect and can be derived - independently on any kinematical coordinate transformation - from: dE = v.dp = c^2.dm .

To Franco Selleri: Dear Franco, there cannot be "theories equivalent to SRT", since SRT is wrong. There is a profound, physical difference between theories with and without a preferred reference frame! Mass doesn´t increases due to uniform motion with respect to a fictive, imaginary IFR.

To Neil Munch: Dear Neil, I hope you will accept that my argument against SRT doesn´t use "shifting assumptions".

To Dennis McCarthy: Dear Dennis, the necessary group properties require the invariant velocity "c" to be unique. Physics with a "medium dependent kinematics" would be a farce! It may well be that the velocity of dislocations in a solid is upper limited by the sound velocity in that solid ; so what?? I wrote over five years ago an article in "Physics Essays" entitled: "From Einstein to Lorentz and then back to Newton", discussing this matter in connection with the ideas of F. Winterberg.

I apologize before all addressants who found themselves, quite unexpectedly, witnesses of a tiresome scientific duel. The formidable, sometimes embarassing, power of INTERNET made possible to reach a positive result in 10 days, which in earlier times could have never happen.

Best wishes to all of you,

George

8-8 - Subject: Both Einsteinian an Lorentzian theories are wrong

Date: Tue, 12 Oct 1999 09:55:23 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

Dear Ron and supporters of the Lorentz transformation (LT),

the advantage of my purely mathematical disproof of SRT is that it is imune to physical arguments about the existence, or absence of "inertial frames of reference", of an "ether", of "neutral observers" of velocity-dependent units of measurement and like.

For years I have hold the opinion that one has to reject SRT for physical, metaphysical and philosophical reasons. I published in 1997 -with Peter Marquardt- a book: "Requiem für die Spezielle Relativität" (the English, extended version, will appear in 2000) which declared -more, or less for tactical reasons- that the algebra of SRT were correct.

ONE HAS TO REALIZE, THAT BY MAINTAINING IN ANY WAY THE LORENTZ TRANSFORMATION ONE OPENS THE DOOR FOR ANOTHER CENTURY OF "RELATIVISTIC PHYSICS", SINCE THE "SPECIAL" (very "special", indeed) RELATIVITY HAS ANYWAY USURPED THE LORENTZIAN MASS-INCREASE- WITH-VELOCITY, ABSOLUTE AND NON-RECIPROCAL "TIME DILATION" and like. THE ARGUMENT THAT THE COMPLETE SOLUTIONS (i.e. including INITIAL CONDITIONS) OF THE COVARIANT EQUATIONS OF MOTION DO NOT SATISFY THE "MINKOVSKI INVARIANT" IS INDEPENDENT ON ANY PHYSICS: IT IS A PURELY MATHEMATICAL ARGUMENT AND THIS IS HIS STRENGTH!!!

The perfide play of "HEADS I WIN, TAILS YOU LOSE" (in Dick Hazelett´s words) HAS TO COME TO AN END!!!

Best wishes,

George

8-9 - Very dear George,

may I emphasize that it is you, and other people like you, which propose similar "arguments" against SR, to have forced me to assume the very unpleasant role of "advocatus diaboli", as you say?! If I do not answer, I am blamed to be impolite (or I am supposed to agree with worthless arguments). If I do answer, then I become unwelcome, because most people seem not to be willing to acknowledge their mistakes (but in the Catholic Church one says that to acknowledge our own sins means to be halfway in the road to heaven!).

Anyway, even in this case I go on in my usual way, really hoping that at last you will be able to sincerely recognize that both your arguments were not so good, and perhaps even to agree with me that, when one finds such simple arguments against SR, it is much more likely that he has misunderstood some point, rather than SR is wrong, or contradictory! When I asked to you, and to other people sharing our same feelings AGAINST SR, to indicate what was in their opinion the BEST (and not the SHORTEST!) anti-relativistic argument, I was sincerely trying to see whether there existed indeed some really good and still unknown weapons to be used against "irrationalistic phyisics", and now I beg you, Wesley, and many others friends: please, let us ascend to an higher level of criticism, otherwise our personal battle (I do not mean, of course, the battle that other people do with other arguments) against "official physics" will indeed be inexorably lost...

By the way, I wish to inform everybody that I am preparing a "virtual book" containing all answers received to my questionary (I have not included comments!), and that I shall send it to all people explicitely confirming to me that they are willing to receive it.

Well, let me now try to answer to your argument, even if I do not wish to go very much into details, with the risk to make some more computational, or worst theoretical, mistakes, which will not show a "contradiction" of SR, but rather another personal mistake of a tired mathematician! For instance, if you want another admission of mistakes from my side, when I have written the "general" equation of a motion in the form x = x(u), t = t(u), I have also introduced the vector (x'(u),t'(u)) calling it the "2-velocity", which is obviously wrong, unless u is the proper time of the particle, namely x'(u)^2 - c^2t'(u)^2 = -1, which is an assumption that I did not introduce explicitely since the beginning (as instead most textbooks do, like for instance O'Neill's one).

Coming back to your point, let me recall that first you claimed that the expression f(t)^2-c^2t^2 was not an invariant (in Minkowski 2-dimensional space-time), except the special case f(t) = ct, under a Lorentz transformation x' = (x-wt)/sqr(1-w^2/c^2) , t' = (t-wx/c^2)/sqr(1-w^2/c^2) (I write w instead of the usual v, since this symbol v will soon be called to assume a different meaning), and I showed to you that this was wrong. If you write the new equation of motion in the new coordinates (x',t'), first you get x' = (f(t)-wt)/sqr(1-w^2/c^2) , t' = (t-wf(t)/c^2)/sqr(1-w^2/c^2), and then you must use the inverse function theorem in the second one of these equations in order to find the final expression of the motion as x' = k(t'), which will be obviously such that:

f(t)^2-c^2t^2 = k(t')^2-c^2t'^2 (for each "corresponding" times t and t').

Then you have added, apparently in answer to my "proof", a new "most physical" consideration: let us suppose for instance that x = f(t) was the solution of a simple relativistic differential equation of motion of the kind

(1) d/dt[mv/sqr(1-v^2/c^2)] = F

(I remark that I have indicated the proper mass simply as m, and not as m°, and that I shall try to avoid apices for derivatives, since apices will have in our context quite a different meaning!), where you say that F is supposed to be a CONSTANT, and we can fix the two initial conditions:

v(0) = 0 , f(0) = 0 (I have put v(t) = dx/dt = df/dt, and changed your solution x(t) by an additive constant in such a way that at t = 0 the moving point is in the origin x = 0, which seems to me better for which follows).

Then, you argue, in the new inertial reference frame "the acceleration F/m is the same", which would mean that the "new" equation of motion is exactly "the same" as before, let us write it as:

(2) d/dt[v'/sqr(1-v'^2/c^2)] = F/m

(where v' is the new velocity of the particle of proper mass m), and then you claim that "the solution will also be the same", with the only one difference that now the two initial conditions become, for the solution of equation (2) (a solution which I shall call x' = f'(t')): f'(0) = 0, v'(0) = df'/dt'(0) = w (here it seems to me that one must arrange the initial conditions as I have previously done).

