Your interpretation is utterly incoherent and unsupported by anything in the text. Einstein merely says a point moving in k must have a value of x' which is constant. In other words, the value of x' for a point moving with k must be constant. Mere obvious kinematics, following from the definition of velocity. Nothing is ever said about x' being ``attached'' to k. Nor is it true that it is measured using moving rods. Rather, x is measured using rods at rest with K, so is vt, and therefore the difference between the two is also a distance measured by rods at rest with respect to K. Your screaming ``Nonsense'' merely shows lack of understanding. The idea that such a distance ``cannot be measured'' is again a figment of your imagination: there is no difficulty whatever in measuring the distance between two moving points.

This discussion has, of course, no meaning: your only point is to denigrate relativity, for purposes best known to you. I have stated the truth of the matter, by following the actual original text (which you were afraid to quote) as closely as possible. For any interested readers who might have been confused by your nonsense, this should be enough. You I do not think worth an additional second of my time.

The spacetime fabric is pushing Mercury to the Sun, it is not moving around the Sun via the Suns gravity, instead the Sun has warped the spacetime fabric and this fabric is PUSHING Mercury into this orbit.

Dear Joel:

Newtons theory was based on Keplar's discovery of elliptical trajectory of planets around the sun. Later Clemence discovered that after completing one orbital period, Mercury did not come back to the exact perihelion of the elliptical orbit but went little further by a small amount. This perihelic advance is 5599.74" / century which Newton's theory could not account for. Einstein's general relativity employed Reimannian geometry to replace elliptical trajectory by geodesic trajectory which solved the problem.

Hello Vikram and thank you for your kind and informative reply,

would you happen to know the formula for Einstein's general relativity employing Reimannian geometry?  I am interested to see how this geometry effected the gravity and how this formula incorporated spacetime again effecting the gravity.

Thanks:)

Joel

Hi and thank you Thierry for your kind and informative reply,

Best,

Joel

"Was it simply via the spacetime fabric adjusting this value?"

There is no "spacetime fabric" with any tangible physical, mechanical/material basis. So, it cannot affect the motion of the planet Mercury, or anything else! There is no role of matter and motion in the concept of "spacetime" to start with!

I posted the following comment in another thread, it is relevant here also:

There is no reality behind “Spacetime” 4D aether. It is an artificial and abstract geometrical construction based on some axioms without any “proof”. Like all geometrical rules; any deduction that are consistent with the premise is true; but has nothing to do with the REAL world. This is the very reason we see paradoxes starting from Zeno to Einstein. There is imperfectness in Newtonian physics, but there are no paradoxes, because it deals with the material/real world.

Space and time are abstractions. There is no “time” as such starting in an infinite past (Newton) or starting in the recent past with a “Big Bang” as in the 4D “spaetime” construct. Nor any space endowed with physical/material attributes. Both space and time are only relational with respect to matter in motion. As Hegel said “It’s essence (matter in motion, A.M.) is to be the immediate unity of space and time; it is time really persisting through space, of space which is made truly distinct through time. …Only in motion have space and time reality”. So, the whole virtual edifice built on the theories of relativity in modern physics has nothing to do with the real world; and everything derived from theses theories are also just mathematics based fantasies.

Please see: “The Philosophy of Space-Time: Whence Cometh Matter and Motion?”:

https://www.amazon.com/Philosophy-Space-Time-Whence-Cometh-Matter/dp/984041884X

From this point of view, Thierry's  materialist approach based on the effect of galactic motion on the perihelion advance of Mercury's motion seems appropriate and credible. 

Hello and thank you Abdul for your kind and informative email.

Best,

Joel

It may in spite of everything be important to refute total nonsense which some people keep spreading around, in spite of having repeatedly been told how things are: we are thus dealing with disinformation, not mere error.

Were the Galaxy's rotation to generate *any* kind of force, due to the fact that the Galactic center is much more distant from the Sun than any of the planets, we would expect, for any force whatever, that it should have the same effect on all planets. But Mercury has an (easily measured) 43 arcseconds/century, whereas neither Venus, Earth nor Mars have a measurable precession. So the cause of Mercury's precession is not due to Galactic rotation.

