Miodrag Mateljević

Hi, the problem is that your reasoning is contradictory. You have to distinguish between the proper length of two rods L0 which is the same for both local observers in F and F' and the length that each observer assigns to the moving rod that passes before him with velocity v, L(v).

The relation is L(v)=L0/gamma.

The observer in F concludes that L'(v)= L0/gamma.

The observer in F' concludes that L(v)= L0/gamma.

It is incorrect to put, as you did

L'(v)=L(v)/gamma ....(1)

L(v)=L'(v)/gamma....(2)

(1) and (2) can only be both correct if gamma=1.

Note that Lorentz Transformations (LTs) are not rigorously derived by assuming time dilation and length contraction. They are derived by assuming that light speed is invariant between moving inertial observers.

Time dilation and length contraction are consequences derived from LTs.

Cheers.

The Lorentz transformations are the linear coordinate transformations between a spatial coordinate and the time coordinate, that leave the wave equation invariant. But what then matters is to focus on the quantities that are invariant under such transformations; the invariant quantities are the only quantities that two observers can compare, the non-invariant quantities are only used to construct the invariants.

So Box f(t,x,y,z)=0 Box' f(t',x',y',z') iff

ct' = ct coshφ + x sinhφ

x' = ct sinhφ + x coshφ

y' = y

z' = z

ct = ct' coshφ - x' sinhφ

x = ct' sinhφ - x' coshφ

y = y'

z = z'

with tanhφ = v/c.

(and there are two other, possible, transformations that involve t and y as well as that t and z)

Everything else follows and is the subject of standard exercises. How Einstein discusses special relativity is now only of historical interest, without any bearing on the technical content.

For instant it's trivial that c(t1-t2) isn't invariant under Lorentz transformations, so c(t1-t2)=0 does NOT imply that c(t'1-t'2)=0 and vice versa. But that doesn't matter.

On the other hand causality is invariant under Lorentz transformations:

c(t1-t2) > 0 c(t'1-t'2) > 0

c(t1-t2) < 0 c(t'1-t'2) < 0.

What is invariant is the interval

c2(t1-t2)2-(x1-x2)2-(y1-y2)2-(z1-z2)2= the same in the primed frame.

Dear colleagues,

Justo Pastor Lambare ,

Preston Guynn,

Stam Nicolis

Thank for useful answers. I am mainly agree with you, but

I would like to point that the question is also related to the papers

[SD]Satadal Datta, A Revisit to Lorentz Transformation without Light, arXiv:2212.03706v1 [physics.class-ph],

[GA] Vasco Guerra and Rodrigo de Abreu, Special Relativity in Absolute Space:

from a contradiction in terms to an obviousness, https://arxiv.org/ftp/physics/papers/0603/0603258.pdf

Thus if we suppose the second postulate we can derive Lorentz Transformation using Minkowski distance. We get the same result

if we substitute the first equation obtain by observer in $S'$ into the second equation obtained by observer in $S$.

It seems to me that from mathematical point of view we can consider some theory roughly speaking using some hypothesis instead of the second postulate.

For example in setting of the paper [SD] whether we can substitute the equation obtain by observer in $S'$ into the equation obtained by observer in $S$ ?

best regards, Miodrag

It doesn't matter, the only thing that matters is that two observers, that are related by a global Lorentz transformation, are equivalent, which means that they will find the same values for quantities that are invariant under Lorentz transformations. The values that they find for quantities that aren't invariant don't matter.

Only quantities that are invariant under such transformations make sense and quantities that aren't invariant are only building blocks for the invariants.

Observers that can't be related by a global Lorentz transformation aren't equivalent, which means that the quantities, that are invariant under Lorentz transformations, will take different values for each observer-which is what gives meaning to the statement that the observers aren't equivalent.

In any case, however, what matters are the quantities that are invariant, not any quantity that isn't. The confusion arises upon focusing on quantities that aren't invariant under global Lorentz transformations. This isn't just wrong-it's meaningless.

“Whether classical derivations of the Lorentz transformations is rigorous ?”

- this thread question really is rather vague - all classical derivations of the Lorentz transformations rigorously follow from corresponding postulates, and so the question would be more clear if would be as – “are the postulates the classical derivations of the Lorentz transformations are based on which are scientifically rigorous ?”

