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Re: Annotated version of SRT

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Am 15.05.2022 um 04:29 schrieb JanPB:
>> But apparently you know how to derive Einstein's equation. So, please
>> >let me know, how that works.
> It's written out in the paper.  Given the equation  (1/2)*(tau_0 + tau_2) = tau_1,
> one differentiates it wrt  x'  and that yields the equation constraining  the
> A  and  D  constants.


Einstein did something VERY nasty:

he reused the symbol tau for two different things.

a) One is a time measure called tau

b) another one is a function called tau.

Now he used the time measure tau from a) in the equation (1/2)*(tau_0 + 
tau_2) = tau_1

But he used the function tau in the partial differential equation.

That tau is a coordinate transformation in form of a function of 
four-vectors, which produces transformed four vectors.

Now we cannot equate both uses of the same symbol, because both denote 
different types of mathematical objects.

But to use a measure in a differential equation would not make sense, 
because tau a) means 'local time measure in system k'.

We can only differentiate functions, hence must use b) here.

The differential equation is derived from a vector equation, which is 
also wrong.

There were a number of errors in the vector equation.

One simple thing is, that tau_0 is not equivalent to 't', because 't' 
has no index, while tau_0 has.

Also an error is, that vectors have brackets and functions have 
brackets, too. This would require a form like "...tau((x,y,z,t))..." 
with double-brackets.

Another error is, that a linear function tau would allow to multiply the 
factor 1/2 into the brackets and from there into the vectors.

This would require x'=0, what is wrong, because for v>0 x'is moving in 
K, hence can be zero only for a certain point in time.


At a different point in time we have t=tau=0.

Now we could plug in t=0 into the vector equation and see, what we get 
for that value:

1/2(tau(0,0,0,0) + tau(0,0,0, x'/(c-v) + x'/(c+v)) = tau(x',0,0,x'/(c-v))


tau is a linear coordinate transformation, hence must transform the zero 
spot of k to the zero spot of K for the condition t=tau=0.

But the vector equation does not, because the point x' is not zero at 
time t=tau=0. Now a linear function tau cannot produce (0,0,0,0) from 
(x',0,0,x'(c-v)) for non-zero x', if also (0,0,0,0) shall transform to 
(0,0,0,0), because that would require a curved function, which is not 
linear.


TH

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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

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