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Equivalence of two definitions of proper time in special relativity

According to Wikipedia, proper time along a timelike world line is defined as the time as measured by a clock following that line.This makes sense to me, but my book defines proper time in the...

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Answer by robphy for Equivalence of two definitions of proper time in special...

Consider two timelike related events.Now draw a worldline for an observer that visits [was present at] both events.The proper time for that worldline is the time elapsed on that observer's...

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Answer by Cryo for Equivalence of two definitions of proper time in special...

I prefer to think of proper time as the 'distance' between the two events in spacetime. Consider some sort of a world-line in a four dimensional spacetime$x^\mu = \left(ct, \mathbf{r}\right)^\mu$Where...

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Answer by Dr. Jerald Feinstein for Equivalence of two definitions of proper...

Proper time was originally defined at the wristwatch time of the local person . . . and still is along with added descriptions that fit various mathematical constructs. Simplicity helps.

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Answer by Nitish Mandal for Equivalence of two definitions of proper time in...

The first one defines time and the second one defines an interval, an interval is between two events, not observers.

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