Length Contraction (Part 1)

As we found out in the previous article, objects moving at constant velocities experience time differently than those at rest. If you’ve ever heard the expression “spacetime,” you might be thinking that if time changes, then space must as well. You’d be right!

The effect on space due to special relativity is known as length contraction. First, let's define what length actually is. Length is the difference in location between one point and another relative to some object. For example, if you are standing in a room with a ruler in your hands measuring a pencil, the length of the pencil would be found by finding the location of the eraser and of the lead, and then taking the difference. These measurements must occur at the same time to find a precise length.

Imagine you are on Earth and watching Bob in a spaceship fly to the Sun, just like in the image at the top of this article. If you time his flight, you might say that it takes him two hours to get there. If we consider the effects of time dilation, let's say with a dilating factor of two, then he might perceive his own travel time as only one hour. We have now established that the times you and Bob experience are different.

Now, due to relative velocities, whatever speed you see Bob going at as he goes to the Sun must be the same speed he sees both you and the Sun go by his spaceship at. For example, imagine you are in a car moving at 50 mph relative to the stationary road you're driving on. Someone standing on the road would obviously see you moving at 50 mph in front of them. Meanwhile, you would perceive yourself and the car at rest, with the road and person moving at 50 mph behind you. It would be nonsensical for them to see you moving at 50 mph, and you see them moving at 30 mph or some other speed.

So you see Bob going at speed v to the Sun in two hours. Bob sees the Sun passing by in one hour at speed v until it reaches him. The only way this is possible is if the distance Bob perceives himself traveling is half the distance that you say he travels! This same logic can be applied for his travel over the Earth and the Sun itself, thus making it clear why in the bottom part of the topmost picture, the Earth, Sun, and space between them all shrinks. (To see why the Earth and Sun would shrink horizontally, just imagine that just like how you traveled the distance of space with the Sun and Earth as the endpoints, the sides of the Sun/Earth can now be the endpoints that you are traveling between. Thus, they must shrink.)

Now, the reason why the spaceship will appear to shrink from your point of view is a little more complicated. It involves other results of special relativity known as relative simultaneity and the rear clock ahead effect. So, stay tuned for an article on that. Only once we can grasp these concepts will we be able to complete our understanding of length contraction.