Re: I dare to relativists to explain local time: t-vx/c²

Den 03.10.2024 06:18, skrev rhertz:

 LOCAL TIME FOR LORENTZ, INTRODUCED IN 1901
 t' = t - vx/c² ;  This is Voigt's Local Time, from 1897.
No explanations given by Voigt, Lorentz or Einstein about the
MATHEMATICAL ARTIFACT vx/c².  This the equivalent of NOISE in
mathematics, an undesired effect.
 t' = t - vx/c² ;  This is Lorentz Local Time, from 1901, presented to
Poincaré.
..............
 β² = c²/(c² - v²)  ; Lorentz Eq. 3 (plagiarized from 1897 Voigt), and
inserted without explanations on his 1904 paper.
 Lorentz, since formulae 4 and 5 on his 1904 paper.
 1904 ORIGINAL LORENTZ TRANSFORMS
 x' = β x  ;  Lorentz Eq. 4
t' = t/β - β vx/c² ;  Lorentz Eq. 5

No, this is not the Lorentz transform.
Lorentz used the Galilean transform first, and then he
"transform these formulae further by a change of variables".
It's is these two transforms together that make the Lorentz transform.
See:
https://paulba.no/div/LTorigin.pdf
He doesn't explain the "change of variables", but the purpose is clear.
To "explain" the Michelson-Morley experiment, Maxwell's equation
must be invariant. (Idea from Poincare.) So "the change of variables"
was what they had to be to achieve that purpose.

  1905 MODIFIED LORENTZ TRANSFORM

In 1905, Einstein introduced (TRICK, out of the blue)  x = X - vt, in

order to get rid of ether.

Lorent's had got rid of the ether, without realising it.
https://paulba.no/div/LTorigin.pdf
Se chapter 3.
The LT transform say that it is impossible to measure the speed
of the ether because the speed of the ether is without physical
consequences.
Einstein started with the second postulate, the speed of light
is invariant (the same in all inertial frames).
So Einstein didn't copy anything, but since the invariance of Maxwell's
equation follows from the invariance of the speed of light,
they ended up with the same transform.

 t' = β (t/β² - vx/c²)
t' = β/c² (t (c² - v²) - vx)
t' = β/c² (t (c² - v²) - vX + v² t) = β/c² (tc² - tv² - vX + v² t)
t' = β (t - vX/c²)

??? :-D

 1905 EINSTEIN'S MODIFIED LORENTZ TRANSFORMS
t' = β (t - vX/c²)
x' = β (X - vt)

It is exactly the same as the Lorentz transform.
--
Paul
https://paulba.no/