Witnessing the Effects of Length Contraction

Summary:

One of the consequences of Einstein's theory of Special Relativity is called length contraction. This means that the 12-inch ruler that you use in your math class would not look 12-inches long if it were moving past you at close to the speed of light. So which length is correct? We define the "proper length" of an object as the length measured when that object is measured at rest. The length at which you would measure an object when it is in motion is always less, but it has to move really fast before you can even begin to see the effects of length contraction! The ruler would appear to shrink the faster it moves, but only in the direction of motion that it is traveling. Finally, when it is traveling at the speed of light, it would appear to have no length.

Materials needed:

  • Bright unidirectional light, preferably a halogen desk lamp or overhead projector
  • 12-inch ruler, wooden or opaque plastic
  • piece of tape

Procedure:

  1. Point the light directly down onto desk surface so it is slightly over 12-inches above the desk.
  2. Lay the ruler down onto the desk surface or across the empty overhead projector so that it is totally illuminated from above. On the overhead you will see the full length of the ruler across the screen.
  3. Tape one end of the ruler down so that it doesn't move or shift.
  4. Slowly lift the other end of the ruler and notice what is happening to the shadow of the ruler on the desk or to the image of the ruler on the overhead projector. You will see the shadow of the ruler slowly shrink as you raise the end of the ruler higher and higher. What happens to the shadow when the ruler is straight up and down?

Explanation:

In this demonstration, the ruler itself never actually changes from its 12-inch length. But as the ruler is tilted and the angle that the ruler makes with the surface gets larger, the shadow of the ruler on the surface will get smaller and smaller. The shadow represents what the ruler would look like to a person at rest. Einstein's Relativity says that the faster the ruler is moving past us the shorter it will look to us. So what are we changing that makes the shadow get shorter? We are changing the angle and we need to link this angle with a speed. The angle represents the speed that the ruler would be traveling past us in order for us to see it appear as its shadow length, instead of its actual 12-inches.