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

Den 19.03.2024 09:50, skrev Richard Hachel:

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

>
We can now review the journey to Tau Ceti.
>
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)

>
According to your equations v = a⋅t and vₘ = a⋅t/2:
===================================================
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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
https://paulba.no/