The other issue is that interaction with other planets also produces precession. The number quoted by Vikram is the total observed precession. A large amount of it can then be accounted for by systematic analysis of all Newtonian effects, that is, all effects involving other planets attracting Mercury, as well as the motion of the Sun caused by other planets' pull. After all this was taken into account, a 43 arcseconds/century remained, which was fully explained by Einstein's general theory of relativity. Further, since Einstein's theory reduces to the Newtonian theory for weak fields, the interaction effects already subtracted from the observed effects are identical in Newton's approach and in Einstein's.

The Einstein field equations simply give a (quite small) correction to Newton's equations of motion in the limit of weak gravitational fields and low velocities. The conceptual bases for the two are quite different, but the final observed results are nearly indistinguishable, the case of Mercury's perihelion advance being one of the few in which classical astronomy could actually observe a discrepancy. With the far higher precision of modern measurements, it has been found necessary to use general relativity quite in general for the high-accuracy computation of planetary motion. Again, good agreement was found.

Hello and thank you Leyvraz for your update.

Best,

Joel

Dear colleague

Newton pointed out that bodies have a tendency, inertia, to continue in whatever direction they are already going, with whatever velocity they have at the moment. That means uniform, rectilineal motion: steady velocity, same direction. Newton actually knew this was what would be later called a geodesic, since « a straight line is the shortest distance between two points ».

Newton then went on to say that to overcome inertia, to overcome this tendency, requires a force: force is what makes a body depart from the geodesic it is (even momentarily) headed on (its direction and speed).

It was then Einstein (and partly Mach before him) who said this does not get to the essence of the question. For Einstein, any coordinate system had to be equally allowable, and in fact, space-time is curved (as already explained by other posters). A body or particle under the influence of gravity actually does travel in a geodesic....i.e., it does what a free particle does. I.e., it does what a particle not under the influence of any force does. So gravity is not a force.

Newton did not realise that space-time could be curved and that then the geodesics would not appear to our sight to be straight lines when projected into space alone. That ellipse you see in pictures of planetary orbits? It is not really there of course since the planet only reaches different points of the ellipse at different times...that ellipse is not what the planet really traverses in space-time, it is the projection of the path of the planet onto a slice of space, it is really only the shadow of the true path of the planet, and seems much more curved than the true path really is.

 The curvature of space-time in the neighbourhood of the earth is really very small ! The path of the earth in space-time would even appear to be nearly straight to an imaginary Euclidean observer who, in a flat five-dimensional space larger than ours, was looking down on us in our slightly curved four dimensional space-time embedded in their world. It's ctct, remember, so the curving around the ellipse gets distributed over an entire light-year, and appears to be nearly straight...and is straight when one takes into account the slight curvature of space-time.)

Regards 

Hello and thank you Saeed for your kind and informative reply,

Best,

Joel

Dear Joel:

Try following link for relativity solution to Perihelic precession of Mercury.

https://www.math.washington.edu/~morrow/papers/Genrel.pdf

Theories of relativity on which modern cosmology is built has persisted too long; propped up by contrived “proofs” of confirmation bias that started with Arthur Eddington and continues till to day. It is time that we call a “spade” a spade. There are many arbitrary pre-suppositions and assumptions both in the construct of the theory and in the experiments to “prove” these theories. In fact most experiments to “prove” these theories are heavily laden with the very theory they are going to prove, such that it becomes mere tautology. A most recent example is the much-trumpeted Higgs boson – (I spoke about it as “futurehuman” in the Guardian in the very Blog of Prof. Jon Butterworth, a key scientist in the (LHC) ATLAS as the Head of the British Team and the Chair of Physics and Astronomy at UCL).

