Abstract There is a certain similarity in the early lives of Planck and of Heisenberg [1,2]. Both had fathers who were professors at the University of Munich, both visited the Maximilians-Gymnasium in Munich, and both went to see a professor in Munich to seek advice for their studies. We have mentioned at the beginning of the Prologue how Jolly in vain tried to dissuade Planck from studying physics. Heisenberg, in his autobiographic book [3], which is devised as a series of conversations, tells us of a similar experience. In the autumn of 1920, when he was about to enter the university, his first choice was mathematics. He wanted not only to do course work but also learn about problems of current interest. This, he thought, he could do best by participating in a professor’s seminar usually reserved to advanced students and Ph.D. candidates. He asked for an interview with Lindemann , the most distinguished mathematician in Munich, who was famous for having proved that the number π is transcendental. But the old professor and the young student found no understanding, partly because Lindemann’s dog noisily interfered. The result was that Heisenberg opted for theoretical physics and went to ask Sommerfeld to be admitted to his seminar. Sommerfeld agreed. At that time Pauli, only a year older than Heisenberg, was already actively doing research under Sommerfeld. The two young men became life-long friends.
Abstract There is a certain similarity in the early lives of Planck and of Heisenberg [1,2]. Both had fathers who were professors at the University of Munich, both visited the Maximilians-Gymnasium in Munich, and both went to see a professor in Munich to seek advice for their studies. We have mentioned at the beginning of the Prologue how Jolly in vain tried to dissuade Planck from studying physics. Heisenberg, in his autobiographic book [3], which is devised as a series of conversations, tells us of a similar experience. In the autumn of 1920, when he was about to enter the university, his first choice was mathematics. He wanted not only to do course work but also learn about problems of current interest. This, he thought, he could do best by participating in a professor’s seminar usually reserved to advanced students and Ph.D. candidates. He asked for an interview with Lindemann , the most distinguished mathematician in Munich, who was famous for having proved that the number π is transcendental. But the old professor and the young student found no understanding, partly because Lindemann’s dog noisily interfered. The result was that Heisenberg opted for theoretical physics and went to ask Sommerfeld to be admitted to his seminar. Sommerfeld agreed. At that time Pauli, only a year older than Heisenberg, was already actively doing research under Sommerfeld. The two young men became life-long friends.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
Heisenberg in Göttingen, Copenhagen and Helgoland Werner Heisenberg studied under Sommerfeld in Munich and was present at the Bohr Festspiele held in Göttingen in 1922 (Sect. 8.2). Although aged only 20, he challenged Bohr's support of Kramers' analysis of the quadratic Stark effect, having studied the paper in detail for Sommerfeld's seminar in Munich. The result was a long walk with Bohr during which they discussed this topic and the more general problems of quantum physics. This encounter made a strong impression on Heisenberg. Much later Heisenberg stated: ‘That discussion, which took us back and forth over Hainberg's wooded heights, was the first thorough discussion I can remember on the fundamental physical and philosophical problems of modern atomic theory, and it has certainly had a decisive influence on my later career. For the first time, I understood that Bohr's view of his theory was much more sceptical than that of many other physicists – for example, Sommerfeld – at that time, and that his insight into the structure of the theory was not a result of mathematical analysis of the basic assumptions, but rather of an intense occupation with the actual phenomena, such that it was possible for him to sense the relationships intuitively rather than derive them formally.’ Heisenberg spent the winter of 1922–1923 working in Göttingen as Born's assistant. The astronomers had made great progress in the use of perturbations techniques within the action–angle formulation of classical dynamics to study the gravitational perturbations of planetary orbits.
The history of physics is not only a sequence of experimental discoveries and observations, followed by their mathematical description; it is also a history of concepts. For an understanding of the phenomena, the first condition is the introduction of adequate concepts; only with the help of the correct concepts can we really know what has been observed. Heisenberg was born on December 5, 1901, in Wurzburg, Germany. His maternal grandfather was the headmaster of the prestigious Maximilian Gymnasium in Munich, and his father, a scholar of ancient Greek philology and modern Greek literature. Heisenberg’s carrier however is regarded as being somewhat controversial due to debate over his activities during World War II. In Heisenberg’s first major paper on quantum theory, he resolved to get rid of any consideration of electron orbits. A cloud chamber is a very simple device for studying particles. They were first used, highly successfully, in the detection of cosmic rays.
