Re: the notion of relativity of simultaneity

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

 The comoving hyperplane (comoving with the observer) is usually called 'hyperplane of the present.

 Absolument.

This is so, because a spacetime diagram uses only two dimensions for space and one for time, because in pseudo-3d it is not possible to depict more dimensions.

 Absolument.

 This 'hyperplane of the present' is therefore depicted as a sheet, but actually means a space.

 Absolument.

 This space is the space of all events, which could be conneted to the place called 'here and now' by the observer,

 Absolument.

if he would use a hypothetical signal with infinite velocity.

This is already the case.
There is no need to imagine an infinite speed of information, because in this case, for the direct observer who "sees" the information arriving, it IS live.
 

 This is, of course, not possible, hence only points are accessible, which are located upon the observers future light cone.

The notion of hypercone of light no longer has any reason to exist, we should no longer use this term which adds nothing, even if it is true that for an external observer B the hyperplane of A is transformed into a hypercone for B in its hyperplane.

But for definitions we do not need to care about such limitations and could regard as 'present', what is placed upon the hyperplane of the present (instead of the positions on the light cone).

Absolument.

TH

R.H.