Re: Langevin's paradox again

Den 11.07.2024 02:02, skrev Richard Hachel:

Le 10/07/2024 à 20:56, "Paul.B.Andersen" a écrit :

Den 09.07.2024 15:47, skrev Richard Hachel:

 The paradox is this: The greatest relativistic physicist in the universe (Richard Hachel) said that the effects of physics
are reciprocal by permutation of observer, and therefore, if we take the INTERNAL mechanism of two watches, each will beat faster than the other, both on the outward and return journey, or during a long circular journey.

Richard Hachel claims:
"each [clock] will beat faster than the other,
both on the outward and return journey"
This is obviously a nonsensical statement.
However, I have chosen to interpret the statement like this:
"Each twin will measure the other twin's clock to beat slower
  than his own clock, both on the outward and return journey".
If this (mutual time dilation) were the case, both twin's clocks
would obviously show the same at the end.
They don't.

 Let's look at the following scenario:
>
- Twin A and twin B are inertial and co-located.
- Twin B accelerates at the proper acceleration 2 c/year
   away from A for 1 light year [ly] in A's rest frame.
- Twin B  coasts (no engine) for 8 light years until he is 9 ly from A.
- Twin B accelerates at 2 c/year towards A. He will reach 10 ly and
   go back to 9 ly when he stops the engine.
- Twin B coasts from 9 ly to 1 ly-
- Twin B accelerates at 2 c/y until he is co-located with A.

The point with this scenario is that both twins are inertial
for most of the journey.
I could obviously have calculated the result from the metric
like I have done with the scenario where twin B is accelerating
during the whole journey:
https://paulba.no/pdf/TwinsByMetric.pdf
(Note that the simulation
   https://paulba.no/twins.html
gives exactly the same result)

>
>
Note:
While B is coasting and inertial we have two inertial twins
moving at the constant speed 0.943 c relative to each other,

Look at the run of the simulation:
https://paulba.no/temp/Twins_run.pdf
You could say:
"When both twins are inertial each twin will measure the other
  twin's  clock to beat slower than his own clock, both on
  the outward and return journey".
Which would make your statement above partly right.
But what happens when twin B is accelerating makes all the difference.

 This value is calculated starting from Minkowsky's four-dimensional space-time which is only one of the possible understandings of Lorentz transformations and the relationships between space and time.

Don't be ridiculous. This is according to SR, and there is only
one possible solution. It doesn't matter if you start with the metric
or the Lorentz transform, the result is the same because the latter
follows from the former.

Mine is directly calculated with the new and direct equation Voi/c=[1+c²/2ax]^-(1/2)
And I find Vo=0.8944c and not Vo=0.943c. The values ​​given are always too high among relativists for instantaneous observable speeds.
 

Yet B ages 9.18 years while A ages 22.63 y.

Which is the only result SR can give.

 That's not what I find.
Tr=11.155 years
To=23,544 years.

Quite.
We know that your "theory" is falsified and gives the wrong results.
SR is however thoroughly tested and never falsified.

 The fact that in my opinion there are two errors comes from the fact that, as I have always said, the instantaneous observable speeds are given too high, this makes an error for To; and the natural times of the accelerated objects are given a little too low, this gives an error for Tr.
 R.H.

Physics isn't a matter of opinion, it is a matter of
experimental evidence.
If you claim SR is wrong, you better give reference
to an experiment which falsify SR.
Here are a few experiments which fails to falsify SR:
https://paulba.no/paper/index.html
--
Paul
https://paulba.no/