Contraction of Length by Time Dilation

introduction

For the theory of relativity to be consistent the length of a moving object must contract in the direction of travel. The higher the velocity the more the contraction, until, at the speed of the light, the object will be measured to have zero length.

Currently no experiment has measured the contraction of length directly. However there is indirect evidence for the phenomenon.

In this section it is shown that length contraction is a direct consequence of time dilation.

animation

The animation depicts a clock and a checked cylinder, as seen in the image below. The two views are of the the same clock and cylinder from two different reference fames.

  • top: stationary relative to the clock with the cylinder moving at 0.866c.
  • bottom: stationary relative to the cylinder with the clock moving at 0.866c.

The four * mark the events when the gauge on the clocks coincide with the ends of the cylinder.

The time recorded on the clock for event 1 must be the same for the two reference frames. Also the time recorded on the clock for event 2 must be the same for the two reference frames.

In the reference frame of the cylinder the clock is moving and so the clock time is running slow. Hence there is a greater distance between the two events than in the reference frame of the clock.

violations

  • The Doppler Effect is not depicted in the animation.
  • The aberration of light is not included in the animation.