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Re: Annotated version of SRT

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Am 13.05.2022 um 08:41 schrieb Thomas Heger:
...
>> After a number of messages exchanged with JanPB, we came to the result,
>> that a mirror stationary in k at same distance to xsi_0 on the xsi-axis
>> would be a valid assumption for the intended setting.
>>
>> These two items move with constant distance along the x/xsi-axis into
>> the direction of higher xsi-values.
>>
>> This 'tandem' is observed from the zero spot of K, which moves with
>> velocity v relative to the system into the negative direction with -v*t.
>>
>> But none of Einstein's equations would fit to that setting.
>>
>> Instead of a coordinate transformation he developed an obscure partial
>> differential equation, which I think is faulty and which I'm unable to
>> associate with the setting from above.
>
>
> This is the equation:
>
> 1/2*(1/(c −v) + 1/(c +v))* ∂τ/∂t = ∂τ/∂x' + 1/(c +v)* ∂τ/∂t
>
>
> As justification for this equation Einstein wrote:
>
> "Hence, if x'  be chosen infinitesimally small,..."
>
> I have complained, that x' cannot be chosen "infinitesimally small",
> because x' was defined as position of the mirror at a fixed position in
> k, but in K-coordinates.
>
> This position is moving in K, to which the variable x' belongs.
>
> The movement of x' in K is rather simple, because it moves with velocity
> v along the x-axis of K.
>
> Now my question was, what these partial derivatives were meant to
> represent, if we have only a one-dimensional problem.
>


It was exceptionally nasty to name the function τ similar to the time 
measure τ, because the function τ is actually a coordinate 
transformation between K and k, which creates four vectors from four 
vectors as input.

These four vectors in k have a time component, which was also called τ.

Now it very important to keep both meanings separated.

Here we have a term ∂τ/∂x', which means a partial derivative of the 
function τ.

This function τ is taking four-vectors from K as input and 'spits' out 
four vectors in system k.

But x' is NOT an independent variable of τ!

x' was defined as the position of a mirror, which had to be at rest in 
respect to the emitter.

The emitter was assumed to be at rest in the center of k, hence has a 
xsi-coordinate of zero.

For the mirror I take a xsi-coordinate of - say - 10.

Now I use the possible setting v=0.

In this case we have an identity of K and k and the x-position of the 
mirror would be x'=10.

Now we plug x'=10 into ∂τ/∂x'.

But what is ∂10 ?????

Does not make much sense. Could be zero, anyhow, because x' is a 
constant with x'=10, what would make ∂τ/∂x' infinite.

And there isn't anything to chose, what would violate Einstein's statement:

"Hence, if x'  be chosen infinitesimally small,..."


TH

...

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Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-05 22:17 -0700
  Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-05 22:34 -0700
  Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-06 08:55 +0200
    Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-06 00:24 -0700
    Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-06 01:15 -0700
      Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-06 01:41 -0700
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-07 07:19 +0200
        Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-07 00:38 -0700
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-08 08:22 +0200
            Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-08 12:33 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-10 07:12 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-10 00:19 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-11 07:55 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-11 11:25 +0300
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-12 07:39 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-12 10:31 +0300
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-12 21:05 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-15 11:26 +0300
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-18 07:38 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-18 16:42 +0300
                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 "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2022-05-19 20:00 +0200
    Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-06 17:09 +0300
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-07 07:32 +0200
        Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-07 13:53 +0300
          Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-07 05:10 -0700
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-08 08:33 +0200
            Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-08 12:34 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-09 07:20 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-09 02:24 -0700
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-09 03:04 -0700
            Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-09 10:14 +0300
              Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-09 00:25 -0700
            Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-18 15:54 +0300
              Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-18 06:17 -0700
                Re: Annotated version of SRT Python <python@python.invalid> - 2022-05-18 15:53 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-18 07:05 -0700
                Re: Annotated version of SRT Python <python@python.invalid> - 2022-05-18 16:58 +0200
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-19 08:57 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-19 11:42 +0300
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-19 06:57 -0700
                Re: Annotated version of SRT nospam@de-ster.demon.nl (J. J. Lodder) - 2022-05-19 16:17 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-19 07:41 -0700
                Re: Annotated version of SRT Python <python@invalid> - 2022-05-19 18:46 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-19 10:22 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-20 09:42 +0200

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