Abstract Although 1900 ended with the classical physics of Newton and Maxwell reigning supreme, that reign did not last long, and Chapter 4 shows why. The first crack in this edifice was the failure to detect the presence of the ether, the medium that supposedly carried electromagnetic waves. Next was Thomson’s discovery of the electron, proving that atoms, believed to have been indestructible, were not: they had a structure. Yet another new development, the discovery of radioactivity, also could not be explained by classical physics. Nor could it explain the experimental data from blackbody radiation measurements, yet Planck’s peculiar formula involving his quantum hypothesis, did so perfectly. It introduced a new fundamental constant, named for him. And while his quantum hypothesis did not gain any traction for five years, in 1905 Einstein used it to explain the photoelectric effect, which classical electrodynamics had been unable to do.
Abstract Although 1900 ended with the classical physics of Newton and Maxwell reigning supreme, that reign did not last long, and Chapter 4 shows why. The first crack in this edifice was the failure to detect the presence of the ether, the medium that supposedly carried electromagnetic waves. Next was Thomson’s discovery of the electron, proving that atoms, believed to have been indestructible, were not: they had a structure. Yet another new development, the discovery of radioactivity, also could not be explained by classical physics. Nor could it explain the experimental data from blackbody radiation measurements, yet Planck’s peculiar formula involving his quantum hypothesis, did so perfectly. It introduced a new fundamental constant, named for him. And while his quantum hypothesis did not gain any traction for five years, in 1905 Einstein used it to explain the photoelectric effect, which classical electrodynamics had been unable to do.
Abstract With the failure of classical physics to explain the experimentally observed black body radiation spectrum, the photoelectric effect and the existence of narrow spectral lines in the light emitted by excited atoms, physicists were forced to reach out for new ideas. Following Planck’s initial “drastic hypothesis” of light “quanta”, Einstein led the way in exploring some of the myriad implications of this idea. In particular, the study of fluctuations led to a new understanding of the interaction of electromagnetic radiation with atoms. Einstein invented the photon by showing, through fluctuation studies, that light emitted by atoms must be in the form of plane waves. These ideas led to the first notions regarding the quantization of matter and its dynamics.
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.
We tried to introduce the idea of quantization in Chapter 9 as a completion of a one semester course. However, we skipped over some really interesting events in the history of Science between 1900 and 1913 when Bohr derived the quantized energy of the H atom. First we want to carry out the 1901 Planck derivation of the formula for blackbody radiation [1]. Many texts just show the curve, write e¼ hn, and move on. As a student, this author found that limited explanation very frustrating since energy quantization is a fundamental concept. Even among graduate texts in quantum mechanics, we are aware of only one that does the complete treatment which we will draw upon for the mathematics [2] but supplement with a narrative that we have found helpful to students over the years. Then in 1905, Albert Einstein (1879-1955), one of the most influential scientists of all time, gave an explanation of the photoelectric effect [3] for which he received the Nobel Prize in 1921. Even reducing our list to essential topics, we need to discuss the Davisson-Germer experiment [4]. The photoelectric effect introduces the idea that light waves can act as particles while the Davisson-Germer experiment showed that particles can act like waves and confirmed the De Broglie equation [5]. However, you can be assured that it will not be as difficult as you might have anticipated and if you can absorb the meaning of just these three key experiments you should be able to begin thinking in terms of quantum mechanics! Despite our slow historical development, this is 2010 and we have to get to the twenty-first century somehow!
Due to the idea of atomism, there were discovered atoms, nucleons, and electrons. The atomic theory incorporated seeds of the idea of infinite divisibility of matter aimed at perceiving the structure of the entire material world. The next step in that perceiving should have been the recognition of ether discovered in Fizeau’s experiment. However, physicists did not recognize the discovery. The neglect of ether in physical theories resulted in physicists’ failure to use the methods of “classic”, Newtonian physics to gain a detailed understanding of atomic structure, and to build a “classic” microworld theory. As consequence, there emerged the quantum hypothesis that became a basis for the quantum physics of microworld. As the quantum hypothesis appeared to be in irreconcilable contradiction with the idea of infinite divisibility of matter, because of the neglect of ether, the quantum physics failed to understand the real structure of electrons and nucleons, even though all the necessary and ample experimental facts there had been obtained on microobject accelerators. Instead of objective ideas of the structure of electrons and nucleons or further development of knowledge regarding the structure of matter, there appeared fake concepts of quarks, myons, pions, bosons, etc., that do not exist in the real material world Experimental evidence as to the lack of indivisible quanta in nature [1] seemed to have fixed the intolerable situation but quantum physicists did not “notice” that.
The behavior of light and its interaction with matter is certainly one of the most interesting phenomena of physics. It has puzzled thinkers and scientists in ancient Greece (Archimedes) and through the Middle Ages, at least since the times of Robert Grosseteste (1168–1235), right up to the theories of Galileo Galilei and Isaac Newton. The classical electromagnetic theory of light (see Tab. 13.1) was beautifully established in the second half of the nineteenth century with the Maxwell equations. Quantum optics is nothing other than the quantum theory of light. It finds its roots in Planck's discovery (1900) that the assumption of energy quantization for a harmonic oscillator allowed us to solve the black-body problem (see Subsec. 1.5.1). The successive early steps that led to the quantization of the electromagnetic field include Einstein's explanation of the photoelectric effect with the introduction of the quantum of light (see Subsec. 1.2.1) and the interpretation of atomic spectra (see Subsec. 1.5.4). Quantum optics is usually not covered by conventional textbooks on quantum mechanics. We include its discussion here for two main reasons: first, because it is a fundamental and advanced application of the basic framework of quantum mechanics, and, second, because in the last 30 years quantum optics has played (and is still playing) a major role in the advancement and understanding of quantum mechanics.
Chapter 2 explains how in constructing quantum mechanics, old ideas had to be discarded and well-established principles had to be modified or even abandoned. First it was necessary to be convinced of the physical reality of the atomic structure of matter; then to show that Newtonian mechanics is not directly applicable to the study of the atom; later to show that Maxwell’s electrodynamics alone does not describe all the elementary processes of interaction between an atom and other quantum particles. The chapter takes us from Planck’s energy quantum to Einstein’s quantization as a universal phenomenon, from Bohr’s quantum atom model, and the early quantization rules, to de Broglie’s waves associated with corpuscles in motion. It ends with a corollary on the electrodynamic nature of quantum mechanics.