Re: the notion of relativity of simultaneity

Le 03/10/2024 à 09:12, Thomas Heger a écrit :

 Sure, but mathematicians use the term 'hyperplane' for a lot of other things, too, which have no connections to time.
 It is like a subspace with one dimension less.

The hyperplane of simultaneity is relative.
A does not have the same as B.
B does not have the same as A.
Romeo has his own hyperplane of simultaneity, Juliet, sitting on this other bench has another one.
When Juliet observes Romeo's hyperplane (if she could make it visible) it is clear that she is not observing a hyperplane, but another geometric figure.
This figure is a virtual hypercone, but it is more difficult to represent, and is not very useful since it is not anyone's hyperplane, but what we could see of someone else's hyperplane.
Note that if I send a mobile at speed Vr (real speed) between Romeo and Juliet, the mobile gradually passes from Romeo's hyperplane to Juliet's hyperplane (tautology).
The hyperplane of this mobile is therefore perpetually changing.
But who should be given priority to transcribe this change? Romeo's hyperplane or Juliet's, since it moves away from one and approaches the other, thus seeing them deform into a hypercone for one (Juliet) and into a hyperplane for the other (Romeo)?
There will therefore be an entanglement of effects, and we will obtain something of the second degree: it is the Lorentz factor g=(1-Vo²/c²)^-(1/2)
R.H.