Physics
Proper Time
Quick fact
Proper time is the only time that is invariant under Lorentz transformations; all observers agree on the proper time between two events along a given worldline.
Why this is interesting
You've heard that moving clocks run slow, but what time does the traveler actually experience? That's proper time—the time you feel on your own wristwatch.
Read the full explanation
Understanding Proper Time
Imagine you're on a spaceship traveling at high speed relative to Earth. Your wristwatch ticks normally according to you, but Earth observers see your clock running slow. The time measured by your watch—your own time—is called proper time. It is the time interval between two events that occur at the same location in your frame. For example, if you blink, the start and end of your blink happen at the same spot relative to you. Proper time is the time you actually experience, and it is always less than the coordinate time measured by a stationary observer due to time dilation.
A deeper explanation
Proper time arises from the spacetime interval, ds² = c² dt² - dx² - dy² - dz², which is invariant. For a clock moving along a path, the proper time Δτ is the integral of √(1 - v²/c²) dt along the worldline. This integral sums up the time experienced by the clock. Because the spacetime interval is invariant, all inertial observers calculate the same proper time for a given path. Proper time is why the twin who travels ages less: their worldline has a shorter proper time. It matters because it provides a frame-independent measure of time, essential for understanding causality and the geometry of spacetime in both special and general relativity.