The Dancing Wu Li Masters (17 page)

As important as was Heisenberg’s introduction of matrix mathematics into the new physics, his next discovery shook the very founda
tions of “the exact sciences.” He proved that, at the subatomic level, there is no such thing as “the exact sciences.”

Heisenberg’s remarkable discovery was that there are limits beyond which we cannot measure accurately, at the same time, the processes of nature. These limits are not imposed by the clumsy nature of our measuring devices or the extremely small size of the entities that we attempt to measure, but rather by the very way that nature presents itself to us. In other words, there exists an ambiguity barrier beyond which we never can pass without venturing into the realm of uncertainty. For this reason, Heisenberg’s discovery became known as the “uncertainty principle.”

The uncertainty principle reveals that as we penetrate deeper and deeper into the subatomic realm, we reach a certain point at which one part or another of our picture of nature becomes blurred, and there is no way to reclarify that part without blurring another part of the picture! It is as though we are adjusting a moving picture that is slightly out of focus. As we make the final adjustments, we are astonished to discover that when the right side of the picture clears, the left side of the picture becomes completely unfocused and nothing in it is recognizable. When we try to focus the left side of the picture, the right side starts to blur and soon the situation is reversed. If we try to strike a balance between these two extremes, both sides of the picture return to a recognizable condition, but in no way can we remove the original fuzziness from them.

The right side of the picture, in the original formulation of the uncertainty principle, corresponds to the position in space of a moving particle. The left side of the picture corresponds to its momentum. According to the uncertainty principle, we cannot measure accurately, at the same time, both the position
and
the momentum of a moving particle. The more precisely we determine one of these properties, the less we know about the other. If we precisely determine the position of the particle, then, strange as it sounds, there is
nothing
that we can
know about its momentum. If we precisely determine the momentum of the particle, there is no way to determine its position.

To illustrate this strange statement, Heisenberg proposed that we imagine a super microscope of extraordinarily high resolving power—powerful enough, in fact, to be able to see an electron moving around in its orbit. Since electrons are so small, we cannot use ordinary light in our microscope because the wavelength of ordinary light is much too long to “see” electrons, in the same way that long sea waves barely are influenced by a thin pole sticking out of the water.

If we hold a strand of hair between a bright light and the wall, the hair casts no distinct shadow. It is so thin compared to the wavelengths of the light that the light waves bend around it instead of being obstructed by it. To see something, we have to obstruct the light waves we are looking with. In other words, to see something, we have to illuminate it with wavelengths smaller than it is. For this reason, Heisenberg substituted gamma rays for visible light in his imaginary microscope. Gamma rays have the shortest wavelength known, which is just what we need for seeing an electron. An electron is large enough, compared to the tiny wavelength of gamma rays, to obstruct some of them: to make a shadow on the wall, as it were. This enables us to locate the electron.

The only problem, and this is where quantum physics enters the picture, is that, according to Planck’s discovery, gamma rays, which have a much shorter wavelength than visible light, also contain much more energy than visible light. When a gamma ray strikes the imaginary electron, it illuminates the electron, but unfortunately, it also knocks it out of its orbit and changes its direction and speed (its momentum) in an unpredictable and uncontrollable way. (We cannot calculate precisely the angle of rebound between a particle, like the electron, and a wave, like the gamma ray). In short, if we use light with a wavelength short enough to locate the electron, we cause an undeterminable change in the electron’s momentum.

The only alternative is to use a less energetic light. Less energetic light, however, causes our original problem: Light with an energy low enough not to disturb the momentum of the electron will have a
wavelength so long that it will not be able to show us where the electron is! There is no way that we can know simultaneously the position
and
the momentum of a moving particle. All attempts to observe the electron alter the electron.

This is the primary significance of the uncertainty principle. At the subatomic level,
we cannot observe something without changing it
. There is no such thing as the independent observer who can stand on the sidelines watching nature run its course without influencing it.

In one sense, this is not such a surprising statement. A good way to make a stranger turn and look at you is to stare intently at his back. All of us know this, but we often discredit what we know when it contradicts what we have been taught is possible. Classical physics is based on the assumption that our reality, independently of us, runs its course in space and time according to strict causal laws. Not only can we observe it, unnoticed, as it unfolds, we can predict its future by applying causal laws to initial conditions. In this sense, Heisenberg’s uncertainty principle is a
very
surprising statement.

