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.
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.
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
By the beginning of the twentieth century, classical physics had accumulated many contradictions that could only be resolved by changing the main concepts of space and time (Einstein’s theory of relativity, Chapter P1) and the laws of motion of particles on atomic scales (quantum mechanics). The first quantum concepts appeared at the very beginning of the century (Planck’s formula for thermal radiation and Einstein’s formula for photoeffect, Chapter P5), but quantum mechanics as a closed science was not constructed until the end of the 1920s.
Even the experts do not understand it the way they would like to, and it is perfectly reasonable that they should not, because all of direct, human experience and of human intuition applies to large objects. Richard P. Feynman Two great intellectual triumphs occurred in the first quarter of the twentieth century: the invention of the theory of relativity, and the rather more labored arrival of quantum mechanics. The former largely embodies the ideas, and almost exclusively the vision, of Albert Einstein; the latter benefited from many creative minds, and from a constant interplay between theory and experiment. Probability plays no direct role in relativity, which is thus outside the purview and purpose of this book. However, Einstein will make an appearance in the following pages, in what some would claim was his most revolutionary role – as diviner of the logical and physical consequences of every idea that was put forward in the formative stages of quantum mechanics. It is one of the ironies of the history of science that Einstein, who contributed so importantly to the task of creating this subject, never accepted that the job was finished when a majority of physicists did. As a consequence, he participated only indirectly in the great adventure of the second quarter of the century: the use of quantum mechanics to explain the structure of atoms, nuclei, and matter.
Along with the exciting experiments that changed the face of physics in the twentieth century, work proceeded feverishly on the theoretical side to rebuild the conceptual world that had been severely shaken. Sometimes the theorists lagged behind the experimentalists, and certain experimental results waited for several years to be explained. And sometimes experiment lagged behind theory, and a new theoretical model waited for years to be verified experimentally. Two great theories left their mark on physics in this century: the theory of relativity, and quantum mechanics. In this chapter we shall briefly review the main ideas of these theories which are vital for the understanding of the atomic world. The theory of relativity The theory of relativity was formulated by the great physicist Albert Einstein. The first part of it (and the important one for us) — the special theory of relativity — was published in 1905, and sprang from the need to explain a puzzling question that exercised the physicists of the nineteenth century: why was it impossible to alter the speed of light, which remained constant (299 792.5 kilometres per second) even when the detector was moving relative to the source of light? In contrast to other physicists, Einstein did not try to explain this phenomenon.
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.
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.