Well, you conclude now that, if one computes this solution f'(t') of (2), one DOES NOT get the previous function x' = k(t'), namely the Lorentz-transformed of x = f(t), and then you claim also that this is a physical absurd of relativity, but this seems to me wrong. [...] If you do explicit, and not extremely difficult, computations, you will see by yourself that once again everything is alright with relativity from a "logical" point of view!

Let me repeat that I hope that you will appreciate my effort of explanation (at least in typewriting!), and that you will not include me between the "fanatical supporters of SR", simply because I feel the duty of pointing out patent mistakes, which, if what I have previously said is correct (I easily admit that I am not a "specialist" in relativity!), would not been allowed to students in a university course. But let me even add that I am rather tired to be always called to "defend" relativity from the objective point of view of simple logical and mathematical truth; why does anybody else not assume this necessary role from now on?, perhaps he will have more success than me in convincing some people that one cannot hope to defeat relativity with such ingenuous theoretical arguments. Moreover, I am persuaded that we cannot confine ourselves only to criticism (we are already all convinced that relativity is not a "good" physical theory), WE NEED TO DEVELOP ALTERNATIVE THEORIES, AND MAKE EXPERIMENTS (which is very difficult), OR AT LEAST PROPOSE EXPERIMENTS...

Again best wishes to everybody from yours most sincerely (and rather depressed)

Umberto Bartocci

8-10 - Very dear George,

just a simple "logical-mathematical analysis" of the question you are calling attention to, in order to check if I have correctly understood your thought. First of all, let me state the following "Theorem" T:

"T - In the 2-dimensional Minkowski space M, with given Lorentzian coordinates (x,t), consider the following second-order differential equation

(1) d/dt[v/sqr(1-v^2/c^2)] = F(x,v,t)

where v(t) = d/dt[f(t)], and call x = f(t) its unique (local) solution satisfying the two initial condition f(T) = X , v(T) = V (I use these unusual symbols in order to avoid, at least as I can, apices and so on...). Consider then a new Lorentz coordinatization of M, with coordinates (x',t'), connected with the previous ones by the Lorentz transformation

x' = (x-wt)/sqr(1-w^2/c^2) , t' = (t-wx/c^2)/sqr(1-w^2/c^2),

and then introduce the " physical problem" corresponding to (1), which is given by the following equation:

(2) d/dt[v'/sqr(1-v'^2/c^2)] = F'(x',v',t'),

with obvious meaning of the symbols, and where F'(x',v',t') is defined as the "new relative force" corresponding to the "old relative force" F(x,v,t):

F(x,v,t) = K1*sqr(1-v^2/c^2) , F'(x',v',t') = K1'*sqr(1-v'^2/c^2),

(K1,K2) is the 2-force in the coordinates (x,t), (K1',K2') is the "same" 2-force in the coordinates (x',t').

Well, having indicated with (X',T') the new coordinates of the event (X,T), let us now introduce the unique solution x' = f'(t') of (2) satisfying the following two initial conditions:

f'(T') = X' , v'(T') = (V-w)/(1-Vw/c^2).

The theorem asserts that this solution x' = f'(t') can be simply obtained by the previous one f(t) by writing first:

x' = (f(t)-wt)/sqr(1-w^2/c^2) , t' = (t-wf(t)/c^2)/sqr(1-w^2/c^2),

and then using the inverse function theorem in the second one of these equations in order to find its inverse expression t = h(t'), and then at last:

x' = f'(t') = [f(h(t'))-w*h(t')]/sqr(1-w^2/c^2)."

Having so clearly and rigorously stated the theorem T, first we have two logical possibilities: either T is true or T is false.

If T is false, then I would agree with you that you are right with your argument, and that you have pointed out a good objection against the "physical interpretation" of SR.

If T is true, there are two subordinate possibilities. The first one, that your argument is simply wrong, and then it must be withdrawn. The second one is that, the previous truth notwithstanding, your argument has still some validity, but then in this case you should state it as clearly as I have tried to do before (without using "terms" whose meaning could be misunderstood...).

I am really very curious to know what your answer will be, and let me explicitely add some comments on the following points on which I STRONGLY AGREE with you:

1) even if this Internet work is very fatiguing, it is true what you say: that "the formidable, sometimes embarassing, power of INTERNET made possible to reach a positive result in 10 days, which in earlier times could have never happen";

2) that I believe, as you do, that indeed there are no experimental indications that the previous "relativistic treatment" of motion's laws has some correspondence in Nature, and that in this direction (even if practically difficult) one should look for that "experimentum crucis" against relativity to which Phipps correctly refers.

3) that I agree with your comments about the physical value of Lorentz transformations (I like very much your remark: "there cannot be ‘theories equivalent to SRT', since SRT is wrong"; of course, in truth there could exist such theories, but they would be wrong as relativity is!!). In particular, I believe that you are right even when you say that: "one has to realize, that by maintaining in any way the lorentz transformation one opens the door for another century of relativistic physics"! There is no reason but "ideological" (the "democracy", and "political correctness", even in science!!) for introducing in physics the mathematical group symmetry between moving reference systems (even of some special kind), and I would even say that there is no reason for considering the problem of finding the "right" coordinate transformation equations x' = x'(x,t),

t' = t'(x,t) as a preliminary, and a fundamental, one. Even if one can carry on the abstract speculations of relativity concerning the natural structure of the "empty" space-time, I think that the fundamental physical question is rather to understand when a natural physical real reference frame, as you say, can be considered as a "good" one, in which some "simple physical laws" hold; then, all the others reference frames moving with respect to one of these, and "near" to it (since I am now talking about reality, one reference frame should be always considered as a local one, both in space that in time!), would very likely be NO INTERESTING, at least at a first approach. To find those equations, and the corresponding transformation laws between physical quantities, will be a secondary problem...

Always friendly wishes from yours truly

Umberto Bartocci

8-11 - Subject: Re: Summing-up

Date: Thu, 14 Oct 1999 08:58:39 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

1/ such an important "theorem" you now propose would have found - since the XIX-th century - his place in the huge literature on differential equations (and would be known under " Bartocci - theorem"!). Had such a theorem existed, Einstein´s brain child would have died as a baby, in hospital!

