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

Den 19.03.2024 21:59, skrev Richard Hachel:

 I have told you many times that if we use low speeds, the observable speeds are the real speeds.
This trotting horse, this motorcycle, this passing train.
What I measure is the reality of things.
>
I also said that the nature of space is such that if we want to have a correct notion of speed, we absolutely must use only one watch and NEVER two watches placed in different places.
 The best measure of time will therefore be the mobile's own time, which goes from A to B, and which clicks during both events. There can therefore be no measurement error.
It notes tau (or Tr).
If I want the real speed of a mobile, in the reference frame where I am, I therefore need the AB measurement in this reference frame, BUT the mobile's own time.
 If I make the mistake of taking time A noted by watch A, and time B noted by watch B, I am using two watches placed in two different theaters, and which will never be naturally in tune, because the universe is not “done like that”. The notion of universal present time is as abstract an notion as the notion of a flat earth.
Now, in relativity, this is what we do every day, and we find a measurement that is false, and therefore a speed that is false.
It doesn't matter for low speeds.
But for relativistic speeds, the measurement errors are considerable, and it "seems" to us that nothing can exceed c.
But it is only an abstract idea that is very difficult to disengage from the human mind.
Vo=Vr/sqrt(1+Vr²/c²)
Vr=Vo/sqrt(1-Vo²/c²)
 We then understand that all real speeds are permitted, but that, by the way we use distinct watches,
an impression of speed Vo appears, and it cannot exceed c.
 But this is only a local illusion.

Let's leave the illusionary world and revert to the real world:
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
https://paulba.no/