Re: [SR] The traveler of Tau Ceti

Den 19.03.2024 09:35, skrev Richard Hachel:

The Traveler of Tau Ceti
 The Tau Ceti Traveler is a relativistic problem imagined by theorist Richard Hachel to describe what would happen to a traveler leaving to join Tau Ceti in accelerated mode.
 We assume that the Sun-Tau Ceti system is stationary.
 We set x=12 light years.
 Thanks to new technology, we use a comfortable acceleration of a=10m/s² (a=1.052ly/y²).
 At the start, we start all the watches. The terrestrial time is noted To=0, the rocket's own time is noted τ=0.
 The problem consists first of determining what the travel time will be for the traveler, and what will be the observable times To (in the terrestrial reference frame) and apparent Tapp (what we see in a powerful telescope) noted by the sedentary observer.

You have in another posting said that the traveller's clock
would show  τ = √(2⋅d/a) = 4.7764 y , and the speed relative to
Tau Ceti would be Vr = a⋅t = 5.0279 ly/y when she passes the star.
Since it is experimentally confirmed that the speed relative
to the star never can exceed c, the theory you have used
to arrive at these predictions is obviously falsified.
The "theory" is obviously Newtonian mechanics with Galilean relativity.

 The problem then consists of determining the instantaneous observable velocity (Voi) at the moment when the rocket will cross Tau Ceti,

What's the point with inventing an apparent (not real)
"observable velocity" which is less than c when you know
  that the real velocity according to your theory is > c?

and its instantaneous acceleration measured in the terrestrial reference frame.

The coordinate acceleration in the terrestrial frame is obviously a.

 Finally, to determine, while we know that the rocket will be 12 light years from the earth at this instant, how far the earth will be from the rocket in the rocket's frame of reference.

According to your theory (NM), the Earth will be 12 ly away from
the rocket measured in the rocket's instant rest frame.
--
Paul
https://paulba.no/