Physicists treat the problem of traveling in the constellation Centaurus
(three bickering suns there) differently from me.
D=4.5ly in their example.
g=10m/s².
They find like me, 5 years and 133 days for the terrestrial observer.
One can thus validate, I think, the calculations since obtained
differently but relating to the same problem.
Where it's weird is that they find it FIRST, then calculate the time taken
by the observer in the rocket THEN. And there, they no longer have the
same result as me.
The oddity comes from the fact that I am good at the FINAL of the problem.
And they only at the first phase. How to explain this? ? ?
Moreover, I proceeded by small integrations, and the result of all my dt'
is the one expected, and not theirs, much too weak.
How to explain that I can give a good final result going through the first
observer
(stellar) to then move on to the second observer (terrestrial)?

Whereas, for them, the reverse is not true. They give a first correct
result, identical to my final result, but their sequence is no longer
consistent with my first result (which one wonders how it could be wrong,
since my second which is correct is based on the first).

I hope to make myself understood.

I say I hope because I know the stupid behavior of some speakers who only
come here to fight, and not to think about some interesting problems.

My first result (traveler himself) was two years and 338 days.

The result they give (and which I think is wrong and based on poorly
established concepts) is two years and 114 days.

The difference is quite considerable.
Anyway, I looked for where could be MY error (although it is still me who
has a FINAL result which we know is absolutely correct), or theirs.

In my calcul, I found nothing very suspicious.

With them, I notice that they proceed by a somewhat dubious infinitesimal
integration, where they
claim that one can neglect the velocity increment in their equation.

It seems weird to me to act like that.

I agree that if we order three million tons of rice from China, and a
grain of rice falls on the boat, we are not going to quibble over the
order of three million tons.

This is called a negligible factor.

But mathematics being an exact science, can we neglect a speed increment
dv, in an equation where we seek the sum of all the increments dt'data
according to the increments dt and the increment dv due to an acceleration
of 10m /s²?

In short, can we say that S dt' = S dt.sqrt(1+(Vr+g.dt)²/c²)
it's the same as S dt' = S dt.sqrt(1+(Vr²/c²) if dt' is very small?
When Vr is small, yes, why not... But when Vr approaches (or exceeds)
light speeds,
which is the case only in this chosen example (since Vr =1,025c) in Hachel
notation, I am not at all sure that to neglect dt at this place, i.e. all
the same dv=g(2dt.t+dt² ) that's such a good idea?

It's a bit like being told that the length of a diagonal of a 3 by 4
rectangle is 7.

It's not that it's wrong that 3+4 is 7.

It's just that if we know Pythagoras, that's 5.

What do you think about that problem?

R.H.

Richard Hachel wrote:

> […] traveling in the constellation Centaurus

You cannot travel in (or to) a constellation as that is merely a projection
of the star background onto a virtual sphere (the celestial sphere) as seen
from a particular vantage point (here: Terra).

The stars of a constellation typically have nothing else to do with each
other and are very far away from each other (i.e. they are NOT neighboring
stars).

For example, the radial distance between Alpha Centauri C (Proxima Centauri)
and Beta Centauri Aa (Hadar) is ≈ 520 light-years.

<https://en.wikipedia.org/wiki/Constellation>

> (three bickering suns there)

The _Alpha Centauri System_ is a trinary (or triple) star system. Only
those three stars are relatively close to each other (compared to the
distances between each of them and other stars):

<https://en.wikipedia.org/wiki/Alpha_Centauri>

PointedEars
--
Two neutrinos go through a bar ...

(from: WolframAlpha)