Despite its intuitive appeal, classical mechanics is just as fraught with conceptual difficulties and problems of interpretation as its quantum replacement. The problems just happen to be rather less obvious, and so more easily overlooked or ignored. Quantum mechanics was born not only from the failure wrought by trying to extend classical physical principles into the microscopic world of atoms and molecules, but also from the failure of some of its most familiar and cherished concepts. To set the scene and prepare for what follows, this Prologue highlights some of the worst offenders, including: space and time; force and energy; the troublesome concept of mass; light waves and the ether; and atoms and the second law of thermodynamics.
Despite its intuitive appeal, classical mechanics is just as fraught with conceptual difficulties and problems of interpretation as its quantum replacement. The problems just happen to be rather less obvious, and so more easily overlooked or ignored. Quantum mechanics was born not only from the failure wrought by trying to extend classical physical principles into the microscopic world of atoms and molecules, but also from the failure of some of its most familiar and cherished concepts. To set the scene and prepare for what follows, this Prologue highlights some of the worst offenders, including: space and time; force and energy; the troublesome concept of mass; light waves and the ether; and atoms and the second law of thermodynamics.
Introduction Quantum mechanics is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities (see in particular [1,4,58–63]). Quantum mechanics should thus be considered a direct continuation of the quantum theory founded by Planck, Einstein and Bohr. Bohr in particular stressed repeatedly, already before the birth of quantum mechanics, that the discontinuities must lead to the introduction of new kinematical and mechanical concepts, so that indeed classical mechanics and its corresponding conceptual scheme should be abandoned [1,4]. Quantum mechanics tries to introduce the new concepts through a precise analysis of what is ‘observable in principle’. In fact, this does not mean setting up the principle that a sharp division between ‘observable’ and ‘unobservable’ quantities is possible and necessary. As soon as a conceptual scheme is given, one can infer from the observations to other facts that are actually not observable directly, and the boundary between ‘observable’ and ‘unobservable’ quantities becomes altogether indeterminate. But if the conceptual scheme itself is still unknown, it will be expedient to enquire only about the observations themselves, without drawing conclusions from them, because otherwise wrong concepts and prejudices taken over from before will block the way to recognising the physical relationships [Zusammenhänge].
Abstract The development of quantum theory was driven by a consistently repeated failure of classical physics to accommodate the results of ever more sophisticated experiments on the microphysical world of radiation, elementary particles, atoms, and molecules. Each break-through in the development of the theory’s conceptual structure was followed (sometimes very rapidly) by new experimental data that just did not fit, pointing to the need for yet further refinements. As is typical in such a radical change in the approach to acquiring scientific understanding, old and often unsuitable concepts were forced into service to meet the needs of the new description. Confusion reigned. The major figures in the theory’s early development took up radically different positions on the theory’s interpretation, and, as we will see, the debate became polarized in ways that remain relevant today.
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.
The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]
As a pointer, and a service to other amateur physicists, I thought it would be useful to sum up the main pitfalls and discoveries I stumbled upon while working my way through Feynman’s Lectures. I call it a Survivor’s Guide to Quantum Physics because – at times – it did feel like going through a jungle, or wading through deep water, or climbing a mountain for which there is no map. Indeed, while there is a tendency to present quantum physics as a coherent set of principles and theory, it is not. At best, it is a toolbox with some novel mathematical techniques, approaches and models. At worst, it tries to present itself as an alternative to classical physics, which it is not. Quantum physics is, in essence, a combination of Maxwell’s equations and the Planck-Einstein relation. That is it. Nothing more. Nothing less. In the QED sector, at least. The one and only quantum is Planck’s quantum of (physical) action, and its physical dimension – a force times a distance times a period (cycle time) – is, unfortunately, not always well understood by those who are supposed to understand it – which is why there is a lot of nonsense around. In short, we hope this short paper might help you to avoid the mistakes I made, and that is to waste time on things you should not waste time on: stuff that is not useful, or plain wrong even. And then I will also try to highlight the little shortcuts or visualizations that may help you to get a much more intuitive grasp of things.
The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism.Here we utilize the concepts of identical and similar preparation procedures to show the conceptual differences between the statistical and the conventional interpretation of quantum formalism.Although the statistical understanding, and its final logical consequence, hidden variables theories (this connexion being explained in the text), have a great intuitive appeal due to its fewer ontological difficulties, both recent experimental results and theoretical developments seem to support an epistemic alternative closer to the conventional one.Nevertheless, we must not rule out the possibility that new theorems or new explanatory principles may modify the reigning supremacy of this interpretation. 1.-Introduction.Although the conventional interpretation of the quantum mechanical formalism (CIQM), very close to the Copenhagen interpretation, is still dominant (is used in almost all textbooks), there are physical situations that ask for an interpretation of the quantum mechanical formalism (QMF) in terms of the Statistical Interpretation of Quantum Mechanics (SIQM) or even for hidden variables theories (HVT).The SIQM and HVT are different research programs, but they are closely related, as we will see further below.To introduce properly the distinctions between the three previous acronyms we will ask an old and apparently simple question.Is the wave function associated to an individual system or to a statistical ensemble?A first tentative answer could be formulated as follows.QMF introduces probabilities, and probabilities are related to statistical ensembles.Otherwise, the same concept of probability would lose its meaning.In QM, if it is said that you would get some concrete result with 0,63 probability it means that if the experiment is carried out 100 times, that concrete result would appear approximately 63 times.Hence, the obvious answer will be that the wave function should be related with statistical ensembles.However, despite its intuitiveness this idea does not capture completely what we want to express.The real problem to analyze could be best introduced with the following example.Imagine that we prepare identically two radioactive atoms with half-life of 30 minutes.By preparation we understand all those theoretical methods and physical procedures necessary to fully characterize the state of the system.It is, thus, a macroscopic reproducible act that lefts the system, without destroying it, in a concrete state after the procedure.In quantum theory, this preparation is represented by a vector state (or a density matrix).Identically in this context will mean identity of procedures, that is that the experimenter has repeated all previous operations, so that there is no difference whatsoever between them.Note, however, that identical preparations are not necessarily followed by identical results, so there is