Redshift is another popular pabulum; where both SR and GR are used to figure out its value and then to “prove” Big Bang origin and expansion of the universe with the help of redshift – where both conclusion and the method are based on GR itself! Supernovae Type 1a is used as a “Standard Candle” to “prove” accelerated universe, but it was shown in many reports that there are widely varying mechanism for SN Type 1A and the “Standard Candle” is anything but standard. In spite of the use of manipulated redshift and non-standard candles; the most recent report finds no evidence for accelerated expansion of the universe: http://www.nature.com/articles/srep35596. This article published in mother of all journals – Nature;  along with many others that go against the theories are routinely ignored; as is the recent report on the modified  Sygnac experiment: https://www.researchgate.net/publication/2177113_Modified_Sagnac_experiment_for_measuring_travel-time_difference_between_counter-propagating_light_beams_in_a_uniformly_moving_fiber

Einstein arbitrarily assumed a finite universe; equivalence principle, 4D “spacetime” aether (field) with tangible physical/material attributes; exclusion of matter and motion etc.; to formulate his theories - pre-suppositions that have no basis at all! Matter in motion is the basis of all positive knowledge and in an infinite universe these theories have no meaning. There is absolutely no reason why the universe should be finite. In fact according to dialectical perspective the universe must be infinite; please see the article: http://www.ptep-online.com/index_files/2014/PP-39-04.PDF . .

Both space and time are abstractions and only relational with respect to matter in motion. As Hegel said “It’s essence (matter in motion, A.M.) is to be the immediate unity of space and time; it is time really persisting through space, of space which is made truly distinct through time. …Only in motion have space and time reality”. https://www.amazon.com/Philosophy-Space-Time-Whence-Cometh-Matter/dp/984041884X. So, the whole virtual edifice built on the theories of relativity in modern physics has nothing to do with the real world; and everything derived from theses theories are also just mathematics based fantasies. 

Most of all Einstein himself expressed doubt about the “continuous field” (spacetime, Higgs etc.) being the basis of objective reality – a pillar on which most of Einsteinian physics is based. He wrote to his friend Besso towards the end of his life, “I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics” A. Pais, Subtle is the Lord …” The Science and the Life of Albert Einstein”, Oxford University Press, (1982) 467,

Article Modified Sagnac experiment for measuring travel-time differe...

Hello and thank you Vikram for the attachment, I scanned it and can see how the spacetime precisely changed the classical solution.

Best,

Joel

Hello and thank you Abdul for your information,

Best,

Joel

Hello and thank you Thierry for your input:)

Best,

Joel

Dear Thierry,

The practice of contriving to “prove“ the almighty theories of modern physics are so wide-spread that physics is losing all credibility. The "discovery of the century", namely the “gravitational waves”, for example did not impress many people and even the Nobel Committee ignored it last year!

There cannot be only one way to look at the universe – a way that was fabricated based on idealized mathematics; devoid of reality and continue to do so contrary to new developments! The real proof of theories can only be realized through social/historical human practice, technology, industry etc. as was the case with Newtonian physics. Except for Quantum Electrodynamics, none of the theories of "New Physics" satisfy this criteria. These are simply made Kosher, through their "power"  of predictability and the contrived and manipulated "proof" of such predictions to retroactively "prove" the theories.  

Before we go much deeper, the all-mighty GR has no credible explanation for the simple fact that spiral galaxies or even the solar system and Saturn’s rings (as you point out above) are flat and particularly the galaxies continue to be so for billions of years after the so called “Big Bang” origin of the universe. The “curving of spacetime” should work in all direction and must eventually give rise spheroid shape to all celestial objects! Even an additional patch to the theory i.e., “dark matter” is of no help!

I have taken on the “COBE” experiment that found “the face of God” and His Big Bang creation; in my article, “Ambartsumian, Arp and the Breeding Galaxies”; and provided an exact opposite view of the universe, the origin and the structures of the galaxies etc.: http://redshift.vif.com/JournalFiles/V12NO2PDF/V12N2MAL.pdf

But official science can continue to ignore ALL contrary experimental evidence and views; but for how long?

Hello Abdul and thank you for your reply,

Best,

Joel

Hello Joel,

This may be the answer to another question, but it is not classical:

There are two articles of Correia and Laskar ( from 2004, on Researchgate); one in Icarus and one in Nature. They rely on intrinsic properties for Mercury, not a tide, but a core-mantle friction. Probably the Newtonian gravity is the major force, but then there are other interaction resulting in a nonlinear problem and chaos which gives that the coupling to sidereal motion is ruling, and in this case it is given by 3/2, which is also a common ratio in acoustics. This dates back to Pythagoras. That is my belief, hitherto, and based on that I wrote all the articles on so-called noncircular orbits. they are an inplane description of an arc of a Keplerian using instead a harmonic to describe the deviance from a circle.

