Abstract This chapter introduces the central mysteries of quantum mechanics. Quantum mechanics is an enormously successful theory that lies at the heart of modern physics, but there is no agreement on how to understand it. Simple experiments with light demonstrate why: in understanding those experiments, we have to shift inconsistently back and forth between thinking of the theory as assigning indefinite, delocalized, but known properties to a system, and assigning definite, localized, but unknown properties (this is called the ‘problem of measurement’). Furthermore, when we break a system into subsystems, the state of the system is not determined by the states of the subsystem (this is called ‘entanglement’), and simple arguments seem to tell us that the physical properties of entangled subsystems can influence one another non-locally—faster than light. These three mysteries—measurement, entanglement, non-locality—need to be addressed by any attempt to make sense of quantum theory.
Abstract This chapter introduces the central mysteries of quantum mechanics. Quantum mechanics is an enormously successful theory that lies at the heart of modern physics, but there is no agreement on how to understand it. Simple experiments with light demonstrate why: in understanding those experiments, we have to shift inconsistently back and forth between thinking of the theory as assigning indefinite, delocalized, but known properties to a system, and assigning definite, localized, but unknown properties (this is called the ‘problem of measurement’). Furthermore, when we break a system into subsystems, the state of the system is not determined by the states of the subsystem (this is called ‘entanglement’), and simple arguments seem to tell us that the physical properties of entangled subsystems can influence one another non-locally—faster than light. These three mysteries—measurement, entanglement, non-locality—need to be addressed by any attempt to make sense of quantum theory.
Abstract This chapter surveys various proposals to interpret—that is, make sense of—quantum mechanics. We could attempt to think of quantum mechanics in purely instrumentalist terms, as an algorithm to predict observed experimental results. But this fits badly with scientific practice and is probably not viable. We could attempt to modify quantum mechanics itself to resolve the paradoxes, and there are some simple models that attempt to do that: some are ‘hidden-variable’ theories that add extra properties to the theory, some are ‘dynamical-collapse’ theories that modify the theory’s equations. But none of these models succeed in reproducing quantum theory’s predictions outside a relatively narrow range of applications. Or we could try to take the apparent indefiniteness of quantum mechanics literally, and interpret it as a theory of many parallel worlds. The correct interpretation of quantum mechanics remains controversial, but the search for understanding and interpretation of the theory has led to very substantial scientific results and is likely to lead to more.
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.
Introduction Chapter 1 dealt with one of the deepest mysteries in modern science: how to explain consciousness. This Part deals with another mystery: how to make sense of quantum mechanics. Both involve a problem of reconciliation with the classical worldview, which is one hint that the two mysteries might be related. A second is that, unlike classical physics, which makes no reference to or allowance for consciousness, quantum theory raises the issue of consciousness and its relationship to the physical world in a very direct way. These hints do not necessarily mean there is a connection between the two mysteries, but by the end of this Part I hope to have shown why it would be natural to look for one. My more immediate aim here is to give the social scientific reader an introductory understanding of the experimental findings of quantum theory, its key concepts, and the debates about its interpretation. The discussion assumes no prior knowledge of quantum physics and makes no use of mathematics. Quantum theory without equations might seem like an oxymoron, and certainly reading this Part will not enable anyone to use quantum theory. But to a perhaps surprising degree it is possible to understand quantum theory without being able to use it. Its findings can be communicated in ordinary language, and the same goes for its main concepts and interpretive debates. One consequence of this has been the emergence of a virtual cottage industry of books on quantum theory for a lay audience. Most are written by physicists, and many are quite good. However, it is not just popular treatments that do without equations: much of the professional philosophical literature does as well. (I draw on both kinds of literature below.) Philosophers of physics are trained to understand the math, of course, which is necessary for a full appreciation of the issues.
The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.
For over nine decades, quantum mechanics has profoundly shaped our understanding of nature, offering explanations for the stability of atoms, the formation of mole cules, the properties of materials, and phenomena such as light or radioactivity. It is essential to modern technologies—from microchips to lasers—and underpins the physics of elementary particles. Yet, despite its successes, it remains a deeply mysterious theory, confronting a central enigma: why does the quantum world behave so differently from everyday reality? Elements such as superposition and quantum entanglement—which allow particles to exist simultaneously in multiple states or remain interconnected regardless of distance—contradict classical world intuitions. This gap between microscopic and macroscopic behavior has given rise to what is known as the “measurement problem,” raising fundamental questions about the nature of reality. Diverging interpretations have led to two major schools of thought: anti-realism, promoted by Niels Bohr, which holds that reality depends on the observer and their interaction with measurement instruments; and realism, supported by Albert Einstein, which argues that quantum mechanics is incomplete and that eality exists independently of observation. Bohr’s complementary philosophy and Heisenberg’s uncertainty principle were central to the formulation of the “Copenhagen interpretation,” which became dominant in the 20th century. However, the persistent opposition of scientists like Einstein and Schrödinger inspired generations of physicists to seek a unification between quantum mechanics and relativity, culminating in new theories such as loop quantum gravity and string theory. Thus, the debate between realism and anti-realism remains alive, and philosophy continues to play a crucial role in exploring the new foundations of physics.
Preface to the 2nd edition. Preface. Acknowledgements. Reality in the quantum world: The quantum revolutions External reality The potential barrier and the breakdown of determinism The experimental challenge to reality Summary of chapter one. Quantum theory: The description of a particle in quantum theory The wavefunction The potential barrier according to quantum mechanics Interference Other applications of quantum theory Summary of chapter two. Quantum theory and external reality: Review of the problem The ensemble interpretation of quantum mechanics The wavefunction as a measure of our knowledge The wavefunction as part of external reality Measurement in quantum theory Interference and macroscopic objects Can quantum mechanics be changed so that it will reduce wavefunctions? Summary of chapter three. Consciousness: The relevance of conscious observers: What is a conscious observer? Does wavefunction reduction require conscious observers? God as the conscious observer The many-worlds interpretation Summary of chapter four. Hidden variables and non-locality: Review of hidden-variable theories The pilot wave The Einstein-Podolsky-Rosen thought experiment Bell's theorem Experimental verification of the non-local predictions of quantum theory Can signals travel faster than light Summary of chapter five. The mysteries of the quantum world: Where are we now? Quantum theory and relativity Where do we go next? Early history and the Copenhagen interpretation A bibliography and some recent opinions A final plea for reality A last look at the wavefunction Conclusions. Recent developments: Models with explicit collapse The Bohm model Many worlds Time and quantum theory A peculiarly quantum measurement Locality. Appendices. Index.