Re: Relativistic aberration

Le 07/08/2024 à 12:05, film.art@gmail.com (JanPB) a écrit :

The visual field differences between observers are known and regardless
of
the details of the motion are always related by a conformal map. This
alone
accounts for things like the appearance of the outline of a moving
sphere,
the Tyrell "rotation", etc.
 Also keep in mind that the two observers, even if they are momentarily
at the same place, will have different visual fields due to the retinas
of their eyes (which are of *finite* extent (i.e., not pointlike))
accounting differently for the visually observed scene because of the
different simultaneity for the two observers.
--

Your post is interesting in the sense that it clearly tries to say things.
It is appreciated.
Even if I do not totally agree with you.
So I can ask you two questions:
"Are you for me or against me when I interpret the Poincaré Lorpetz transformations as Poincaré described them?"
I interpret them literally, and not like Python (who is crazy) and not like Paul B Andersen (who is intelligent and courageous), because I interpret them as a translation, and not as a rotation.
I do not vary in y or z. Secondly, it is necessary to clarify things:
According to Hachel, and always in accordance with logic, with truth, and with the equations of Poincaré, who was not weak in mathematics, the notion of simultaneity is invariant by change of observer JOINT at the moment of measurement, what varies for them is the INTERNAL CHRONOTROPY, and not the notion of simultaneity.
For example, a terrestrial observer observes the simultaneous bursting of three supernovae (it is very improbable but let's admit it) in very different places of the cel, and at very different distances.
At this moment, a rocket crosses the solar system at 0.8c (we admit that it is technologically possible on the Ox axis of R (earth reference frame).
Simplicity (and the TLs) shows that the terrestrial observer and the rocket observer will perceive the three explosions at the same time. This obviously implies that they see the same simultaneous universe. Nothing that is perceived by one is not perceived by the other and vice versa. Likewise, nothing that is not perceived by one is perceived by the other.
Both see the universe in perfect simultaneity.
Simply, things are spatially seen as through a distorting mirror, and we must apply x'=(x+Vo.To)/sqrt(1-Vo²/c²) for the x component.
The t component does not vary. t'=t=0.
The To component varies To'=(To+x.Vo/c²)/sqrt(1-Vo²/c²), but that's not relevant here.
The problem is that we confuse t and To too much (t being real time measured by real watches, To being a useful, but abstract, unit).
R.H.