 Proper mean lifetime

The mean lifetime of an unstable particle measured in its rest frame, using elapsed proper time. In the exponential decay model, survival to proper time $\tau$ has probability $e^{-\tau /{\tau }_0}$. For constant Lorentz factor $\gamma$, time dilation gives laboratory mean lifetime $\gamma {\tau }_0$. A mean lifetime is a statistical mean, rather than a fixed decay time.