The Dancing Wu Li Masters (7 page)

Some experiments show that light is wave-like. Other experiments show equally well that light is particle-like. If we want to demonstrate that light is a particle-like phenomenon or that light is a wave-like phenomenon, we only need to select the appropriate experiment.

According to quantum mechanics there is no such thing as objectivity. We cannot eliminate ourselves from the picture. We are a part of nature, and when we study nature there is no way around the fact that nature is studying itself. Physics has become a branch of psychology, or perhaps the other way round.

Carl Jung, the Swiss psychologist, wrote:

Jung’s friend, the Nobel Prize-winning physicist, Wolfgang Pauli, put it this way:

If these men are correct, then physics is the study of the structure of consciousness.

The descent downward from the macroscopic level to the microscopic level, which we have been calling the realm of the very small, is a two-step process. The first step downward is to the atomic level. The second step downward is to the subatomic level.

The smallest object that we can see, even under a microscope, contains millions of atoms. To see the atoms in a baseball, we would have to make the baseball the size of the earth. If a baseball were the size of the earth, its atoms would be about the size of grapes. If you can picture the earth as a huge glass ball filled with grapes, that is approximately how a baseball full of atoms would look.

The step downward from the atomic level takes us to the subatomic level. Here we find the particles that make up atoms. The difference between the atomic level and the subatomic level is as great as the difference between the atomic level and the world of sticks and rocks. It would be impossible to see the nucleus of an atom the size of a grape. In fact, it would be impossible to see the nucleus of an atom the size of a room. To see the nucleus of an atom, the atom would have to be as high as a fourteen-story building! The nucleus of an atom as high as a fourteen-story building would be about the size of a grain of salt. Since a nuclear particle has about 2,000 times more mass than an electron, the electrons revolving around this nucleus would be about as massive as dust particles!

The dome of Saint Peter’s basilica in the Vatican has a diameter of about fourteen stories. Imagine a grain of salt in the middle of the dome of Saint Peter’s with a few dust particles revolving around it at the outer edges of the dome. This gives us the scale of subatomic particles. It is in this realm, the subatomic realm, that Newtonian physics has proven inadequate, and that quantum mechanics is required to explain particle behavior.

A subatomic particle is not a “particle” like a dust particle. There is more than a difference in size between a dust particle and a sub
atomic particle. A dust particle is a
thing
, an object. A subatomic particle cannot be pictured as a thing. Therefore, we must abandon the idea of a subatomic particle as an object.

Quantum mechanics views subatomic particles as “tendencies to exist” or “tendencies to happen.” How strong these tendencies are is expressed in terms of probabilities. A subatomic particle is a “quantum,” which means a quantity of something. What that something is, however, is a matter of speculation. Many physicists feel that it is not meaningful even to pose the question. It may be that the search for the ultimate “stuff” of the universe is a crusade for an illusion. At the subatomic level, mass and energy change unceasingly into each other. Particle physicists are so familiar with the phenomena of mass becoming energy and energy becoming mass that they routinely measure the mass of particles in energy units.
^*
Since the tendencies of subatomic phenomena to become manifest under certain conditions are probabilities, this brings us to the matter (no pun) of statistics.

Because there are millions of millions of subatomic particles in the smallest space that we can see, it is convenient to deal with them statistically. Statistical descriptions are pictures of crowd behavior. Statistics cannot tell us how one individual in a crowd will behave, but they can give us a fairly accurate description, based on repeated observations, of how a group as a whole behaves.

For example, a statistical study of population growth may tell us how many children were born in each of several years and how many are predicted to be born in years to come. However, the statistics cannot tell us which families will have the new children and which ones will not. If we want to know the behavior of traffic at an intersection, we can install devices there to gather data. The statistics that these devices provide may tell us how many cars, for instance, turn left during certain hours, but not
which
cars.

Statistics is used in Newtonian physics. It is used, for example, to explain the relationship between gas volume and pressure. This relation is named Boyle’s Law after its discoverer, Robert Boyle, who lived in Newton’s time. It could as easily be known as the Bicycle Pump Law, as we shall see. Boyle’s Law says that if the volume of a container holding a given amount of gas at a constant temperature is reduced by one half, the pressure exerted by the gas in the container doubles.

Imagine a person with a bicycle pump. He has pulled the plunger fully upward, and is about ready to push it down. The hose of the pump is connected to a pressure gauge instead of to a bicycle tire, so that we can see how much pressure is in the pump. Since there is no pressure on the plunger, there is no pressure in the pump cylinder and the gauge reads zero. However, the pressure inside the pump is not actually zero. We live at the bottom of an ocean of air (our atmosphere). The weight of the several miles of air above us exerts a pressure at sea level of 14.7 pounds on every square inch of our bodies. Our bodies do not collapse because they are exerting 14.7 pounds per square inch outward. This is the state that we usually read as zero on a bicycle pressure gauge. To be accurate, suppose that we set our gauge to read 14.7 pounds per square inch before we push down on the pump handle.

Now we push the piston down halfway. The interior volume of the pump cylinder is now one half of its original size, and no air has been allowed to escape, because the hose is connected to a pressure gauge. The gauge now reads 29.4 pounds per square inch, or twice the original pressure. Next we push the plunger two thirds of the way down. The interior volume of the pump cylinder is now one third of its original size, and the pressure gauge reads three times the original pressure (44.1 pounds per square inch). This is Boyle’s Law: At a constant temperature the pressure of a quantity of gas is inversely proportional to its volume. If the volume is reduced to one half, the pressure doubles; if the volume is reduced to one third, the pressure triples, etc. To explain why this is so, we come to classical statistics.

