Fear of Physics (18 page)

 

 

As strong as the connection between the particle realm and our own may be, the progress of twentieth-century physics has not been confined to providing new perspectives just on phenomena beyond our direct perception. I want to return, in stages, from the extremes of scale I have been discussing to ones that are more familiar.

Nothing is more direct than our perception of space and time. It forms a crucial part of human cognitive development. Well-known milestones in animal behavior are categorized by changes in spatial and temporal perception. For example, a kitten will walk unabashedly over a Plexiglas-covered hole until a certain age at which the animal begins to appreciate the dangerous significance of empty space beneath its feet. So it is all the more remarkable that we should discover, at the beginning of the twentieth century, that space and time are intimately connected in a way that no one had previously suspected. Few would dispute that Albert Einstein’s discovery of this connection through his special and general theories of relativity constitutes one of the preeminent intellectual achievements of our time. With hindsight,
it is clear that his leaps were strikingly similar to those of our cave dweller.

As I have discussed, Einstein based his theory of relativity on the desire to maintain consistency with Maxwell’s electromagnetic theory. In this latter theory, I remind you that the speed of light can be derived a priori in terms of two fundamental constants in nature: the strength of the electric force between two charges and the strength of the magnetic force between two magnets. Galilean relativity implies that these should be the same for any two observers traveling at a constant velocity relative to each other. But this would imply that all observers should measure the speed of light to be the same, regardless of their (constant) velocity or the velocity of the source of the light. Thus, Einstein arrived at his fundamental postulate of relativity: The speed of light in empty space is a universal constant, independent of the speed of the source or the observer.

In case the intuitive absurdity of this postulate has not hit home completely, let me give you another example of what it implies. In order to capture the White House in these times, it appears necessary for the winning political party to show that it encompasses the center, while the other party is either right or left of center. Some incredulity is therefore aroused when, before the election, both parties claim to have captured the center. Einstein’s postulate, however, makes such a claim possible!

Imagine two observers in relative motion who pass by each other at the instant one of them turns on a light switch. A spherical shell of light will travel out in all directions to illuminate the night. Light travels so fast that we are normally unaware of its taking any time to move outward from the source, but it does. The observer, A, at rest with respect to the light bulb, would see the following shortly after turning on the light:

She would see herself at the center of the light sphere, and observer B, who is moving to the right relative to her, would have moved some distance in the time it took the light to spread out to its present position. Observer B, on the other hand, will measure these same light rays traveling outward as having the same fixed speed relative to him and thus as traveling the same distance outward relative to him, by Einstein’s postulate. Thus, he will see
himself
as being at the center of the sphere, and A as having moved to the left of center:

In other words, both observers will claim to be at the center of the sphere. Our intuition tells us this is impossible. But, unlike politics, in this case both protagonists actually
are
at the center! They must be if Einstein is right.

How can this be? Only if each observer somehow measures space and time differently. Then while one observer perceives that the distance between herself and all points on the sphere of light is the same and the distance between the other observer and the sphere is less in one direction and greater in another, the other observer can measure these same things and arrive at different answers. The absolutism of space-time has been traded for the absolutism of light’s velocity. This is possible, and in fact all the paradoxes that relativity thrusts on us are possible, because our information about
remote
events is indirect. We cannot be both
here
and
there
at the same time. The only way we can find out what is happening
there
now is to receive some signal, such as a light ray. But if we receive it
now,
it was emitted
then.

We are not accustomed to thinking this way, because the speed of light is so great that our intuition tells us that nearby events that we see
now
are actually happening
now.
But this is just an accident of our situation. Nevertheless, it is so pervasive an accident that had Einstein not had the fundamental problems of electromagnetism to guide him in thinking about light, there is probably no way he would have been able to “see” beyond the cave reflection we call
now.

When you take a picture with your camera, you are accustomed to imagining it as a snapshot in time: This is when the dog jumped on Lilli while she was dancing. This is not exactly true, however. It does represent an instant, but not in time. The light received at the camera at the instant the film recorded the image at different points on the film was emitted at different times, with
those points displaying objects farthest from the camera emitting their light the earliest. Thus, the photo is not a slice in time but, rather, a set of slices in space at different times.

