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| Introduction | xi | ||||
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| Appendices | 251 | (14) | |||
| Notes | 265 | (8) | |||
| Bibliography | 273 | (4) | |||
| Index | 277 |
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Chapter One
Mach's Shadow
During the first conversation between Albert Einstein and Werner Heisenberg, Einstein was critical of Heisenberg's "new quantum mechanics." Heisenberg tried to defend the new theory: He pointed out that in its formulation he followed the requirements of Ernst Mach, the same requirements that guided Einstein in his discovery of Special Relativity. Einstein, however, did not budge. His astonishing comment "It is the theory which decides what we can observe" made a deep impression on young Heisenberg. This conversation was a precursor of the celebrated Bohr-Einstein debate.
* * *
All physicists of the last century saw in classical physics a firm and final foundation for all physics, yes, indeed, for all natural science.... It was Ernst Mach who, in his History of Mechanics , shook this dogmatic faith; this book exerted a profound influence upon me in this regard while I was a student. --Albert Einstein
1. The New Quantum Mechanics
On April 28, 1926, a young lecturer from the University of Göttingen addressed the physics colloquium at the University of Berlin. The colloquium was a venerable institution, attended by the entire staff of the physics department, a department that was, at the time, the center of physics research in Germany and beyond.
The name of the speaker was Werner Heisenberg, and the audience he addressed was august indeed. It included Max Planck, who started the quantum revolution in 1900 with his discovery that light is emitted and absorbed in discrete packets of energy called "quanta," Max yon Laue, who deciphered the nature of X-rays and revolutionized the study of crystals, Walter Nernst, who discovered the third law of thermodynamics, and Albert Einstein.
The subject of Heisenberg's lecture was "the new quantum mechanics," a theory that he developed in 1924 and 1925 in collaboration with Max Born and Pascal Jordan. The word new distinguishes the theory from what is now called "early quantum mechanics," a collection of theories formulated by Max Planck, Albert Einstein, Niels Bohr, and others during the first two decades of the twentieth century.
The new theory provided "a coherent mathematical framework, one that promised to embrace all the multifarious aspects of atomic physics." Its discovery was an impressive achievement. And yet the presentation was bizarre. The theory was supposed to account for atomic phenomena, but Heisenberg was very careful not to describe what is going on inside atoms; in particular, he was careful not to address the burning issues of the day--"quantum jumps" and "the wave-particle duality."
The term "quantum jumps" refers to a model of the hydrogen atom that Niels Bohr proposed more than a decade earlier. According to Bohr's model, atoms are like miniature solar systems: The light electrons revolve around massive nuclei, just as the planets revolve around the sun. But there is a crucial difference: In the case of the solar system there is no special reason for the planets to be at particular distances from the sun. They just happen to occupy the orbits in which we find them; they might just as well have occupied other orbits. In Bohr's model, however, only certain orbits are "allowed." One never finds electrons anywhere except at these allowed orbits. But since they do change orbits, they must be capable of "jumping" from one allowed orbit to another. It is precisely during such jumps that an atom emits or absorbs packets, or "quanta" of light, also known as "photons." What is the nature of these quantum jumps? Should one think of an electron inside an atom as a little object circulating around a nucleus in an allowed orbit and, in some circumstances, jumping to another allowed orbit? If so, why don't we ever see an electron while it is jumping? This was one issue that Heisenberg was careful to avoid.
The other major issue that he ignored was "the wave-particle duality." In everyday life particles and waves are very different entities. A particle is an object that moves in space, while a wave is a pattern of vibrations that propagates from one place to another. The pattern is carried by a medium, but the particles that make up the medium do not go with the wave. Consider, for example, what happens when one drops a pebble into a quiet pond. A circular wave starts propagating, but the water particles do not move away from the pebble. They simply vibrate up and down, and these vibrations cause the circular pattern to travel further and further away from the place where the pebble was dropped.
In everyday life a phenomenon can be either a particle or a wave; it cannot be both. If an object travels, it is a particle. If a pattern travels while the medium in which it travels just vibrates, it is a wave. A tennis ball is a particle. Sound is a sequence of waves. As we will see, however, this clear distinction was put into question by the results of experiments on light and on electrons. In some circumstances light and electrons behave as if they were particles; in others, as if they were waves. What are they, really? This issue became known as "the wave-particle duality."
