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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.physics.relativity
Subject: Re: Definition : relativistic (or not) hyperplane
Date: Fri, 4 Oct 2024 11:52:14 +0300
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On 2024-10-03 18:13:33 +0000, Richard Hachel said:

> A hyperplane of simultaneity is a geometric concept used mainly in 
> relativistic physics.
> In a four-dimensional orthonormal framework (three dimensions of space 
> and one dimension of time), it represents the set of points in 
> space-time that are considered simultaneous for a given observer; the 
> hypersurface that contains all the events that, for him, occur at the 
> same time.
> This "hyperplane of the present", which is represented as a horizontal 
> sheet, therefore actually represents a three-dimensional space.

A hyperplane is a subspace of a multi-dimensional space that fully
contains those straight lines that have at least two pints in common
with the subspace. Often but not always the term is used only for
subspaces that are at least three-dimensional.

-- 
Mikko