This “timelike” nature of space is normally not perceived because of the disparity between human spatial scales and the distances light can travel in human time scales. For example, in one-hundredth of a second, the length of time of a conventional snapshot, light travels approximately 3,000 kilometers, or almost the distance across the United States! Nevertheless, even though no camera has such a depth of field,
now,
as captured in a photograph, is not absolute in any sense. It is unique to the observer taking the picture. It represents “here and now”
and
“there and then” to each different observer. Only those observers located at the same
here
can experience the same
now.

Relativity tells us that, in fact, observers moving relative to one another
cannot
experience the same
now,
even if they are both
here
at the same instant. This is because their perceptions of what is “there and then” will differ. Let me give you an example. While I don’t intend to rehash all the standard presentations in elementary texts on relativity, I will use one well-known example here because it is due to Einstein, and I have never seen a better one. Say that two observers are on two different trains, moving on parallel tracks at a constant velocity with respect to each other. It doesn’t matter who is actually moving, because there is no way to tell, in an absolute sense, anyway. Say that at the instant these two observers, located in the center of their respective trains, pass each other, lightning strikes. Moreover, say that it strikes
twice,
once at the front and once at the back of the trains. Consider the view of observer A at the instant he sees the light waves due to the flashes:

Since he observes the flashes simultaneously from either end of the train, and he is located in the center of his train, he will have no choice but to infer that the two flashes occurred at exactly the same time, which he could refer to as
now
although it was actually
then.
Moreover, since observer B is now to the right of A, B will see the flash from the right-hand lightning bolt before he sees the flash from the left-hand bolt.

This normally doesn’t bother anyone, because we would all ascribe the difference in time of observation for B to the fact that he was moving toward one source of light and away from the other. However, Einstein tells us that there is no way for B to observe such an effect. The speed of both light rays toward him will be the same as if he were not moving at all. Thus, B will “observe” the following:

From this, B will infer—because (a) he sees one flash before the other, (b) the light was emitted from either end of a train in
which he is sitting at the center, and (c) the light was traveling at the same speed in both directions—that the right-hand flash occurred before the left-hand flash. And for him, it actually did! There is no experiment either A or B can perform that will indicate otherwise. Both A and B will agree about the fact that B saw the right flash before the left flash (they cannot disagree about what happens at a single point in space at a single instant), but they will have different explanations. Each explanation will be the basis of each person’s
now.
So these
nows
must be different. Remote events that are simultaneous for one observer need not be simultaneous for another.

The same kind of thought experiments led Einstein to demonstrate that two other facets of our picture of absolute space and absolute time must break down for observers moving relative to one another. A will “observe” B’s clock to be running slowly, and B will “observe” A’s clock to be running slowly. Moreover, A will “observe” B’s train to be shorter than his own, and B will “observe” A’s train to be shorter than his own.

Lest the reader think that these are merely paradoxes of perception, let me make it clear that they are not. Each observer will
measure
the passage of time to be different and will
measure
lengths to be different. Since, in physics, measurement determines reality, and we don’t worry about realities that transcend measurement, this means that these things are
actually
happening. In fact, they are happening every day in ways that we can measure. The cosmic rays that bombard the Earth every second from space contain particles with very high energies, traveling very close to the speed of light. When they hit the upper atmosphere, they collide with the nuclei of atoms in the air and “break up” into a shower of other, lighter elementary particles. One of the most common of the particles that gets produced in this way
is called a
muon.
This particle is virtually identical to the familiar electrons that make up the outer parts of atoms, except that it is heavier. We presently have no idea why an exact copy of the electron exists, prompting the prominent American physicist I. I. Rabi to protest, “Who ordered that?” when the muon was discovered. In any case, the muon, because it is heavier than the electron, can decay into an electron and two neutrinos. We have measured the lifetime for this process in the laboratory and found that muons have a lifetime of about one-millionth of a second. A particle with a lifetime of one-millionth of a second traveling at the speed of light should go about 300 meters before decaying. Thus, muons produced in the upper atmosphere should never make it to the Earth. Yet they are the dominant form of cosmic rays (other than photons and electrons) that do!