Re: [SR] Usefulness of real velocities in accelerated relativistic frames of reference.

Den 19.03.2024 10:17, skrev Richard Hachel:

Le 18/03/2024 à 22:12, "Paul B. Andersen" a écrit :

 A rocket is stationary on  Earth, When its clock show  τ = 0 and
the Earth clock show t = 0 the rocket engine starts an give
the rocket a constant proper acceleration a = 10 m/s².
 a = 10 m/s² = 1.05265 ly/y/y   c = 1 ly/y  d = 12 ly
 >> According to SR:
================
>
The rocket will pass Tau Ceti at the terrestrial time:
  t = √((d/c)²+2⋅d/a) = 12.9156 y

 Absolutely.
 

The proper time of the rocket when it passes Tau Ceti is:
  τ = (c/a)⋅arsinh(a⋅t) = 3.13894 y

 Here is the error.

No error!
What SR predicts is not a matter of opinion,
it is a matter of fact.
So _ACCORDING TO SR_:
======================
The proper time of the rocket when it passes Tau Ceti is:
  τ = (c/a)⋅arsinh(a⋅t) = 3.13894 y
The speed of the rocket in the terrestrial frame
when it passes Tau Ceti is:
   v = a⋅t/√(1 + (a⋅t/c)²) = 0.9973 ly/y
Facts. Indisputable!

Physicists use the Minkowskian metric and it is not correct.

So you are saying that the predictions of SR are wrong
because the metric is wrong.
You are of course free to have that opinion, but remember that
SR is confirmed by innumerable experiments, and falsified by none.

You have to use (I understand that this is confusing) the Newtonian equation.
Physicists absolutely need to understand something:
the rocket is AT REST in its frame of reference, and it is from start to finish.

Everything happens, for her, as if the surrounding space were accelerating by 10m/s² around her.

Ah! This is an old, rather stupid misconception:
The twins must age equally because of the symmetry,
both the speed and acceleration of the other twin
are equal for both twins.
This is obviously nonsense. SR do predict that
the twin's age differently. Math don't lie!
https://paulba.no/pdf/TwinsByMetric.pdf
Consider this simple thought experiment:
Two rockets A and B are instantly side by side.
A is accelerating at 10m/s², B is inertial.
Will "everything happen to the astronaut in A as if
she were inertial, and B and the surrounding space were
accelerating by 10m/s² around her"?
Think of it. The answer is rather obvious.

The big complaint (because it's confusing when you don't have 40 years of thinking on the subject like me) is to say: "Yes, but the more time passes, the more the surrounding space will contract. for the rocket, and therefore Vr=a.Tr is no longer valid".

It's pathetic, and a bit sad, to have thought in 40 years
to come up with utter nonsense.

<snip nonsense>

--
Paul
https://paulba.no/