Relativity · undergrad

Proper Time

The time measured by a clock moving along a worldline.

Published Apr 26, 2026 · 1 min

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Definition

For timelike motion,

d\tau = \frac{1}{c}\sqrt{-ds^2}.

For speed $v$ in an inertial frame,

d\tau = dt\sqrt{1-\frac{v^2}{c^2}}.

A structured path through Lorentz symmetry, intervals, and proper time.

The symmetry of spacetime itself, derived from the constancy of the speed of light.

The invariant spacetime distance preserved by Lorentz transformations.