The speed at which a clock has to travel to run at a rate that is one-third the rate of a stationary clock is

Question

Quizplus · Accepted Answer

The correct answer is derived from the time dilation formula in special relativity, $\Delta t' = \Delta t / \sqrt{1 - v^2/c^2}$, where $\Delta t'$ is the dilated time, $\Delta t$ is the proper time (time measured by a stationary observer), $v$ is the velocity of the moving clock, and $c$ is the speed of light. To make a clock run at one-third the rate of a stationary clock, we set $\Delta t' = 3\Delta t$, leading to $1/\sqrt{1 - v^2/c^2} = 3$. Solving for $v/c$, we get $v/c = \sqrt{1 - (1/3)^2} = \sqrt{8/9}$, which is approximately 0.943.

The Speed at Which a Clock Has to Travel to Run