Werner Heisenberg, co-discoverer of quantum mechanics, was born on December 5, 1901, in Würzburg, Germany, the second son in a scholarly family. His father, August Heisenberg, initially taught at a gymnasium but after his Habilitation was appointed Professor of Greek Philology at the University of Munich in 1911. Werner’s teachers in Munich made observations about the 10-year-old which seem prescient today (but which probably characterize bright children everywhere): “He has an eye for what is essential and never gets lost in details…great interest and thoroughness, and ambition.” Heisenberg excelled over the other boys at skiing and chess. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
It is appropriate in this year, when we celebrate the 50th anniversary of quantum mechanics, and during which we have been saddened by the death of one of its leading founders, Werner Heisenberg, to reminisce about the formative years of the new mechanics. At the time when the foundations of physics were being replaced with totally new concepts I was a student of physics. I sat in the colloquium audience when Peter Debye made the suggestions to Erwin Schrödinger that started him on the study of de Broglie waves and the search for their wave equation. It was from Heisenberg, as his first doctorate student, that I caught the spirit of research, and that I received the encouragement to make my own contributions.
Abstract A short personal and historical account of the field of radiation interacting with (two-level) atoms is given. Subsequent to 1963, developments and extensions have been extensive and fruitful. One of the most fortunate changes in my life came in late 1957. I was looking for a thesis advisor, after two years of graduate course-work at Stanford. I chanced to see a notice of an upcoming lecture by a professor named Edwin T Jaynes. I could not understand from the announcement what he intended to talk about, but I was searching; I went to find out. That decision was a very lucky one. Ed was talking about a subject that inspired him then, and had been for many years, namely his concept of 'Max-Ent'. 'Maximum-Entropy' is a subject now close to my heart also. Ed's very-clear, well-thought-out papers, spread over many subsequent years, are transforming the field of probability (albeit too gradually) to the 'subjective' outlook of Bayes. (A recent book 'Maximum Entropy and Ecology' [1] will probably convert many nay-sayers to 'Max-Ent'.) I went into Ed's office (late 1957) and asked if I could work with him on a thesis. Did he have a problem for me? Yes, he did. Somewhat to my surprise, he asked me to look into the 'maser problem', involving a comparison of the semi-classical theory of radiation to a proper quantum treatment. To make a two-year story short, Ed's guidance was expert. (I imagine that if another of Ed's students (e.g. Joe Eberly) had come into his office fifteen minutes before me, the 'Jaynes–Cummings' (J–C) model would now perhaps be called otherwise, e.g., the 'J–E' model). In the two-year time frame (∼1958–60), Ed had a number of other PhD dissertation students whom I knew; these included Joe Eberly, Doug Scalapino, Baldwin Robertson, Larry Davis and Mike Duggan. My thesis work under Ed reminds me of a story about Michelangelo and his famous 'Pieta'. Michelangelo was an old man about then, so he hired a young craftsman to do much of the physical work: 'chip here, carve there, cut off here, eliminate this, etc'. When the beautiful Pieta was finished, the young man was heard to say, 'I didn't realize before this that I was so talented'. Experiments by Clauser in 1972 on Bell's inequalities (e.g. [2]) showed them to be correct, and indicated that semi-classical alternatives to quantum electrodynamics were not viable. Working with Stuart Freedman, these were the first experimental tests of the predictions of Bell's theorem, the first observation of quantum entanglement, as well as the first experimental observation of a violation of a Bell inequality. The perturbation formulation of quantum radiation theory has long been rife with vexing infinities. Ed always insisted that only experiment can end an argument, so he and his students had been sensibly exploring semi-classical theory. This was not only because of the serious failings of standard QED, but more importantly because of the fact that (an improved) semi-classical theory was able to predict both spontaneous emission, with the correct Einstein coefficients, and the Lamb shift. These two effects have long been thought only possible in the quantum radiation domain (cf [3]). Ed readily accepted losing his bet with Franken about what experiment had to say about the Lamb shift. What is clear is that this bet of $50 with Peter Franken stimulated so much subsequent research that this bet played an important role in generally furthering the field of quantum optics. How did 'J–C' come to be published as it did in the IEEE [4]? Ed was not well known for the extravagant use of words, rather for