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I am working my way thought Hartle's Gravity. In Section 5.4 he states that "The straight lines along which free particles move in spacetime are paths of

__proper time" and proceeds to proof that "in flat space time the proper time is a curve of extremal proper time".__

*longest*Can someone explain why it actually are the paths with longest proper time? Light travels along path with zero proper time. Is that a longest path (normal paths being negative)?

Thanks

Bas