We cannot apply Newton’s laws of motion to an individual particle that does not have an initial location and momentum, which is exactly what the uncertainty principle shows us that we cannot determine. In other words, it is impossible, even in principle, ever to know enough about a particle in the subatomic realm to apply Newton’s laws of motion which, for three centuries, were the basis of physics.
Newton’s laws do not apply to the subatomic realm
.
^*
(Newton’s
concepts
do not even apply in the subatomic realm.) Given a beam of electrons, quantum theory can predict the probable distribution of the electrons over a given space at a given time, but quantum theory cannot predict, even in principle, the course of a single electron. The whole idea of a causal universe is undermined by the uncertainty principle.

In a related context, Niels Bohr wrote that quantum mechanics, by its essence, entails:

Yet there is another startling implication in the uncertainty principle. The concepts of position and momentum are intimately bound up with our idea of a thing called a moving particle. If, as it turns out, we cannot determine the position and momentum of a moving particle, as we always have assumed that we could, then we are forced to admit that this thing that we have been calling a moving particle, whatever it is, is
not
the “moving particle” we thought it was, because “moving particles” always have both position and momentum.

As Max Born put it:

Whatever it is that we are observing
can
have a determinable momentum, and it
can
have a determinable position, but of these two properties,
we must choose
, for any given moment, which one we wish to bring into focus. This means, in reference to “moving particles” anyway, that we can never see them the way they “really are,” but only the way we choose to see them!

As Heisenberg wrote:

The uncertainty principle rigorously brings us to the realization that there is no “My Way” which is separate from the world around us. It brings into question the very existence of an “objective” reality, as does complementarity and the concept of particles as correlations.

The tables have been turned. “The exact sciences” no longer study an objective reality that runs its course regardless of our interest in it or not, leaving us to fare as best we can while it goes its predetermined way. Science, at the level of subatomic events, is no longer “exact,” the distinction between objective and subjective has vanished, and the portals through which the universe manifests itself are, as we once knew a long time ago, those impotent, passive witnesses to its unfolding, the “I”s, of which we, insignificant we, are examples. The Cogs in the Machine have become the Creators of the Universe.

If the new physics has led us anywhere, it is back to ourselves, which, of course, is the only place that we could go.

The importance of nonsense hardly can be overstated. The more clearly
we experience something as “nonsense,” the more clearly we are experiencing the boundaries of our own self-imposed cognitive structures. “Nonsense” is that which does not fit into the prearranged patterns which we have superimposed on reality. There is no such thing as “nonsense” apart from a judgmental intellect which calls it that.

True artists and true physicists know that nonsense is only that which, viewed from our present point of view, is unintelligible. Nonsense is nonsense only when we have not yet found that point of view from which it makes sense.

In general, physicists do not deal in nonsense. Most of them spend their professional lives thinking along well-established lines of thought. Those scientists who establish the established lines of thought, however, are those who do not fear to venture boldly into nonsense, into that which any fool could have told them is clearly not so. This is the mark of the creative mind; in fact, this
is
the creative process. It is characterized by a steadfast confidence that there exists a point of view from which the “nonsense” is not nonsense at all—in fact, from which it is obvious.

In physics, as elsewhere, those who most have felt the exhilara
tion of the creative process are those who best have slipped the bonds of the known to venture far into the unexplored territory which lies beyond the barrier of the obvious. This type of person has two characteristics. The first is a childlike ability to see the world as it is, and not as it appears according to what we know about it. This is the moral of the (child’s?) tale, “The Emperor’s New Clothes.” When the emperor rode naked through the streets, only a child proclaimed him to be without clothes, while the rest of his subjects forced themselves to believe, because they had been told so, that he wore his finest new clothing.

The child in us is always naive, innocent in the simplistic sense. A Zen story tells of Nan-in, a Japanese master during the Meiji era who received a university professor. The professor came to inquire about Zen. Nan-in served tea. He poured his visitor’s cup full, and then kept on pouring. The professor watched the overflow until he no longer could restrain himself.

“It is overfull. No more will go in!”

