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The Harvard Review of Philosophy

What is the Problem of Measurement?

Simon Saunders, The Harvard Review of Philosophy

Published Jan 1, 1994• 18 citations
Publisher

Abstract

Q UANTUM MECHANICS, TOGETHER WITH RELATIVITY, are the basis of most of what we know of the very large, the very small, and the very fast.And in all of these areas our knowledge is extensive.It would be hard to say how good these theories are; arithmetic, one might say, is good mathematics.For all that, there is a problem, a strange and amorphous difficulty: it is the problem of measurement.This problem has become much more interesting, and much more pressing, as a result of some recent developments.Hitherto the difficulty has been so peculiar, and so formless, that physicists have on the whole thought it a matter of philosophy.But that is not quite right (or that is what I shall argue).It is certainly philosophical, but it is also a matter of methodology, a question of what physics is to do; and now the matter has come to seem quite pressing.In this sense the measurement problem has become a problem for physics.But what is the problem of measurement?As a first stab, we can say this: on the basis of quantum mechanics, there is a difficulty in accounting for the

DOI
10.5840/harvardreview1994411

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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.

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In Quirks of the Quantum, Samuel Chase Coale argues that the twentieth century is the quantum era, riddled with all of the indeterminacies, blurriness, and entanglements that he attributes to quantum theory, which he describes as the “philosophical basis for quantum physics” (1). He acknowledges that “to truly understand quantum mechanics as a science, one would have to study mathematics,” which he readily admits his book does not undertake. Instead, he relies on the “tropes, metaphors and models” (ibid.) that scientists have published about the implications of quantum theory. He thus distinguishes mathematical formulae from philosophical constructions, privileging the latter over the former. Philosophy, however, does not provide a “basis” for quantum mechanics; rather, quantum mechanics describes the phenomena, and then philosophy struggles with what the physical theory implies.Coale makes wide-ranging references to what quantum physicists, including Neils Bohr, have thought about these implications. Strangely, he does not include in his account Karen Barad's excellent Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. A former physicist, Barad develops the quantum philosophy of Neils Bohr into an approach she calls agential realism, which insists that humans and nonhumans are ineluctably bound together in the production of meaning. She argues that quantum mechanics demonstrates the “ontological inseparability of intra-acting agencies,” which emerge as separate entities only as a result of “cuts” we make to simplify phenomena and render them susceptible to measurement and analysis (148). Although her conclusions are similar to Coale's, her approach is distinguished by a deep knowledge of quantum mechanics as a mathematical theory, and her formulations are rigorous and precise. Her absence from Coale's book is the more notable because his analysis needs an infusion of the kind of deep thinking that Barad embodies. By contrast, his book engages in a discursive inflation of quantum physics, wherein the rigor and precision it has as a physical theory is buried under an avalanche of verbiage that makes quantum physics appear so broad and vague that almost anything can fit under its umbrella.A good example of this problem is the way in which Coale uses “entanglement.” In quantum mechanics, it refers to the correlation of the quantum characteristics of two subatomic particles. For example, when two photons interact (say, by pumping a laser beam through a nonlinear crystal such as beta-barium borate, which splits some of the photon stream into photon pairs with correlated polarizations), they can become entangled such that their wave functions (i.e., the eigenstates described by their superpositions) are coordinated. If they are then separated, measurement on one of them determines how the wave function for the other will collapse, even if they are by then far apart. The distance (and time intervals) separating the two photons can be quite large; entanglement has been shown to operate as far removed as fourteen miles. Moreover, it also operates on the macroscale, for example in the ability of migratory birds to sense the inclination of the earth's magnetic field (via entangled electrons in the molecules of their eyes). This is mysterious to the extent that no one knows how or why the particles become coordinated, but it is nevertheless quite distinct from such uses of “entanglement” that would include, for example, two lovers becoming entangled with one another or the World Bank becoming entangled in the global economic system. Citing Patrick O'Donnell, Coale appropriates the word to mean, following O'Donnell, “the complex relationship between self, objects, and the world” (164), which stretches the meaning so far that it leaves quantum mechanics (or quantum theory, as Coale would have it) far behind.In similar fashion, Coale assimilates to quantum theory most of deconstruction, especially the indeterminacy, undermining of origins, and undecidability that Jacques Derrida brilliantly developed in Of Grammatology and later works. 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He mentions in the introduction that he found several articles on quantum theory and references of quantum phenomena in DeLillo's notebooks at the Harry Ransom Humanities Research Center at the University of Texas at Austin. These bear fruit in his readings of DeLillo's novels, especially his fine reading of The Body Artist and the section on DeLillo's Underworld, arguably the best interpretation in the book. This section alone almost justifies the price of admission.Were Coale to frame his book as a contribution to postmodern literary criticism, it would take its place among many other such books and articles as a well-written and interesting contribution that makes good observations about a number of important authors and their works. By insisting that all of this fits under quantum theory, he overreaches what the theory can justly claim and, in the process, dilutes the effectiveness of his book. 