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

Le 19/03/2024 à 20:44, "Paul B. Andersen" a écrit :

Den 19.03.2024 09:50, skrev Richard Hachel:

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

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We can now review the journey to Tau Ceti.
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Both Earth and Tau Ceti are considered to be inertial.
>
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.
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a = 10 m/s² = 1.05265 ly/y/y   c = 1 ly/y  d = 12 ly

 Richard Hackel uses 10 m/s² = 1.052 ly/y²
but my value above is more precise.
(A year is ≈ 356.25 days, not 365 days)

 If you want.

According to your equations v = a⋅t and vₘ = a⋅t/2:
===================================================
>
d =  ∫a⋅t⋅dt + 0 ly = a⋅t²/2  => t = √(2⋅d/a)
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The proper time of the rocket when it passes Tau Ceti is:
 τ = √(2⋅d/a) = 4.7764 y

 

Absolutely.

 

The speed of the rocket in the terrestrial frame
when it passes Tau Ceti is:  v = a⋅t = 5.2860 ly/y

 My typo:  v = a⋅t = 5.0279 ly/y
 

Yes, Vr=5.0245c

 So your "theory" is identical to NM and predicts
that there is no limit to the speed of the rocket
in an inertial frame of reference.
 You know of course that experimental evidence
show that the speed of an object can't exceed c,
so why do you promote a "theory" you know is false?
 

 BUT: Vo=0.980c
 Observable speeds Vo is not real speeds Vr,

 :-D
 How do you think that inventing a speed that isn't real
can change the fact that your "theory" predicts that it
is no limit to the speed of the rocket in an inertial
frame of reference, and therefore is falsified?
--
Paul

 My Dear Paul, I have begged you many times to try to understand what I was saying, and I believe that is an impossible task because you do not WANT to understand.
 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.
Paul! Breathe! Exhale!
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.
Paul! Breathe! Exhale!
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.
Paul! Breathe! Exhale!
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.
In reality, instantaneous transfers of information are evident (Aspect's experience) if one understands what one is doing.
R.H.