2/ I have to point out that the forces F and F´in (1) and (2) are different "creatures":

a) F in (S) is derived from the "proper force" F° = m°a° in (S°) by applying (against the basic rules) a "Lorentz transformation with a time variable velocity v(t), F° being independent on both position and velocity in (S°) , while F´ in (S´) is derived via the Lorentz transformation with the uniform velocity V between (S´) and (S).

b) The velocity-dependent masses m(v) = m°/sqr(1 - v^2/c^2) and

m(v´) = m°/sqr(1 - v^2/c^2) are introduced - against the basic rules, too - with the obviously non-uniform velocities v(t) and v(t´) WITHIN the reference frames (S) and (S´), respectively. The only escape from this inconsistency would be the absence of any force in both (S) and (S´), thus reducing the physical systems under investigation in (S), respectively (S´) to structureless mass-points and to apply the Lorentz transformation with uniform relative velocity V to the total linear momentum

P = m(v1).v1 + m(v2).v2 = M.V in (S), where M = m(v1) + m(v2) , thus obtaining P´= m(v´1).v´1 + m(v´2).v´2 = M´.V

with v´1 = (v1 + V)/(1 + v1.V/c^2) ; v´2 = (v2 + V)/(1 + v2.V/c^2).

This derivation, consistent with the "basic rules" of SRT has been done by David Bohm and restricts the application of m = g(v).m° to COLLISION - TYPE PROBLEMS, with particles in "ASYMPTOTI-CALLY FREE (i.e. FAR FROM THE "INTERACTION REGION")STATES ! This disqualifies at once the the entire PARTICLE DYNAMICS based on the FORCE CONCEPT , quite independently on the "Bartocci theorem".

c) In your notation:

x´= [f(t)-wt]/sqr(1-w^2/c^2) ; t´[t-wf(t)/c^2]g(w)

it would seem that x´ and t´ were independent on v and v´ . This is however

false, since v and v´ enter the solutions x(t) and x´(t´) via the variable masses m°.g(v) and m°.g(v´), respectively. On top of it, v and v´ had to add up "hyperbolically" to w = (v + v´)/(1 + v.v´/c^2) .

I think that you - as a logical scientist - will realize now the falsity of T.

It is good that you agree in the other three points with me.

Best wishes,

George

8-12 - Very dear George,

just a few words to say that I have received your message, and that I am happy to see that your opinion is at least very clear. I would be very happy too if theorem T was wrong, it would indeed be a good point against SR. I shall try to work about it, but before I shall ask to some competent people...

Ciao, il tuo UB

8-13 - Subject: Re: Summing-up

Date: Thu, 14 Oct 1999 09:52:51 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

when under "competent people" you mean Establishment physicists, it would be a serious error "to ask" them. You can "tell them" after you realized the falsity of the theorem.

In the attachment I send you a manuscript draft containing a specific example of the complete solution of an equation of motion, including initial conditions.

Best regards,

George

8-14 - Subject: Final version

Date: Fri, 15 Oct 1999 20:26:39 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

Dear truth searchers,

in the attachment you will find the final version of the article proving the incompatibility between "Minkovski space" and particle dynamics. SRT is therefore wrong on purely mathematical grounds, too!

I wish to all of you a pleasent weekend !

George

Attachment: MINKOVSKI.doc

8-15 - Dear Umberto and Franco,

leaving problems connected with the methodology of physics (very interesting in themselves) apart, the clean demonstration of the incompatibility of STR with particle dynamics is now DEFINITIVE.

Best wishes to all of you,

George

8-16 - Very dear George,

you have blamed me a few days ago because I would exhibit sometimes the famous Hilbert's arrogance ("physics is too much important to be left to physicists"). Well, I do not like Hilbert's attitude towards the foundations if mathematics, but let me say that in this case he was quite right, and that his consideration was not at all arrogant! Having studied for a while your problem I realize, with great modesty, that to study physics is much more difficult than to study mathematics, and that all physicists should be good mathematicians too (the inverse is not necessary).

I am writing once again to you in response to your mail expressing surprise and scepticism in order to the validity of the assertion that I called "theorem T". Well, let me say that one can PROVE, and without much trouble, that statement in its most generality, without confining oneself to special cases (constant forces and so on). This "theorem" is not worth to be called "Bartocci theorem", as you say, not even a "theorem"! It is quite an "exercise" in elementary calculus applied to relativistic dynamics, and that is all - it is nothing compared to nowadays high level original research.

Let me start coming back to the very beginning of our discussion, and summing up my argument, namely that when you take the relativistic equation of motion in the "relative form" (let us continue to discuss the 2-dimensional space-time case; moreover, I shall assume from now on that both the proper mass and the light's speed are equal to the unity):

(1) d/dt(v/sqr(1-v^2)) = F(x,v,t) = relative force

in some IFR (x,t), and you take one of its solutions x = f(t) (v = dx/dt) satisfying

(2) f(t°) = x° , v(t°) = v° ,

then the corresponding "Lorentz-transformed" function x' = f'(t'), in a new IFR (x',t'), satisfies the corresponding "right" equation

(1') d/dt(v'/sqr(1-v'^2)) = F'(x',v',t') = relative force in the new IFR

AND the initial conditions

(2') f'(t'°) = x'° , v'(t'°) = v'° ,

where: (x'°,t'°) is the event corresponding to (x°,t°) , and v'° is the relativistic composition of velocities: v'° = (v°-w)/(1-wv°) .

As a friend I shall try to typewrite for you (almost) all details, but you can check the truth of this "theorem" by yourself, at least in some special case. Needless to say, I do not enter into physical questions, like for instance if the "relativistic dynamics laws" are experimentally meaningful (founded) or not (I have my own doubts even about a personal full understanding of the "phyisical situation"). I just study a well definite abstract theory, according to its own internal rules. For this reason, I cannot say whether some other of your arguments is correct or not, but I assert explicitely that you appear to me surely wrong when you assert that "the initial conditions are non-covariant", and that your argument is a "purely mathematical disproof of SRT", I repeat that I intend to confute ONLY these particular issues. In my friendly opinion, if you wish to accept it, you should stop to look for such an impossible thing (against SRT are quite enough "philosophical and physical reasons", I agree with what you have written to Ron Hatch), and I begin to understand why many "official" physicists do not wish to pay any attention to claims concerning such "findings"...

Coming back to our main argument, and trying to do everything since the very beginning, start from the standard covariant differential motion equation in SR, which asserts the identity between the 2-acceleration (A1,A2) and the 2-force (K1,K2). This means that the derivative of the

2-velocity (V1,V2) = (dx/dT,dt/dT) WITH RESPECT TO THE PROPER TIME T is equal to (K1,K2), and since dT=sqr(1-v^2)*dt, where v = dx/dt is the "ordinary" velocity in the "first" IFR (x,t) we are introducing, we get at last (putting h = 1/sqr(1-v^2), and k its inverse, k = h^-1 = sqr(1-v^2)):

(3) d/dT(V1,V2) = d/dT(hv,h) = (K1,K2),

which is the same as

d/dt(hv,h) = (k*K1,k*K2).

This splits in the following two differential equations

d(hv)/dt = k*K1 = F (relative force)

d(h)/dt = k*K2 = kv*K1 = Fv

(since the 2-acceleration is orthogonal to the 2-velocity, because the ds^2 of this last one is constant - equal to -1 - we have K1*V1 - K2*V2 = 0, whence K2 = v*K1, as I have written).