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Q UANTUM MECHANICS, TOGETHER WITH RELATIVITY, are the basis of most of what we know of the very large, the very small, and the very fast.And in all of these areas our knowledge is extensive.It would be hard to say how good these theories are; arithmetic, one might say, is good mathematics.For all that, there is a problem, a strange and amorphous difficulty: it is the problem of measurement.This problem has become much more interesting, and much more pressing, as a result of some recent developments.Hitherto the difficulty has been so peculiar, and so formless, that physicists have on the whole thought it a matter of philosophy.But that is not quite right (or that is what I shall argue).It is certainly philosophical, but it is also a matter of methodology, a question of what physics is to do; and now the matter has come to seem quite pressing.In this sense the measurement problem has become a problem for physics.But what is the problem of measurement?As a first stab, we can say this: on the basis of quantum mechanics, there is a difficulty in accounting for the
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.
In Quirks of the Quantum, Samuel Chase Coale argues that the twentieth century is the quantum era, riddled with all of the indeterminacies, blurriness, and entanglements that he attributes to quantum theory, which he describes as the “philosophical basis for quantum physics” (1). He acknowledges that “to truly understand quantum mechanics as a science, one would have to study mathematics,” which he readily admits his book does not undertake. Instead, he relies on the “tropes, metaphors and models” (ibid.) that scientists have published about the implications of quantum theory. He thus distinguishes mathematical formulae from philosophical constructions, privileging the latter over the former. Philosophy, however, does not provide a “basis” for quantum mechanics; rather, quantum mechanics describes the phenomena, and then philosophy struggles with what the physical theory implies.Coale makes wide-ranging references to what quantum physicists, including Neils Bohr, have thought about these implications. Strangely, he does not include in his account Karen Barad's excellent Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. A former physicist, Barad develops the quantum philosophy of Neils Bohr into an approach she calls agential realism, which insists that humans and nonhumans are ineluctably bound together in the production of meaning. She argues that quantum mechanics demonstrates the “ontological inseparability of intra-acting agencies,” which emerge as separate entities only as a result of “cuts” we make to simplify phenomena and render them susceptible to measurement and analysis (148). Although her conclusions are similar to Coale's, her approach is distinguished by a deep knowledge of quantum mechanics as a mathematical theory, and her formulations are rigorous and precise. Her absence from Coale's book is the more notable because his analysis needs an infusion of the kind of deep thinking that Barad embodies. By contrast, his book engages in a discursive inflation of quantum physics, wherein the rigor and precision it has as a physical theory is buried under an avalanche of verbiage that makes quantum physics appear so broad and vague that almost anything can fit under its umbrella.A good example of this problem is the way in which Coale uses “entanglement.” In quantum mechanics, it refers to the correlation of the quantum characteristics of two subatomic particles. For example, when two photons interact (say, by pumping a laser beam through a nonlinear crystal such as beta-barium borate, which splits some of the photon stream into photon pairs with correlated polarizations), they can become entangled such that their wave functions (i.e., the eigenstates described by their superpositions) are coordinated. If they are then separated, measurement on one of them determines how the wave function for the other will collapse, even if they are by then far apart. The distance (and time intervals) separating the two photons can be quite large; entanglement has been shown to operate as far removed as fourteen miles. Moreover, it also operates on the macroscale, for example in the ability of migratory birds to sense the inclination of the earth's magnetic field (via entangled electrons in the molecules of their eyes). This is mysterious to the extent that no one knows how or why the particles become coordinated, but it is nevertheless quite distinct from such uses of “entanglement” that would include, for example, two lovers becoming entangled with one another or the World Bank becoming entangled in the global economic system. Citing Patrick O'Donnell, Coale appropriates the word to mean, following O'Donnell, “the complex relationship between self, objects, and the world” (164), which stretches the meaning so far that it leaves quantum mechanics (or quantum theory, as Coale would have it) far behind.In similar fashion, Coale assimilates to quantum theory most of deconstruction, especially the indeterminacy, undermining of origins, and undecidability that Jacques Derrida brilliantly developed in Of Grammatology and later works. He does the same with postmodernism, so that it begins to seem almost a branch of quantum physics rather than a philosophical and cultural movement with complex roots in cultural, economic, and technological developments. For example, John Johnston in Information Multiplicity: American Fiction in the Age of Media Saturation argues persuasively that the postmodern American novel has been distinctively shaped by the glut of information that the Internet and contemporary communication media make available, a point also made by Fredric Jameson in his seminal study Postmodernism, or the Cultural Logic of Late Capitalism. Yet for Coale, “that