The present conference takes place in the same year that celebrates the centenary of Albert Einstein. Hence it is a good occasion to reflect on those problems which have been at the core of Einstein’s intellectual activity. Undoubtedly the foundation of quantum mechanics (QM) is one of these problems. It is known that Einstein was never convinced by the interpretation of quantum mechanics accepted, in his times and still now, by the majority of physicists. The fact that he was sharing this skepticism with people like Schrödinger and, most of all, the fact that no convincing answer, to the doubts of these people, had emerged in a more than half a century old debate, helped in keeping alive the attention of a growing number of people on this problem.The crucial issue is that the standard interpretation of QM has some physical implications which are experimentally verifiable and which, for several years, have been thought to be incompatible with relativity theory (the so‐called “quantum nonlocality”). On the other hand alternative, more intuitive, interpretations (such as the ensemble interpretation) seemed to be ruled out from very well confirmed experimental data.The way out from this impasse has required a deep analysis of the connections between mathematics and physics as well as the emergence of new ideas both in mathematics (non‐Kolmogorovian probabilities) and in physics (the theory of adaptive systems).The Einstein centenary is a good occasion for a short survey of these developments with the goal of answering the intriguing question posed in the title of the present paper.
The present conference takes place in the same year that celebrates the centenary of Albert Einstein. Hence it is a good occasion to reflect on those problems which have been at the core of Einstein’s intellectual activity. Undoubtedly the foundation of quantum mechanics (QM) is one of these problems. It is known that Einstein was never convinced by the interpretation of quantum mechanics accepted, in his times and still now, by the majority of physicists. The fact that he was sharing this skepticism with people like Schrödinger and, most of all, the fact that no convincing answer, to the doubts of these people, had emerged in a more than half a century old debate, helped in keeping alive the attention of a growing number of people on this problem.The crucial issue is that the standard interpretation of QM has some physical implications which are experimentally verifiable and which, for several years, have been thought to be incompatible with relativity theory (the so‐called “quantum nonlocality”). On the other hand alternative, more intuitive, interpretations (such as the ensemble interpretation) seemed to be ruled out from very well confirmed experimental data.The way out from this impasse has required a deep analysis of the connections between mathematics and physics as well as the emergence of new ideas both in mathematics (non‐Kolmogorovian probabilities) and in physics (the theory of adaptive systems).The Einstein centenary is a good occasion for a short survey of these developments with the goal of answering the intriguing question posed in the title of the present paper.
Quantum theory is a phenomenally successful cornerstone of physics. But a recent poll among quantum physicists shows that there is still little agreement on what the theory tells us about physical reality. Yet precious bits of consensus are emerging. As always, Albert Einstein was ahead of his time. Quantum theory was still in its infancy, its formalism a mere sketch, and its implications only beginning to be realized. Yet Einstein, in 1917, already spotted what would trouble him throughout his lifetime. He concluded that the nascent theory, which he had helped initiate, seemed to leave “time and direction of elementary processes,” such as the spontaneous emission of radiation from a molecule, “to chance” 1. Einstein's conclusion was visionary. It was also incredibly bold, for it suggested a radical departure from the powerful, centuries-old deterministic and causal worldview of classical physics. But Einstein also immediately expressed his discomfort with the idea of fundamental chance. In fact, his worries were just the seed of what would turn into one of the longest and most heated debates in the history of physics. What does quantum theory mean, and what does it tell us about the nature of reality? Some of the brightest minds in physics locked horns over these issues. Besides Einstein, there were Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Pascual Jordan, Carl Friedrich von Weizsäcker, Wolfgang Pauli, and Richard Feynman, just to name a few. Ask anyone today working on foundational questions in quantum theory and you are likely to hear that there is still no consensus on many of these questions—all the while, of course, everybody seems to be in perfect agreement on how to apply the quantum formalism when it comes to making experimental predictions. Remarkably, there has never been any serious attempt to find out what the current opinions of the community really are and how they may be correlated. We jumped on the opportunity and polled 33 participants at a 2011 conference on “Quantum Physics and the Nature of Reality” (Fig. 1) 2. (We hasten to add that our poll is to be understood as merely a snapshot and certainly cannot claim to be representative.) As soon as we had collected the questionnaires, the respondents eagerly asked to hear the results. Evidently, we had not been the only curious party. What did we find? The fundamental questions, it seems, still elicit radically different responses. Take the quantum state—represented by the wavefunction—as an illustration. The wavefunction is the central mathematical symbol of quantum mechanics. It allows us to make incredibly accurate predictions, be it in atomic, molecular, or solid-state physics. But how are we to interpret it? Is it itself a physical property, or does it merely represent our knowledge? Our poll revealed a tie between these two positions. And not only that: a third of respondents preferred a mix of both viewpoints—perhaps a sign that a more nuanced view, or even a synthesis of views, may be on the horizon. Only 3% of those polled thought that quantum states never refer to a single system but only to ensembles of systems. Perhaps this departure from the ensemble view—a view that, we suspect, remains more popular in the physics community at large—has to do with the fact that experiments with single quantum systems have become routine in today's quantum-information laboratories. Sharp disagreement was in evidence on another deep question. Abraham Pais, Einstein's biographer, recalled that “during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it” 3. Putting the issue differently, are the physical properties