It is very simple to check that the previous TWO equations reduce to just ONE, and then we can simply write, as you did since the beginning:

(4) d(hv)/dt = F .

Well, since the expression (3) we started with is covariant, in a new IFR (x',t') connected with the first by the LT (suppose w =/= 0)

x' = (x-wt)/sqr(1-w^2) = z*(x-wt) , t' = (t-wx)/sqr(1-w^2) = z*(t-wx)

(I shall write from now on z in place of 1/sqr(1-w^2)),

we obviously have, in the new coordinates,

(3') d/dT(V1',V2') = d/dT(h'v',h') = (K1',K2')

which, as before, reduces to

(4') d(h'v')/dt' = F'

(here F' must be the "correct" new relative force, equal to k'*K1').

If you take a solution x = f(t) of (2), which satisfies the two initial conditions x° = f(t°) , v° = v(t°), it will be then obvious "a priori" that

x' = f'(t') will be a solution of (2'), where f'(t') is the function computed as follows. Write first:

x' = z*(f(t)-wt) , t' = z*(t-w*f(t)),

and then use the inverse function theorem in the second one of these equations in order to find its inverse expression t = g(t'), and then at last you get the required solution as:

(5) x' = f'(t') = z*[f(g(t'))-w*g(t')].

Since the identity t' = z*[g(t')-wf(g(t'))] will hold by definition for each value of t', from this identity you can deduce:

f(g(t')) = w^-1*[g(t')-z^-1*t'] ,

which gives for the solution (5) also the following useful expression:

(6) x' = f'(t') = w^-1*[z^-1*g(t')-t'] .

Your "purely mathematical disproof of SRT" pointed out the possibility that this solution of (4') would NOT satisfy the "right" initial conditions, which would be, in your words, "not covariant". Well, it is a very simple exercise to show that, quite on the contrary, if you put

x'° = z*(x°-wt°) , t'° = z*(t°-wx°),

one has indeed:

f'(t'°) = x'° ,

and

v'(t'°) = df'/dt'(t'=t'°) = (v°-w)/(1-wv°) ,

as "theorem T" asserted, and this is the conclusion.

Let me remark that the last identity is perhaps a bit more difficult to obtain. You must start from the identity we used before,

t' = z*[g(t')-w*f(g(t'))]

and make the derivative (with respect to t') of both sides:

1 = z*[dg/dt'-w*(df/dt)*(dg/dt')] .

From this identity you can get the following espression for dg/dt':

dg/dt' = 1/(z*[1-w*(df/dt)]) = 1/(z*(1-wv)) ,

from which, using (6), one can at last deduce, for each value of t', as it MUST be (and not only for t'°!):

v' = df'/dt' = w^-1*[z^-1*dg/dt'-1] = w^-1*[((1-w^2)/(1-wv))-1] =

= w^-1*[(1-w^2-1+vw)/(1-wv)] = w^-1*[w*(v-w)/(1-vw)] =

= (v-w)/(1-vw) !

I hope that you will be persuaded by this objective simple computations, and as usual I send to you my best greetings,

Umberto

P.S. There is some other points in your mails which I should have to comment, for instance assertion (c) of your Summing-up ("In your notation..."), but I am sure that you will realize by yourself that it is not so important to go on discussing this rather improductive argument. Anyway, let me say at least that v cannot "enter" as an "independent variable" in the solution x(t), which I have called f(t), since v is simply defined as dx/dt! For instance in your particular case of a constant relative force, F(x,t) = H = constant, a simple solution of equation (4), as you have correctly stated in one of your last communications, can indeed be obtained by integration of v = dx/dt = Ht/sqr(1+H^2*t^2), in which of course only t, and H, do appear. Gone so far, let me even try to make a last attempt to convince you that I am right in this special case, which is rather complicated (very far from your assertion that, since the relative motion of the two IFR is uniform, then forces and acceleration remain equal!) but not impossible to handle.

The equation we are starting with, in the first IFR, is

d(hv)/dt = H ,

one of its solutions is, as we said, an integral of Ht/sqr(1+H^2*t^2). Let us choose, supposing H =/= 0 (and putting for instance H = 1)

x = f(t) = sqr(1+t^2) .

Now find the right Lorentz-transformed function x' = f'(t') of the previous one, which can be obtained by first finding the inverse of

t' = z*[t-w*f(t)] = z*[t-w*sqr(1+t^2)],

which is

t = g(t') = zt'+wz*sqr(1+t'^2),

and then operating the corresponding substitution in

x' = z*[f(t)-wt] = z*[sqr(1+t^2)-wt].

You will get a rather complicated expression x' = f'(t'), which you can check is a solution of the corresponding second order differential equation

d(h'v')/dt' = F'(x',v',t') ,

whose right-hand side term is determined by:

F' = k'*K1' = (1-v'^2)*z*sqr(1+g(t')^2)-(1-v'^2)*wz*g(t')

[as a matter of fact, we have now (K1,K2) = (K1,v*K1) = (h,hv), since we have supposed F = k*K1 = H = 1 and then K1 = k^-1 = h, from which identities you can get at last:

K1' = z*K1-wz*K2 = zh-wzhv = z*sqr(1+t^2)-wzt =

= z*sqr(1+g(t')^2)-wz*g(t') ] .

(As usual, I have thought and I have written very fastly, and I hope not to have made too many mistakes. But, I repeat, if I have made some "essential" mistake, I shall give up all this research!)

8-17 - Very dear George,

excuse me if I bother you again (and all other "recipients", most of them I do not know!), but I did not resist in doing explicitely all computations which I left just outlined in the P.S. of my last mail - the computations concernig your "exercise" - and I found many new things which I HAVE to communicate to you. These things were in part unexpected for me, and I do apologize for that, but let me even state once again that I AM NOT particularly COMPETENT, an expert, in relativity. I was always a teacher in Geometry and History of Mathematics, I was never a teacher in Relativity, and the difference between an expert, and an "amateur" like me, is exactly this: the expert knows IN ADVANCE, in force of his experience, what the right answers will be, while the amateur has to find them by himself, sometimes even with great effort...

In the particular case we were discussing, the Lorentz-covariance of the solutions of a motion's equation in Minkowski space, INCLUDING the initial conditions, all my general analysis was quite correct, but I could have solved your exercise much better. In other words, I have not made mistakes, fortunately!, but I was INCOMPLETE. As a matter of fact, I realized very late that you were right at least in one point (but, as a matter of fact, I never asserted the contrary, I had to see all the explicit proof before!), namely that if you take the equation

(1) d/dt(v/sqr(1-v^2)) = F(x,v,t) = relative force

(let me recall that we are considering the 2-dimensional Minkowski space, with Lorentz coordinates (x,t), and that we assume both the proper mass and the light's speed to be equal to one)

in the case F = constant, say for instance F = 1, then this relative force IS INDEED EXACTLY THE SAME in the new Lorentz coordinates (x',t'):

x' = (x-wt)/sqr(1-w^2) = z*(x-wt) , t' = (t-wx)/sqr(1-w^2) = z*(t-wx).