When Heisenberg presented his theory at the physics colloquium he was careful to avoid anything that seemed like a description or a presentation of a model. He confined himself to the presentation of a mathematical procedure for calculating the results of experiments. He was, incredible as this may sound, firmly convinced that in doing so he provided a full explanation of the atomic phenomena he was discussing! Young Heisenberg, like young Einstein before him, was thinking and working under the long shadow of Ernst Mach.
2. The Legacy of Ernst Mach
Nowadays the ideas of Ernst Mach are hardly known, even among intellectuals. His name is remembered only in the context of the term "Mach number," a unit of measurement of the speed of airplanes. The name of the unit was chosen to honor Mach's contribution to the study of aerodynamics; his contributions to philosophy are all but forgotten. At the turn of the century, however, Ernst Mach was a towering figure, influential not only in physics and philosophy but even in sociology and politics. No less a leader than Vladimir Ilych Lenin found it necessary, in 1908, to set aside his pressing duties as the head of the Bolshevik party and devote a few months to the writing of a voluminous book, Materialism and Empiriocriticism , devoted in large measure to the refutation of Mach's philosophy. Lenin saw the spread of Mach's views as a threat to Carl Marx's philosophy of "dialectical materialism," which was the theoretical foundation of the communist revolution he was preparing.
The forbidding term "empiriocriticism" is the name of Mach's philosophical system, The system must have been "in the air" in the latter part of the nineteenth century, because it was proclaimed, more or less simultaneously and independently, by two thinkers, Ernst Mach and Richard Avenarius. Empiriocriticism is both a philosophical system regarding the nature of reality and a philosophy of science. The following summary of some of its main ideas will give a taste of Mach's thought.
Science, according to Mach, is nothing more than a description of facts. And "facts" involve nothing more than sensations and the relationships among them. Sensations are the only real elements. All the other concepts are extra; they are merely imputed on the real, i.e., on the sensations, by us. Concepts like "matter" and "atom" are merely shorthand for collections of sensations; they do not denote anything that exists. The same holds for many other words, such as "body."
Mach carried his philosophy to its logical conclusion. Consider the case of a pencil that is partially submerged in water. It looks broken, but it is really straight, as we can verify by touching it. Not so, says Mach. The pencil in the water and the pencil out of the water are merely two different facts. The pencil in the water is really broken, as far as the fact of sight is concerned, and that's all there is to it.
Since science is, for Mach, just the description of facts, it does not aim at finding the math about reality. It does not aim at finding the truth about anything. Its sole function is the achievement of "economy of thought," the description of the greatest possible number of facts using the smallest possible mental effort. A law of nature is valuable not because it is, in any sense, true but because it is a concise description of a large number of facts. Consider, for example, the phenomenon of free fall. One way to describe it is to create an enormous collection of data coveting all the results of all the experiments conducted with falling bodies. Another way is to formulate the law of free fall, the law that says that the velocity of the falling object keeps increasing at a constant rate. According to Mach, the second way is superior to the first only because it is more economical. As far as "understanding" goes, both ways are equal.
Empiriocriticism arose as a reaction to the speculative German philosophy of the nineteenth century, an entangled, verbose mess of intricate "world-views," having little to do with either empirical evidence or clarity of thought. In this climate the simplicity, directness, and compelling logical coherence of Mach's presentations were a breath of fresh air. Many scientists were fascinated. Mach's approach cut through persistent dichotomies, e.g., matter vs. mind, and demanded an unprecedented rigor of thought. Every concept used in science had to have an "operational definition": One was not allowed to name a quantity unless one could specify how it could be measured. This led to fruitful reexamination of basic concepts, such as space, time, and energy. Yet this call for a precision of thought was deeply problematic. It was arrived at on the basis of faulty metaphysics, as we shall see.
Lenin was right, I believe, when he considered Mach a great physicist and a small philosopher. The blatant fallacies in Mach's philosophical arguments have been pointed out by many, Lenin and Einstein included. Einstein accepted Mach's system in his youth and disowned it in his forties. We will come to Einstein's thoughts on the matter in the next section. Here I will limit myself to a few critical comments of my own.
