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I was thinking about what it would mean for space to be continuous, but time to be discrete, and wondering if such ideas have been explored, or even how the math on such a vector space would work. In my mind, this would make the physics rotationally invariant still, since time as a single dimension can only undergo one rotation that will always map onto a previous time on an evenly spaced metric. Or is it that this discontinuity in the translational symmetry for time would violate the invariance too?

Anyhow, I'm very new to the mathematics used to talk about all this stuff, is there a place to get a good crash-course with applications along the way to demonstrate it?