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Clocks and Relativity: Time Dilation Calculations

30-Oct-2010

## Introduction

Relativity theory predicts that clocks traveling at speed run slow. The greater the speed the slower a clock runs compared to a stationary clock. There are more complex equations but for modest, human scale velocities the fractional change in clock frequency is given by Δf/f = −½v²/c² , where v is velocity (meters/second). This is often refered to as kinematic time dilation, or simply SR (special relativity).

Relativity theory also predicts that clocks in a gravitational field run slow. Thus a clock at sea level runs slower compared to a clock up on a mountain (where gravity is slightly less). The greater the altitude the faster a clock runs compared to a clock at sea level. There are more complex equations but for modest, human scale elevations the fractional change in clock frequency is given by Δf/f = +gh/c² , where h is elevation difference (meters). This is often refered to as gravitational time dilation, or simply GR (general relativity).

So both speed and mass change clock rate and the combined effect is: Δf/f = gh/c² − ½v²/c²

The following graphs show the relationship between velocity, elevation, and change in clock rate.

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