 Hello Lena and thank you for your update,

my understanding that Einstein's Spacetime fabric for gravity and Mercury's orbital correction for this via his Relativity was very precise.

Thank you. I hope some day I will reach this level of understanding. There is also much fractal interactions. According to Einstein, curvature is important. I agree, and I think 3/2 is related to pi/2 in some sense and that the difference (0.07) may be driving processes from a sublevel. It could be that the sidereal rotation involves an elongation in the orbital direction which contributes to the orbital motion. Or occasionally the orbital motion is less curved than other times.

Thierry: You have not proved, to my knowledge, that the Galactic center can do anything to Mercury.

But far more to the point, you show Olympian disdain (or more likely lack of understanding) for my main contention: whatever the Galactic center may do to the Solar system must, in essence, be *uniform*. With a great deal of good will, I might accept the fact that the influence you postulate *could* have the requisite size. It most certainly, at Galactic distance, *could not* distinguish between Mercury and Mars. But Mercury has a very observable perihelion precession, whereas Mars has none. It is hard to imagine how anyone could suggest such astrology, now that the Dark Ages are a few centuries behind us.

``As for the other planets, my paper shows, indeed, that the perihelion advance strongly reduces with distance from the Sun.''

How and why are they reduced? If you attribute it to the Sun's motion through the Galaxy, this motion has a radius of curvature R much larger than all interplanetary distances. Hence all planets should, in leading order of 1/R, be equally affected. Yet Venus Earth and Mars have negligible precessions. In your theory, this cannot be explained.

I used a description ( noncircular orbits) r =r0+resin(fwt), where r0 is the radius of a circle and re is a generalised eccentricity w is the orbital angular velocity and t is time and f is a factor that is e.g. 2 for a tide and can take other values. I find this a useful model in many cases, since differential equation often are not valid but for short times or spatial domains. From this, you may construct an invariant ( I called it Tti, it is the Pythagorean identity, with notations of spatial parts from this). The spatial part and time will then be small increments compared with the one in the larger circle.

You can't expect an extended space fabric to conquer other local forces, I thought everyone knew that now.  In electronics and modern chaos they determine time in other fashions than Einstein did.

I hope to find time reading Thierry de Mees paper, with higher order modeling. But I think that after I understood them there will still be some questions, e.g. that magnetism may be stronger at the shadow side on the planet where lower temperature or other phenomena compared with Roche forces. Other higher order models e.g. Hyperion accounts for the non-spherical shape of the orbiting object, but in that model they maintain the elliptical orbit, and the sidereal motion is nonconstant. It is ofcourse interesting how that would affect what we call gravity? Could one fabric that 

For Mercury, photos show that it is anisotropic spherical.

I don't see why you should disregard the results of Correia and Laskar (2204), giving that the (3/2) spin is due to a core-mantle friction,

unless you doubt it, or you wish to consider the isolated problem of a perihelium shift.

I assume the latter. If you  extend to densities, you may compare the calculation I did for the inner moon of Mars, it is called .. Close force ... I do not think it is so useful to describe Mercury, but it describe another large stone that is not kepler- Newtonian, also mentioned by Thierry de Mees.

Ahead of time, I accidently wrote the year (2204), it should be 2004 for the reference to Correia and Laskar. It is also a version in Icarus.

'Mercury's capture into ... ' is found by google

I  find this clockwork model useful, attached.  In view of that, nowadays, many defines time from a clock frequency, and that is the case in all computer applications for example.  

@ Thierry: In your last post, you seem to imply that absolute rectilinear motion can cause observable effects, such as the Mercury perihelion precession. This may work in your model, whatever that is, but it will not work with any correct form of the Heaviside/Jefimenko equations, since these are manifestly Lorentz invariant, as indeed pointed out by Jefimenko.

@ Thierry: ``Where is your reference claiming that Heaviside/Jefimenko equations would be "manifestly Lorentz invariant"? ''

I guess you are right on one point: I should have said: manifestly *covariant*. But that is quite enough to prove that no effect such as Mercury precesion can arise from uniform motion.