In other words, F' = F !

The proof is very easy, without doing all complicated calculations I started to do in my mail, which were in any case correct:

F' = k'*K1' = (1-v'^2)*z*sqr(1+g(t')^2)-(1-v'^2)*wz*g(t')

K1' = z*K1-wz*K2 = zh-wzhv = z*sqr(1+t^2)-wzt =

= z*sqr(1+g(t')^2)-wz*g(t')

(the meaning of the symbols was specified in that mail).

As a matter of fact, it would have been enought to observe that when you consider the ds^2 of the 2-force (K1,K2) you get

(K1)^2 - (K2)^2 = (K1)^2 - (vK1)^2 = (1-v^2)*(K1)^2

which is exactly F^2 !!

I am very sorry not to have previously "seen" this obvious identity, which semplifies all things. Your "problem"

(2) d/dt(v/sqr(1-v^2)) = 1

becomes indeed, in the new IFR,

(2') d/dt'(v'/sqr(1-v'^2)) = 1 ,

and when you take the particular solution of (2) given by

x(t) = sqr(1+t^2) ,

which satisfies the initial conditions

x(0) = 1 , v(0) = 0 ,

you can easily get the "corresponding" solution of (2') exactly as I have said in my mail. First write

sqr(1-w^2)*t' = t-w*x(t) = t-w*sqr(1+t^2),

then write the "inverse"

sqr(1-w^2)*t = t'+w*sqr(1+t'^2),

and then do the corresponding substitution in

x'(t') = [x(t)-wt]/sqr(1-w^2) = [sqr(1+t^2)-wt]/sqr(1-w^2) .

You get indeed a rather complicated expression, but it is very easy to check that it satisfies the RIGHT initial conditions, which are the following. Since the "initial" event (1,0) becomes in the new coordinates

(1/sqr(1-w^2),-w/sqr(1-w^2)) ,

what you have to check is simply that:

x'(-w/sqr(1-w^2)) = 1/sqr(1-w^2))

v'(-w/sqr(1-w^2)) = -w (which is the "relativistic" composition of 0 and -w),

which are both TRUE.

You could be not persuaded that the previous x'(t') is really a solution of (2'), and computations are indeed rather laborious, but I can suggest to you even a SHORTER WAY. Start from (2), and try to prove directly that

v' = (v-w)/(1-vw) (which is the relativistic composition of velocities!)

is indeed a solution of (2'), where v = dx/dt = t/sqr(1+t^2) .

You have of course to use the identity

sqr(1-w^2)*t' = t-w*sqr(1+t^2),

which gives

sqr(1-w^2)*dt' = dt-wv*dt = (1-wv)*dt,

and then you easily get

d/dt'(v'/sqr(1-v'^2)) =

= [sqr(1-w^2)/(1-wv)]*d/dt[((v-w)*(1-vw)^-1)/sqr(1-v'^2)] =

= [sqr(1-w^2)/(1-wv)]*d/dt[(v-w)/sqr(1-v^2)*sqr(1-w^2)) =

= [sqr(1-w^2)/(1-wv)]*[d/dt(v/sqr(1-v^2)*sqr(1-w^2)) +

- (w/sqr(1-w^2))*d/dt(1/sqr(1-v^2)] =

= (1-wv)^-1*[1-wv] = 1 !!

(don't forget that the "second" relativistic differential equation of motion gives to you

d/dt[1/sqr(1-v^2)] = K2*sqr(1-v^2) = K1*v*sqr(1-v^2) = F*v = v).

These computations seem to me rather instructive, aren't they?!

I repeat that I am very sorry not to have "seen" all these identities before, and I hope that you will agree with after this new and better attempt to prove that your asserted "incompatibility between Minkovski space and particle dynamics" is wrong.

Ciao, Umberto

9 - Complete mathematical computations notwithstanding, all my efforts of clarification were quite useless. Here they are some examples of mails and replies.

9-1 - Subject: Re: Final form

Date: Mon, 18 Oct 1999 19:58:16 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

as I already explained, for a = a° = constant the x-component of the force is not changed when you go to (S) and (S´), so the equation for v´ is - as far as this point is concerned - OK. What is not OK is the application of the Lorentz transformation to the transition from (S°) to (S), since (S°) IS NEVER INERTIAL! This fact alone should have sufficed to disqualify SRT! Taking into account the y- and z-components of the force in (S) and (S´) is no rescue to SRT, while the t-component doesn´t enter the 3D equation of motion. The only equations of motion which are Lorentz-COVARIANT are the Maxwell FIELD equations with partial derivatives, in vacuum. However, the electric and magnetic field intensities do not have to fulfil a "Minkowski invariant" and a "hyperbolic composition law". No solution of a differential equation/equation of motion, with the exception of x = ct, will satisfy a "Minkowski invariant"; "they are different worlds" like Tom Phipps put it. The specific example is, indeed, very useful.

I would suggest you to try to publish YOUR T-THEOREM in Phys. Rev. Letters. Were it correct, it sould have to be included in all physics courses, textbooks and monographies.

Ciao,

George

9-2 - Very dear George,

as I already told you, theorem T seems to me quite an obvious thing, and it is no worth of great attention (the things which I have published are much more deep and difficult). Of course, I am getting old, and perhaps I am wrong in claiming its truth (I would not say that I have made mistakes in computations, I have checked things twice; but I am not sure to have understood all subtleties of relativistic dynamics, and to have computed in the correct way the relative force in coordinates (x',t')), but now it is up to you to convince the scientific world of your claims, I have no such interesting claims to do [...] If you do not believe to me, I suggest that you contact some competent (and honest!) scientist (I suppose that there exist someone, somewhere in the world! - one is surely Mamone, mat@unipg.it), in order to avoid possible further mistakes...

Ciao, always friendly wishes, Umberto

9-3 - Subject: Final polishing

Date: Tue, 19 Oct 1999 11:00:50 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

Dear truth searchers,

this is the fate of manuscripts: to be rewritten over and over again! (Microsoft Words makes it much easier than in old times...). I think the new comments between Eqs. (23) and (27) will add more force to the main argument. Enjoy it!

Best wishes to all of you,

George

Attachment: MINKOWSKI 2.doc

9-4 - Subject: Re: Final polishing - Please delete if not interested in this discussion!

Date: Wed, 20 Oct 1999 13:59:54 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

I had much more calculational errors in my specific example, than I imagined. All together they do not change the content of the main argument.

Best regards,

George

Attachment: MINKOWSKI 3.doc

9-5 - Subject: Refinements

Date: Fri, 22 Oct 1999 13:32:23 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

Dear friends,

the improved text in the attachment is confidential for the time being. Please read carefully the ABSTRACT and the IMPORTANT NOTE and tell me if you agree that:

1/ The derivation of the LT requires x´(0) = x(0) = 0 for t´= t = 0.

