deserve kudos for organizing the conference (2002) on the future of Quantum Mechanics and publishing (2005) the book, “Quo vadis Quantum Mechanics?”1 through Springer, as one of the important Frontier collections. Seminar’s notion could be found in A. J. Leggett’s paper (Ch. 6) where he cites the “reasons for speculating that the linear formalism of standard quantum mechanics may break down at some stage between the level of the atom and human consciousness. ” (p. 83). The contributors have responded differently to this stated notion and the issue revolves around whether nature is deterministic or probabilistic and whether we are dealing with a closed or open system. This is what this book is about with opinions favoring the notion, and the opinions on the contrary. In this one Volume one could observe a collection of papers on quantum mechanics from sixteen of today’s most eminent theoretical physicists, two of them are already Nobel winner. The contributions are studded with introspection, conservatism, disinterested search for the root of quantum mechanics in classical theories, incisive formulation (L.
deserve kudos for organizing the conference (2002) on the future of Quantum Mechanics and publishing (2005) the book, “Quo vadis Quantum Mechanics?”1 through Springer, as one of the important Frontier collections. Seminar’s notion could be found in A. J. Leggett’s paper (Ch. 6) where he cites the “reasons for speculating that the linear formalism of standard quantum mechanics may break down at some stage between the level of the atom and human consciousness. ” (p. 83). The contributors have responded differently to this stated notion and the issue revolves around whether nature is deterministic or probabilistic and whether we are dealing with a closed or open system. This is what this book is about with opinions favoring the notion, and the opinions on the contrary. In this one Volume one could observe a collection of papers on quantum mechanics from sixteen of today’s most eminent theoretical physicists, two of them are already Nobel winner. The contributions are studded with introspection, conservatism, disinterested search for the root of quantum mechanics in classical theories, incisive formulation (L.
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.
When investigating various interpretations of quantum mechanics one notices that each interpretation contains an element which escapes a complete and full description. This element is always associated with the stochasticity of the individual event in the quantum measurement process. It appears that the implications of this limit to any description of the world has not been sufficiently appreciated with notable exceptions of, for example, Heisenberg, Pauli and Wheeler. If we assume that a deeper foundation of quantum mechanics is possible, the question arises which features such a philosophical foundation might have. It is suggested that the objective randomness of the individual quantum event is a necessity of a description of the world in view of the significant influence the observer in quantum mechanics has. It is also suggested that the austerity of the Copenhagen interpretation should serve as a guiding principle in a search for deeper understanding. In recent years, a significant increase of interest in the foundations of quantum mechanics can be observed. This increase is certainly related to the immense progress made during the last two decades in experiments with individual quantum systems. This technological progress has made it possible to really perform more and more of the famous gedanken experiments which were so important in the early days of the theory. Not only did these experiments confirm the theory in every detail, they also opened up avenues for new experimental directions which might even lead some day to new technology. While such applications are certainly still far away, areas like quantum cryptography[1], quantum computation[2] and interaction-free measurement[3], just to name a few examples, certainly deserve the attention they receive. All this activity has also drawn more attention to the problems of understanding and interpreting quantum mechanics. It seems that there, a definitive consensus has not yet been reached. As witnesses quote authorities like Feynman as saying[4]: I think can safely say that nobody today understands quantum mechanics, whereby he apparently included himself, or like Roger Penrose[5], who describes his opinion remarking that while the theory agrees incredibly well with experiment and while it is of profound mathematical beauty, it makes absolutely no sense. Why did even physicists who have contributed so significantly to quantum theory Feynman was even rewarded the Nobel Prize for one of its mathematical formulations choose such emphatic and strong formulations? Why is it that the average physicist hears very little about such problems during his/her education? Why is the comprehension of the theory very often focused on formalism while questions that probe for deeper meaning are usually not tackled? To take a closer look at the situation, let us turn to a brief analysis of the interpretation of quantum mechanics. We note that there are at least two levels of interpreting a formalism, a physical theory. The first, basic, level supplies the rules that determine which element of the formalism corresponds to which measurable quantity or to which observable fact in a concrete experimental situation. Theses rules are a large, mostly not explicated but only implicit, set of instructions. These instructions concern the manner of working with the statements of the theory in order to obtain predictions for future experiments or events, and they concern the instructions on how to proceed in experiment in order to demonstrate or test a theoretical
