Theories of the Universe: How Can You Be in Two Places at Once?
How Can You Be in Two Places at Once?
Now that we've spent a good amount of time talking about all the different kinds of time, let's get to the bottom of it all. If the nature of time hasn't appeared to be relative to you yet, then by doing another thought experiment I think you'll discover what Einstein did—time, like motion, is relative. For this experiment, we won't be going to outer space. Instead we'll just use a train and some mirrors to show that what appears to be a simultaneous event actually reveals that time flows differently for each of us.
Many objects in the universe send out radio waves, and a radio telescope can be used to detect them. A large, curved, metal dish collects the radio waves and reflects them to a focus point above the center of the dish, rather as the curved mirror of a reflecting telescope gathers light waves from space. By detecting radio waves coming from galaxies and other objects in space, radio telescopes have discovered the existence of many previously unknown bodies, such as invisible giant stars that emit only x-rays and black holes.
We begin our thought experiment by measuring the distance between two poles alongside a railroad track and then find the midpoint between them. You are carrying a right angle mirror that allows you to see both poles when you stand at the midway point. Out of the sky two bolts of lightening strike the two poles simultaneously. You watched this occur in the mirror to verify that indeed the light struck both poles at the same time.
At this point, a train appears coming down the track with a friend of yours onboard who also has a right angle mirror. As the train arrives at the midway point, lightening strikes the two poles again. You observe the event as occurring simultaneously as before, but your friend doesn't. Why not?
To figure out the difference in time intervals for someone traveling close to the speed of light and someone stationary, Einstein developed a mathematical formula that he called the relativity factor. It adjusts for the difference in time between two frames of reference. For example, a person traveling in a spaceship at half the speed of light would have a 15 percent shorter time interval than someone at rest on earth. For every hour that goes by on board the spaceship, one hour and nine minutes goes by on earth. That's because 115 percent of 60 minutes is 69 minutes.
She sees the bolt hit the pole she's moving toward first and then sees the other bolt hit the pole behind her. The light has a shorter distance to travel from the pole that the train is moving toward than it does from the pole that the train is moving way from. Since the speed of light is constant regardless of the source, the only thing that can account for both of you seeing different events is that time must be relative. So a determination of whether or not two events are simultaneous depends on how you are moving as well. And since we are all in one way or another moving continually about through space, whatever happens to us in a different time also necessarily happens to us in a different space.
That simple thought experiment we just did lies at the core of Einstein's theory of special relativity. With time now understood as being relative, there was a significant result that had to be dealt with. What happens to time as we speed up the rate we're moving at? And if we travel as fast as light travels, what happens to time? And is time the only thing affected by light speed? What about space? To answer those questions we need to look at special relativity in a little more detail.
Keeping Track of Time
A common thought experiment in physics will be used to explain the slowing down of clocks. We're going to incorporate something called a light clock to illustrate this. This clock is made of two parallel mirrors with a photon bouncing back and forth between them. A round trip of the photon makes one tick. And let's say that there are a million ticks for every second. We also have a counter hooked up to the clock to show how many ticks have gone by. If I timed the dropping of a ball from the top of my house to the ground and the counter registered three million ticks, that means it took three seconds for this event to occur.
Now let's imagine that you're sitting at a table that has the light clock and it's just ticking away. On the other end of the table, a second light clock slides by at constant velocity. What will be revealed to us is that the moving clock will tick at a different rate than the stationary clock. How is this possible?
Well, let's look at the path that the photon must take in the sliding light clock from our stationary perspective. Now we're only going to observe one tick to illustrate the principle behind this experiment.
Einstein's famous theory of special relativity was described in a paper of his called On the Electrodynamics of Moving Bodies. He never called it the theory of relativity. That name was given to it years later by other scientists.
The photon starts from the base of the clock and moves to the upper mirror. But it must move at an angle as the clock slides by; otherwise it would bounce off into space. The photon bounces off the upper mirror and again travels a diagonal path to the lower mirror. Look at the figure below to get a clearer idea of how this works.
The motion of the photon in the sliding light as seen from a stationary perspective.
Now, remember that motion is relative, so from the point of view of the moving light clock, it is stationary and we are moving. That means that the photon is just traveling straight up and down from that perspective, even though from our point of view it is moving diagonally. Notice also that from our point of view, the distance that the photon travels is longer on the diagonal than within the up and down movement of the stationary clock. Since the speed of light is constant, regardless of motion, the distance the moving photon has to cover is longer than the stationary photon and therefore there will be less frequent ticks. The moving light clock will run slower! And guess what happens the faster it moves? The clock runs slower and slower until it stops altogether at the speed of light. There is no time at the speed of light. Time stops! Whether it's a light clock or any other type of mechanical, electric or atomic clock, the principle is the same.
As an object approaches the speed of light, the time intervals, or the rate at which time passes, change. This is called time dilation. Time intervals are periods of time between events and they dilate or become longer as you approach the speed of light.
This explanation is what lies behind the many examples of time dilation found in introductory books on relativity. One of the classic stories is of the two twins. One stays home on earth while the other takes off on a journey through outer space. Many years pass. The twin on earth grows old, but the twin who was whizzing around the galaxy at close to light speed comes back still young. Time had slowed down for the space traveler from the point of view of his twin on earth and that is why he appears young. According to the space traveler, however, time has not slowed. The biological aging process remained the same, his clocks kept normal time and everything seemed “normal.” Relativity is a property of time, not of clocks.
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.
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