One role of science is to explain phenomena, and an explanation is different from "economy of thought." Consider the example of tides. People made accurate tables of the times of high and low tides in many locations, but the phenomenon of tides was not understood until Newton came along and explained it as the joint effect of the gravitational pull of the sun and the moon on the waters of the oceans. This discovery did not make it possible to calculate the times of high and low tides in specific locations. These depend on many complicated factors, such as the contours of the shores, the depth of the oceans at other locations, and so on; the complexity of these factors makes it impossible to calculate the tables of tides on the basis of Newton's laws. Newton's discovery did not lead to economy of thought; the tide tables continued to be produced from the records of local observations. But it did explain the phenomenon of tides.
Furthermore, the view of science as merely a system for thought economy is contrary to the experiences of many great scientists. They experience their acts of discovery as acts of seeing into the hidden workings of nature, not as acts of figuring out how to condense large bodies of information into "economical" packages. Heisenberg himself described his experience of discovering the new quantum mechanics in the following words:
At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures that nature had so generously spread out before me.
It seems to me that Mach's view is especially deficient in that it limits "the real" to the sensory. It implies that the attempts to explore the depths of reality are meaningless, because reality does not have any depth! And yet, sometimes, while listening to a piece of music, we feel that the sounds are merely a vehicle, and what they convey is something else, something that resonates in us on a level that is deeper than that of an ordinary sensation.
3. "It Is the Theory Which Decides What We Can Observe"
When Heisenberg's lecture was over, Einstein invited the young lecturer to accompany him on his walk home. The opportunity to have a conversation with Einstein must have been exciting for Heisenberg, and he must have expected to receive a pat on the back. After all, his achievement in atomic physics was accomplished using the same approach that guided Einstein two decades earlier when he discovered Special Relativity, the theory that revolutionized the concepts of space and time! Einstein arrived at his theory by following Mach's approach and analyzing very carefully the operational meaning of the statement "Two events that took place far away from each other happened at the same time." Similarly, Heisenberg arrived at the new quantum mechanics by analyzing very carefully what was actually being measured in atomic experiments. In doing that he was guided, in fact, by a comment of Einstein's, reported to him by a friend, to the effect that "physicists must consider none but observable magnitudes while trying to solve the atomic puzzle."
To Heisenberg's surprise and dismay, however, Einstein did not like what he had heard at the colloquium. He criticized Heisenberg for following his own advice!
"You don't seriously believe," Einstein said, "that none but observable magnitudes go into a physical theory?"
"Isn't that precisely what you had done with relativity?" Heisenberg protested. "After all you did stress the fact that it is impermissible to speak of absolute time, simply because absolute time cannot be observed; that only clock readings, be it in the moving reference frame or the system at rest, are relevant to the determination of time."
"Possibly I did use this kind of reasoning," Einstein responded, "but it is nonsense all the same ... on principle it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe."
" It is the theory which decides what we can observe! " What did Einstein mean?
Look at Figure 1.1. What do you see? I showed it to two of my friends, Alan, a musician, and Jane, an electrical engineer. Alan said, "This is a bunch of lines. I have no idea what they mean." Jane got excited when she saw the picture. "This must be a photograph of a cloud chamber event," she said. "Most of these sluggish lines must represent slow electrons. But look at this line across the picture! This is a really fast one!"
Both Alan and Jane saw facts. But they saw two different sets of facts. Alan had no interest in physics; he did not know the theory behind the photographs, so what he observed was almost meaningless. Jane, who had studied physics, knew that a cloud chamber is a detector of atomic and subatomic particles, and she knew how it works: It is a transparent jar that contains supercooled gas, that is, a gas that has not condensed to become liquid, in spite of being cold enough to do so. Supercooled gas is unstable. Any slight disturbance, such as the passage of an electron, is enough to trigger condensation along the path of passage; the tiny drops of liquid that show up in the photograph indicate the trajectory of the electron. She was not thinking about that when she looked at the photograph, and yet it was this theory that determined what she observed.
And there is more. Alan too saw something, a picture that looked like a collection of lines. To see even that much, he too relied on theory. Both Alan and Jane know the principles of photography; and they understand seeing as a process that is initiated by light impinging on the retina and continues with signals traveling through the nervous system and reaching the brain. "Along this whole path," Einstein explained, "from the phenomenon to its fixation in our consciousness, we must be able to tell how nature functions, must know the natural laws at least in practical terms, before we can claim to have observed anything at all." The understanding of photography and of seeing need not be explicit. I believe that this is the import of Einstein's phrase "at least in practical terms." Perhaps the word "theory" should have been replaced by the word "paradigm," which includes both explicit and tacit knowledge and belief. At any rate, there is no question that theory, i.e., explicit knowledge, and belief as to how nature works do each play an essential part in an act of observation.