The air (a gas) in our pump is composed of millions of molecules (molecules are made of atoms). These molecules are in constant
motion, and at any given time, millions of them are banging into the pump walls. Although we do not detect each single collision, the macroscopic effect of these millions of impacts on a square inch of the pump wall produces the phenomenon of “pressure” on it. If we reduce the volume of the pump cylinder by one half, we crowd the gas molecules into a space twice as small as the original one, thereby causing twice as many impacts on the same square inch of pump wall. The macroscopic effect of this is a doubling of the “pressure.” By crowding the molecules into one third of the original space, we cause three times as many molecules to bang into the same square inch of pump wall, and the “pressure” on it triples. This is the kinetic theory of gases.

In other words, “pressure” results from the group behavior of a large number of molecules in motion. It is a collection of individual events. Each individual event can be analyzed because, according to Newtonian physics, each individual event is theoretically subject to deterministic laws. In principle, we can calculate the path of each molecule in the pump chamber. This is how statistics is used in the old physics.

Quantum mechanics also used statistics, but there is a very big difference between quantum mechanics and Newtonian physics. In quantum mechanics, there is no way to predict individual events. This is the startling lesson that experiments in the subatomic realm have taught us.

Therefore, quantum mechanics concerns itself only with group behavior. It intentionally leaves vague the relation between group behavior and individual events because individual subatomic events cannot be determined accurately (the uncertainty principle) and, as we shall see in high-energy particles, they constantly are changing. Quantum physics abandons the laws which govern individual events and states
directly
the statistical laws which govern collections of events. Quantum mechanics can tell us how a group of particles will behave, but the only thing that it can say about an individual particle is how it
probably
will behave. Probability is one of the major characteristics of quantum mechanics.

This makes quantum mechanics an ideal tool for dealing with subatomic phenomena. For example, take the phenomenon of common radioactive decay (luminous watch dials). Radioactive decay is a phenomenon of predictable overall behavior consisting of unpredictable individual events.

Suppose that we put one gram of radium in a time vault and leave it there for sixteen hundred years. When we return, do we find one gram of radium? No! We find only half a gram. This is because radium atoms naturally disintegrate at a rate such that every sixteen hundred years half of them are gone. Therefore, physicists say that radium has a “half life” of sixteen hundred years. If we put the radium back in the vault for another sixteen hundred years, only one fourth of the original gram would remain when we opened the vault again. Every sixteen hundred years one half of all the radium atoms in the world disappear. How do we know which radium atoms are going to disintegrate and which radium atoms are not going to disintegrate?

We don’t. We can predict how many atoms in a piece of radium are going to disintegrate in the next hour, but we have no way of determining
which
ones are going to disintegrate. There is no physical law that we know of which governs this selection. Which atoms decay is purely a matter of chance. Nonetheless, radium continues to decay, on schedule, as it were, with a precise and unvarying half life of sixteen hundred years. Quantum theory dispenses with the laws governing the disintegration of individual radium atoms and proceeds directly to the statistical laws governing the disintegration of radium atoms as a group. This is how statistics is used in the new physics.

Another good example of predictable overall (statistical) behavior consisting of unpredictable individual events is the constant variation of intensity among spectral lines. Remember that, according to Bohr’s theory, the electrons of an atom are located only in shells which are specific distances from the nucleus. Normally, the single electron of a hydrogen atom remains in the shell closest to the nucleus (the ground state). If we excite it (add energy to it) we cause it to jump to a shell farther out. The more energy we give it, the farther out it jumps. If we stop exciting it, the electron jumps inward
to a shell closer to the nucleus, eventually returning all the way to the innermost shell. With each jump from an outer shell to an inner shell, the electron emits an energy amount equal to the energy amount that it absorbed when we caused it to jump outward. These emitted energy packets (photons) constitute the light which, when dispersed through a prism, forms the spectrum of one hundred or so colored lines that is peculiar to hydrogen. Each colored line in the hydrogen spectrum is made from the light emitted from hydrogen electrons as they jump from a particular outer shell to a particular inner shell.

What we did not mention earlier is that some of the lines in the hydrogen spectrum are more pronounced than others. The lines that are more pronounced are always more pronounced and the lines that are faint are always faint. The intensity of the lines in the hydrogen spectrum varies because hydrogen electrons returning to the ground state do not always take the same route.

Shell five, for example, may be a more popular stopover than shell three. In that case, the spectrum produced by millions of excited hydrogen atoms will show a more pronounced spectral line corresponding to electron jumps from shell five to shell one and a less pronounced spectral line corresponding to electron jumps from, say, shell three to shell one. That is because, in this example, more electrons stop over at shell five before jumping to shell one than stop over at shell three before jumping to shell one.

In other words, the probability is very high, in this example, that the electrons of excited hydrogen atoms will stop at shell five on their way back to shell one, and the probability is lower that they will stop at shell three. Said another way, we know that a certain number of electrons probably will stop at shell five and that a certain lesser number of electrons probably will stop at shell three. Still, we have no way of knowing
which
electrons will stop where. As before, we can describe precisely an overall behavior without being able to predict a single one of the individual events which comprise it.

This brings us to the central philosophical issue of quantum mechanics, namely, “What is
it
that quantum mechanics describes?” Put another way, quantum mechanics statistically describes the overall behavior and/or predicts the probabilities of the individual behavior of what?