Abstract Six years after Kelvin made this claim, he hedged: “Physics is essentially complete: There are just two dark clouds on the horizon.” He picked the right clouds: One hid relativity; the other, quantum mechanics. But before we look behind those clouds, we tell a bit more of the nineteenth-century physics we today call “classical.” We will describe the phenomenon of “interference,” which demonstrates something to be a widely extended wave. We will need the concept of electric field. Light is a rapidly varying electric field, and it is with light that the quantum enigma first arose. We will also talk of energy and its “conservation,” its unchanging totality. And we will briefly tell of Einstein’s theory of relativity. Its well-confirmed but hard-to-believe predictions are good psychological practice for the “impossible-to-believe” implications of quantum theory. There’s somewhat more in this chapter than you actually need to know in order to understand the quantum enigma. But it’s good background.
Abstract Six years after Kelvin made this claim, he hedged: “Physics is essentially complete: There are just two dark clouds on the horizon.” He picked the right clouds: One hid relativity; the other, quantum mechanics. But before we look behind those clouds, we tell a bit more of the nineteenth-century physics we today call “classical.” We will describe the phenomenon of “interference,” which demonstrates something to be a widely extended wave. We will need the concept of electric field. Light is a rapidly varying electric field, and it is with light that the quantum enigma first arose. We will also talk of energy and its “conservation,” its unchanging totality. And we will briefly tell of Einstein’s theory of relativity. Its well-confirmed but hard-to-believe predictions are good psychological practice for the “impossible-to-believe” implications of quantum theory. There’s somewhat more in this chapter than you actually need to know in order to understand the quantum enigma. But it’s good background.
Abstract Toward the end of the nineteenth century Lord Kelvin, one of the best known and most respected physicists at that time, commented that “only two small clouds” remained on the horizon of knowledge in physics. In other words, there were, in Kelvin’s view, only two sources of confusion in our otherwise complete understanding of material reality. The two clouds were the results of the Michelson-Morley experiment, which failed to detect the existence of a hypothetical substance called the ether, and the inability of electromagnetic theory to predict the distribution of radiant energy at different frequencies emitted by an idealized “radiator” called the black body. These problems seemed so small that some established physicists were encouraging those contemplating graduate study in physics to select other fields of scientific study where there was more opportunity to make original contributions to knowledge. What Lord Kelvin could not have anticipated was that efforts to resolve these two anomalies would lead to relativity theory and quantum theory, or to what came to be called the new physics.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
At the close of the nineteenth century, we stood on the threshold of one of the greatest periods of science, in which the entire world and understanding of science would be shaken to the core and greatly modified. This explosion of knowledge led ultimately to that same information revolution that we live in today. Planck and Einstein showed that light was not continuous but made of small corpuscles that today we call photons. Einstein changed the understanding of mechanics with his theory of relativity: airplanes became conceivable; radio and television blossomed; and the microelectronics industry, which drives most of modern technology, came into being. New areas of science were greatly expanded and developed, and one of these was quantum mechanics, which is the story to be told here. Yet, the development of quantum mechanics and the leadership of Niels Bohr have distorted the understanding of quantum mechanics in a strange way. There are some who would say that Bohr set back the real understanding of quantum mechanics by half a century. I believe they underestimate his role, and it may be something more like a full century. Whether we call it the Copenhagen interpretation, or the Copenhagen orthodoxy, it is the how for the continuing mysticism provided by Mach that is still remaining in quantum mechanics. It is not the why. Why it perseveres and why it was forced on the field in the first place is an important perception to be studied. In this book, I want to trace the development of quantum mechanics and try to uncover the why.
I conclude the first part of this book by carrying the story up to 1928, to the lightning flash in Eddington's mind produced by Dirac's paper on the wave equation of the electron. Setting out the context and Eddington's thinking about it is a very different matter for quantum mechanics and relativity. Both theories are commonly expressed in austere mathematical language. In the case of relativity the basic ideas behind the mathematics are now well understood and can be set out with little complication. These ideas were mostly already clear to Eddington. But for quantum mechanics the mathematics, yoked to the wealth of experimental results, drove the development of the theory at a breakneck speed, mostly without anyone pausing for deeper understanding. It is indeed only in the last decade that it has become generally accepted that quantum mechanics still lacks any coherent interpretation. To explain Eddington's context it is therefore necessary to say something about the mathematical formalism. It is true, as will become clear, that Eddington was a little more sceptical than most, but by and large the mathematics drove him as it did those directly working in the theory. I begin, then, with a description of that part of the early (pre-1925) history of quantum mechanics that was in Eddington's mind in 1923. Then I explain what happened in 1925–6 and Eddington's reaction to it. The chapter concludes with Dirac's relativistic wave equation of 1928 and Eddington's further reaction to that. The old quantum theory What is now called the old quantum theory arose at the turn of the century. Two related experimental contradictions with classical physics played important roles in this.
Science has developed through a variety of investigations more or less over the time scale of human existence. On this scale, quantum mechanics is an extremely young field, existing essentially for only just over a century. Even our understanding of classical mechanics has existed for a comparatively long period—roughly having been formalized with Newton's equations published in his Principia Mathematica , in April 1686 (1687). Up until the very end of the nineteenth century, mechanics in the form of Newton's laws were comfortable, being understood and accepted by all who dealt with the motion of reasonable bodies. With the turn of the new century, however, mechanics would be shaken to its roots. The change began already on December 14, 1900, when Planck (1900) presented his new theory of black-body radiation to the German Physical Society, and this change would affect mechanics in physically small structures (and lead to quantum mechanics). Mechanics of large bodies would similarly be changed in 1905 with the arrival of Albert Einstein's (1905a) relativity theory. In this book, we will deal with only the first of these two great breakthroughs.
Unlike special relativity, quantum mechanics was not the inspired product of one mind. It developed, in fits and starts, over a period of 25 years (1900–1925), and many cooks stirred the broth. Even now, a century later, quantum mechanics raises profound conceptual questions. Every competent physicist can “do” quantum mechanics, and the predictions it makes are in spectacularly good agreement with experimental results; there can be little doubt that quantum mechanics is “right.” On the other hand, as Richard Feynman once remarked, “nobody understands quantum mechanics.” I'll tell the story in two parts. First the history (how the essential pieces of the puzzle were assembled), and then the implications (what the finished picture has to say about our world). Photons Like relativity, quantum mechanics began with the study of light. In both cases, this historical association is misleading. Relativity, really, has nothing to do with light – to be sure, it involves that magic speed limit, c , and of course the most familiar thing that travels at speed c is light. So light is a convenient vehicle for introducing the subject. But it is perfectly possible to imagine a universe in which there is no such thing as light, and yet relativity might still be valid. Quantum mechanics, too, starts with light – in this case the “quantum” of light (the photon). But, as it turns out, this is just one rather specialized example of much more general principles – in fact, a rather bad example, because photons are by their nature relativistic (they travel at the speed of light), and it would be more natural to begin with the quantum mechanics of slow-moving objects, in analogy with Newtonian mechanics.