Why is there a Minus in Spacetime Interval Formula?

[DimReg]

That's well into the realm of "physically possible according to theory", or leaning heavily on the theory. In what sense could I meet up with an earlier version of myself? Everything I know about SR tells me that isn't even remotely possible. Are there "real world" examples of this, or is it strictly hypothetical?

EDIT: Reading about the Gödel metric the wiki seems to say it is possible to "See" an earlier version of yourself. I see that as a world of difference...womp womp womp...I can "see" old light that I shouldn't be able to "see". That said I still don't know about CTCs or what they are.

Einstein said this in retort to the metric "It will be interesting to weigh whether these are not to be excluded on physical grounds."

A CTC is a physically accessible path (for massive particles) that forms a complete loop. So essentially you end up at the same point of time and space, after some finite proper time. I don't really want to get into the details of causal structure, it's a huge topic and my ability to replicate it from memory is not exceptional. However, CTC's are typically considered unphysical, and there are some reasons to believe there are no CTC's outside of just "they are confusing" (in order for there to be an initial value formulation, space-time has to be globally hyperbolic, which has no CTC's).

My point with CTC's was just to note that the relative minus sign in the minkowski metric is not by itself enough to ensure causality. That said, there aren't any CTC's in minkowski space, but it's just one of many examples of a metric without CTC's. So while the minkowski metric ensures causality, causality does not ensure the minkowski metric.

 

[nitsuj]

My point with CTC's was just to note that the relative minus sign in the minkowski metric is not by itself enough to ensure causality. That said, there aren't any CTC's in minkowski space, but it's just one of many examples of a metric without CTC's. So while the minkowski metric ensures causality, causality does not ensure the minkowski metric.

Ah, thank you, your point went over my head. It'll take some time to "see" why that is; it doesn't "jump out at me".

Perhaps I feel too strongly that the simple logic of causality has a physical significance & that properly defined measurements do too.