As to my authority for that claim, I cite Jefimenko, Chapter 9, Intro: ``We shall present illustrative examples demonstrating the use and power of relativistic transformations applied to gravitational and cogravitational equations. Then we shall briefly discuss the ``covariant formulation'' of gravitational and cogravitational equations''. In Section 9-2, he goes into the details of the covariant formalism for his theory of gravity.

So much for Jefimenko, who was a capable physicist, and no liar. As for you, I cannot believe you so incompetent as not to be able to understand the point of Jefimenko's Chapter 9. Nor can I accept the possibility that you are so completely careless as to propagate Jefimenko's ideas without having read the book at least up to Chapter 9. So I regretfully come to the conclusion that you are merely a slightly deranged individual, who attacks mainstream physics in whatever manner he sees fit, and makes up both theory, experiment and authority to suit the caprice of the day. In other words, a compulsive liar.

Now you will say ``ad hominem'': by no means. The ad hominem argument consists in arguing against a theory by criticising the person who defends it. I have described the theory, more fairly than you have, and I then criticise *you* (not the theory) for lying about it. Calling a liar, a liar, is not being ad hominem, it is being honest towards a community of readers who might otherwise be deceived concerning your good faith.

``Not Jefimenko is indeed the liar, you are!'' You are really good! I actually said that Jefimenko was a competent  physicist, and no liar. I accused *you* of being a liar, which you once more prove by this misquotation.

As to your claim that Jefimenko was using words such as covariance in a personal sense, it is, once more, incorrect: could you quote one single of the equations of Section 9-1 that does not exactly correspond to the usual Lorentzian expressions?  You cannot (except if there were some typo) since Jefimenko claims to hve obtained them from direct correspondence out of the Maxwell equations. More lying on *your* part (not on Jefimenko's: do not slander him so readily).

Finally, you have not answered my remark concerning the changes in the electric field: if you want to do the calculation of the orbit around a moving center, you must take all this into account. If you do not wish to use LT, do the calculation in detail, correctly, and you will find a precession of 

zero.

Affectionately yours,

Francois

``It depends on which book you talk of, of course'' Stop equivocating: I mentioned explicitly Chapter 9 of Jefimenko's book ``Gravitation and Cogravitation''. Are you scared of facing facts?

As for your peculiar interpretation of Jefimenko's attitude towards Lorentz covariance (which he explicitly accepts in Chapter 9 of his book), do you have any quotation of Jefimenko's to support it? Considering your record on truthfulness, you can hardly expect us to take your unsupported word for it. Note that I have always introduced specific quotations and references to bolster my claims: you seem averse to such honest practices.

Further: ``You have not the slightest idea what cogravitational equations mean!"

That is quite possible. But I do not need their meaning to find their solution. The Lorentz invariance correctly described in Chapter 9 trivially allows to find the exact motion of a mass in motion around a far heavier mass, which is itself in uniform rectilinear motion. And it trivially follows that no precession arises.

Quite so. But his equations *are* covariant, and the fact can be used to compute the solutions of his equations. In particular, the final sentence you quote clearly states that covariance fully applies to Jefimenko's equations: it merely changes the (irrelevant) *form* of the equations. So a problem can, without affecting its essence, be solved either in the covariant or in the traditional framework.

For the problem you state, covariance is the easiest way to solve it, and to see that your solution is wrong.

The transformations listed in Jefimenko's Chapter 9 Section 1, are exactly the usual Lorentz transfo9rmations, and Jefimenko *never* says otherwise. The LT correctly understood mean what they mean, and cannot be reduced to pointless mantras about time slowing down. The LT is a mathematical tool, which must be used correctly. It can be used when the theory is covariant, which GEM emphatically is. This means that LT''s can be used to simplify the calculat6ions, and one thus immediately shows that the orbit around a rectilinearly moving Sun is just as closed, or not closed, as when the Sun is at rest.

And everyhting *you* are saying about GEM is a brazen lie. No theory deserves such a persistent calumniator, even one quite as wrong as is GEM.

GEM is, of course, wrong: it predicts Mercury precession incorrectly, gives wrong results for gravitational radiation,predicts half the value for light deflection and more. But it *is* covariant: even a quite wrong theory can be defined in such a way as to satisfy, at the very least, relativistic covariance. No contradiction there. I would suggest you start by understanding the theory you try to ram down everybody's throat. Maybe you could start by working out possible differences between the transformations given in Jefimenko 9-1, and ordinary Lorentz transformations, as defined in Einstein 1905. If you find any, do tell.