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se , suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N -particle system in its 6N -dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic effects. On the other hand, actual events are not postulated to occur exclusively in brains. They are more generally associated with the formation of records. Records are necessarily part of the total state of the universe: it is obvious that the state of the universe cannot undergo a Schrödinger dynamics and at the same time record its own history. `The full universe consists therefore of an exceedingly thin veneer of relatively sluggish, directly observable properties resting on a vast ocean or rapidly fluctuating unobservable ones.' The present ideas also bear on how the world should be seen to develop. While conventional cosmology encounters problems as to how to define the intial conditions, which would enter the governing equations of motion, here `the boundary conditions are set not at some initial time, but gradually by a sequence of acts that imposes a sequence of constraints. After any sequence of acts there remains a collection of possible worlds, some of which will be eliminated by the next act.' Connected with those acts is `meaning': there has always been some speculation about the special significance of local properties in our understanding of the world. One could argue that correlations (even the quantum correlations found, e.g., in the EPR-experiments) were as real as anything else. But also Stapp stresses the special role of locality: the `local observable properties, or properties similar to them are the natural, and perhaps exclusive, carriers of meaning in the quantum universe. From this point of view the quantum universe tends to create meaning.' This sounds like an absolute concept: meaning not with respect to something else, but defined intrinsically---not easy to digest. The role of consciousness in the developing quantum universe requires more attention. `The causal irrelevance of our thoughts within classical physics constitutes a serious deficiency of that theory, construed as a description of reality.' This is taken to be entirely different within quantum mechanics. `The core idea of quantum mechanics is to describe our activities as knowledge-seeking and knowledge-using agents.' `21st century science does not reduce human beings to mechanical automata. Rather it elevates human beings to agents whose free choices can, according to the known laws, actually influence their behaviour.' An example with respect to perception is discussed: `Why, when we look at a triangle, do we experience three lines joined at three points and not some pattern of neuron firings?' The brain `does not convert an actual whole triangle into some jumbled set of particle motions; rather it converts a concatenation of separate external events into the actualization of some single integrated pattern of neural activity that is congruent to the perceived whole triangle.' How convincing is this proposal? It is hard to tell. I think Henry Stapp did a good job, but there are tight limitations to any such endeavour. Quantum mechanics is often strange indeed, but it also gives rise to our classical world around us. For the emergence of classicality jumps and measurement projections (the basic phenomena connected with those fundamental events of choice) are not needed. Therefore, I doubt whether the explanation of the evolution of our world really allows (or requires) that much free choice. On the other hand, most scientist will agree that empirical science was not possible without free will: we could not ask independent questions if this asking was part of a deterministic trajectory. The fact that the result of a quantum measurement is indeterminate (within given probabilities) does certainly not explain free will. How about the type of measurment? The experimentalist will have to assume that he can select the pertinent observable within some limits. But given a certain design the so-called pointer basis (producing stable measurement results) is no longer a matter of free choice. `The main theme of classical physics is that we live in a clocklike universe.' Today it is often assumed that the universe was a big (quantum-) computer or a cellular automaton. Many would be all too happy to leave that rather restrictive picture behind. But where to go? Stapp suggests giving consciousness a prominent role: `The most profound alteration of the fundamental principles was to bring consciousness of human beings into the basic structure of the physical theory.' How far we are able to go in this direction will depend on the amount of concrete research results becoming available to support this view.
