Re: Einstein cheated with his fraudulent derivation of Lorentz transforms

On Thu, 6 Feb 2025 7:27:30 +0000, Thomas Heger wrote:

Am Mittwoch000005, 05.02.2025 um 23:51 schrieb rhertz:
....

See:
https://paulba.no/paper/Electrodynamics.pdf
Read §3
  Theory of the Transformation of Co-ordinates and
  Times from a Stationary System to another System in
  Uniform Motion of Translation Relatively to the Former
>
On the first page (page 5) Einstein defines the coordinate systems.
The "stationary system"  K(t,x,y,z) coordinates are Latin letters
The "moving system"      k(τ,ξ,η,ζ) coordinates are Greek letters
>
So the Galilean transform is: ξ = x - vt

>
Sure, but that wasn't what Einstein wrote.

>
NO, innoble animal! ξ is the name of the horizontal axis in the moving
frame k.

correct (without the insult, of course).
>

ξ(x') = x' in the moving frame. I attached a graphic to clarify this
but, with your "dog vision" you missed it.

>
There wasn't a function named ξ in Einstein's text.
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Because x' has a Latin letter 'x' in it, it was meant as a coordinate
belonging to system K.
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Therefore the equation ξ = x - vt was meant, while x' = x - vt was
written.
>
x' should be capable of reflecting a light beam, hence a mirror should
be placed there.
>
This would fit to the term 'If we place x' = x - vt...' but not to the
equation.
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That's why it is hard to say, what actually was meant with x'.
>
>

x' = x - vt is the well known Galilean transform, along with τ = t' = t.
>

But that " τ = t' = t " wasn't, what Einstein had in mind.
>

>

You will _not_ find this anywhere in Einstein's paper.

The x' is a point in the stationary system K, it is NOT
a coordinate in the moving system k.
>
So x' = x - vt is a _moving_ point in K.
And since x' is moving with the speed v, it will be stationary
relative to k.

NO. you are confused. I attached again a diagram that represent this
part. If you can't see it with your newsreader, open this site with any
browser (Chrome, Firefox, etc.).


I'll quote Einstein, then I'll clarify what he wrote:

QUOTE: "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 ζ, η, ζ, τ, 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.

We first define τ as a function of x', y, z, and t. To do this we have
to express in equations that τ is nothing else than the summary of the
data of clocks at rest in system k, which have been synchronized
according to the
rule given in § 1". END QUOTE.


1) He's announcing that he FORCES a relationship between K(x,y,z,t) and
k(ζ,η,ζ,τ) in terms of τ(x',y,z,t), a function that relates (x,t) in K
to any point (x',τ) in k.

2) He needs to do that, because he's targeting the equations (which he
already
knew, from Poincaré modification of 1904 Lorentz):

τ = β (t - vx/c²)
ζ = β (x - vt)


Being β = 1/√(1-v²/c²)

SEE? He's looking for τ(x',y,z,t) = τ(x-vt,y,z,t). Do you understand so
far?

He's anticipating a result (petitio principii), and he WILL CHEAT/FUDGE
to obtain such relationship between K and k coordinates, by using
Taylor.

3) By using x' on k, he's replacing the previous rod r_AB by a moving
VIRTUAL ROD r_AB located between ζ=0 and ζ=x'. By doing so, he can make
the virtual rod
infinitesimally small, which grant him the right to apply Taylor around
the
origin ζ=0, with an infinitesimal separation from ζ=0 given by x'.

4) If x' had been a fixed coordinate on the stationary frame K, then the
thought experiment WOULD HAVE HAD NO SENSE, because as x'=x-vt, the
duration
of the experiment would have been t=x/v. After that time x/v, x' would
be
behind ζ=0 and progressively moving to the left of the origin of k.

5) It's proven that the equation

1/2 (τ₀ + τ₂) = τ₁

is valid ONLY for an observer measuring time moving along with the frame
k.

The equation IS NOT VERIFIED when he replaced times τ₀,τ₁,τ₂ measured in
k
with times PERCEIVED from the stationary frame K, which I demonstrated
in a
post above. These times are:


τ₁ = t₀ + x'/(c-v)

t₂ = t₀ + x´/(c–v)+ x´/(c+v)


So, his modification by stating x' as infinitesimally small:


1/2 [τ(0,0,0,t) + τ(0,0,0,t + x'/(c-v) + x'/(c+v)] = τ[(x',0,0,t +
x'/(c-v)]

that replaces the correct equation

1/2 (τ₀ + τ₂) = τ₁

is INCORRECT, because HE WANTS TO RELATE variables in K(x,y,z,t) and
k(ζ,η,ζ,τ) FORCEFULLY, without any mathematical validity. And this, plus
the hacking of Taylor results prove that such relationship is false, and
can't
be obtained in that way, unless he cheats and fudge, what he did.


6) I quote Einstein's writing explaining how the ray of light behave:

QUOTE: "From the origin of system k let a ray be emitted at the time τ₀
along the X-axis to x', and at the time τ₁ be reflected thence to the
origin of the coordinates, arriving there at the time τ₂; we then must
have

1/2 (τ₀ + τ₂) = τ₁
END QUOTE

I hope that you may understand that he's re-writing his thought
experiment
from Point §2, but now with the REAL TIMES MEASURED IN k. It's the only
way
that

1/2 (τ₀ + τ₂) = τ₁

is verified.

For him, x' is the substitution of the extreme B in the rod r_AB, only
that now he can make the length of the virtual rod x' infinitesimally
small, to apply Taylor around ζ=0.

No, the point x' MUST be stationary in K !!
>
If it is stationary in k, if would not move in respect to the emitter in
the center of k and we had no use for the velocity v.
....
TH

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