# Trying to speak correctly of spacetime intervals and how to compare them

Is it correct to speak of "magnitude of a spacetime interval"?

For instance, considering a pair of (distinct) events, $A$ and $B$, which are lightlike separated, is it correct to say that "the magnitude of the spacetime interval of event pair $A$ and $B$ is equal to 0"?

Further, considering two pairs of (distinct) events, both of which are spacelike separated, is it correct to say that "the ratio between the magnitudes of the spacetime intervals of these two pairs of events is a real number"?

Likewise, considering two pairs of (distinct) events, both of which are timelike separated, is it correct to say that "the ratio between the magnitudes of the spacetime intervals of these two pairs of events is a real number"?

Finally: Is "$s[ P, Q ]$" an appropriate notation to abbreviate "the magnitude of the spacetime interval of event pair $P$ and $Q$"?

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Sure, why not? The signature of either (+,-,-,-) or (-,+,+,+) is completely arbitrary. As for your last question, you're free to invent any notation you like. – jld Mar 15 '13 at 9:05
@elfmotat "[...] why not?" Well, I'd like to avoid possible confusion of the spacetime interval magnitude with the quantity (real number?) "$s^2$" which often appears in discussion of spacetime intervals; e.g. in en.wikipedia.org/wiki/Spacetime_interval (Those numbers "$s^2$" might become cumbersome when considering the triangle inequality etc. And, in fact, I don't even know how to name them unambiguously either.) Perhaps, what I'm trying to get at is best called "proper separation" of a pair of events. "you're free to invent any notation" Not if it's used otherwise already. – user12262 Mar 15 '13 at 15:52