If the theory decides what we can observe, how is it possible to come up with a new theory, then confirm it by observations? The theory that "determines what we can observe," Einstein explained, contains many elements. The discovery of a new theory involves changing one of these elements and keeping the others intact. For example, analyzing Figure 1.1, one can come up with a new theory about the electron; but the theories of supercooled gases, and of the principles of photography, stay the same. As we will see later on, Heisenberg made his second great leap, the discovery of the celebrated uncertainty principle, precisely through such a reinterpretation of what seemed like electron trajectories in a cloud chamber.
Listening to Einstein's explanations, Heisenberg was torn between his belief in Mach's doctrine, with which he was not prepared to part, and the realization that Einstein was right. "The idea that a good theory is no more than a condensation of observations in accordance with the principle of thought economy surely goes back to Mach," he said, "and it has, in fact, been said that your relativity theory makes decisive use of Machian concepts. But what you have just told me seems to indicate the very opposite. What am I to make of all this, or rather what do you yourself think about it?"
Einstein responded by explaining that he was no longer an adherent of Mach's philosophy. He regarded Mach as being too naive. He suggested considering simple everyday concepts, like the word "ball." What does the word "ball" mean? Is it merely the result of thought economy, a condensation of the sensory experiences that involve balls? No, Einstein argued. We are convinced that the ball really exists , and this feeling of actual existence goes beyond thought economy. It means, for example, that we expect the ball to give us new experiences in the future; we associate with the word "ball" possibilities and expectations, which a mere condensation of past experiences does not include. Einstein saw Mach's ideas as naive, because Mach assumed that he knew what it means "to observe" and did not appreciate the complexity of an act of observation. He did not realize, for example, that "it is the theory which decides what we can observe."
4. Leaving Mach Behind
The conversation between Einstein and Heisenberg moved on to other subjects, such as the question of what can and cannot be described by an acceptable quantum theory. Einstein believed that the new quantum theory presented by Heisenberg was deficient, that it left too many issues unresolved. Heisenberg admitted that the theory was still too new to tackle the thorniest issues. They parted without an agreement, but with the expectation of continuing their discussions in the future.
The conversation with Einstein must have been, for Heisenberg, a disappointing experience. And yet Einstein's statement "It is the theory which decides what we can observe" made a strong impression on him and was later instrumental in leading him to the discovery of the uncertainty principle.
Unbeknownst to either of them, this conversation was the first move in what was to become the most remarkable controversy in twentieth-century physics. Because of the differences in age and stature in the scientific world (Heisenberg was twenty-five, fresh out of graduate school, while Einstein, at forty-seven, was at the height of his acclaim), Heisenberg was in no position to confront Einstein with a new, revolutionary paradigm about the task of physics, especially since the Machian position he was trying to defend was, indeed, indefensible. By the autumn of 1927, however, Einstein met his match.
Niels Bohr, the man who discovered the first successful model of the atom, was, more or less, a contemporary of Einstein and, just like Einstein, an acknowledged authority on the foundations of physics. The Solvay Conference in Brussels, in 1927, was the site of the first powerful clash between these two great thinkers, who, while having the highest respect for each other, totally disagreed about practically everything concerning the budding quantum theory. Their clash was a clash of paradigms. The disagreement about the quantum theory uncovered a basic disagreement about what physical reality is and what can be known about it.
In the discussions that took place between Einstein and Bohr, Mach was left behind. Both thinkers were too mature and too profound to take Mach seriously. By the 1920s Einstein had replaced his earlier adherence to Mach's philosophy with his own version of realism, a belief in an objective world, the existence of which is independent of acts of perception. Bohr came from an altogether different philosophical tradition. Influenced by Harald Høffding, who was, in turn, influenced by Søren Kierkegaard, Bohr was neither interested in Mach nor attached to realism. When it became clear that Einstein's version of realism was incompatible with quantum mechanics, Bohr made heroic yet vain efforts to move Einstein away from his cherished philosophical stance. Believing that quantum mechanics is a fundamental theory, he tried to usher Einstein into the new philosophical vistas that quantum mechanics opened up, but failed. As we go along we will explore these vistas, as well as Einstein's brilliant defense of his philosophical position. The presentation of this philosophical position is the subject of the next chapter.
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