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buybuydandavis comments on Why is the A-Theory of Time Attractive? - Less Wrong Discussion
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If time were topologically a loop, wouldn't both A and B theories be inaccurate representations of time?
They'd still work locally, but not globally.
I don't think B-theory, broadly construed, would be incompatible with that. B-theory is basically just treating space-time as an integrated entity, rather than having radically different ontologies for space and time. It doesn't require time to be partially ordered, any more than it requires spatial directions to be partially ordered.
I would think it does. Time without ordering aint much like time to me. YMMV.
But that was my point. You don't get well defined global ordering if time loops.
There are spacetimes, most notably the Godel Universe, where time is both a loop and not a loop. Some time directions (from the same spatial point) loop around, others go on forever, never getting close to the point of origin. You can still say, however, that it is compatible with the timeless B-like approach. There is no way to construct this spacetime by taking an A-like fixed spatial slice and evolving it forward in time using the Einstein equations. (There is a loophole, however, where one can lift the Godel universe from flat space using a twisted timelike fiber, but that's a different story.)
One has becoming. The other doesn't.