of objects well defined before we actually measure them? Half of the respondents in our poll believed that they sometimes were, while the other half said that they never were. These two positions correspond to radically different ways of understanding the function of measurement: either as simply ascertaining—at least sometimes—of what is already there, or as an act of genuine creation. The role of measurement is also at the heart of another perennial favorite of foundational discussions, the measurement problem. The measurement problem highlights a curious fact about quantum theory: while the act of measurement assumes a fundamental role, it is not described—not without interpretive contortions, anyway—by the dynamical law of quantum theory, the Schrödinger equation. For decades, the measurement problem was seen by many as the main stumbling block for quantum theory, sparking a storm of rivaling attempts to deal with this perceived issue. Today, the waters seem to have calmed and attention shifted elsewhere, as only less than a fourth of respondents consider the measurement problem “a severe difficulty threatening quantum mechanics.” Changing attitudes are also evident when it comes to the issue of chance Einstein had brought to light in 1917. Today, the question of the randomness of quantum events no longer seems to be all that contentious. Most of our respondents accepted randomness as irreducible or a fundamental concept in nature (or both). Less than one-tenth of respondents thought that quantum randomness was merely apparent rather than fundamental, and no one believed in a hidden determinism governing quantum events. We wish we could hear Einstein's opinion today. Why have attitudes and priorities changed? It's hard to say, but we think there may be several driving forces. The rapid ascent of quantum information science has not only led to applications such as secure cryptography and the promise of lightning-fast quantum computers, but has also shed new light on foundational problems and handed us new tools for addressing them. Our poll shows that these tools are considered a welcome addition, with three-fourths seeing quantum information as a breath of fresh air for foundational investigations. There is also optimism about the future technological development of quantum information, with more than 75% of respondents expecting a working and useful quantum computer to be realized within the next fifty years. Such optimism might be rooted in the astonishing experimental progress we have witnessed over the past decades, another driving force behind changing attitudes. We are now at stage where almost perfect experimental control of single quantum systems has been achieved. The 2012 Nobel Prize in physics was awarded for just such experiments. This has put at our fingertips the ability to actually carry out the thought experiments—or approximations thereof, at any rate—that the founders of quantum theory had dreamed up. Take Schrödinger's cat. In 1935, Schrödinger wanted to illustrate what seemed to him an absurd prediction of the new theory: that the strange quantum superpositions of the atomic world can be amplified to everyday objects. Schrödinger's object of choice was a cat in a specifically prepared box. Quantum theory then suggested that the state of the cat should become transformed into a bizarre quantum superposition of being simultaneously alive and dead. But what Schrödinger had intended as a “burlesque” 4 thought experiment is now approaching experimental reality. Over the last decades, researchers have become increasingly skilled in breeding small versions of Schrödinger's cat. While they don't involve actual cats, they do already involve large biological molecules. Our respondents, it seems, were inspired by such developments. A solid two-thirds majority declared that they don't expect any fundamental limit in this enterprise of observing larger and larger objects in superpositions of macroscopically distinct states. No limit, then, for quantum theory—something that Bohr had already suggested when he, in some of his early thought experiments, considered apparatuses that included macroscopic parts behaving in quantum-mechanical ways. There are other new trends. Why do people seem to be much more at ease with relativity theory than with quantum theory? For one, both special and general relativity theory are grounded in a few simple physical principles. By contrast, quantum theory is lacking such a foundation and is instead based on a rather abstract mathematical body. Today, several researchers are out to change this situation, trying to derive quantum theory from a small set of physical or information-theoretic principles. They hope that in this way, we will understand why we have this peculiar theory to begin with. A majority in our poll regarded such “reconstructions” of quantum theory as giving useful insights, indicating once more that any new tool that promises fresh insights is embraced with an open mind. To be sure, many (albeit not all) of the questions we asked in the poll are interpretive questions. This means that unless we should find out some day that quantum theory is in fact not always valid—in which case we would have to rethink the whole game—experiments arguably can't play the role of the arbiter. Some physicists will conclude from this that we need not bother with such questions, and relegate them to philosophy. We think this is too quick. Many ideas in physics didn't come out of thin air, but came about when someone started looking at a problem with a certain philosophical disposition. In this sense, we may think of the plurality of views in quantum mechanics as productive. Every interpretation highlights some aspect of quantum theory, is particularly suited for explaining particular phenomena, and may inspire new technologies—such as the quantum computer—or even new physics. What, then, does the future hold? Half of the respondents in our poll believe that in fifty years from now, we will probably still be coming together for conferences on the fundamental questions of quantum theory. But what kinds of questions will be on the agenda? Will we still be worrying about the same problems as today? Or will these problems have been solved—or found to be less relevant—and our focus shifted to new questions once again? Who knows. But the location of the conference where we conducted the poll may tell a story. It was the place of a monastery, and a central position in the battle between Catholics and Protestants during the seventeenth century. Many of the questions that were hotly debated back then are no longer of interest to many people today, and other, new questions have since taken center stage in our society. Maybe some of the battles over the interpretation of quantum theory will meet a similar fate.
