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

Groups > sci.physics.relativity > #584168

Re: Annotated version of SRT

Show all headers | View raw

Am 26.04.2022 um 08:52 schrieb JanPB:
> On Monday, April 25, 2022 at 10:02:19 PM UTC-7, Thomas Heger wrote:
>> Am 25.04.2022 um 21:22 schrieb JanPB:
>>> On Monday, April 25, 2022 at 12:52:14 AM UTC-7, Thomas Heger wrote:
>>>> Am 24.04.2022 um 10:52 schrieb JanPB:
>>>>
>>>>>> But even if so, x' would still be zero.
>>>>>
>>>>> Yes, you get x' = 0 for the emitter/receiver because its location
>>>>> by construction of this experimental setup satisfies x = vt at
>>>>> all times t, hence the corresponding x' value is:
>>>>>
>>>>> x' = x - vt = 0
>>>>>
>>>>> throughout.
>>>> Here you actually agree, that x'=0 must be true.
>>>
>>> For the *light source*.
>> No, this is wrong because Einstein had a different setting:
>>
>> [quote]
>>
>> "From the origin of system k let a ray be emitted at the time τ'along
>> the X-axis to x' and at the time τ_1 be reflected thence to the origin of
>> the coordinates, ..."
>>
>> [/quote]
>>
>> The system k was the moving system, hence Einstein wanted a moving
>> emitter and a stationary mirror.
>
> Both the light source and the mirror are stationary in  k  because that's how
> the (1/2)*(tau_0 +tau_2) = tau_1 criterion has been set up previously (in section 1).

The coordinates in k had small Greek letters as names.

Therefore x' must be a coordinate from system K.

On the other hand, the origin of the ray needs a coordinate in k, too, 
which had to be xsi=0.

If now the mirror is stationary in respect to xsi=0, it cannot have a 
fixed position in K, but should move to 'the right' with velocity v.

So, your statement cannot be true, even if your argument with the 
equation you have quoted is correct.

But a mirror stationary in respect to the emitter cannot possibly be 
meant, because in this case we would not have a use for velocity v.

Actually the system K could be left away entirely in this case.

So, something is wrong, because every possible interpretation would 
require to change something a little.

In effect we are lost and should think about an interpretation, where 
the number of errors is minimized.

Your proposal would fit to the equation (1/2)*(tau_0 +tau_2) = tau_1, 
but would render the subsequent equations useless.

Also missing is in this case a defintion of x'.

Emitter and mirror should not coincide, but should have a little 
distance. But what distance is appropriate?

The next question would be, how we make use of system K in a scenario, 
which does not include system K.


>> The mirror should be located at x', because the text says so.
>
> Yes.
>
>> Because the zero spot of k has the x-coordinate in K of
>> xsi_0 = x_0 * v*t
>
> If you say "x-coordinate", then don't say "ksi".  So again: if we assume,

The naming convention of Einstein was, that the moving system k had 
small Greek letters as symbols for the coordinate values and the system 
K had small Latin letters.

So xsi would be the equivalent to x, but in system k, while x belongs to 
K, with xsi=x+v*t.

  xsi=x+v*t could be transformed to x= xsi - v*t, what looks quite 
similar to Einstein's equation x'=x-v*t, especially if we exchange the x 
for xsi and the x' for x.

But you are right, that in this case the equation

(1/2)*(tau_0 +tau_2) = tau_1

cannot be kept, if v is not equal to 0.

So, there is actually no possibility, which would leave the text intact, 
hence we need to decide for a ssolution, which minimzes errors.




> as Einstein did, that:
>
> (1) the ray is emitted from the origin of  k,
>
> (2)  the origins of  K  and  k  coincide when  t = 0  and  tau = 0,
>
> (3)  the ray is emitted at some  K-time  value of  t_0,

No, that is not a possibility.

If the ray is emitted at t =tau=0, the ray would point away from the 
zero spot of K, where the mirror should be placed. That would exclude 
the possibility of a reflection.

The reason: if emitter and mirror coincide, the ray would point away 
from the mirror, wherever the ray is pointed to.

