Re: the notion of relativity of simultaneity

Am Donnerstag000003, 03.10.2024 um 14:49 schrieb Richard Hachel:

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.
 

Sure:
The observer see remote events 'live'.
But he sees remote events also delayed!
What we see in the night sky is NOT happening now, but earlier than now.
We see events now, which happenend the longer ago the further  away.
It is therefore patently irrelevant, what the observer sees, because these impressions are pictures, we receive from the past.
The 'real thing' is supposed to exist, but remains invisible for a long time.
This 'real thing' is invisible, but real, while our impressions are visible, but not real.
We would need to correct this error 'by hand', because we cannot see, what is happening now.
Such a correction isn't that difficult, since we only need to take the delay into consideration.
A certain shell around the observer represents a certain set of points, from where we receive simultaneous signals at the same time.
For other shells further away or closer to us, we need to add or subtract the delay relative to that shell mentioned above.
If we reduce that shell to zero radius, we would need to measure only delay.
This delay should be used to compensate the time needed for signals to travel from remote events to the observers.
What is happening now, that will be seen with such a delay later.
Therefore, the (hyperplane of the) present is real, but cannot be seen,
It is constructed by assuming a hypothetical signal, which needs no time to travel, hence is here once emitted.
This does not exist, but that doesn't matter for a definition.
TH
..

>
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.