paucity, clarity and economy. After about two years of working with Ed, he said to me one day, 'You have enough, write it up'. He also said 'We should publish'. (This was around early 1960). About this same time, I was contacted by someone from a new research lab just starting in Newport Beach, California (called 'Aeroneutronic', a division of Ford), asking if I would come to work there. I thought it sounded about right as an approximately two–three year position: repay some debts and look around at other possibilities (especially academe?). I left around June 1960 to take up this position in the research lab in Newport Beach. At about this same time (∼late 1959), Ed was moving to his new 'chair' at Washington University in St Louis. I proceeded as quickly as I could to put together a thesis after arriving in Newport Beach; I wrote about what I had done, as best as I could in my naiveté about such undertakings. I wrote of the work I had done under Ed's kind and patient guidance for the two years in Palo Alto. I soon remembered that Ed had done a recent Stanford Microwave Lab report on our project; his writing was so much better than mine that I thought it witless to put out something as 'uneven' as I had written by then. At just this time that I was cobbling together a thesis, a consultant at Aeroneutronic, Jay Singer of UC Berkeley EE department, approached me in the hall, (no tele-commuting then!) asking if I might have something to contribute to a special issue of a journal of the IEEE he was editing, on the subject of 'Quantum Electronics'. (Comment: One of the earliest predecessors to the MRI, Jay Singer was then measuring the blood flow in rat tails and human arms; he holds two key MRI patents). I said I thought I did have something. The journal sounded appropriate, so I soon handed my 'thesis' to Jay, put Ed's name first (of course, since it consisted so largely of his words from the Microwave Lab report, but also since Ed was my 'guru'), ...and that was that...done [4]. From my perspective, it seemed to subsequently sink to the bottom of the sea, not to be seen by me again for many years until the elegant Walther–Rempe–Klein (WRK) experiments of 1987 on long-time coherent radiative behavior appeared [5]. They confirmed the long-time quantum-theoretical results of Eberly, Narozhny and Sanchez-Mondragon [6]. Bob Buley and I, while at Aeroneutronic, had published in the field of lasers [7], based on the J–C model. We found very strange, puzzling 'chaotic' output of a 'Q-switched' laser. When computer time-steps were changed, the chaos didn't disappear. It was about then (∼June 1963) that both Bob and I headed elsewhere: I to the early-forming UC Riverside Physics Department as Assistant Professor, and Bob to a company in Santa Barbara. Our work on the mysterious 'chaotic' laser effect then ended (the term 'chaos' was not yet in the physics lexicon); Bob was the computer expert, our non-linear laser problem demanded rigorous numerical computations, and I was not savvy with the (then) 'refrigerator-sized' computers at UCR. P W Milonni has greatly extended this work (cf [8]). Mike Tavis, my graduate student at UCR around 1965, extended the J–C model to N atoms [9]. (We have more recently collaborated in a further study of this and other extensions of J–C.) The silence and zero feedback from the 'J–C', Buley and 'T–C' papers for so many years following 1965 was a bit deafening, so I thought it would be best that I go mostly onto other topics. One day in about 1989, I got a tap on the shoulder from a colleague at UCR: 'I saw your name in the title of a paper'. ('Huh?'). An astonishing number of exciting and important new topics have emerged since the 1987 WRK experiment, providing an ever-branching tree of both new theory and experiment. It is tempting to entitle this piece as 'Get your name in print: Diagonalize a 2 × 2'. References [1] Harte J 2011 Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Series in Ecology and Evolution) (Oxford: Oxford University Press) [2] Freedman S J and Clauser J F 1972 Experimental test of local hidden-variable theories Phys. Rev. Lett. 28 938 [3] Stroud C R Jr and Jaynes E T 1970 Long-term solutions in semiclassical radiation theory Phys. Rev. A 1 106 [4] Jaynes E T and Cummings F W 1963 Comparison of quantum and semiclassical radiation theories with application to the beam maser Proc. IEEE 51 89 [5] Rempe G, Walther H and Klein N 1987 Observation of quantum collapse and revival in a one-atom maser Phys. Rev. Lett. 58 353 [6] Eberly J H, Narozhny N B and Sanchez-Mondragon J J 1980 Periodic spontaneous collapse and revival in a simple quantum Phys. Rev. Lett. 44 1323 [7] Buley E R and Cummings F W 1964 Dynamics of a system of N atoms interacting with a radiation field Phys. Rev. 134 A1454 [8] Milonni P W, Shin M-L and Ackerhalt J R 1987 Chaos in Laser–Matter Interactions (Singapore: World Scientific) [9] Tavis M and Cummings F W 1968 Exact solution for an N -molecule—radiation-field Hamiltonian Phys. Rev. 170 379