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Re: Annotated version of SRT

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Am 18.05.2022 um 19:02 schrieb JanPB:
> On Sunday, May 15, 2022 at 12:53:05 PM UTC-7, I wrote:
>>
>>> He used partial derivatives, for what there was no
>>> reason, because the other variables (y/eta and z/zeta) were not involved.
>>
>> They were but their values were identically zero, so Einstein
>> didn't include them in the equation.
>
> Sorry, I got carried away by the other part of the derivation. Here the answer
> is that the derivatives wrt  y  and  z  are not present because in the first  tau
> equation the variable  x'  is not present in the  y  and  z  slots of  tau.

x' is not a variable!
x' denotes the location of the mirror at rest in k, but measured in 
K-coordinates.

That position is in some distance d from the emitter of the zero spot of 
k. This distance was not named 'd', nor even mentioned, but should exist.

Therefore, I assume d would be the name for the disatnce between emitter 
and mirror in k. d is arbitrary (because not specified), but assumed as 
a constant value, because the mirror is assumed to be at rest in k.

The position of the mirror is moving in K as x', but that does not make 
x' a variable.

> That's why in order to calculate  dtau/dy  and  dtau/dz  it's necessary to set up
> tau  equations with the  y  and  z  variables present (that's what setting up the
> mirror in the  Y  and  Z  directions does).


What is dtau/dy?

tau is a time measure in k and y a coordinate in K.

So: how do we interpret dtau/dy?

something like: a small variation of the y-coordinate in K is 
corresponding to a small variation of the time tau in k?

As that is absurd, we need to aply the other meaning of 'tau' here, 
which is a function!

That function is a coordinate transformation between k and K.

The input values of tau are four vectors in k and the output 
corresponding four-vectors in K.

To use partial derrivatives was actually correct, because only one 
coordinate y was considered.

But Einstein used x', which is NOT a variable of that function.

TH

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Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-12 11:33 -0700
  Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-12 21:28 +0200
    Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-13 08:41 +0200
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-14 06:43 +0200
      Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-14 19:49 -0700
        Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-15 08:34 +0200
          Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-15 12:53 -0700
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-18 08:01 +0200
            Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-18 10:02 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-20 09:32 +0200
    Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-14 19:29 -0700
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-15 08:50 +0200
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-19 08:39 +0200
        Re: Annotated version of SRT Python <python@python.invalid> - 2022-05-19 11:03 +0200
          Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-19 06:56 -0700
        Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-19 02:05 -0700
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-20 09:17 +0200
            Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-20 15:10 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-21 08:38 +0200
            Re: Annotated version of SRT Python <python@python.invalid> - 2022-05-21 18:41 +0200
              Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-21 11:51 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-22 07:29 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-21 23:10 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-30 07:19 +0200
        Re: Annotated version of SRT "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2022-05-19 20:00 +0200

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