That you cannot even understand what your favourite author writes, let alone distinguish which parts of it are right or wrong, is pitiful indeed. That you then try to teach the rest of us how to do physics, could mildly amuse, or arouse a low level of contempt, no more.

``far from excellent'' is kindness itself. The ill-called paper is pure bilge. It adds to the 2 postulates a series of disjointed remarks, which are either wrong (for example ``the postulate of simultaneous validity of Galilei and Lorentz transform''!!) or which are, in fact, needed to establish both Newtonian and relativistic mechanics. That Mr. Danci chooses to see in the multiple tacit assumptions he finds in classical mechanics (both Newtonian and relativistic) only a weakness of relativity, is of course merely a way of displaying his personal bias.

As for my ``scolding'' you, I fear you overrate yourself: it was never  my intent to give you such a level of recognition.

``As for the Galilean transformation used by Einstein in his 1905 paper, IT IS THERE, plain and clear in his text. Isn't it a pity that you can't understand it?''

The shoe, once more, is on the other foot. You, in the dubious company of thousands of other incompetents (and possibly a few truly evil individuals) confuse the computation of relative velocity with the addition of velocities. Relative velocity between two objects, a quantity measured within one single reference frame, is obtained (in any kind of theory, whether relativistic or otherwise) by adding or subtracting the velocities of the two objects. If, on the other hand, an object 1 moves with a velocity v1 in a frame B, which itself moves with a velocity v2 with respect to frame A, then the velocity of object 1 in frame A is obtained by relativistic addition of velocities.

Einstein does use the computation of relative velocities in his derivation of the Lorentz transform, he does not, of course, use a Galilean law of addition of velocities. It *is* a pity you *will* not understand it (for my guess is, you probably do understand it, but attempt to confuse everyone else. Not really ``heroic'', I would rather call it revolting).

``the statements of Einstein, Born, Pauli, Lowdin, Mermin, Valentini, and many others, are just "disjointed remarks"!?''

Mr. Danci has indeed merely made a telegraphic summary of various remarks  made, in some cases, by highly regarded physicists. My main point, which you characteristically leave out of your rejoinder, is that all of those ``hypotheses'' underlie both Newtonian and relativistic dynamics They could thus be viewed as a weakness for mechanics in general, but surely not for SRT specifically.

It is a bit painful to read your misunderstandings. Einstein defines k to be the moving system and K to be at rest. He states that if a point has a constant position in the moving system k, then x'=x-vt, where x and t are coordinates *in the system at rest* called K, is time independent. There are no transformations from one system to the other involved here: only quantities in the system at rest. The coordinates in the moving system are denoted by Greek letters.

No mixture of Galilei transformations with Lorentz transformations in Einstein. Plenty of confusion of just about everything under the Sun in the Danci-de Mees-Gehrcke-Mitis-Lenard association.

So let me quote Einstein fully:

``To any system of values x , y , z , t , which completely defines the place and time of an event in the stationary system, there belongs a system of values xi, eta, zeta and tau determining that event relatively to the system k , and our task is now to find the system of equations connecting these quantities.

In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.

If we place x’= x − vt , it is clear that a point at rest in the system k must have a system of values x’ , y , z , independent of time.''

The coordinates of the event in k are thus defined to be xi, eta, zeta and tau (greek letters!). The letter x' is computed from the K quantities x, y, z and t. It is nowhere stated to be anything like a coordinate of the event in k. It is simply claimed that, if the event is at rest with respect to k, then the quantities x', y, z are independent of time t. This follows from the definition of velocity and has nothing to do with *any* kind of transformation, let alone either Galileo or Lorentz!

The idea of a ``system of values which pertains to k'' comes from you, and you alone. Einstein merely makes the remark that x', y and z are constant in the case of rectilinear motion. This is in fact true without any hypothesis on any kind of transformation, since all the quantities involved (x, y, z and t, as well as x') are measured in terms of the K coordinates.

``Therefore the observer of K *calculates* the distance x' and assumes it to have the length of a moving rigid ruler attached to k.

