General Spacetime
The coordinate-independent definition of the square of the line element ds in spacetime is:
In terms of coordinates:
where for this case the indices α and β run over 0, 1, 2, 3 for spacetime.
This is the invariant interval - the measure of separation between two arbitrarily close events in spacetime. In special relativity it is invariant under Lorentz transformations; in general relativity it is invariant under arbitrary invertible differentiable coordinate transformations.
Read more about this topic: Line Element, Line Elements in 4d Spacetime
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—Denis Diderot (1713–1784)