Jean-Pierre Messager (known as Python) showed his opposition to my formula
relating to the observable speed in relation to the proper time (of the
object or of the rocket).

I wrote:
Vo=aTr/sqrt(1+a².Tr²/c²)

This equation is obviously correct.

But it is better to put the equation
of the speed Vo as a function of the observable time To in the terrestrial
reference frame.

I think that's what he wanted.

We then have:
Vo= sqrt[2ax/(1+(2ax)²/c²)]

Les deux réponses sont équivalentes. L'un est donnée en fonction de Tr
(temps propre), l'autre, de To (temps terrestre), mais c'est la même
chose.

R.H.

Richard "Hachel" Lengrand (M.D.) wrote:
....
> I wrote:
> Vo=aTr/sqrt(1+a².Tr²/c²)
>
> This equation is obviously correct.

No equation is obviously correct. Throwing it out of your hat is
ridiculous.

Assuming that your "Tr" is what is usually called tau (i.e. proper
time of the uniformly accelerated traveler) the correct equation
is :

v = c*tanh(tau*a/c)

v is the instaneous speed of the traveler in Earth's frame.

And I can deduce it from Lorentz Transformations.

> But it is better to put the equation
> of the speed Vo as a function of the observable time To in the
> terrestrial reference frame.
>
> I think that's what he wanted.
>
> We then have:
> Vo= sqrt[2ax/(1+(2ax)²/c²)]

No.

v = at/sqrt(1+(at/c)^2)

Check your derivation, if you have one.

Richard Hachel wrote:

> I wrote: Vo=aTr/sqrt(1+a².Tr²/c²) This equation is obviously correct.
> But it is better to put the equation of the speed Vo as a function of
> the observable time To in the terrestrial reference frame.

A speed can only be registered by local time to a remote observed target.
Never the opposite.

Le 18/04/2022 à 13:47, Python a écrit :
> Richard "Hachel" Lengrand (M.D.) wrote:
> ...
>> I wrote:
>> Vo=aTr/sqrt(1+a².Tr²/c²)
>>
>> This equation is obviously correct.
>
> No equation is obviously correct. Throwing it out of your hat is
> ridiculous.
>
> Assuming that your "Tr" is what is usually called tau (i.e. proper
> time of the uniformly accelerated traveler) the correct equation
> is :
>
> v = c*tanh(tau*a/c)
>
> v is the instaneous speed of the traveler in Earth's frame.
>
> And I can deduce it from Lorentz Transformations.
>
>> But it is better to put the equation
>> of the speed Vo as a function of the observable time To in the
>> terrestrial reference frame.
>>
>> I think that's what he wanted.
>>
>> We then have:
>> Vo= sqrt[2ax/(1+(2ax)²/c²)]
>
> No.
>
> v = at/sqrt(1+(at/c)^2)
>
> Check your derivation, if you have one.

There are three ways to calculate v.

Either we go through the proper time of the object (usually the rocket),
or we go through the time of the external observer (terrestrial).

If we go through the proper time Tr (which you can call tau if you want),
we set:
Vo=aTr/sqrt(1+a².Tr²/c²)

If we go through the distance noted by the observer, we note:
Vo= sqrt[2ax/(1+(2ax)²/c²)]
Or, Vo/c = [c²/2ax + 1]^(-1/2)

If we go by Vr :
Vr²=2c²[sqrt(1+To².a²/c²)-1] then Vo=Vr/sqrt(1+Vr²/c²)

R.H.

On Monday, April 18, 2022 at 8:44:31 AM UTC-7, Richard Hachel wrote:
> Le 18/04/2022 à 13:47, Python a écrit :
> > Richard "Hachel" Lengrand (M.D.) wrote:
> > ...
> >> I wrote:
> >> Vo=aTr/sqrt(1+a².Tr²/c²)
> >>
> >> This equation is obviously correct.
> >
> > No equation is obviously correct. Throwing it out of your hat is
> > ridiculous.
> >
> > Assuming that your "Tr" is what is usually called tau (i.e. proper
> > time of the uniformly accelerated traveler) the correct equation
> > is :
> >
> > v = c*tanh(tau*a/c)
> >
> > v is the instaneous speed of the traveler in Earth's frame.
> >
> > And I can deduce it from Lorentz Transformations.
> >
> >> But it is better to put the equation
> >> of the speed Vo as a function of the observable time To in the
> >> terrestrial reference frame.
> >>
> >> I think that's what he wanted.
> >>
> >> We then have:
> >> Vo= sqrt[2ax/(1+(2ax)²/c²)]
> >
> > No.
> >
> > v = at/sqrt(1+(at/c)^2)
> >
> > Check your derivation, if you have one.
> There are three ways to calculate v.
>
> Either we go through the proper time of the object (usually the rocket),
> or we go through the time of the external observer (terrestrial).
>
> If we go through the proper time Tr (which you can call tau if you want),
> we set:
> Vo=aTr/sqrt(1+a².Tr²/c²)
>
> If we go through the distance noted by the observer, we note:
> Vo= sqrt[2ax/(1+(2ax)²/c²)]
> Or, Vo/c = [c²/2ax + 1]^(-1/2)
>
> If we go by Vr :
> Vr²=2c²[sqrt(1+To².a²/c²)-1] then Vo=Vr/sqrt(1+Vr²/c²)
>
> R.H.

Do they allow total nutters to practice medicine in France? No wonder France is so deep into shit.

Le 18/04/2022 à 17:52, "Dono." a écrit :

>> Vo=aTr/sqrt(1+a².Tr²/c²)

>> Vo= sqrt[2ax/(1+(2ax)²/c²)]
>> Or, Vo/c = [c²/2ax + 1]^(-1/2)
>> Vr²=2c²[sqrt(1+To².a²/c²)-1] then Vo=Vr/sqrt(1+Vr²/c²)

>> R.H.

> shit.

No comment.

R.H.

On Monday, 18 April 2022 at 13:47:26 UTC+2, Python wrote:
> Richard "Hachel" Lengrand (M.D.) wrote:
> ...
> > I wrote:
> > Vo=aTr/sqrt(1+a².Tr²/c²)
> >
> > This equation is obviously correct.
> No equation is obviously correct. Throwing it out of your hat is

Oh, stinker Python is opening its muzzle again,
and trying to pretend he knows something.
Tell me, poor stinker, what is your definition of
a "theory" in the terms of Peano arithmetic?
See: if a theorem is going to be a part of a theory,
it has to be formulable in the language of the
theory. Do you get it? Or are you too stupid even for
that, poor stinker?