An so Einstein attached the SYSTEM OF VALUES x', y, z to system k which all are referred to the origin of k.''

Pure imagination: all coordinates linked to k have been defined to be Greek letters. x' can be computed, or for that matter measured, in K. In relativity, x' is the constant distance between the origin of k and the point x fixed with respect to the origin of k (that is, moving together with k) *as measured using rods belonging to the system at rest K*. There is no statement to the contrary in the whole text, and the peculiar interpretation you give is wrong, that is, it belongs to you alone. Read the text and do not put your own mistaken ideas into it.

Your interpretation is utterly incoherent and unsupported by anything in the text. Einstein merely says a point moving in k must have a value of x' which is constant. In other words, the value of x' for a point moving with k must be constant. Mere obvious kinematics, following from the definition of velocity. Nothing is ever said about x' being ``attached'' to k. Nor is it true that it is measured using moving rods. Rather, x is measured using rods at rest with K, so is vt, and therefore the difference between the two is also a distance measured by rods at rest with respect to K. Your screaming ``Nonsense'' merely shows lack of understanding. The idea that such a distance ``cannot be measured'' is again a figment of your imagination: there is no difficulty whatever in measuring the distance between two moving points.

This discussion has, of course, no meaning: your only point is to denigrate relativity, for purposes best known to you. I have stated the truth of the matter, by following the actual original text (which you were afraid to quote) as closely as possible. For any interested readers who might have been confused by your nonsense, this should be enough. You I do not think worth an additional second of my time.

Systematic lying, dear Valentin, even with caps on, will get you nowhere. x' *is* measured with resting rods, and it is, self-evidently, constant when thus measured. Anything else is your imagination running wild and trying desperately to avoid facing facts. But of course, the daylight of truth is damaging to denizens of Transylvania.

Dear Valentin,

x' is not a Cartesian coordinate measured in k. If m is a material point whose coordinates in K are x, y, z, t, and if m is constantly at rest in k, then there are mathematical functions f (x, y, z, t) whose values does not depend on t.

x' = x-vt is an example of these functions. This particular function is the definition of the fact that k is animated by a uniform translational motion with respect to K. This is not a transformation of coordinates between k and K.

>

Dear Valentin,

x' is not a Cartesian coordinate measured in k. If m is a material point whose coordinates in K are x(t),  y(t), z(t), t, and if m is constantly at rest in k, then there are mathematical functions f [ x(t), y(t), z(t),  t ] whose values does not depend on t.

x' = f [ x(t), y(t), z(t), t ] = x(t) - v t is an example of these functions. This definition of relative motion is used both by classical and special relativity kinematics. It is a postulate in both theories.

Could you cast this format into universality, by combining it with Lorenz invariance?

It would be a postulate, in that way, to assume thar re scales with some length L, related to v0, as (1-v 2/v0 2)1/2L, where v0=wOrO

Dear Valentin,

k is in uniforme translational motion with respect to K with the velocity v.

If x(t), y(t), z(t) are the cartesian coordinates in K of a material point of the universe:

1/ what relations must be satisfied by these functions in order to be able to affirm that this material point is constantly at rest in K?

2/ what relations must be satisfied by these functions in order to be able to affirm that this material point is constantly at rest in k?

you don't need to calculate the coordinates in k to provide a mathematical answer to these questions.

Continuing reading, I think 'my result' ( or it is the Pythagorean identity for a relative motion) is more independent, and since not a translational motion it would be difficult to cast in this framework. It may be suitable to describe how light creates shadows and reflexions. It may also invoke the twinkling that the eye uses.

Somehow this discussion deviated, because everything non-newtonian was not explained by Einstein and most things non-newtonian or non-Kepler, do not relate to light.

``You need to know where the values come from, and what they mean. Once you assume x' is constant in k, that has a meaning in Physics as a measurement in a coordinate system of k.''

You need to know what the values mean: how true! The rest is incorrect, however: x' is constant in time (no one said anything about ``constant in k'') when a point is moving with velocity v along the x axis. x, by definition, is the number of (resting) yardsticks needed to connect the resting origin of K with the position x of the moving point m at time t. The fact that the point is moving in no way stops us from measuring its position at a given time t with resting yardsticks (we might, for example, take a photograph at time t of the position, or any of a large number of alternate possibilities). Once we have a fixed marker for the position the point occupied at time t, we can measure the distance with resting rods easily.

