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DiracPool said:I have to agree with Copernicus, I don't see what we gain by pretending that time (or space) isn't imaginary. Depending on how you set up your delta S squared, it could be either one. You can try to explain that away somehow, but I think Minkowski's trick of replacing the Y axis with ict and treating the Lorentz transformation as a rotation is the most instructive approach to understanding the invariant interval.
Minkowski's trick is useful, if you stop with Special Relativity.
If you wish to move to on General Relativity (or do Special Relativity with different coordinates), you'll likely get stuck.
In the end, using the metric [itex]g_{ij}[/itex] is the best way to go.
There is a famous passage in Misner Thorne Wheeler's Gravitation:
"Farewll to ict"
http://www.google.com/search?q="farewell+to+ict"+gravitation