Proper time

Definition

Proper time is the time interval measured by an observer who is at rest relative to the event being timed. It is considered the shortest possible time interval between two events.

5 Must Know Facts For Your Next Test

1. Proper time is denoted by $\tau$ and is measured in the frame where both events occur at the same location.
2. Proper time is invariant, meaning it remains constant across all reference frames.
3. The relationship between proper time and coordinate time involves the Lorentz factor: $\Delta t = \gamma \Delta \tau$.
4. Proper time can be calculated using the equation $\Delta \tau = \sqrt{1 - v^2/c^2} \, \Delta t$, where $v$ is velocity and $c$ is the speed of light.
5. In a spacetime diagram, proper time corresponds to the length of the world line that connects two events.

Review Questions

Related terms

Time Dilation:

A phenomenon in which a clock moving relative to an observer runs slower compared to a clock at rest with respect to that observer.

Lorentz Factor:

$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$, a factor that appears in several equations of special relativity, accounting for how measurements of space and time change for different inertial observers.

Spacetime Interval:

$s^2 = (ct)^2 - x^2 - y^2 - z^2$, an invariant quantity in special relativity that combines distances in space and intervals in time between events.