People just want to know the root cause of Lorentz transformations. Personally, I recommend everyone to look for this root cause in the flow movement, but not in a 3-dimensional space, but in a 4-dimensional one. Our Euclidean space is orthogonal to the flow and therefore we do not see it.

“…Minimum amount of assumptions for deriving the Lorentz transformation….Surprisingly enough, as much as about 125 years after its first proposal, there are still a lot of articles about the derivation of the Lorentz transformation. Why? Which variant you are recommending?….”

- the derivation of Lorentz transformation with minimum amount of assumptions exists soon 120 years – the Poincaré derivation 1905 [published 1906]: Lorentz transformations are derived by only one condition: of invariance of quadratic form s2=x2+y2+z2-t2 [in the equation the speed of light, c=1] in mathematical 4D space, where the t-dimension is mathematically imaginary one;

- and this derivation is given seems last at least 100 years in all textbooks with the SR.

That is another thing, that Poincaré understood that real Matter’s, 4D in those times [and in mainstream physics till now], spacetime is really Euclidian one, and in Matter there cannot be some imaginary dimensions; and that the derivation above is some interesting mathematical fact, which, though, can be important physically, but he hadn’t some ideas in this case.

That is another thing, that in 1908 Minkowski postulated that real Matter’s spacetime is as that is in Poincaré derivation above, and postulated that that is so because of the Relativity Principle is so extremely potent, if omnipotent, that imaginary either space or time dimensions are real, and in the Lorentz transformations letters x,y,z,trelate to all/every point in the spacetime,

- “discovering” by this postulating the “fundamental relativistic properties of space/time/spacetime and effects” – “space contraction”, “time dilation”, etc.

The Minkowski SR version – including the “properties ” and “effects” above, remain be standard theory in mainstream physics,

- despite that really all that in the SR is/are really only transcendent – and wrong, claims, since really everything in this fundamentally cannot, and so doesn’t exist in the objective reality.

This transcendence was – and is till now - in the mainstream quite logically inevitably because of that in the mainstream philosophy and sciences all really fundamental phenomena/notions, first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, were/ are fundamentally completely transcendent/uncertain/irrational,

- and so in every case when mainstream author(s) addressed(ss) to some really fundamental points – in this case what are space/time/spacetime – what is necessary ~ at least 150 years already at formulation of physical theories postulates, the postulates, again - quite inevitably logically - can be, and are, only some transcendent mental construction; and so really the mainstream theories [not only SR/GR] are such constructions.

The fundamental phenomena/notions above can be. and are, rigorously scientifically defined only in the really philosophical 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- and at application to concrete informational system “Matter” in the Shevchenko-Tokarevsky’s informational physical model

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics , which is based on the conception.

Including in the model it is rigorously scientifically explained – what are Lorentz transformations and why they are as they are; and after understanding of the explanation the derivation of the transformations

- in, of course, fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [5]4D spacetime with metrics (at least) (cτ,X,Y,Z,ct), which fundamentally cannot be “contracted”/ “dilated”/ “curved”, etc., is rather simple – Matter is rather simple logical system and to derive the transformations – and all other general fast bodies mechanics equations – it is enough to know only Pythagoras theorem.

Cheers

Proofs of the Lorentz Transformation must make the assumption that the axial shift is not there or or erroneously it cancels, or that the transverse and axial shift are independent effects. Links to relevant proofs:

The first attached Link has the proofs tat the axial Doppler shift and the gravitational Doppler shift changes observed time and distance. It then goes on to proofs the impacts of relativistic velocities like changing observed constants of particles with rest mass. The second is effects not in most texts of high velocity on beam flux. https://drive.google.com/file/d/1jR23mwgUEMqFNNVuWhzy2Zei9ZPnecK5/view?usp=sharing--------------------------------------- https://drive.google.com/file/d/1SJ3adTk9XmBWAV-6RoLE3UNV0hz5keGG/view?usp=sharing--------------------------------------------------------------------------------------------- Thanks for your time. Samuel Lewis Reich, [email protected]

A general property of any physical symmetry is that the volume of the phase space is conserved.

Proofs of the Lorentz Transformation must make the assumption that the axial shift is not there or or erroneously it cancels, or that the transverse and axial shift are independent effects. Links to relevant proofs:----------------

https://drive.google.com/file/d/0B_EuaRUutBrtMkRnMEZ2SmNVQ0FETWpOV29yaWo3bWs3aXN3/view?usp=drive_link&resourcekey=0-igyEAMLGwSdYUNybHyBdlQ------------------------------------------------

A link to the effect of high vewlocities on flux of beams:---------------------

https://drive.google.com/file/d/1SJ3adTk9XmBWAV-6RoLE3UNV0hz5keGG/view?usp=sharing------------------------------------

Thank you for or time.

Samuel Lewis Reich ([email protected])