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

Den 18.03.2024 10:52, skrev Richard Hachel:

Le 17/03/2024 à 14:43, "Paul B. Andersen" a écrit :

Don't be ridiculous.
An intelligent Doctor and scientist like you will obviously
understand that since the equations:
  Speed of rocket in inertial frame:             Vr=a.Tr
  Average speed of rocket in the inertial frame: Vrm=(1/2)Vr
  are valid _only_  in Newtonian Mechanics with Galilean relativity,
  then the theory which is consistent with said equations
  is Newtonian Mechanics.
>
Or don't you? :-D

 I don't understand why a man like you, who has repeatedly shown in his speeches that he has a good command of his subject, cannot listen to what I say.

I am listening to what you say.
You say:
Speed of rocket in inertial frame:             Vr=a.Tr
Average speed of rocket in the inertial frame: Vrm=(1/2)Vr
These statements are valid _only_ in Newtonian Mechanics
with Galilean relativity, so the theory which is consistent
with said equations is Newtonian Mechanics.
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.
a = 10 m/s² = 1.05265 ly/y/y   c = 1 ly/y  d = 12 ly
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)
The rocket will pass Tau Ceti at the terrestrial time:
  t = √(2⋅d/a) = 4.7764 y
The proper time of the rocket when it passes Tau Ceti is:
  τ = √(2⋅d/a) = 4.7764 y
The speed of the rocket in the terrestrial frame
when it passes Tau Ceti is:  v = a⋅t = 5.2860 ly/y
The average speed is: vₘ = a⋅t/2 = 2.6430 ly/y
Note that d/vₘ = 4.5403 y < t    Why :-D
According to SR:
================
The rocket will pass Tau Ceti at the terrestrial time:
  t = √((d/c)²+2⋅d/a) = 12.9156 y
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
The average speed is:
   vₘ = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t = 0.9291 ly/y
Note that  vₘ/v > 1/2
==========================================================================

I will never question your intellectual qualities.
I have begged you many times to breathe calmly as you read me.
What I blame you for is your impatience and your lack of listening.
You tell me, Paul, that my equations are Newtonian physics, which is both untruthful and at the same time proof that you are not reading me correctly.

The point is that with the starting point v = a⋅t and vₘ = a⋅t/2
you can't get anything but Newtonian mechanics.

 I beg you, once again, to look at this, and tell me if these are Newtonian equations.

I see a number of equations with no definition of the entities in
the equations. So they are meaningless.
But i guess they all are inconsistent with your equations
v = a⋅t and vₘ = a⋅t/2

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 R.H.
 

--
Paul
https://paulba.no/