Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.physics.relativity > #585341

Re: Annotated version of SRT

Show all headers | View raw

Am 15.05.2022 um 04:49 schrieb JanPB:
..

>>>
>>>
>>> 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",
>
> This is just the 1905 way of saying "let's differentiate this equation
> with respect to  x' ".

That function (NOT equation) was tau and can only differentiated to its 
variables. But x' is not a variable.

In the meant context x' can be treated as a constant.

x' is actually moving in system K, but not in system k.

For the possible case v=0 we have K=k, hence this identity is a possible 
setting, where x' is actually a constant.

Now you cannot differentiate function in respect to constants. That 
would be nonsense, because 'small variations of a constant' are an oxymoron.




>> because x' was defined as position of the mirror at a fixed position in
>> k, but in K-coordinates.
>
> The differentiation means we consider several instances of the experiment,
> each at different  x'  value, and compute the limit of the relevant difference quotient.

'The experiment' cannot be carried out, anyhow, because inertial 
movement of a pair of an emitter and a mirror, seen from a remote 
location in (fast) relative motion, is nothing you could possibly do in 
real.

So, we have here a 'thought experiment', which you do not need to carry 
out with different values for the distance between mirror and emitter.

> In this case the transformation is presumed linear, so it's only necessary to
> consider TWO instances of the experiment, each at different values of  x',
> so Einstein's use of calculus here is an overkill meant to shorten the process.

Well, I think this equation is plain wrong.

And as this particular equation is essential for the entire paper, there 
will be no remainder, if the error is removed.


> It's not wrong.
>
>> 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.
>
> I don't think this is something I can teach you on a forum like this.

A link to the derivation would be sufficiant.

I think, this partial differential equation is nonsense.

  reason:

he attempted to derive a function, which was meant as coordinate 
transformation between system K and k.

As system k is actually the same as system K, but set into motion to 
velocity v, I would simply add the displacement between K and k and the 
case is closed.

For what reason did he develop that partial differential equation, in 
the first place?



>> But there are more problems than that.
>
> There are no problems there.
>
>> E.g. the term ∂τ/∂x' looks like an inverse of a velocity.
>
> Sigh.
>
>> But that was not meant, because we have a very tricky problem here:
>> τ meant two different things, which were only named with the same symbol τ
>> (what I have regarded as very obscure).
>
> I think it's best to leave it at that. You are WAY too confused to be able
> to follow an ASCII forum explanations. I mean it completely sympathetically,
> it would be nice to have a beer in Paris (and visit Daniel Roth at St-Sulpice)
> but one simply cannot physically teach anyone fluent German in 15 minutes.

I see it like this:

Einstein tried to differentiate the (unknown) function tau in respect to 
the constant x'. He used partial derivatives, for what there was no 
reason, because the other variables (y/eta and z/zeta) were not involved.

That looks (at least at first sight) like complete nonsense to me.

If you are able to justify the equation, anyhow, I would like to hear 
from you, how you would do that.


TH
>

Back to sci.physics.relativity | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

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

csiph-web