“Like this cup,” Nan-in said, “you are full of your own opinions and speculations. How can I show you Zen unless you first empty your cup?”

Our
cup usually is filled to the brim with “the obvious,” “common sense,” and “the self-evident.”

Suzuki Roshi, who established the first Zen center in the United States (without trying, of course, which is very Zen), told his students that it is not difficult to attain enlightenment, but it is difficult to keep a beginner’s mind. “In the beginner’s mind,” he told them, “there are any possibilities, but in the expert’s there are few.” When his students published Suzuki’s talks after his death, they called the book, appropriately,
Zen Mind, Beginner’s Mind
. In the introduction, Baker Roshi, the American Zen Master, wrote:

The beginner’s mind in science is wonderfully illustrated by the story of Albert Einstein and his theory of relativity. That is the subject of this chapter.

The second characteristic of true artists and true scientists is the firm confidence which both of them have in themselves. This confidence is an expression of an inner strength which allows them to speak out, secure in the knowledge that, appearances to the contrary, it is the world that is confused and not they. The first man to see an illusion by which men have flourished for centuries surely stands in a lonely place. In that moment of insight he, and he alone, sees the obvious which to the uninitiated (the rest of the world) yet appears as nonsense or, worse, as madness or heresy. This confidence is not the obstinacy of the fool, but the surety of him who knows what he knows, and knows also that he can convey it to others in a meaningful way.

The writer, Henry Miller, wrote:

The songwriter Bob Dylan told a press conference:

An example of this kind of faith in the realm of physics was the theory of light quanta. In 1905, the accepted and proven theory of light was that light was a wave phenomenon. In spite of this, Einstein published his famous paper proposing that light was a particle phenomenon. Heisenberg described this fascinating situation this way:

That is exactly what happened. Einstein’s thesis led to the wave-particle duality from which quantum mechanics emerged, and with it, as we know, a way of looking at reality and ourselves that is vastly different from that to which we were accustomed. Although Einstein is known popularly for his theories of relativity, it was his paper on the quantum nature of light that won him the Nobel Prize. It is also a fine example of confidence in nonsense.

What is nonsense and what is not, then, may be merely a matter of perspective.

“Wait a minute,” interrupts Jim de Wit. “My uncle, Weird George, believes that he is a football. Of course, we know that this is nonsense, but Uncle George thinks that
we
are mad. He is quite certain that he is a football. He talks about it constantly. In other words, he has abundant confidence in his nonsense. Does this make him a great scientist?

No. In fact, Weird George has a problem. Not only is he the only person who has this particular perspective, but also this particular perspective is in no way relative to that of any other observer, which brings us to the heart of Einstein’s special theory of relativity. (Einstein created two theories of relativity. The first theory is called the special theory of relativity. The second theory, which came later and is more general, is called the general theory of relativity. This chapter and the next are about the first theory, the special theory of relativity).

The special theory of relativity is not so much about what is relative as about what is not. It describes in what way the relative aspects of physical reality appear to vary, depending upon the point of view of different observers (actually depending upon their state of motion relative to each other), but, in the process, it defines the nonchanging, absolute aspect of physical reality as well.

The special theory of relativity is not a theory that everything is relative. It is a theory that
appearances
are relative. What may appear to us as a ruler (physicists say “rod”) one foot long, may appear to an observer traveling past us (very fast) as being only ten inches long. What may appear to us as one hour, may appear to an observer traveling past us (very fast) as two hours. However, the moving observer can use the special theory of relativity to determine how our ruler and our clock appear to us (if he knows his motion relative to us) and, likewise, we can use the special theory of relativity to determine how our stick and our clock appear to the moving observer (if we know our motion relative to him).

If we were to perform an experiment at the same moment that the moving observer came past us, both we and the moving observer would see the same experiment, but each of us would record different times and distances, we with our rod and clock and he with his rod and clock. Using the special theory of relativity, however, each of us could transpose our data to the other’s frame of reference. The final numbers would come out the same for both of us. In essence, the special theory of relativity is not about what is relative, it is about what is absolute.

However, the special theory of relativity does show that appearances are dependent upon the state of motion of the observers. For example, the special theory of relativity tells us that (1) a moving object measures shorter in its direction of motion as its velocity increases until, at the speed of light, it disappears; (2) the mass of a moving object measures more as its velocity increases until, at the speed of light, it becomes infinite; and (3) moving clocks run more slowly as their velocity increases until, at the speed of light, they stop running altogether.