The distance measured with rods at rest with respect to K is thus x. This follows amongst others from the original text:

`` We now imagine space to be measured from the stationary system K by means of the stationary measuring-rod, and also from the moving system k by means of the measuring-rod moving with it; and that we thus obtain the co-ordinates x , y , z , and xi, eta ,zeta respectively''

So x is measured by rods at rest with respect to K, So, clearly, is vt, since velocity is defined (quite generally) as the ratio of the space covered in time t, divided by the time in which it is covered, where both the space and the time are measured in the resting frame. So vt is also a number of yardsticks at rest. But then x-vt, which is x', is the number of yardsticks at rest separating the (moving) origin of k from the moving point m. So it is the distance separating m from the origin of k, which is constant since that origin and m move at the same velocity, measured in yardsticks at rest with respect to K.

But, being constant, it is constant in whatever units it is measured. Your claim ``As I said above, the distance x' is constant only if it can be measured by rigid rods in k.'' is untenable: the two rods differ by a constant factor, so the distance x' is constant, but it is also measured in terms of rods at rest with respect to K. The distance xi separating m from the origin of k as measured by yardsticks moving together with k, is also constant, of course.

The quantity xi does indeed give a meaningful *coordinate* in k, since it is defined (see text above) as the distance separating the origin of k from the point m *measured with rods moving with respect to K but at rest with respect to k*. The quantity x' has the same meaning, except that it is measured in terms of rods at rest with respect to K. No Galilean transform.

Your further remarks are equally wrong: describing the motion of two bodies moving at velocities v1 and v2 if the whole motion is described in one and the same frame, is a problem, the solution of which does not depend on how we transform frames: when a single frame is involved, we need no transform. So two particles, the first one at the origin the second one at L, moving with velocities v1 and v2, will always meet at a time t=L/(v1-v2), since that is simply given by the solution of the equation

x1(t) = v1*t = x2(t) = v2*t + L

which is true whenever velocity is correctly defined, and has no connection to any kind of transformation. v2-v1 is then correctly defined to be the relative velocity, and is a quantity independent of any kind of transformations.

Total nonsense, but I guess we should agree to disagree. I cannot say, of course, that I repeat what you have said: in as many ways as I know how to, I have stated that x' is measured with the yardsticks of K, just as x and vt are: if two distances are measured with the same yardsticks, then so is their difference. Thus x' is measured with a yardstick at rest with K, not moving with k. According to you ``x' is the distance between origin of k and a point at rest in k. Therefore x' is constant in k, and can be deemed as constant only in k by employing the rods of k.'' That is simply false and repeating it will not mend matters. The first part is true enough: x' is the distance between a point fixed with respect to k, and the origin of k. But that is time-independent in any units you care to measure it in. It can perfectly well be measured using yardsticks at rest with respect to K. The part of your statement I put in bold is thus wrong.

As for your rigidity postulates, they belong to you, and you alone. Rods must, indeed, maintain their proper length as they are moved around, but moving rods are allowed to appear shorter, when measured using rods at rest. Neither Born nor Einstein ever stated anything to the contrary.

Simply said: any quantity can be measured in any frame: that is what frames are for. Objects do not, in any way, *belong* to frames. Frames are simply means to describe the position and time of occurrence of events. By the way, an event is instantaneous, and thus is not moving. You cannot tell, at any given point, whether the event one measures corresponds to a moving point, or one at rest.

As to rigidity, of course, Born wrote a lot about it. It is just completely irrelevant to the derivation of the LT, and utterly different from anything you write. No ``rigidity postulate'' is needed for relativity.

Dear friends, maybe, Einstein's theory or mistakes is much more simple. Please see:

 https://www.researchgate.net/publication/313822831_Contradiction_between_invariance_of_speed_of_light_and_Lorentz_transformation

Working Paper Contradiction between invariance of speed of light and Loren...

@ Yin Zhu

The formulation of Special Relativity using Lorentz Transform may involve a mathematical fallacy; at least in its popular presentation. Please watch the following video: https://www.youtube.com/watch?v=xrun8KUyYm4