Re: Well...

Le 24/04/2024 à 22:51, Paul B. Andersen a écrit :

Den 24.04.2024 03:08, skrev Richard Hachel:

We set To²=Tr²+Et²
>
It’s great, life is above all very easy.
>
We take Stella, we calculate her proper time (Tr=4.776 years), her improper time (validated by Terrence, To=12.915 years), her constant speed Vo=0.929c, her distance traveled to Tau Ceti (12al).

 Why do you not define the scenario properly?

It seems to be a typical cranks' habit, doesn't it?

This is a twin scenario where twin A and B both are present at
two events.
Event #0 is that A and B are co-located at the Earth
Event #1 is that A and B are co-located at Tau Ceti
 Given:
In the inertial frame where the Earth and Tau Ceti
are stationary, the distance between them is L = 12 ly.
 Twin A is travelling at the constant speed v = 0.929 ly/y
At Event #0 twin B is stationary, and is accelerating at
the constant proper acceleration 1.052 ly/y².
 The coordinates of event #0 are t₀ = 0, x₀ = 0
The coordinates of event #1 are t₁ = L/v = 12.9171 y, x₁ = L = 12 ly

>
We take Bella, in an accelerated reference frame at 1.052 ly/year², we calculate its proper time, its improper time, and the distance traveled.

 "Improper time" is given, t₁ = 12.9171 y
 According to SR:
Proper time of A:  τ_A = L/γ⋅v = 4.7804 y
Proper time of B:  τ_B = (c/a)⋅arsinh(a⋅t₁/c) = 3.1404 y
 -----------------------
 You like to dream up equations for relativistic speeds which
you believe can't be proven false in the real world.
 You are wrong.
 There are _lots_ of experiments with particles moving with
speed close to c, and even the proper times of particles
at relativistic speeds are measured (muons in storage ring).
 All these experiments which are performed in the real world
confirms SR and falsifies RRH.
 WHY DO YOU KEEP POSTING YOUR FORMULAS WHICH YOU KNOW ARE PROVEN WRONG?

A mix of stupidity, stubbornness, arrogance and ignorance I would say.
His claim is highly suspicious to begin with because a property
depending on a choice of frame of reference (equal distances i.e.
equal spatial paths) cannot imply a frame-independent property
(equality of proper elapsed time). Except, of course, if this
property is always true (like in Galilean Relativity) but then
the condition of equal distances is pointless.
Hachel (aka M.D. Lengrand, go figure!) claims is not only refuted by
experiments but can be proven contradictory and violating the principle
of Relativity (if you assume Galilean Relativity wrong, where elapsed
proper times for both travelers are equal by nature).
Just consider the cinematic of the accelerated traveler from the
point of view of the inertial frame of the other one.
Hachel/Lengrand agrees that if the inertial frame is Earth's one
in such an identical situation elapsed proper times will be
different. But not when the considered frame is the inertial
traveler's one!!! This is obviously contradictory and making
the inertial traveler's frame a absolute one (!!!).
When presented with such obvious logical facts, M.D. Lengrand is
whining like a pig and put his head in sands. As usual...