Science without Representation

Galileo set the agenda for modern physical science by requiring it to explain how such apparent features of our world as colours, sounds, tastes and smells are produced by a colourless, silent, tasteless and odour-free reality. Van Fraassen calls this the Appearance from Reality Criterion. He acknowledges our enormous advances in physics since Galileo’s day, but argues that these have in the end come about by abandoning this along with other completeness criteria associated with necessity, determinism and causal explanation. The appearances physics (as practised and preached by the Copenhagen developers of quantum mechanics) has declined to explain are ‘the contents of measurement outcomes’. Even if that theory is superseded (or if fundamental physics develops in accordance with a new interpretation under which the Criterion can be satisfied) our view of science must be forever modified in the light of this historical episode. (291)1 I think van Fraassen is right to see the development of quantum mechanics as a turning point for physical science with a profound moral for philosophy, and not just for the philosophy of science. But the moral is not that even a completely successful physical theory may fail to account for the appearances by showing how they arise within the reality it represents. The moral is more radical: it is that a physical theory – even a fundamental theory – may be completely successful in all its applications without offering a representation of reality at all. The quantum challenge to the Appearance from Reality Criterion is presented in the final pages of the last chapter of Scientific Representation, a mature and densely structured work that sets out to chart the analytic topography of a significant part of contemporary philosophy of physical science. Since I endorse much of van Fraassen’s new cartography, I begin by reviewing what I take to be common ground before addressing his challenge. That measurement is a form of representation is a central theme of Scientific Representation to which van Fraassen devotes two chapters. In Chapter 6 he addresses the physical correlate of measurement – the physical interaction between the object of the measurement and some measuring device whose final reading yields the outcome of the measurement. As he says If that interaction is in the theory’s domain, the theoretical description will be of this interaction in the same terms as any other physical interaction, and involve no terms that signify anything intensional or intentional. (143) What the outcome reveals is not directly what the measured object is like, but what it ‘looks like’ in that measurement set-up. (183) Not all measurements are equally good. Some are carried out incompetently, others rely on flawed techniques. It is at best a coincidence when the outcome of a bad measurement reveals what the measured object is like. Van Fraassen is not making this obvious point. At times he seems to be making the correct, but less obvious, point that our taking a measurement outcome to reveal what the measured object is like is hostage to the fortunes of the theory in whose light we interpret its significance. The outcome of a measurement provides a representation of the entity (object, event, process) measured, by displaying values of some physical parameters that – according to the theory governing this context – characterize that object. (179–80) In the course of his insightful discussion of measurement, Van Fraassen makes several important points we should take to heart. Measurement is not just the assignment of numbers according to rules. Rather, locating something in logical space is the over-arching concept under which all actions of measurement can be arrayed. This is the only stopping point we have found in the successive generalization of the notion of number-assigning. (172–73) On all these points I expect, or at least hope for, wide agreement with van Fraassen. But his attachment to constructive empiricism continues, and here I part company with him, leaving our common ground. These days a great deal of activity undertaken in scientific research laboratories is directed towards measuring magnitudes pertaining to objects or events that van Fraassen would count as unobservable since they elude our unaided sense organs: consider measurements of the mass of a neutrino or of the black hole at the centre of our galaxy, the temperature near the centre of the sun, the anomalous magnetic moment of the muon, the value of the Weinberg angle in the unified electro-weak theory or even the width and helical angle of the DNA molecule. I venture that most scientists engaged in such activity believe that they are aiming to find out the value of the magnitude in question on the measured object. Not so, according to van Fraassen. He would maintain that (at least in some of these examples) their true purpose is to locate the supposed object in the logical space of theory so as to preserve empirical adequacy – science’s real goal. Meeting that goal is what science is about, for the constructive empiricist. That leaves it up to the individual scientist whether to believe there are any neutrinos, black holes, muons, electro-weak interactions or DNA molecules: commitment to the sun is not optional, but the status of its centre seems less clear! Here, we see a less innocent interpretation of the phrase ‘what it ‘looks like’ in that measurement set-up’, according to which ‘looking like’ something need not imply that thing exists. This may not be an interpretation van Fraassen means to