With the awesome authority that we have given it, science is telling us that our faith has been misplaced. It appears that we have attempted the impossible, to disown our part in the universe. We have tried to do this by relinquishing our authority to the Scientists. To the Scientists we gave the responsibility of probing the mysteries of creation, change, and death. To us we gave the everyday routine of mindless living.
The Scientists readily assumed their task. We readily assumed ours, which was to play a role of impotence before the ever-increasing complexity of “modern science” and the ever-spreading specialization of modern technology.
Now, after three centuries, the Scientists have returned with their discoveries. They are as perplexed as we are (those of them who have given thought to what is happening).
“We are not sure,” they tell us, “but we have accumulated evidence which indicates that the key to understanding the universe is you.”
This is not only different from the way that we have looked at the world for three hundred years, it is opposite. The distinction between the “in here” and the “out there” upon which science was founded, is becoming blurred. This is a puzzling state of affairs. Scientists, using the “in here—out there” distinction, have discovered that the “in here—out there” distinction may not exist! What is “out there” apparently depends, in a rigorous mathematical sense as well as a philosophical one, upon what we decide “in here.”
The new physics tells us that an observer cannot observe without altering what he sees. Observer and observed are interrelated in a real and fundamental sense. The exact nature of this interrelation is not clear, but there is a growing body of evidence that the distinction between the “in here” and the “out there” is illusion.
The conceptual framework of quantum mechanics, supported by massive volumes of experimental data, forces contemporary physicists to express themselves in a manner that sounds, even to the uninitiated, like the language of mystics.
Access to the physical world is through experience. The common denominator of all experiences is the “I” that does the experiencing. In short, what we experience is not external reality, but our interaction with it. This is a fundamental assumption of “complementarity.”
Complementarity is the concept developed by Niels Bohr to explain the wave-particle duality of light. No one has thought of a better one yet. Wave-like characteristics and particle-like characteristics, the theory goes, are mutually exclusive, or complementary aspects of light. Although one of them always excludes the other, both of them are necessary to understand light. One of them always excludes the other because light, or anything else, cannot be both wave-like and particle-like at the same time.*
How can mutually exclusive wave-like and particle-like behaviors both be properties of one and the same light? They are not properties of light. They are properties of our interaction with light. Depending upon our choice of experiment, we can cause light to manifest either particle-like properties or wave-like properties. If we choose to demonstrate the wave-like characteristics of light, we can perform the double-slit experiment which produces interference. If we choose to demonstrate the particle-like characteristics of light, we can perform an experiment which illustrates the photoelectric effect. We can cause light to manifest both wave-like properties and particle-like properties by performing Arthur Compton’s famous experiment.
In 1923, Compton played the world’s first game of billiards with subatomic particles, and, in the process, confirmed Einstein’s seventeen-year-old photon theory of light. His experiment was not conceptually difficult. He simply fired x-rays, which everybody knows are waves, at electrons. To the surprise of most people, the x-rays bounced off the electrons as if they (the x-rays) were particles! For example, the x-rays which struck the electrons glancing blows were deflected only slightly from their paths. They did not lose much energy in the collision. However, those x-rays which collided more nearly head-on with electrons were deflected sharply. These x-rays lost a considerable amount of their kinetic energy (the energy of motion) in the collision.
Compton could tell just how much energy the deflected x-rays lost by measuring their frequencies before and after the collision. The frequencies of those x-rays involved in near head-on collisions were noticeably lower after the collision than before it. This meant that they had less energy after the collision than they had before the collision. Compton’s x-rays were impacting with electrons exactly the way that billiard balls impact with other billiard balls.
Compton’s discovery was intimately related to quantum theory. Compton could not have revealed the particle-like behavior of x-rays if Planck had not discovered his fundamental rule that higher frequency means higher energy. This rule permitted Compton to prove that the x-rays in his experiment lost energy in a particle-like collision (because their frequencies were lower after the collision than before the collision).
The conceptual paradox in Compton’s experiment shows how deeply the wave-particle duality is embedded in quantum mechanics. Compton proved that electromagnetic radiations, like x-rays, have particle-like characteristics by measuring their frequencies! Of course, “particles” don’t have frequencies. Only waves have frequencies. The phenomenon which Compton discovered is called Compton scattering, in honor of what happens to the x-rays.
In short, we can demonstrate that light is particle-like with the photoelectric effect, that it is wave-like with the double-slit experiment, and that it is both particle-like and wave-like with Compton scattering. Both of these complementary aspects of light (wave and particle) are necessary to understand the nature of light. It is meaningless to ask which one of them, alone, is the way light really is. Light behaves like waves or like particles depending upon which experiment we perform.
