Theories of the Universe
The Faster You Go, the Shorter You Get
You now know that time is affected by motion. And since time and space are inseparable, that means that space is affected by motion as well. Let's pay a visit to Casey and his cosmic locomotive. You ask him if he would participate in a science experiment, and of course, he couldn't be happier. You explain to him that you want to measure the change in the length of his locomotive as he shoots down the railroad tracks at close to light speed.
You get out your 100-foot tape measure and use it to find out how long his stationary train is. Okay, you did that. But now you realize that you can't measure its length while it's zooming past you, so you devise another method to do that. Remember that distance, or in this case the length of the locomotive, is equal to its speed times the elapsed time. You take out your stopwatch, which you always carry for experiments like this, and figure that if you start the watch the moment the tip of the train goes past you and stop it when the tail end goes by, you'll know the length.
As we learned in the last section, from Casey's perspective on board the train, he's stationary while you appear to be zooming by. That means that it will appear that your stopwatch is running slower too. This will result in a measurement of the locomotive that will be shorter, because if the watch is running slower, the elapsed time will be shorter, and consequently, when you do the math, the length of the train will be shorter than when it's at rest. Casey hops onboard, drives the train past you at 98 percent of light speed, and sure enough you not only perceive the train to be 80 percent shorter than at rest, but your stopwatch calculations verify this as well. Is your head zooming past you at light speed yet?
I have one last conceptual stretch for you before closing this section. We've discussed motion in relation to time and motion in relation to space. How about addressing the combination: motion through the space-time continuum? This gets a little tricky, but hang in there. The essential idea that I'll try to explain is one that Einstein believed to be at the heart of special relativity. And that is that an object's motion is shared through all four dimensions, the three of space and the fourth of time.
Hendrik Lorentz (1853-1928) was a Dutch physicist who received the Nobel Prize in Physics in 1902 for his work on the theory of electromagnetism. His later work provided the bridge between Maxwell's work and Einstein's special theory of relativity. He developed the so-called Lorentz transformation equations, which describe the way space and time are distorted for objects traveling at a sizable fraction of the speed of light.
We all know what it's like to move through space—we do it all the time. But even if we're sitting still and not moving through space, we're still moving through time. When we set up a luncheon, we move through space to get there and arrive at an appointed moment “in time.” I think this is already familiar, because of our previous discussion of time. So let's take this a step further. We know that when an object moves through space relative to us, its clock will run slower compared to ours. We saw that in the experiment with the light clock. This can be explained in another way as well.
If an object is stationary, relative to us, all of its motion is being used to travel through only one dimension: time. As soon as it begins to move, some of its motion is being diverted to moving through space, so there is no longer as much motion being used to travel through time, so time goes by slower, and that's why the clock of a moving object runs slower than one that is stationary, get it? The speed of an object through space reflects how much of its motion through time is being diverted. The faster it moves through space, the more its motion is being diverted away from moving through time, so time slows down.
Here's the final part. There is a limit to an object's maximum speed through space. And, of course, we know what that limit is. Right? It's the speed of light. There is nothing that can travel faster. That means that all of the object's motion is wrapped up in moving at the maximum speed through space. It has diverted its motion through time to accomplish this. Because there is no motion left for time … there is no passage of time at the speed of light. The photons from the big bang are all still the same age today as when they first emerged.
Excerpted from The Complete Idiot's Guide to Theories of the Universe © 2001 by Gary F. Moring. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.