The modern proof of Lorentz transformations makes you laugh

quite simply because there is no physical or mathematical proof.

Lorentz transformations are a universal law of nature.

Likewise, the modern proof of the mass energy equivalence E=mc^2 is laughed at simply because this formula has no physical or mathematical proof.

The mass energy equivalence E=mc^2 is a universal law of nature.

So what is this complex and little-known story?

Besides Wikipedia's errors, "Lorentz derived the transformation from the special theory of relativity, as well as from the Lorentz force." The true story is that the giant Noble Prize scientist H. Lorentz, while working extensively on accelerated electrons, experimentally observed and introduced the Lorentz transformation equations as EMPERICAL equations. Maybe he knew there was no proof.

What happened later was that the giant A. Einstein managed to prove this formula via his thought experiment on the sphere of light.

In fact, Einstein's derivation is based on the constancy of the speed of light c.

This means that Einstein didn't add anything because Lorentz transformations imply the constancy of the speed of light and vice versa.

What else

Einstein then derived the mass energy equivalence formula E=mc^2 via another thought experiment by merging Lorentz transformations with Newton's law of motion in its general form F=d/dt)partial mv.

Again, Einstein didn't add anything here because the mass energy equivalence formula E=mc^2 implies Newton's law and vice versa.

1-A rigorous reformulation of Einstein's derivation of the theory of special relativity, IJISRT review, February 2022.

“…Are Lorentz transformations a paradox?

The modern proof of Lorentz transformations makes you laugh and the modern proof of mass energy equivalence E=mc^2 keeps you laughing.…..”

- there is nothing paradoxical in Lorentz transformations, and their derivations by Lorentz and further by Einstein are quite legitimate, since the derivations are based on the well confidential experimental data – as all other equations in physics are principally derived.

That is another thing, that the interpretation/using of Lorentz transformations in the SR-1905 and in [standard now in mainstream physics] SR-1908, where it is postulated

- in the 1905 version that the transformations act in Matter because of that there is a mystic omnipotent “light” that makes that so; so there exist no the absolute Matter’s spacetime, and so all/every inertial reference frames are absolutely completely equally equivalent and legitimate;

- in 1908 version it is postulated, instead the light, that there exist omnipotent “World law” - the SR relativity principle, and so the same as in the 1905 version above,

- is really not “paradoxical”, but fundamentally wrong, and so from the postulates above any number of senseless directly, rigorously, and unambiguously follow, the simplest one is the Dingle objection to the SR, not so simple, but fundamentally wrong are “discovered ” in the SR/GR “fundamental relativistic properties and effects” – “space contraction”, “time dilation”, “spacetime curvature”, which fundamentally don’t exist, Matter’s spacetime is fundamentally absolute, and fundamentally cannot be “contracted”, etc.

However the Galileo-Poincaré relativity principle is really extremely potent, and so the SR, till it is based on this principle is really well, and quite seriously, applicable in everyday physical practice.

The equation E=mc2 is really true and great equation; though was obtained by Einstein at consideration of energy-mass balance at radiating of photons; but it can be derived in general case, see the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics , see Eqs.(3-4)

In the paper the physical sense of the Lorentz transformations is explained, including the transformations are derived. Really for derivation of the transformations – and most of other fast bodies mechanics equations, besides Eq.(3) - it is enough to know Pythagoras theorem, on Planck scale Matter is rather simple informational system.

Cheers

Lorentz Transforms, 'spacetime", gamma factor, m = m0 x gamma, SR, GR etc. are all artificial and brain-cooked abstract mental/geometrical constructs; to make the velocity of light an absolute constant. But all of these are false, with no basis in objective reality.

“The Mystery of the Lorentz Transform: A Reconstruction and Its Implications for Einstein's Theories of Relativity and cosmology” : INSPIRE>HEP: https://inspirehep.net/literature/2158754

"New Physics – The Negation of Einstein’s Theories of Relativity" Article New Physics -The Negation of Einstein's Theories of Relativi...

Back in 1965, Lévy-Leblond certainly « christened “Carroll group” [a new limit of the Lorentz group] because of its seemingly paradoxical physical contents ».

Preprint On the unexpected fate of scientific ideas: An archeology of...

So yes, it can be quite some fun...

It is possible that the lotentz transformation may be in-between the two, but is also explains the nature of evolving relative frames at light speed, the transformations themselves can reduce to simple pythagorean descriptions in which the x and y axis remains constant where z axis is simply a transformation of the x axis and time is simply a transformation of the x axis travelling near light speeds in which time dilation takes place in the forth axis of time. There are many other interpretations to the lorentz transformation, in which we can say a single axis tranformation is simply a modifications of the other axis due to various relative motion, this can also be true for different observers if they choose to perceive an event differently.

I also find lorentz transformation fascinating as it also underlines the philosophical and abstract nature of reality. Nevertheless it is still an important tool in mordern physics, a theory can be incomplete or inaccurate but that does not mean it cannot have value.

"a theory can be incomplete or inaccurate but that does not mean it cannot have value."

The theory that is the subject of this discussion is NOT "incomplete or inaccurate"; which is the attribute of any scientific theory. This theory is FALSE, a FICTION, a mental FABRICATION from the abstract geometry of Pythagoras; has no relevance for objective reality and science. All inferences and deductions made from this and relativity theories in the realms of cosmology (Big Bang creation, dark/black cosmic entities etc.) and quantum physics (God Particle, Matter Myth etc.) are deceptions, absolute fictions of no value to science. The only value of this new mythology lies with monopoly capitalism and the Vatican, who promote this mythology as their ruling idea, to pacify the exploited and subjugated mortals.

" Quō Vādis Theoretical Physics and Cosmology? From Newton's Metaphysics to Einstein's Theology!: Article Quō Vādis Theoretical Physics and Cosmology? From Newton's M...

Lorentz Transforms, "spacetime". gamma factor, relativistic mass, SR, GR etc., are mental and mathematical fabrications; all derived from the false “axiomatic truth” that light photons are massless and their velocity c is an absolute and universal constant. Some new considerations

New Physics II – Quantum-Dialectical Derivation of New Mass-Energy Relation Invalidates Einstein’s Famous Equation E = mc2

https://www.gsjournal.net/Science-Journals/Research%20Papers/View/9900