Our friend Paul B.Andersen who is one of the best posters on "physics",
and who produces very beautiful pdfs, did not, unfortunately, answer a
question of capital importance,
because it brings into play all the logic, beauty and precision of the
theory of relativity as long as it is understood correctly.

It's a shame, because I appreciate his often competent and detailed
answers.

I posed the problem of the Tau Ceti traveler, a thought experiment
invented some time ago by Doctor Hachel (that's me).

This thought experiment is very simple, and always the same.

We send a space traveler to Tau Ceti, located 12 ly from earth, and we do
so with a constant acceleration motion of about 10m/s² to ensure
artificial gravity in his large ship.

We set a=1.052 ly/y²

We ask when the rocket will pass the 11 ly point and when the rocket will
arrive in the Tau Ceti system (12 ly).

So far, so good.

Paul B. Andersen and Richard Hachel pose the same equation, obtained by
different, but identical, and scientifically correct reflections.

To=(x/c).sqrt(1+2c²/ax)

Let To(11)=11.9127 y
To(12)=12.9156 y

We will then ask something completely fantastic and disorienting: what
is the average speed of the rocket between these two points?

We also ask the question:
What is the instantaneous speed of the rocket as it passes
at point (11ly) and at point (12ly)?

There are therefore three speeds to be determined.

And there, my dear friends, perhaps we will enter the post
the most important and interesting in the whole history of
"sci.physics.relativity".

In manus tuas, Domine.

R.H.

On 2023-10-12 17:00:47 +0000, Richard Hachel said:

> Our friend Paul B.Andersen who is one of the best posters on
> "physics", and who produces very beautiful pdfs, did not,
> unfortunately, answer a question of capital importance,
> because it brings into play all the logic, beauty and precision of the
> theory of relativity as long as it is understood correctly.
>
> It's a shame, because I appreciate his often competent and detailed answers.
>
> I posed the problem of the Tau Ceti traveler, a thought experiment
> invented some time ago by Doctor Hachel (that's me).

Anyone who's been here for a while who doesn't know that "Doctor"
Hachel is you probably doesn't care.

By the way, you still haven't revealed which university awarded your
doctorate in a scientific subject, preferably physics and definitely
not medicine.

--
athel -- biochemist, not a physicist, but detector of crackpots

On Thursday, October 12, 2023 at 11:00:51 AM UTC-6, Richard Hachel wrote:
>
> Our friend Paul B.Andersen who is one of the best posters on "physics",
> and who produces very beautiful pdfs, did not, unfortunately, answer a
> question of capital importance,
> because it brings into play all the logic, beauty and precision of the
> theory of relativity as long as it is understood correctly.
>
> It's a shame, because I appreciate his often competent and detailed
> answers.
>
> I posed the problem of the Tau Ceti traveler, a thought experiment
> invented some time ago by Doctor Hachel (that's me).
>
> This thought experiment is very simple, and always the same.
>
> We send a space traveler to Tau Ceti, located 12 ly from earth, and we do
> so with a constant acceleration motion of about 10m/s² to ensure
> artificial gravity in his large ship.
>
> We set a=1.052 ly/y²
>
> We ask when the rocket will pass the 11 ly point and when the rocket will
> arrive in the Tau Ceti system (12 ly).
>
> So far, so good.

I don't think so, see below.

> Paul B. Andersen and Richard Hachel pose the same equation, obtained by
> different, but identical, and scientifically correct reflections.
>
> To=(x/c).sqrt(1+2c²/ax)
>
> Let To(11)=11.9127 y
> To(12)=12.9156 y
>
> We will then ask something completely fantastic and disorienting: what
> is the average speed of the rocket between these two points?
>
> We also ask the question:
> What is the instantaneous speed of the rocket as it passes
> at point (11ly) and at point (12ly)?
>
> There are therefore three speeds to be determined.
>
> And there, my dear friends, perhaps we will enter the post
> the most important and interesting in the whole history of
> "sci.physics.relativity".
>
> In manus tuas, Domine.
>
> R.H.

The rocket won't make it to 11 ly. After traveling for 6 months,
it was doing 0.466c:

https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

and collided with a denizen of the Oort cloud at 0.124a ly from earth.

https://en.wikipedia.org/wiki/Oort_cloud

Blooie!! I'm afraid that traveling at such high speeds will be
fraught with significant dangers. Better find some other way
to travel.