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Physics in a Nutshell

Proving special relativity: episode 4

While Einstein's theory of special relativity is one of the most mind-bending and nonintuitive ideas of the last century, it turns out that there is a single insight that makes it all far more sensible.

Over the past few Physics in a Nutshell columns, we have talked about Einstein's theory of special relativity and how the operational experience of particle accelerators shows that the theory is true. But there's a difference between knowing that something is true and understanding why it is true. It is the nonintuitive logic of special relativity that makes so many people resist believing it. But it will all make sense when you understand just a relatively small number of ideas.

The first is the fact that space and time are really the same thing. This is not at all obvious, but it becomes clear when one considers how two observers view a common object (you don't even need to invoke Einstein). For instance, suppose you sit by the side of the road. As far as you are concerned, you don't move. On the other hand, a person driving by at 60 miles per hour will say that your position is changing. Every hour, your position is 60 miles farther away from him. As far as the other person is concerned, your position depends on his time. Space and time are mixed, much the same in the same way that up-down and left-right are essentially equivalent.

Once you've accepted the equivalence of space and time and the existence of space-time, we're almost home free. Our final important point is cinchy to accept in comparison: All things travel at just one speed the speed of light. In fact, as you sit there, perhaps eating a muffin on your morning coffee break, you are traveling at the speed of light. At such a breakneck speed, perhaps you should hold onto your coffee and muffin just a tad bit more carefully, no?

In relativity, space and time should be thought of as equivalent in the same way that the north-south direction is relatable to the east-west direction. Then it becomes easy to see how an object with a single speed can travel entirely through time, entirely through space or in a mixture.

The idea that you are traveling at such an incredible speed seems absurd, but wait for the catch: You are traveling at that speed through time. That is, assuming that you are not moving at all through space, your motion is exclusively through time.

So what happens if you start moving through space? Well, since you are moving at a single speed, that means that your motion through time must be less. Let's think of a more familiar example to illustrate that point. Suppose you are out in the Utah Salt Flats or some other location that is flat for miles in every direction. Suppose further that you are in a car set to go at precisely 20 miles per hour. You can drive toward the east at 20 mph, but if you do so, you are not moving north at all. You could also drive north, but without any motion east. Or you could travel in a mixture of north and east.

It's much the same thing in relativity. If you are moving at a steady 186,000 miles per second — the speed of light — through space, that leaves no velocity left over to move through time. If you are moving at nearly the speed of light through space, but not exactly, then you have a little velocity left over to move through time, and so your motion through time is slow. And if you are not moving through space, time moves as quickly as it can.

Once you realize that time and space are interchangeable and that objects travel through space-time at a single speed, the peculiarities of relativity become much easier to understand. With a little practice, relativity can even become intuitive. Intuitive-and-right is a great label for any theory.

—Don Lincoln

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