2/ The two IFR´s (S) and (S´) always recede from each other.

3/ "Radar distances" with non-simultaneous ends are different from ordinary distances with simultaneous ends.

4/ A massive particle moves from x[t(2)] to x[t(1)] with the variable velocity v , while in the "finite interval form" of the "Minkowski scalar invariant" the interval x[t(2)] - x[t(1)] is ALWAYS c.[t(2) - t(1)] .

In retrospect I regreat the many errors on "the tortuous way of truth" (to paraphrase Stefan...) and I am really grateful to you for the sharp criticism which served as cathalist. I think my case is a typical example of the working style of many physicist, who start with a physical idea and later try to provide the mathematical support -as expressed by Franco, too.

Best wishes to all of you,

George

Attachment: MINKOWSKI 4.doc

9-6 - Subject: The missing link

Date: Tue, 26 Oct 1999 19:31:49 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

Dear truth searchers,

It seems that, after a sleepless night, I found the necessary completion of the purely mathematical argument against SRT.

It boils down to the following remark: Even if one subtracts the initial position from the space coordinates, i.e.

(ct)^2 - [x - x(0)]^2 - [y - y(0)]^2 - [z - z(0)]^2 = (ct)^2 - [r(t) - r(0)]^2

this expression will till contain the initial velocity W -which is reference frame dependent, with the consequence that the "Minkowski invariant" is not invariant at all! My initial statement: "Particle dynamics is incompatible with the ´Minkowski invariant´" retains, therefore, its validity. Moreover, the argument is quite general, making the specific example superfluous. This point is very important, since the number of examples with explicit solutions in closed analytical form is hardly greater than one. Umberto´s "T-Theorem" is therefore invalid, since the function f(t) contains the arbitrary parameter W . I hope that Umberto will suceed to overcome his ´professional proud´ and feel - like myself - relieved.

Best wishes to all of you,

George

9-7 - Very dear George,

I have no professional proud at all (I am neither a great mathematician, nor a good mathematician!), I just feel that mathematics is the better form of thought we have at our disposal for an objective "understanding" of reality (and for communicating between us). For instance, sometimes I do not understand what you say, but just because I have not enough physical culture, and imagination: a mathematician is usually much more precise in the definition of the concepts, and the terms, he is using, even when they could be considered "obvious".

As far as "theorem T" is concerning, I repeat to you that it is quite a true theorem, and that there is no possibility of any divergence of opinion. Either this theorem is true, or it is false, and the decision can be achieved exclusively by means of objective calculus. If you want, you can read my proof, and point out where is a possible mistake (of course, this is not enough in order to say that the theorem is false, perhaps it is just my proof which is wrong, or incomplete; one should find a particular case in which the assertion of the theorem is not true - you seemed at first inclined to believe that already the case of a constant relative force would give such a counterexample, I hope that you have changed idea after the explicit computations I sent to you in my last mail, in the case F = 1).

I state once again "theorem T" thereafter, in order to avoid further misunderstandings, and to make things "trascendentally clear". Moreover, I repeat my invitation to submit your sensational claims, that: "SRT is wrong as a mathematical theory", and that: "Particle dynamics is incompatible with the Minkowski invariant", to some good physical journal, and wait to see what the answers of the referees will be. I am not playing a "double game", I would really be very happy if you are right, but unfortunately I sincerely believe that you are not (I feel much more sensible Larson's opinion, that: "If there was a theoretical flaw it would have been found long ago", and that: "If we try to come up with theoretical arguments to show how special relativity is wrong, we will lose"...).

"Theorem T - In the 2-dimensional Minkowski space M, with given Lorentzian coordinates (x,t), consider the following second-order differential equation:

(1) d/dt[v/sqr(1-v^2/c^2)] = F(x,v,t) = relative force

where v(t) = d/dt[x(t)], and call x = f(t) its unique (local) solution satisfying the two initial conditions:

(2) f(t°) = x° , v(t°) = v°.

Consider then a new Lorentz coordinate mapping of M, with coordinates (x',t'), connected with the previous ones by some Lorentz transformation

x' = (x-wt)/sqr(1-w^2/c^2) , t' = (t-wx/c^2)/sqr(1-w^2/c^2),

and introduce the function x' = f'(t') [the Lorentz-transformed of x = f(t)] in the following way. Write first the "motion equations" in the new coordinate system:

x' = (f(t)-wt)/sqr(1-w^2/c^2) , t' = (t-wf(t)/c^2)/sqr(1-w^2/c^2),

and use the inverse function theorem in the second one of these equations in order to find its inverse expression t = h(t'). Then you get at last:

(3) x' = f'(t') = [f(h(t'))-w*h(t')]/sqr(1-w^2/c^2).

Well, having so done, if you introduce the "corresponding physical problem" of (1), which is given by the following equation:

(1') d/dt[v'/sqr(1-v'^2/c^2)] = F'(x',v',t'),

[with obvious meaning of the symbols - here F'(x',v',t') is defined as the "new" expression of the relative force, corresponding to the "old" expression:

F(x,v,t) = K1*sqr(1-v^2/c^2) , F'(x',v',t') = K1'*sqr(1-v'^2/c^2);

(K1,K2) is the 2-force in the coordinates (x,t), (K1',K2') is the "same"

2-force in the coordinates (x',t')],

and you call (x°',t°') the new coordinates of the event (x°,t°):

x°' = (x°-wt°)/sqr(1-w^2/c^2) , t°' = (t°-wx°/c^2)/sqr(1-w^2/c^2),

then the previous function (3) defines the unique solution of (1') which satisfies the following two initial conditions, "corresponding" to those expressed by (2):

(2') f'(t°') = x°' , v'(t°') = (v°-w)/(1-wv°/c^2)."

P.S. This is exactly the theorem I stated at the beginning of our discussion, and that I proved some day later. I can just add that one can prove that the connection between F(x,v,t) and F'(x',v',t') is much more easy than I believed at the beginning, remember that I overlooked that the square of the relative force is exactly the ds^2 of the 2-force:

F^2 = (K1)^2-(K2)^2 = (K1)^2 - (v^2)*(K1)^2 = (1-v^2)*(K1)^2...

P.P.S. In this solution x = f(t) there are NOT independent variables, or parameters, as you say (you call it W, which I suppose is my previous v°), but you can also introduce a "theorem T" for the "general integral" of (1) and (1'), introducing the Lorentz-correspondent not of the event (x°,t°), but of the "phase" (x°,v°,t°), which is (x°',v°',t°'), where v°' = (v°-w)/(1-wv°)...

Always friendly wishes from yours most sincerely

Umberto Bartocci

(I am sending this mail to some people to which I owe an answer since a lot of time, apologizing for my great delay, but I was really very busy in trying to settle the following question once for all...)