The “we” that does the experimenting is the common link that connects light as particles and light as waves. The wave-like behavior that we observe in the double-slit experiment is not a property of light, it is a property of our interaction with light. Similarly, the particle-like characteristics that we observe in the photoelectric effect are not a property of light. They, too, are a property of our interaction with light. Wave-like behavior and particle-like behavior are properties of interactions.
Since particle-like behavior and wave-like behavior are the only properties that we ascribe to light, and since these properties now are recognized to belong (if complementarity is correct) not to light itself, but to our interaction with light, then it appears that light has no properties independent of us! To say that something has no properties is the same as saying that it does not exist. The next step is this logic is inescapable. Without us, light does not exist.
Transferring the properties that we usually ascribe to light to our interaction with light deprives light of an independent existence. Without us, or by implication, anything else to interact with, light does not exist. This remarkable conclusion is only half the story. The other half is that, in a similar manner, without light, or, by implication, anything else to interact with, we do not exist! As Bohr himself put it:
…an independent reality in the ordinary physical sense can be ascribed neither to the phenomena nor to the agencies of observation.1
By “agencies of observation,” he may have been referring to instruments, not people, but philosophically, complementarity leads to the conclusion that the world consists not of things, but of interactions. Properties belong to interactions, not to independently existing things, like “light.” This is the way that Bohr solved the wave-particle duality of light. The philosophical implications of complementarity became even more pronounced with the discovery that the wave-particle duality is a characteristic of everything.
When we left off telling the story of quantum mechanics, the tale had progressed as follows: In 1900, Max Planck, studying black-body radiation, discovered that energy is absorbed and emitted in chunks, which he called quanta. Until that time, radiated energy, like light, was thought to be wave-like.
This was because Thomas Young, in 1803, showed that light produces interference (the double-slit experiment), and only waves can do that.
Einstein, stimulated by Planck’s discovery of quanta, used the photoelectric effect to illustrate his theory that not only are the processes of energy absorption and emission quantized, but that energy itself comes in packages of certain sizes. Thus physicists were confronted with two sets of experiments (repeatable experiences) each of which seemed to disprove the other. This is the famous wave-particle duality which is fundamental to quantum mechanics.
While physicists were trying to explain how waves can be particles, a young French prince, Louis de Broglie, dropped a bomb which demolished what was left of the classical view. Not only are waves particles, he proposed, but particles are also waves!
De Broglie’s idea (which was contained in his doctoral thesis) was that matter has waves which “correspond” to it. The idea was more than philosophical speculation. It was also mathematical speculation. Using the simple equations of Planck and Einstein, de Broglie formulated a simple equation of his own.* It determines the wavelength of the “matter waves” that “correspond” to matter. It says simply that the greater the momentum of a particle, the shorter is the length of its associated wave.
This explains why matter waves are not evident in the macroscopic world. De Broglie’s equation tells us that the matter waves corresponding to even the smallest object that we can see are so incredibly small compared to the size of the object that their effect is negligible. However, when we get down to something as small as a subatomic particle, like an electron, the size of the electron itself is smaller than the length of its associated wave!
Under these circumstances, the wave-like behavior of matter should be clearly evident, and matter should behave differently than “matter” as we are used to thinking of it. This is exactly what happens.
Only two years after de Broglie presented this hypothesis, an experimenter named Clinton Davisson, working with his assistant, Lester Germer, at the Bell Telephone Laboratories, verified it experimentally. Both Davisson and de Broglie got Nobel Prizes, and physicists were left to explain not only how waves can be particles, but also how particles can be waves.
The famous Davisson-Germer experiment, which was done by accident, showed electrons reflecting off a crystal surface in a manner that could be explained only if the electrons were waves. But, of course, electrons are particles.
Today, electron diffraction, an apparent contradiction in terms, is a common phenomenon. When a beam of electrons is sent through tiny openings, like the spaces between the atoms in a metal foil, which are as small or smaller than the wavelengths of the electrons (isn’t this ridiculous—“particles” don’t have wavelengths!), the beam diffracts exactly the way a beam of light diffracts. Although, classically speaking, it can’t happen, here is a picture of it.*
It was disconcerting enough when light, which is made of waves, began to behave like particles, but when electrons, which are particles, began to behave like waves, the plot became unbearably thick.
The unfolding of quantum mechanics was (and still is) a drama of high suspense. Werner Heisenberg wrote:
I remember discussions with Bohr [in 1927] which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighboring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed to us in these atomic experiments.2
Subsequent experiments were to reveal that not only subatomic particles, but atoms and molecules as well have associated matter waves. The title of Donald Hughes’s pioneer book, Neutron Optics, provides eloquent testimony of the merger between waves and particles to which Prince de Broglie’s doctoral thesis gave birth. Theoretically, in fact, everything has a wavelength—baseballs, automobiles, and even people—although their wavelengths are so small that they are not noticeable.
