special relativity

Length Contraction

Now is not absolute

introduction

For the theory of relativity to be consistent the length of a moving object, in the direction of travel, must contract. 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 phenomenan.

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 from two different reference fames.

  • top: stationary relative to the clock
  • bottom: stationary relative to the cylinder

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.