Consider the upper half of the hyperbola(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

(ct)^2 - x^2 = a^2

[/tex]

where [itex] a^2 [/itex] is a positive constant. The spacetime distance between any point on this curve and the origin is the positive number a. A thought experiment helps give this some physical meaning to me: If I'm at x=0 with a set of identical clocks, and at time = 0 I simultaneously throw them all at different speeds along the x-axis, then the time on every clock when it hits the curve will be the same (a).

Now consider the right half of the hyperbola

[tex]

(ct)^2 - x^2 = b^2

[/tex]

where [itex] b^2 [/itex] is a negative constant. The spacetime distance between any point on this curve and the origin is also a constant, but I don't know of an analogous thought experiment to help give this hyperbola physical meaning.

Any suggestions?

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# About invariant hyperbolae

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