Really the transformations are based first of all on the Galileo-Poincaré relativity postulate that all physical objects/events/effects/processes in Matter – and corresponding physical laws that describe/govern the objects/events/effects/processes in Matter – exist and happen by the same way in any/every inertial reference frame [further “frame”]. Including really, say, if a light flash happens in the middle of a Galileo ship’s cabin, the light must simultaneously hit the cabin’s ends as that happens in a “stationary” tavern on a beach; from what, say, evidently follows that the hits that are simultaneous for observer in the cabin are non-simultaneous for observer in the tavern, provided that the light propagates in absolute space with speed that doesn’t depend on its source speed.

Both – the relativity principle and isotropic constancy of measured in some frame speed of light were/are confirmed experimentally, i.e. both these postulates are based on experiments that were/are made. But any number of experiments principally cannot prove anything, besides that if one experiment results are inconsistent with a theory, that proves that the theory isn’t at least completely, correct.

That above was the base of the Lorentz-[Poincaré] 1904 theory, which was developed just provided that Matter’s spacetime is absolute, and, though experimentally it is impossible to observe absolute motion in 3D space – as that Poincaré stated, from this by any means it doesn’t follow that that that doesn’t happen – always and in parallel with observed motion in concrete frame.

Correspondingly in the 1904 theory the letters x,y,z,tin Lorentz transformations relate to some really, of course, transcendent/undefined scientifically “local space” and “local time” in the absolute spacetime,

- but in the SR the relativity principle is completely absolutized , and so it is postulated that there is no absolute Matter’s spacetime, all/every frames are absolutely completely equivalent and legitimate; and the letters x,y,z,t in Lorentz transformations so relate to all/every points in the concrete frame’s spacetime, at that so the “relativistic properties and effects”- “space contraction”, “time dilation”, etc., were “discovered” – i.e. really simply postulated as some properties of the Lorentz .transformations.

From the postulates that there is no absolute Matter’s spacetime, all/every frames are so absolutely completely legitimate and equivalent, and that the Lorentz transformations are as in the SR above, immediately completely directly, rigorously and unambiguously any number of completely rigorously senseless consequences follow, the simplest and evident one is the Dingle objection to the SR,

- from what again completely rigorously by completely rigorous proof by contradiction it follows that Matter’s spacetime is absolute, and so the frames aren’t completely equivalent, while there can exist the really preferred frames that are at rest in the absolute 3D space.

Real physical sense of the Lorentz transformations and relativity principle can be, and is, clarified only in the Shevchenko-Tokarevsky’s informational physical model , in this case see

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics;

- including in the model it is shown that the absolute motion can be observed and absolute velocity can be measured yet now, more see https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible.

More see the linked above papers, here only note that there exist no “local space” and “local time”, and, of course, no “space contraction”, “time dilation”, etc., since really the letters x,y,z,t in Lorentz transformations relate only to spacetime points that are occupied at a given time moment by rigid bodies and rigid systems of the bodies; and so only concrete moving bodies’ lengths are contracted, and only in concrete moving bodies internal processes are slowed [say, unstable moving particle lives longer], at that fundamentally nothing happens with space/time/spacetime, that is fundamentally impossible at all.

At that Matter is rather simple logical system, and so to derive really clearly scientifically the Lorentz transformations and most of main equation in fast bodies dynamics it is enough to know the Pythagoras theorem.

Cheers

Stam Nicolis , Preston Guynn and Justo Pastor Lambare ,

One specific fact is at the base of the derivation of the Lorentz Transformations and it is quite arbitrary and show quite a shaky base.

LT are based on a synchronization technique or internal synchronization, true by stipulation, assuming that the SOL is c one-way.

Although the Sagnac effect does not clash with SR directly, it tells clearly the following. Light emitted at once in two opposite direction in a closed loop of length L and detected by an observer in motion (interferometer) shows an arrival delay due to different path length (than L) crossed to reach the interferometer in motion.

EM waves departing in absolute sync arrive at the interferometer with a phase difference (absolute desync) which corresponds to a time difference of 2*gamma*vL/c2 measured by a clock comoving with the interferometer.

