What is the relationship between phase space and space-time?

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Loren Booda
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How would you describe the intersection between phase space and space-time?
 
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Intersection? Spacetime is the configuration space of a single classical point particle. That particle's phase space is the cotangent bundle of spacetime.

I know very little about these things, but I hope that I at least got the above right. The best place to read more about such things is almost certainly "Mathematical methods of classical mechanics" by V.I. Arnold.