Re: [SR] The traveler of Tau Ceti

Le 20/03/2024 à 20:18, "Paul B. Andersen" a écrit :

Consider an inertial observer in space.
She has instruments like clocks and telescopes and computers,
so she can measure the speed of a passing rocket relative
to herself.
Please don't say that this in principle is impossible in the real world.
 Eleven such observers (O_0 ..O_10) are stationary relative to each
other, and are arranged along a straight line with 1 light year
between them.
A rocket which is accelerating at the constant proper acceleration
a = 1 c per year is instantly at rest relative to O_0.
The rocket is moving along a line parallel to the line of observers.
 c = 1 light year per year.
 Please show what you think the observers O_1 to O_10 would
measure the speed of the rocket to be relative to themselves.
  Paul

The answers I can give you are very simple as long as you understand correctly what I am saying.
But I repeat again and again, observable speeds are not real speeds. This is very important to understand, because you will realize that things will logically start to go wrong.
If you use real speeds (Vr) you will no longer have any problems, and the equations will remain both simple and true.
If you use traditional observable velocities (v or Vo)
you will notice that the observable speeds can be different for various observers present in the same frame of reference. Which may seem absurd if we do not understand that, precisely, these speeds are not real but a distortion of what is real.
I can easily give you all the equations you need.
Here you are asking me what is the instantaneous observable velocity for each point placed on the path as the rocket passes in front of it.
We have :
Voi/c=[1+c²/2ax]^(-1/2)
That's not what the relativists say.
They give too high instantaneous speeds (like you).
But that’s THEIR problem.
Same thing for clean times. They give clean times that are too low.
tau=sqrt(2x/a)
To=(x/c).sqrt(1+2c²/ax)
R.H.