9-8 - Subject: Re: The missing link

Date: Wed, 27 Oct 1999 20:53:36 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

in your eagerness to defend the mathematical consistency of SRT you totally neglected one of the main actors: THE "MINKOWSKI INVARIANT". My claim was that the solution of the dynamical equation of motion violates the "Minkowski invariant". The way of replacing r(t) with r(t) - r(0) - suggested by Tom Phipps - doesn´t save the situation, since r(t) contains the initial velocity V - an arbitrary parameter, indeed. You will find in SRT books no discussion on the role of initial conditions. In the GRT the "principle of Mach" was hoped to replace the boundary conditions in a closed univesrse with no boundaries. Your T-theorem is irrelevant to my argument if it leaves the "Minkowski invariant" out of discussion.

Best regards,

George

9-9 - Very dear George,

excuse me, but I really do not understand you. First you said that theorem T was wrong (your words: "If such an important "theorem" you now propose was true, it would have found - since the XIX-th century - his place in the huge literature on differential equations (and would be known under " Bartocci - theorem"!). Had such a theorem existed, Einstein´s brain child would have died as a baby, in hospital!", "T-Theorem is therefore invalid"), now you say that it is "irrelevant". I could produce a detailed analysis of your mathematical "arguments" against SR, showing that they were always wrong, and that I always pointed out to you where was the mistake. Not to quote some of the previous ones (like the "terrible" things of Shaozhi and Xiangqun, or Ishiwata, or Theimer, etc.), recently first you said that an equation of motion x = x(t) is not Lorentz covariant (with the exception of x = ct !), which is not true. Then you added that you meant a solution of a second order relativistic differential equation of motion:

d/dt[v/sqr(1-v^2/c^2)] = F(x,v,t), which would have been (in your words) not Lorentz covariant, if one had taken into account also the initial conditions, and once again I showed to you, by proving theorem T, that this too was not true. What can I do more?, of course the quite obvious theorem T can be irrelevant if you change once again your argument, it is not an "universal theorem" against ALL pseudo-arguments against SR, but in your place I would stop in trying to find such "arguments", WHICH DO NOT EXIST (cannot possibly exist!).

Sempre un caro ciao,

il tuo Umberto

P.S. I know very well the difference between invariance and covariance, it is in some of the previous "arguments" that things are expressed in a quite "obscure" way...

9-10 - Subject: Re: The missing link

Date: Thu, 28 Oct 1999 14:25:18 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "umberto bartocci" <bartocci@dipmat.unipg.it>

Dear Umberto,

the Law of Parkinson "Everything which could go wrong, will go wrong" applies to you with a slight modification: "Everything which could be misunderstood, will be misunderstood."...

- The point is not that ´a force cannot be made covariant with the LT. It was shown long time ago that any law can be formulated in general covariant form, but this fact is lacking physical content. My point was, and is, I repeat, that THE SOLUTIONS OF THE DYNAMICAL EQUATIONS OF MOTION ARE INCOMPATIBLE WITH THE "MINKOWSKI INVARIANT". Now, mathematically, the LT is derived as THE TRANSFORMATION WHICH LEAVES THE EXPRESSION (ct)^2-x^2 INVARIANT. Therefore, accurately speaking, your T-Theorem is OK, so long you don´t mention the "Minkowski Invariant". The consequence of the equations of motion, however, is that THE INVARIANT IS INCOMPATIBLE WITH PARTICLE DYNAMICS and the LT -rather than the theorem as such- is, indeed, IRRELEVANT. I admit that my formulation "if your theorem were correct, it would be a very important one" was not accurate, since your starting point is the LT, rather than (ct)^2 - x^2. This expression is indeed invariant, provided t and x (y, z) are INDEPENDENT coordinates. But the essence of particle dynamics is that they are DEPENDENT.

- I confess you that I , too, was unable to understand Ishiwata´s argument in its initial form. Later I found the statement : "The concept of invariant scalar is compatible with the fundamentals of the Einstein special relativity in the four-dimensional space-time when and only when it is equal to zero. This fact was emphasized by Ishiwata." by M. Z. v. Krzywoblocki in "A Critical Review of Thermodynamics"(1970, Mono Books Corp., Baltimore, Univ. of Pittsburg series, Stuart, Brainard and Gal-Or, Editors, ISBN 72-122028, p. 146) which impressed me. After realizing the incompatibility of the MI with particle dynamics, the statement of Ishiwata regains its weight. Only x = ct satisfies MI.

- Theimer´s statement "The relative velocity between (S) and (S´) cannot be reciprocal, if the units of measurement in the two IFR´s are different. Gertrude Walton and Tom Phipps already agreed with this and I assume that Franco accepts this argument, too. For Mendel Sachs " c is just an universal conversion factor", the difference between one- and two-way light velocity is not worth mentioning, although he also says that in the observer frame on has to use different measurement units than in the "proper" frame.

- The solution of the equation of motion is, of course, not invariant -although the equation self is- since the initial conditions are not invariant. The same point was emphasized by Fock, Rosen and others with respect to the boundary conditions in the general theory of relativity. Their non-covariance perturbed the "aesthetical beauty of the theory", therefore the great attractiveness of Mach´principle.

Best wishes,

George

9-11 - Subject: Re: Some thoughts

Date: Sat, 30 Oct 1999 12:09:45 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

Dear Friends,

after rethinking the whole issue, I conclude that my statement about the incompatibility between particle dynamics and "Minkowski Invariant" is correct. The root of misunderstanding between Umberto Bartocci and myself was, that he takes the validity of Lorentz transformation (LT) for granted: solves the equation of motion in (S), applies the LT to obtain x´(t´) and concludes that both x(t) and x´(t´) satisfy the MI. This reasoning is, however, tautological, since the LT and MI imply each other. What has to be done -and I did it- is to solve the equation of motion in (S), then solve the equation of motion in (S´), calculate

(ct)^2 - x^2 and (ct´)^2 - x´^2 by taking initial conditions into account, see that the "MI" is not invariant and drop it TOGETHER with the LT. If the "Minkowski invariant" is no invariant, then the Lorentz transformation itself is no more valid. The MI is compatible with Maxwell´s field equations, but these are incomplete without a force equation and an equation of motion for a discrete charge in the field. Maxwell´s equations, which are generally covariant, do not provide t-dependent x, y, z coordinates which violate the MI. Mendel Sachs is once more right: SRT is compatible only with FIELD THEORY; it is INCOMPATIBLE WITH PARTICLE DYNAMICS and with equations of motion.