That is the same as saying that the measured light-time clockwise is not the same as the measured light-time counterclockwise. Each Em-wave brings a contribution of gamma *vL/c2 , one in anticipation of the detection and the other in delay of detection.

The central synchronization which can be used in a rotating disk (which is independent on the speeds of the synchronization signals), provides the same result as the absolute sync, intrinsic in the Sagnac setup. For two clocks at distance H, along a disk, there is a variation of the measured light-time of light_time_diff=gamma*vH/c2 (same as the Sagnac correction in GPS base stations)

On the contrary, going back to the initial point, with an internal synchronization, as the one which stipulates SOL one-way as c (the Einstein-Poincarè sync proc), clocks would not be able to spot such difference of light-time . They will simply have the "impression" that once applied the procedure their clocks are synchronized, but they are actually desynchronized by that light_time_diff.

The natural synchronization is the absolute, the one intrinsic in the Sagnac type configurations, or one which is irrespective of the signal speed, that brings inevitably to a quite important difference with what is found otherwise.

Basically the stipulation does not hold, since it states that simultaneity is non invariant which is instead an invariant.

Assuming that SOL depends on whether it is "going" or "coming back" makes no sense to me. How can it know if its returning or not? What is the speed upon returning?

When something makes no sense to me I prefer to assume I do not understand it instead believing the rest are stupid. I believe that is the differece between a crackpot and a reasonable person.

it is the measurement on a moving frame. Sagnac effect is an experimental evidence (laser gyros), and it has a peculiar and easy explanation and consequences.

The topic has been extensively described in my previous post, you are invited to give specific claims to specific parts. A generic reply like that is just what a a crank, not a scientist, would provide.

Stefano

My question was very simple, clear and concrete.

Of course, you can choose to ignore it if you wish but you cannot say it does not exist.

How can light change speed because it is returnig back? How does it know that it is going back from where it first came. I agree that you only mesure the mean value. The point is whether it is reasonable to asume that it has to change its value only because is returning.

For instance, supose two light beams depart from the same place but one is being reflected to where it first came while the other leaves its sourse for the first time.

It seems to me that according to the two way principle they should propagate at different speeds.

Preston Guynn ,

the synch arrives at once to all parts so there is no effect of rotation on time..

>

I advise you to study the topic much metter because what you are saying makes little sense, have a look at what is said by a well known relativist..

Article Ways to resolve Selleri's paradox

Sagnac experimental setup actually shows the stipulation, that the vx/c2 in LT is just an "observer dependent" term which together with the internal sync procedure of Poincarè, provides the "impression" that the SOL one-way is constant in every frame of reference.

That does not mean that LT clashes with Sagnac, because as a matter of fact it is possible, in non simple way, to find Sagnac's results through SR.

Actually to a certain extent some results of SR can be found through Sagnac in a straighforward and reliable way.

Preston

All you said seems correct and reasonable. However, to elevate Thomas presecession to a fundamental principle seems strange. Thomas precession is a mere corollary of LT, a kinematic effect.

Justo Pastor Lambare ,

Let's consider one frame (ECI FRAME of earth), where light is isotropic to a very good approximation and one measures the 2way as c, SOL one-way is c.

From a moving system (in ECI frame not considering gravitation), where two clocks were set in absolute sync in motion (circular motion also Sagnac case). If one measures the SOL with the help of such two clocks, the SOL measured will depend also on the retardation of light in reaching a moving target or approaching the moving target represented by the term gamma*vH/c2

in such case light will be measured as a c/(1+IvI/c) or c/(1-IvI/c), but in the frame which is the preferred one it is postulated isotropic.

Preston Guynn ,

yes it is the speed which Maxwell found as a ratio of the vacuum EM constant, that occurred thanks to considering a preferred frame where SOL is isotropic, or more isotropic than in relative moving frames.

Stefano Quattrini

Now I realized my question was silly or at least easy to answer to. That only confirms what I said at the beginning: the difference between a crackpot and a rational person is that the last one can correct his mistakes and is capable of changing his mind.

The short answer to my concern is that when a medium like the aether exists there is no problem with an anisotropic behavior of light speed for an observer moving through that medium.

Justo Pastor Lambare ,

Yes. Sagnac by the way was not a crackpot for sure....