Also: rays are not momentary events, but have a duration, what does not 
fit to a time t=0.

Also: time should remaind the independent variable, hence all values for 
time should be possible.


>
>      THEN:
>
> (a) the  K  x-coordinate  x_0 of the emission satisfies:  x_0 = v*t_0,
>
> (b) the  K  x-coordinate  x  of the light ray pulse at subsequent times
> t  satisfies:L  x = x_0 + v*(t - t_0).

To apply a duration of the light beam would be a very bad idea!

The equation was not about a pulse. Meant was the duration of the travel 
of the ray between emitter and a mirror and on the way back. The length 
of the pulse was irrelevant.

We are still discussing the question, where we want to place the mirror 
and which state of motion this mirror had.

My proposal was, that Einstein meant a scenario, where the emitter is 
placed at point xsi=0 in k and the mirror is placed at x'=0 in K.

Your proposal was, that the emitter was placed at xsi=0 in k and the 
mirror at a point x'=xsi_mirror= -something (a negative xsi-value, 
unknown, but fixed).

Unfortunately both proposals would cause trouble in subsequent parts of 
the text, though different trouble in different parts.



> (Note that for  t = t_0  we get  x  = x_0,  as expected.)
>
> But  x = x_0 + v*(t - t_0)  means that  x - v*t = x_0 - v*t_0.
>
> By item (a) the RHS is equal to zero.  Hence the combination  x - v*t
> is equal to zero for all times  t  following the emission (until the
> reflection which alters this pattern). Einstein labels this combination
> by  x'.
>
> Similar consideration yields  x' = constant  (NOT equal to zero) for the mirror.

You should say, which coordinate system you mean.

Above you wrote, that mirror and emitter would not move inrespect to 
each other. That would say, that x' is actually a xsi coordinate in k. 
That would need to have a negative value, because the mirror should be 
placed in the direction of the beam, which was assumed to point towards 
smaller values (to the left).

In this scenario, the system K could be left away entirely, because it 
would not be involved in the situation anymore.

That in turn would exclude the use of coordinates from K (x, y, z and t) 
and from velocity v.

And that would leave a lot of empty space in the following text.



>> we end up at the zero spot of K, if we subtract v*t from xsi_0.
>>> The differentiation OTOH is taken with respect to the *mirror* position
>>> (denoted by x' by the abuse of notation) which is nonzero (obviously).
>> No, x' is OBVIOUSLY the zero spot of K.
>>
>> It makes no sense to write partial differential equations for a problem,
>> where only the x-axis is involved.
>
> Both sides are functions of  x'  so they can be differentiated
> with respect to  x'.

No. The function tau is a function of time, which produces a value for x 
at time t, with:
tau(t)=x=v*t

You could also mean a function tau(x)=t, but that would not make much 
sense, because you cannot possibly say, that time would be depending on 
the coordinates of a point.



>> But still we cannot differentiate a
>> fixed position, at least not in K.
>
> When you perform differentiation, you consider multiple instances of the
> function values and evaluate the resulting difference quotient limit.

Sure, but how do you do this with zero?

If you have only a fixed value of zero, there would be nothing to change.

We can change time, however, and let the clocks run for some time, say a 
day.

After that day the position x had still the value zero.

That is, btw, the reason, why time must be the independent variable and 
not the x-coordinate of the mirror.

> In this case one considers instances of the experiment with different
> values of  x'.

Sure. It is possible to chose other places for the mirror, as long as 
the mirror remains at that position.

But the position was not yet specified, anyhow, hence any possition is 
possible, as long it remains fixed.

>
>> Seen from the emitter, the mirrors moves and we have the usual relation
>> v= x'/d tau.
>
> Again, a typo?

No. I meant a velocity of the mirror, which is measured with measures 
from system k.

You had a different setting, where v=0, while I used the defintion of v 
as velocity of system k in respect to system K, where v<>0.

This velocity is v = x'/d tau

>
>> Now Einstein used the inverse 1/v in his equation, what is blatant nonsense.
>
> There is no  1/v  there.