flow of information suggests the quantum flux, constantly in motion with islands of possible comprehension like the tracks and trails of ‘particles’ that are measured in individual experiments” (109). The importance of globalization, the complex economic structures emerging from late capitalism, the transformations the web has wrought—all these in Coale's analysis become subsets of quantum physics.Within the limits of his methodology, which are significant, Coale provides good readings of several postmodern authors, including Joan Didion, Tim O'Brien, Thomas Pynchon, Paul Auster, and Don DeLillo. Although many have discussed the fragmentation, nonlinear narratives, lack of coherent subjectivities, and indeterminacy of novels by these writers as postmodern constructions, for Coale they become manifestations of quantum theory (not surprisingly, since he sees postmodernism itself as a branch of the same). With chapters on the quantum flux, quantum style, and death as quantum dissolution, he combines good readings with inflated claims for them as manifestations of quantum theory. The exceptions to this quantum inflation are his discussions of DeLillo's novels. He mentions in the introduction that he found several articles on quantum theory and references of quantum phenomena in DeLillo's notebooks at the Harry Ransom Humanities Research Center at the University of Texas at Austin. These bear fruit in his readings of DeLillo's novels, especially his fine reading of The Body Artist and the section on DeLillo's Underworld, arguably the best interpretation in the book. This section alone almost justifies the price of admission.Were Coale to frame his book as a contribution to postmodern literary criticism, it would take its place among many other such books and articles as a well-written and interesting contribution that makes good observations about a number of important authors and their works. By insisting that all of this fits under quantum theory, he overreaches what the theory can justly claim and, in the process, dilutes the effectiveness of his book. Without a doubt, we need more informed criticism of the interactions between literature, culture, and science, but such work is more effective when it focuses on the specificities of scientific theories and their complex entanglements with cultural and technological practices. Lest it fall under Coale's quantum umbrella, I should add that I do not intend in this formulation a reference to quantum theory!
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing physics is regarded as a creative activity to develop a meaningful description of the world, then one has to carefully discriminate between the two notions: An observer's account of experience - consitutive to meaning - is hardly expressed exhaustively by the formal framework of an interaction within one particular theory. We develop a corresponding perspective onto central terms in quantum mechanics in general, and onto the measurement problem in particular.
In this magisterial work, Roland Omnès takes us from the academies of ancient Greece to the laboratories of modern science as he seeks to do no less than rebuild the foundations of the philosophy of knowledge. One of the world's leading quantum physicists, Omnès reviews the history and recent development of mathematics, logic, and the physical sciences to show that current work in quantum theory offers new answers to questions that have puzzled philosophers for centuries: Is the world ultimately intelligible? Are all events caused? Do objects have definitive locations? Omnès addresses these profound questions with vigorous arguments and clear, colorful writing, aiming not just to advance scholarship but to enlighten readers with no background in science or philosophy. The book opens with an insightful and sweeping account of the main developments in science and the philosophy of knowledge from the pre-Socratic era to the nineteenth century. Omnès then traces the emergence in modern thought of a fracture between our intuitive, commonsense views of the world and the abstract and--for most people--incomprehensible world portrayed by advanced physics, math, and logic. He argues that the fracture appeared because the insights of Einstein and Bohr, the logical advances of Frege, Russell, and Gödel, and the necessary mathematics of infinity of Cantor and Hilbert cannot be fully expressed by words or images only. Quantum mechanics played an important role in this development, as it seemed to undermine intuitive notions of intelligibility, locality, and causality. However, Omnès argues that common sense and quantum mechanics are not as incompatible as many have thought. In fact, he makes the provocative argument that the "consistent-histories" approach to quantum mechanics, developed over the past fifteen years, places common sense (slightly reappraised and circumscribed) on a firm scientific and philosophical footing for the first time. In doing so, it provides what philosophers have sought through the ages: a sure foundation for human knowledge. Quantum Philosophy is a profound work of contemporary science and philosophy and an eloquent history of the long struggle to understand the nature of the world and of knowledge itself.
Ever since the beginning of quantum mechanics, the measurement problem has been a subject of sometimes discontinued but nevertheless recurrent concern. As students, most physicists have raised questions about it, but the spectacular and renewed successes of quantum theory were a strong incentive for them to work out applications without further worrying about foundations. In each generation, however, some dissatisfaction reemerges, which leads to slow progress, and we may expect that the measurement problem will some day be cleared up rather than forgotten. The situation recalls statistical mechanics, the foundations of which still give rise to scientific discussions, in spite of more than one century’s achievements. Actually, the paradoxes of irreversibility and of Maxwell’s demon share some common features with quantum measurements, to wit, they involve probabilities in a crucial fashion and their explanation requires elucidating the role of the observer.