‘Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One’. These views were contained in a letter written by Albert Einstein to Max Born in December 1926. Though the following year would see the completion of work on the theoretical foundation of the modern physics of atoms and particles, Einstein was never to change his judgement and remained firmly convinced that ‘this business […] contains some unreasonableness’. He was unwilling to sacrifice his own ideas as to the cognitive scope of science even in the face of the important results being achieved by the new theory. To the undeterministic findings of quantum mechanics he opposed his belief in the ‘possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability of their occurrence’. For this reason he chose to live with the isolation of his scepticism and dissent, ironically accepting the reputation as a obstinate heretic that he had won over the years among his colleagues, and worked to the end on his own research programme to develop a unified field theory of rigorously causal nature. As is generally known, Einstein carried on a strong scientific and philosophical dispute with the defenders of the so-called official interpretation of quantum mechanics.
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.
‘Sprache und Wirklichkeit in der modernen Physik’ is the title of a lecture Heisenberg gave in 1960 at the Bayerische Akademie der Schönen Künste. The polemics that had accompanied the establishment of quantum mechanics were over by then and the so-called problems of its foundations had lost much of their initial interest. Einstein had been dead for some years. Right up to the end he had expressed his profound dissatisfaction with a theory which, in his opinion, had something unreasonable about it. With the volume dedicated to him by the community of physicists and philosophers, the long debate between Bohr and Einstein had come to an end. It had been a disappointing conclusion, marked by the reaffirmation of the respective viewpoints of two scientists who by now found great difficulty even in defining a common code of communication. As though seeking to narrow the gap between them, Heisenberg took the opportunity to underline the existence of a common feature in their contributions to 20th century physics. Their discoveries had in fact made it possible to recognize that ‘even the fundamental and most elementary concepts of science, such as space, time, place, velocity, have become problematic and must be re-examined’. The conceptual and cognitive implications of relativity and of quantum mechanics were obviously different but Heisenberg maintained that both theories asked the same question: ‘Does the language we use when we speak of experiments correspond to the artificial language of mathematics which, as we know, describes real relationships correctly; or has it become separated from it so that we must be content with imprecise linguistic formulations and only return to the artificial language of mathematics when we are forced to express ourselves with precision?’.
The founding fathers of quantum mechanics had already perceived the essence of the difficulties of quantum mechanics; today, after almost a century, the discussions are still lively and, if some very interesting new aspects have emerged, at a deeper level the questions have not changed so much. What is more recent, nevertheless, is a general change of attitude among physicists: until about 1970 or 1980, most physicists thought that the essential questions had been settled, and that “Bohr was right and proved his opponents to be wrong”. This was probably a consequence of the famous discussions between Bohr, Einstein, Schrödinger, Heisenberg, Pauli, de Broglie, and others (in particular at the Solvay meetings [1–3], where Bohr's point of view had successfully resisted Einstein's extremely clever attacks). The majority of physicists did not know the details of the arguments. They nevertheless thought that the standard “Copenhagen interpretation” had clearly emerged from the infancy of quantum mechanics as the only sensible attitude for good scientists. This interpretation includes the idea that modern physics must contain indeterminacy as an essential ingredient: it is fundamentally impossible to predict the outcome of single microscopical events; it is impossible to go beyond the formalism of the wave function (or its generalization, the state vector ∣ψ) and complete it.
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.