Sure, because he wrote del tau /del x'
  in the equations in the middle of page 6

Since there is no 'del' in the position (because the position is fixed), 
I took x'.

But possibly you are right, and I should use zero in the denominator 
instead.

>
>> This is nonsense, because the possible case of v=0 would produce an
>> infinite term.
>
> Sure but there is  1/(c-v)  and  1/(c+v)  there.

Actually I meant the next equation a little below.

That does not contain  1/(c-v)  and  1/(c+v).
>
>> I have complained about this fact a number of times, but instead of a
>> positive reply I was called a nutcase.
>
> You claim something that's not there.

Sure, it was my interpretation of the text.

Seemingly my interpretations were not correct, despite serious efforts 
to understand the text correctly.


Therefore I leave it to you and allow you to decide, where the emitter 
and the mirror shall be placed.

...


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> - 2022-04-22 09:00 +0200
  Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-22 01:41 -0700
    Re: Annotated version of SRT Dong Vassilikos <saox@cowrpsho.rb> - 2022-04-24 12:23 +0000
  Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-22 15:39 +0200
    Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-22 07:11 -0700
    Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-23 07:55 +0200
      Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-23 03:34 -0400
        Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-23 11:52 +0200
          Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-23 05:49 -0700
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-24 08:07 +0200
            Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-24 01:52 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-25 09:52 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-25 12:22 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-26 07:02 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-25 23:52 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-26 22:24 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-26 17:35 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-27 07:59 +0200
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-28 07:14 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-28 01:45 -0700
                Re: Annotated version of SRT Rady Konoe <akde@oakoradn.en> - 2022-04-28 09:03 +0000
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-29 08:08 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-29 20:51 -0700
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-29 21:03 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-30 07:47 +0200
                Imbecile Thomas Heger perseveres "Dono." <eggy20011951@gmail.com> - 2022-04-30 07:00 -0700
                Re: Imbecile Thomas Heger perseveres Richard Hachel <r.hachel@tiscali.fr> - 2022-04-30 14:44 +0000
                Re: Imbecile Thomas Heger perseveres "Dono." <eggy20011951@gmail.com> - 2022-04-30 08:19 -0700
                Re: Imbecile Thomas Heger perseveres Richard Hachel <r.hachel@tiscali.fr> - 2022-04-30 15:28 +0000
                Re: Imbecile Thomas Heger perseveres Odd Bodkin <bodkinodd@gmail.com> - 2022-04-30 15:33 +0000
                Re: Imbecile Thomas Heger perseveres Richard Hachel <r.hachel@tiscali.fr> - 2022-04-30 17:56 +0000
                Re: Imbecile Thomas Heger perseveres Thomas Heger <ttt_heg@web.de> - 2022-04-30 20:15 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-30 19:02 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-01 10:15 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-02 00:15 -0700
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-02 00:40 -0700
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-28 16:44 +0000
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-28 23:15 -0700
                Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-29 14:30 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-29 06:45 -0700
                Re: Annotated version of SRT Richard Hachel <r.hachel@tiscali.fr> - 2022-04-30 19:50 +0000
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-30 21:43 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-29 08:22 +0200
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-29 12:52 +0000
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-29 13:06 +0000
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-29 06:47 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-01 09:59 +0200
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-05-01 12:16 +0000
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-02 08:03 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-01 23:31 -0700
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-02 00:18 -0700
        Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-24 07:49 +0200
          Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-24 01:23 -0700
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-24 11:08 +0200
              Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-24 05:14 -0700
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-24 12:46 -0700
                Re: Annotated version of SRT Dong Vassilikos <saox@cowrpsho.rb> - 2022-04-24 21:09 +0000
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-25 10:23 +0200
              Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-24 12:56 -0400
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-25 10:09 +0200
                Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-25 11:51 -0400
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-26 07:22 +0200
      Re: Annotated version of SRT Cody Sakellariou <yall@ckcldcdd.ar> - 2022-04-23 07:59 +0000
      Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-23 12:56 +0000

csiph-web