Light Clocks and Time Dilation

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Time dilation is an intriguing implication of Einstein's special theory of relativity. The light clock is an elegant illustration of this effect, relying only on a knowledge of the Pythagorean theorem and the invariance of the speed of light.


Imagine a clock that keeps time by reflecting a pulse of light back and forth between two mirrors; one tick of the clock is defined as contact between the light pulse and the lower mirror. Now imagine three identical clocks, viewed from a reference frame in which two clocks are at rest and a third is moving at high velocity. Observers in this reference frame see the light pulse of the moving clock travel a greater distance than the light pulses in the stationary clocks, but since they must measure the same speed for all light pulses, they observe fewer ticks on the moving clock than on the stationary clocks—that is, time appears to pass more slowly for the moving object. An observer in the rest frame of the third clock would witness an identical effect: two clocks flying by at high velocity appear to tick more slowly than the single stationary clock.

In this Demonstration, is the speed of light, is the velocity of the moving clock (ranging between 0 and 0.9 ), is the distance between the mirrors of each clock, and is , the factor by which the moving light pulse's path is lengthened, and therefore the factor by which time appears to dilate.


Contributed by: Quentin Sedlacek (March 2011)
Based on a program by: Howard Georgi
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.