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  • Definition : relativistic (or not) hyperplane

    From Richard Hachel@21:1/5 to All on Thu Oct 3 18:13:33 2024
    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.

    R.H.

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  • From Mikko@21:1/5 to Richard Hachel on Fri Oct 4 11:52:14 2024
    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

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