Best wishes to all of you,

George

9-12 - Subject: Re: Minkowski, Sherwin, EPR & more tests

Date: Mon, 1 Nov 1999 14:41:02 +0100

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: Delbert7@aol.com, bartocci@dipmat.unipg.it

Dear Del,

I need more time to think over the rest of your message, but I have to react to the first part, which distorts my fundamental argument into a "purely conceptual" one. ("Conceptual" being used by you in a condescending sense, like in: "poor guy, he is busy with conceptual ideas, rather than with reality....."). The big fuss about "special" relativity was, I remind you, due exactly to the supposed "conceptual revolution" in our ideas about space and time. Moreover, Umberto is defending "special" relativity as a "purely mathematical theory", without connection to real world.

Your criticism is at rather low level, namely to claim that I were not familiar with the distinction between invariance in different, relatively moving IFR´s and a quantity conserved within one IFR. When I stressed the non-invariance of initial conditions, I was talking all the time about the initial velocities in DIFFERENT IFR´s. And I was talking all the time about x(t) and x´(t´), in (S) and (S´), respectively. You are unwilling to confront my central argument:

THE "MINKOWSKI INVARIANT" (MI) IS INCOMPATIBLE WITH ANY EQUATION OF MOTION DIFFERENT FROM x = ct. MI presupposes 4 (four) INDEPENDENT COORDINATES, WHILE PARTICLE DYNAMICS HAS AS GOAL FINDING THE DEPENDENCE OF x, y, z ON THE TIME PARAMETER.

The "great relativistic paradigm change" was the implantation of a"new paradigm" in the theory developed by Lorentz, Larmor, Poincaré, a new "conceptual" foundation, i.e., just what you disconsider, Del. The mathematics was all the time the same, while the Lorentzian ABSOLUTE effects were usurpated by the Einsteinians. Starting with Ives,Jánossy, Builder,Bohm, Bell, Vigier -to name only the best known- the "school of Neo-Lorentzianism developed under our eyes, justifying -of course- Einsteinian STR. The tactic used all along was : "Heads I win, Tails, you lose" (Richard Hazelett). I tried to summarize the situation in 1995 ("From Lorentz to Einstein and then back to Newton", Physics Essays, Vol. 8, Nr. 4, 591-594).

George

9-13 - Subject: Re: Four Space Events, Bell, Shadows, Sherwin, Parallelism and Experiments

Date: Sun, 14 Nov 1999 17:02:01 +0100

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: Delbert7@aol.com, bartocci@dipmat.unipg.it

Dear Del,

as a matter of fact, you got my attention since the Santa Fe meeting of NPA. My interest was aroused by John Chappell´s mentioning you as a "veteran particle accelerator designer, who declared that he didn´t use SRT in this job". My personal experience revealed you as a very fine, gentleman-type person; unfortunately (from my point of view) you turned out to be a Neo-Lorentzian, thus obviously a (conscious, or unconscious) apologet of "special" relativity. I say ´obviously´ since the Lorentzian ("active") and the Einsteinian ("passive") interpretations of the Lorentz transformation (LT) are seen as just two views of one and the same "genial" kinematic theory. The sad thing is that after WWI the theory of Larmor- Lorentz-Poincaré started to be ascribed to Einstein and since then all the non-reciprocal, absolute velocity effects of the aether theory have been usurped by SR. As pointed out by Dick Hazelett 20 years ago, this tactic of "Heads I win, tails you lose" contributed decisively to the survival of a contradiction ridden theory for almost a century. Since the LT is common to both aether and SR theory, their acceptance could (!) contribute to the perpetuation of the present confused situation in physics.

The almost generally accepted view is that the LT is the transformation

leaving Minkowski´s MI = (ct)^2 -(x^2 + y^2 + z^2) invariant. Now, the only theory in which the time and space coordinates -in the form of time and space partial derivatives- occur in a symmetric way (on equal footing, so to say) is Maxwell´s theory of electromagnetic field. The very meaning of vector FIELDS is that of vector-functions taking some continuously distributed values at the points (x, y, z, t) of a spacetime continuum. Some specific value of - let me say - the electric field at the "point x, y, z" at the "moment t" is "an event" in the four dimensional Minkowski space. This picture was introduced by Leonhard Euler in fluid dynamics. The independent variables x, y, z, t -which you, Del, call X, Y, Z, T, do not move with the electromagnetic field; their totality constitute the very background space! In the Lagrangean description of a fluid -introduced by the same Euler- on the other hand, the three spatial variables belong, so to say, to the moving particle of fluid and are TIME DEPENDENT. You correctly wrote that that x, y, z, t in MI refer to ONE, delta-localized EVENT, which in a relatively moving inertial frame of reference would be described by x´, y´, z´, t´. You also correctly state that the dynamics of a discrete particle is described by three CONTINUOUS, time-dependent variables, since MOTION IS CONTINUOUS. You actually accept openly that MI and particle dynamics refere to different things! The contradiction in the attempt to apply SRT to particle dynamics is, therefore, obvious! And, of course, it´s not me who has "conceptual difficulties"; "special" (very special, indeed) relativity is, as I already pointed out, a tragic confusion between Eulerian and Lagrangean descriptions! (Don´t forget that it was me who suggested Umberto Bartocci to use Greek xi, eta and zeta in particle dynamics.....).

Very sincerely yours,

George

10 - The "fire" seemed then extinguished, or perhaps a further opinion exchange on this matter was considered useless (and this would have been indeed true). But it was not so, since just a few days ago I received the following public message:

Subject: Minkowski´s invariant

Date: Wed, 10 May 2000 10:18:12 +0200

From: "George Galeczki" <nc-galeczge@netcologne.de>

To: "Gertrud Walton" <Sapere.Aude@btinternet.com>

Dear Mrs. Walton,

I shall quote in toto an abstract by Susumu Ishiwata published in the Bulletin of the American Physical Society (Ser.11, Vol. 13, p. 662, 1968), to which I referred several times in the past:

"GJ2. Inconsistency of Special relativity. Susumu Ishiwata, Fairleigh Dickinson University.

The invariance of interval is one of the hypotheses in the special relativity. Mathematically speaking, it is a perfectly consistent generalization. However, it has not been realized that the hypothesis is physically incompatible with the concept of 4-dimensional continuum, except when the interval vanishes; that is, except when the Lorentz transformation is applied to light. A thorough examination of this limitation in the applicability of the lorentz transformation discloses a crucial fact that, should the limitation be overlooked and the Lorentz transformation be applied to others than the light as in the special relativity, there no longer exists non-zero relative velocity v that satisfies Einstein´s symmetry requirement, k(v) = k(-v) , in 4-dimensional space. Once these facts are fully understood, it cannot be denied that the special relativity is physically inconsistent and various experimental results, which have been considered to prove the correctness of the theory, have nothing to do with it. For, there is absolutely no relationship between the relative velocity the experimentalists consider in practical measurements and the relative velocity in the special relativity, the existence of which has just been denied."

I have tried - with partial success - to persuade my discussants on the correctness of Ishiwata´s statement. I ask you for the last time to help me explain the failure of the "generalized (non-zero) Minkowski invariant" for individuals like Bartocci, Selleri, Phipps - among others.

Best regards,

George Galeczki