De Broglie himself was not very helpful in explaining his theory. It predicted what the Davisson-Germer experiment proved: that matter, like electrons, has a wave-like aspect. His equation even foretold the wavelength of these waves. Nonetheless, no one knew what these waves actually were (no one does yet). De Broglie called them waves which “correspond” to matter, but he did not explain what “correspond” meant.
Is it possible for a physicist to predict something, calculate equations which describe it, and still not know what he is talking about?
Yes. As Bertrand Russell put it:
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.3
This is why the physicists at Copenhagen decided to accept quantum mechanics as a complete theory even though it gives no explanation of what the world is “really like,” and even though it predicts probabilities and not actual events. They accepted quantum mechanics as a complete theory because quantum mechanics correctly correlates experience. Quantum mechanics, and, according to the pragmatists, all science, is the study of correlations between experiences. De Broglie’s equation correctly correlates experiences.
De Broglie merged the wave-particle paradox which came to light (hissss) through the genius of Thomas Young (double-slit experiment) and Albert Einstein (photon theory). In other words, he connected the two most revolutionary phenomena of physics, the quantum nature of energy and the wave-particle duality.
De Broglie presented his matter-wave theory in 1924. During the next three years quantum mechanics crystallized into what it essentially is today. The world of Newtonian physics, simple mental pictures, and common sense disappeared. A new physics took form with an originality and force that left the mind reeling.
After de Broglie’s matter waves came the Schrödinger wave equation.
De Broglie’s matter waves seemed to Erwin Schrödinger, the Viennese physicist, a much more natural way of looking at atomic phenomena than Bohr’s planetary model of the atom. Bohr’s model of hard, spherical electrons revolving around a nucleus at specific levels and emitting photons by jumping from one level to another explained the color spectrum of simple atoms, but it said nothing about why each shell contains only a certain number of electrons, no more and no less. It also did not explain how the electrons do their jumping (for example, what is happening to them between shells).*
Stimulated by de Broglie’s discovery, Schrödinger hypothesized that electrons are not spherical objects, but patterns of standing waves.
Standing waves are familiar phenomena to anyone who has played with a clothesline. Suppose that we tie one end of a rope to a pole, and then pull it tight. On this rope there are no waves at all, either standing or traveling. Now suppose that we flick our wrist sharply downward and then upward. A hump appears in the rope and travels down the rope to the pole where it turns upside down and returns to our hand. This traveling hump (figure A) is a traveling wave. By sending a series of humps down the rope, we can set up the patterns of standing waves shown below, and more that are not shown.
The simplest of these is the pattern shown in figure B. This pattern is formed by the superposition of two traveling waves, a direct one and a reflected one traveling in the opposite direction. It is the pattern, not the rope, which does not move. The widest point in the standing wave remains “stationary,” and so do the points at the ends of the standing wave. These points are called nodes. There are two of them in the simplest standing pattern, one at our hand and one at the pole where the rope is attached. These stationary patterns, superpositions of traveling waves, are called standing waves.
No matter how long or short our rope is, there can be only a whole number of standing waves on it. That is, it can have a pattern of one standing wave, or a pattern of two standing waves, or a pattern of three, four, five, and so on, standing waves but it can never have a pattern of one and one half standing waves, or a pattern of two and one fourth standing waves. The standing waves must divide the rope evenl
y into whole sections. Another way to say this is that we can increase or decrease the number of standing waves on a rope only by a whole number of them. This means that the only way that the number of standing waves on a rope can increase or decrease is discontinuously (that word, again!).
Furthermore, standing waves on a rope cannot be just any size. They always will be restricted to those lengths which divide the rope evenly. The actual size of the waves depends upon how long the rope is, but no matter what length the rope, there will be only certain lengths which divide it evenly.
All of this was old stuff in 1925. Plucking a guitar string establishes patterns of standing waves on it. Blowing air into an organ pipe creates standing wave patterns in it. What was new was Schrödinger’s realization that standing waves are “quantized” the same way that atomic phenomena are! In fact, Schrödinger proposed that electrons are standing waves.
In retrospect, this is not as fantastic as it first sounds. At the time, however, it was a stroke of genius. Picture an electron in orbit around a nucleus. Each time the electron completes a journey around the nucleus, it travels a certain distance. That distance is a certain length, like our rope was a certain length. Similarly, only a whole number of standing waves, never a fraction of one, can form in this length. (Length of what is an unanswered question.)
Schrödinger proposed that each of these standing waves is an electron! In other words, he proposed that electrons are the segments of vibrations bounded by the nodes. A drawing of this is on the next page.
So far, we have talked about standing waves on a line, like a clothesline or a guitar string, but standing waves also occur in other mediums, like water. Suppose that we throw a rock into a round pool. Waves radiate from its point of entry. These waves are reflected, sometimes more than once, off different sides of the pool. When the reflected traveling waves interfere with each other they create a complex pattern of standing waves which is our old friend, interference.