The Wigner Centennial Conference was held in Pécs, Hungary, on 8–12 July 2002. Eugene Paul Wigner was born in Budapest on 17 November 1902 and left us on 1 January 1995 in Princeton, USA. Numerous other conferences and conference sessions were also held during 2002 to commemorate the centennial year of his birth, because so many wished to pay tribute to him. It would, of course, take a major international effort to review thoroughly all the contributions Wigner made in all branches of physics and for the cause of world peace. The purpose of the Wigner Centennial Conference was to enrich and enhance the research lines initiated by Wigner. The conference was particularly interested in assembling young researchers who will develop and expand those research lines in the future. Indeed, there were many papers of current interest, including symmetry problems in quantum mechanics and quantum field theory, group theoretical issues, foundations of quantum mechanics, nuclear physics, chemical physics, the phase-space formulation of quantum mechanics, as well as quantum computing, information and entanglement problems. In 1932 Wigner published a seminal paper entitled 'On the quantum correction for thermodynamic equations' ( Phys. Rev. 40 749--759) in which he introduced a fundamental tool for quantum mechanics known these days as the Wigner function. The Wigner function has a long history, but began to gain its major strength in quantum optics during the 1970s. Since then, it has become the primary scientific language for squeezed states of light dealing with multi-photon coherent states. The Wigner function is also the basic language for transition from classical to quantum mechanics through phase-space. It therefore plays a major role in detecting quantum effects in processes routinely regarded as classical. Indeed, most optical instruments have been based on classical optics; it is, however, a great challenge to find quantum effects in those devices. This itself is an important subject. Wigner initially formulated the Wigner function to understand thermodynamic effects in physical systems, and thus it plays an important role in studying entropy in measurement processes, statistical mechanics and chemical physics. Physicists do not seem to fully appreciate the fact that Wigner functions can be used for the purpose of group representations. For instance, the single-mode and two-mode squeezed states are isomorphic to the Lorentz groups O(2,1) and O(3,2), respectively. This can be done very cleanly within the framework of the Wigner phase-space approach. By combining two of Wigner's main research areas, namely group theory and the Wigner function, we can construct a very rich field of physics. This is a future possibility for today's young physicists. Turning to computing, a man or woman is born with ten fingers, which constitute a natural computer based on decimal numbers. Indeed, the Chinese developed an abacus for dealing with decimal numbers. Slide rules perform additions, but they can do multiplications in the logarithmic scale. In the 1940s, another Hungarian scientist named John von Neumann observed that vacuum tubes could perform 'yes or no' logic. His observation led to the computer age in which we live. It is interesting to note that both Wigner and von Neumann came from the same high school in Hungary, the Budapest Evangelikus Gimnazium. Likewise, Eugene Wigner began to worry about the language that atoms speak even before the present form of quantum mechanics was formulated. He published in 1929 a book entitled 'Group Theory and its Applications to Quantum Mechanics of Atomic Spectra'. This is, in fact, the first book on quantum computing. Physicists do not yet seem to appreciate this aspect of Wigner's contribution, but eventually they will. If we are seriously interested in building quantum computers, we should use atoms. We should then develop mathematical algorithms to use group theory of atomic spectra for numerical computation. This is what Wigner left to us as a homework. The Wigner Centennial Conference was dedicated to Wigner's future rather than to his past. Indeed, we are very happy to note that many young physicists presented their new research results at this conference. We regret that this special issue cannot include all the subjects covered at the Conference. We are, however, very fortunate to have so many excellent papers on Wigner functions, quantum optics and quantum information, as well as quantum computing. The special issue is not meant to be the conference proceedings. The papers included here have been refereed according to the standards of Journal of Optics B: Quantum and Semiclassical Optics and publication was not restricted to the participants of the Conference. This is indeed a special issue dedicated to the above-mentioned subjects.
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.
A little while ago I was asked to give a lecture at the very elegant Weisman Art Museum in Minneapolis on an assigned title: “Elegance in Physics.” As I get older, the things I'm asked to do get stranger, so I wasn't surprised. Alarmingly, the older I get, the stronger is my inclination to do the peculiar ones. So I accepted the invitation, and soon found myself brooding, not, as I had imagined, about the glory of the eternal verities, but about the highly contentious nature of elegance in physics. Here is the first such difference of opinion I came upon. In a lecture at Fermilab with a title similar to the one I was given, Subrahmanyan Chandrasekhar talked about “harmoniously organizing a domain of science with order, pattern, and coherence.” He cited five examples of such pinnacles of exposition, one of them being Paul Dirac's celebrated book, Principles of Quantum Mechanics. “The translucence of the eternal splendor through material phenomena,” Chandrasekhar remarked, “[is] made iridescent in these books.” Keeping that iridescent translucence firmly in mind, consider the following remarks of the eminent mathematician Jean Dieudonné: When one arrives at the mathematical theories on which quantum mechanics is based, one realizes that the attitude of certain physicists in the handling of these theories truly borders on delirium … One has to ask oneself what remains in the mind of a student who has absorbed this unbelievable accumulation of nonsense, real hogwash! It would appear that today's physicists are only at ease in the vague, the obscure, and the contradictory [1]. What is Dieudonné talking about? He is addressing the approach to quantum mechanics laid out in Dirac's book. Elegance in physics is as much in the eye of the beholder as it is in any other field of human endeavor. Dirac's formulation appeals to physicists because, by being a little vague and ambiguous about its precise mathematical structure, it enables them to grasp and manipulate the physical content of the theory with a clarity and power that would be greatly diminished if one were distracted by certain complicating but fundamentally uninteresting mathematical technicalities. But for mathematicians, those minor technical matters lie at the heart of the subject. Quantum mechanics becomes ill-formulated and grotesque if it does not properly rest on impeccable mathematical foundations.