There is no other reason why a preferred frame was abandoned except for an apparent simplicity at the beginning (LT) to end into negative energies (Dirac) and infinities and re-normalization (Feynman) to an impossible integration with gravitation.

That M&M experiment did not detect what M&M expected is non disputable, what they expected (an interference fringe shift testifying 30Km/s) was not the right thing to expect that's all. Expecting an aether in the form they imagined was simply unrealistic. Sagnac effect, with M&M device could be detected and it was done in the Michelson and Gale experiment, a much larger and sensitive interferometer which detected earth's rotation speed. That means that Earth's is a preferred frame for light, a local preferred frame.

yes, although it is unknown what such a background is and how it reacts to gravitational phenomena.

Preston Guynn ,

First never mentioned a time keeper to be at the center of the disk.

What is needed is just a generator of a signal (if you are in air you can use sound) located in the center of rotation which generates a pulse which reaches at once the RIM of the disk (SYMMETRY) where clocks are located to set their timestamps to 0. That makes the simultaneity of clocks absolute also because what happened (at variance with Einstein Poincarè sync procedure) is independent on the signal speed..

You better study carefully these things before arguing in the way you did it because as a matter of fact the one who is not willing to learn anything is you.

The scientific answer to the thread question is given in SS post on page 1, 2 days ago now; so for the readers who want to know the answer see the pointed SS post and links in the post.

However further some rather vivid series of really physically strange posts, which even looks as specifically organized by addressing to a few “specific” posters 2 days ago now, appeared. In the series really only one point looks as rational for somebodies, who don’t know what the SR on sufficient level, including for some possible the thread readers:

“…The short answer to my concern is that when a medium like the aether exists there is no problem with an anisotropic behavior of light speed for an observer moving through that medium..….”

- really this problem in most cases doesn’t exist, since any physical and everyday humans practice observations of external environment aren’t “arbitrary”, in every case some material instruments are used. Including in this case of measurement of one-way speed of light, for what is necessary to have at least two synchronized distant clocks for measurement time moments of distant events, and scaled rule for the distance measurement;

- while Matter is based on a number of fundamental and universal laws/links/constants so, that in Matter the Galileo-Poincaré relativity principle acts, which govern all material objects/events/effects/processes in Matter so, that inertialy moving observers can observe, including measure, the same objects/events/effects/processes by the same way;

- what happens because of all/every material objects know physics, including the instruments, completely exactly, and behave at existence and interactions in full accordance with this principle.

Correspondingly if an inertial observer know physics enough, and so sets his scaled rule and the distant clocks in accordance with the relativity principle – really specifically in accordance with Lorentz transformations, and concretely, say, by using Einstein-Poincaré the clocks synchronization, he will measure isotropic one-way speed of light independently on with what speed he moves;

- or, if he sets the instruments by some other way, he will discover any speed of light anisotropy – and not only, though, he will make many other marvelous discoveries, which have no relation to objective reality, which, again, knows physics completely correctly..

That’s all, the relativity principle is extremely mighty principle, and so, say, Poincaré stated that the absolute 3D space motion in the, of course, fundamentally absolute Matter’s spacetime – where so some, fixed in the at least in the 3D space, “aether” can be so placed, really cannot be observed.

However really, since the fact that Matter’s spacetime is absolutely for sure absolute - since from opposite – and postulated in the SR assumption any number of senseless consequence follow, the simplest and evident for any normal human is the Dingle objection to the SR,

- observation of the absolute motion really is only some technological task, which can be solved yet now, see 2-nd linked paper in the pointed SS post.

Cheers

Preston Guynn,

Dear Miodrag Mateljević ,

To my understanding the derivation of LT is mathematically rigorous, it involves the postulate of the one-way SOL assuring the validity of the synchronization procedure adopted (Einstein Poincare' INTERNAL synch procedure).

Physically, the one-way SOL measurement is synchronization dependent. Sagnac effect shows that if one uses absolute synchronization the measured SOL in a moving frame is not isotropic.

If one considers Tangherlini Transformations (absolute synchronization), he finds the same effects which, in this case, it is not due to an offset of the clocks but it is due to the non isotropic measurement of SOL.