In an accelerated movement, as for example in the problem of Tau Ceti,
created by the immense celestial luminary doctor Richard Hachel (that's
me), we describe things like this.
An interstellar rocket will be launched from the earth, with on board
an infant named Bella, who we will not confuse with Stella who will leave
on a Galilean journey, while Bella leaves on an accelerated journey, while
her brother Terrence, born the same day, stay on earth.
We choose, for the purposes of the cause, a precise acceleration of
1.052al/year² in order to maintain a constant artificial gravity of
approximately 10m/s².
It is assumed that Tau Ceti is located exactly 12 feet from the earth.
It is an equation that doctors must know by heart among other
equations, much like we learn by heart our multiplication tables, its
remarkable identities, or the main trigonometric equalities such as
sinµ²+cosµ²=1.
This simple equation is this:
To=(x/c)/sqrt(1+2c²/ax)
It gives the time that the journey will last for a terrestrial observer,
and is in agreement with what all the doctors in the world say. We thus
have the time taken to reach any point of the journey.
We therefore immediately have the duration of the journey: 12.9156 years.
That is approximately 12 years and 334 days (taking into account that a
year is 335.25 days on average).
We can even give the apparent time of the journey, that is to say what
Terrence sees in his telescope when his sister reaches Tau Ceti.
Tapp=24.9156 years.
On this, I repeat, everyone agrees, which attempts to confirm the
reality of things,
even for people who fiercely deny any relativistic phenomenon.
But we must now go further, and ask ourselves the double question of
instantaneous speeds
and average speeds.
History of completing the equations which define the whole of a
journey, accelerated, in a correct way.
So we are going to ask the reader to think about two seemingly simple
things?
What will be the average observable speed (Vom) of the trip upon
arrival at Tau Ceti?
What will be the equation for the instantaneous observable speed (Voi)
at each point of the rocket's path?
Is there a relationship between Voi and Vom? If yes, which one and what
is its reciprocal?
So far so good, no one has thought of making death threats to me. It's
good.
No more if I start to help the reader, and if I assume that for the
final trip, the average observable speed will be Vom=x/To
Or, since x=12 and To=12.9156: Vom=0.9291c
So far so good for everyone.
It's after that that it gets complicated, no one can answer this little
problem due to intellectual incapacity or total ignorance of the
relativistic reality described by me. Everything then collapses into
theoretical, scientific and experimental horror.
With, icing on the cake, this contemptuous: "We are very strong, very
intelligent, and if the RR had flaws, that is recognizable, and it is not
a moron like you who will explain things better than the big bridges
physical."
Here, facing the doctor, the moron is the reader, filled as he is with
ill-gotten certainties, and therefore, ipso facto, with unjustified
arrogance.
I'll let you answer the various questions asked, if you have the
courage. I remind you that the level is classified [hard] knowing that I
do not think that a single doctor in the world can answer correctly
without making huge blunders since no one seems to master the correct
spatio-temporal geometry, nor simply the notion of speed real different
from the notion of observable speed (not to be confused with apparent
astronomical speed which is something else again).
R.H.