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  • Compactified Minkowski?

    From Julio Di Egidio@21:1/5 to All on Mon Jun 9 13:39:07 2025
    I am trying to compactify Minkowski space, but all I manage
    to get is kinds of clovers or squares, while what I'm after
    is circles (i.e. the locus of points whose *proper* distance
    from the origin is constant).

    See <https://www.desmos.com/calculator/b2bl9jiwo8>

    Note that I would like to keep it in terms of (y,x) coords,
    as that naturally maps to the (t,x) of space-time.

    Can anyone suggest scaling formulas (or fix the diagram)?

    -Julio

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  • From sobriquet@21:1/5 to All on Mon Jun 9 17:37:16 2025
    Op 09/06/2025 om 13:39 schreef Julio Di Egidio:
    I am trying to compactify Minkowski space, but all I manage
    to get is kinds of clovers or squares, while what I'm after
    is circles (i.e. the locus of points whose *proper* distance
    from the origin is constant).

    See <https://www.desmos.com/calculator/b2bl9jiwo8>

    Note that I would like to keep it in terms of (y,x) coords,
    as that naturally maps to the (t,x) of space-time.

    Can anyone suggest scaling formulas (or fix the diagram)?

    -Julio


    https://en.wikipedia.org/wiki/Motor_variable#Compactification

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  • From Julio Di Egidio@21:1/5 to Julio Di Egidio on Mon Jun 9 19:41:12 2025
    On 09/06/2025 13:39, Julio Di Egidio wrote:
    I am trying to compactify Minkowski space, but all I manage
    to get is kinds of clovers or squares, while what I'm after
    is circles (i.e. the locus of points whose *proper* distance
    from the origin is constant).

    See <https://www.desmos.com/calculator/b2bl9jiwo8>

    Note that I would like to keep it in terms of (y,x) coords,
    as that naturally maps to the (t,x) of space-time.

    Can anyone suggest scaling formulas (or fix the diagram)?

    Never mind, here it is, at least the upper portion: <https://www.desmos.com/calculator/3j9sqkymsf>

    The scaling is the obvious one component-wise. Drawing
    full diagrams in Desmos makes things quite more complicated,
    indeed I have not actually computed `f_e` as that require
    the inverse scaling...

    -Julio

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