All of this is from the point of view of an observer to whom the object is moving. To an observer traveling along with the moving object, the clock keeps perfect time, ticking off sixty seconds each minute, and nothing appears to get any shorter or more massive. The special theory of relativity also tells us that space and time are not two separate things, but that together they form space-time, and that energy and mass are actually different forms of the same thing, mass-energy.

“This is not possible!” we cry. “It is nonsense to think that increasing the velocity of an object increases its mass, decreases its length, and slows its time.”

Our cup runneth over.

These phenomena are not observable in everyday life because the velocities required to make them noticeable are those approaching the speed of light (186,000 miles per
second
). At the slow speeds that we encounter in the macroscopic world, these effects are virtually undetectable. If they were, we would discover that a car traveling down the freeway is shorter than it is at rest, weighs more than it does at rest, and that its clock runs slower than it does at rest. In fact, we even would find that a hot iron weighs more than a cold one (because energy has mass and heat is energy).

How Einstein discovered all of this is another version of “The Emperor’s New Clothes.”

Only Albert Einstein looked at two of the major puzzles of his day and saw them with a beginner’s mind. The result was the special theory of relativity. The first puzzle of Einstein’s time was the constancy of the speed of light. The second puzzle of Einstein’s time was the uncertainty, both physical and philosophical, about what it means to be moving or not moving.
^*

“Wait a minute,” we say. “What is uncertain about that? If I am sitting in a chair and another person walks past me, then the person walking past me is in motion, and I, sitting in my chair, am not in motion.”

“Quite right,” says Jim de Wit, appearing on cue, “but still, it is not that simple. Suppose that the chair in which you are sitting is on an airplane and that the person walking past you is a stewardess. Suppose also that I am on the ground watching both of you go by. From your point of view, you are at rest and the stewardess is in motion, but from my point of view, I am at rest and
both
of you are in motion. It all depends upon your frame of reference. Your frame of reference is the airplane, but my frame of reference is the earth.”

De Wit, as usual, has discovered the problem exactly. Unfortunately, he has not solved it. The earth itself hardly is standing still. Not only is it spinning on its axis like a top, it and the moon are revolving around a common center of gravity while both of them circle the sun at eighteen miles per second.

“That’s not fair,” we say. “Of course, it is true, but the earth does not seem to be moving to us who live on it. It is only in motion if we change our frame of reference from it to the sun. If we start playing that game, it is impossible to find anything in the entire universe that is ‘standing still.’ From the point of view of the galaxy, the sun is moving; from the point of view of another galaxy, our galaxy is moving; from the point of view of a third galaxy, the first two galaxies are moving. In fact, from the point of view of each of them, the others are moving.”

“Nicely said,” laughs Jim de Wit, “and that is exactly the point. There is no such thing as something being absolutely at rest, unequivocally not moving. Motion, and the lack of it, is always relative to something else. Whether we are moving or not depends upon what frame of reference we use.”

The discussion above is
not
the special theory of relativity. In fact,
the discussion above is a part of the Galilean relativity principle which is over three hundred years old. Any physical theory is a theory of relativity if, like Jim de Wit, it acknowledges the difficulty of detecting absolute motion or absolute nonmotion. A theory of relativity assumes that the only kind of motion that we ever can determine is motion, or lack of it, relative to something else. Galileo’s principle of relativity says, in addition, that the laws of mechanics are equally valid in all frames of reference (physicists say “co-ordinate systems”) that move uniformly in relation to each other.

The Galilean relativity principle assumes that somewhere in the universe there exists a frame of reference in which the laws of mechanics are completely valid—that is, a frame of reference in which experiment and theory agree perfectly. This frame of reference is called an “inertial” frame of reference. An inertial frame of reference simply means a frame of reference in which the laws of mechanics are completely valid. All other frames of reference moving uniformly, relative to an inertial frame of reference, are also inertial frames of reference. Since the laws of mechanics are equally valid in all inertial frames of reference, this means that there is no way that we can distinguish between one inertial frame of reference and another by performing mechanical experiments in them.