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Modern Physics

Proper Time

dτ=dtγ=dt1−v2c2d\tau = \frac{dt}{\gamma} = dt\sqrt{1 - \frac{v^2}{c^2}}

Proper time is the time measured by a clock moving with the object. It is always shorter than coordinate time measured by a stationary observer.

Variables

d\tau
Proper time interval
s
dt
Coordinate time interval
s
\gamma
Lorentz factor
unitless
v
Velocity
m/s
c
Speed of light
m/s

Derivation

The proper time is an invariant quantity in special relativity.

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Common questions

What is the Proper Time formula?

Proper Time is written dτ= dt/γ= dt√(1 - v²/c²). Proper time is the time measured by a clock moving with the object. It is always shorter than coordinate time measured by a stationary observer. It belongs to Modern Physics, under Special Relativity.

What are the units in dτ= dt/γ= dt√(1 - v²/c²)?

In SI units, d\tau is proper time interval, measured in s; dt is coordinate time interval, measured in s; \gamma is lorentz factor (dimensionless); v is velocity, measured in m/s; c is speed of light, measured in m/s.

How is the Proper Time formula derived?

The proper time is an invariant quantity in special relativity. The result is dτ= dt/γ= dt√(1 - v²/c²).