allow. But to exclude it by requiring that the only measurements are on observables, yielding appearances as their outcomes, would be to ride roughshod over scientific usage of the term ‘measurement’. I take his discussion of the measurement of spin-component of (unobservable!) silver atoms by a Stern–Gerlach device to provide evidence of his conformity to that usage. To begin to explain my disagreement with van Fraassen about the correct moral to draw from the development of quantum theory, I return to his discussion of the physical correlate of measurement in Chapter 6. As he notes, this was tailored to fit the peculiar features of quantum mechanics. The result shows enough evidence of strain in the fabric to prompt the concern that quantum measurement is a topic unto itself. In a justly influential paper, the physicist John Bell concluded that no fit should be attempted. In his view the word has had such a damaging effect on the discussion [of the foundations of quantum mechanics] that I think it should now be banned altogether in quantum mechanics.2 One of Bell’s charges against the word ‘measurement’ was that the word comes loaded with meaning from everyday life, meaning which is entirely inappropriate in the quantum context. When it is said that something is ‘measured’ it is difficult not to think of the result as referring to some pre-existing property of the object in question.3 The outcome does not reveal a prior state for an individual silver atom, but the frequencies in the outcome do give information about the prior state in which the source prepares what it sends out. (155–56) His example illustrates van Fraassen’s general theory of the physical correlate of measurement. This is intended to apply to physical theories in which the relation between physical state and measurement outcome is only characterizable in terms of probabilities. What is required of a measurement interaction is just that the final state of the apparatus be appropriately correlated to that of the measured object, for each of a wide class of initial object states. The key Criterion for the Physical Correlate of Measurement therefore requires only that these states agree in the probabilities they assign – on the one hand to the measured parameter of the object, and on the other hand to the ‘pointer position’ parameter of the apparatus. This is problematic, since the probabilities in each case are for measurement outcomes. If we were looking for a way to restore some kind of veracity to measurement by moving to probabilities, then we have made no progress. Satisfaction of the probabilistic Criterion for the Physical Correlate of Measurement would have given us what we wanted only if each individual outcome whose probability is specified were itself veracious. Van Fraassen disagrees we can see now that Veracity is honored at some appropriate level…. In practical terms it is precisely the source on which the measurement, taken as a whole, is performed. (155–56) In assessing this response to the problem we need to distinguish two claims: When a Stern–Gerlach magnet is considered part of an apparatus for measuring the spin component of a silver atom, it is the second claim that is relevant. A Stern–Gerlach apparatus is not a device for performing a quantum measurement on the atom’s source: its function is to perform (typically) non-veracious quantum measurements on individual silver atoms. The relative frequencies with which silver atoms are detected in various locations beyond the magnet constitute the outcome of a measurement on the source that prepared them. Each detection of an individual silver atom at a specific location beyond the magnet constitutes the outcome of a measurement on that atom. Quantum measurements of spin-component (or the analogous magnitude polarization) are now routinely carried out on individual spin 1/2 atoms including silver (respectively, photons) without regard to their source, and sometimes when this source is unknown. The quantum-mechanical representation of such a system’s state is by a qubit: quantum measurements on individual qubits are fundamental to the flourishing new field of quantum computation. A qubit represents the simplest kind of quantum state, and the only universally acknowledged role of any quantum state in the theory is to assign a probability for each outcome of any possible measurement on the system whose state it is.5 The way these probabilities are assigned guarantees that no quantum measurement on an individual system can reliably reveal its previously unknown quantum state. But as van Fraassen correctly notes, the frequencies of outcomes of one kind of measurement on similar systems do give information about their common quantum state, and by combining the frequencies of outcomes of enough different kinds of measurements on similar systems one can reliably estimate that state. Van Fraassen returns to quantum mechanics in Chapter 13 to argue that its development shows science is not bound by the demand to explain how the appearances are produced by the underlying reality it represents. The appearances in question are the outcomes of quantum measurements, and the failure of quantum mechanics to use its representations to explain their production is intimately connected to the notorious quantum measurement problem. In the course of his argument van Fraassen offers an empiricist dissolution, or rather dismissal, of that problem. In response, I shall argue that the quantum measurement problem could be remedied only by stronger pragmatist medicine. The pragmatist moral of the development of quantum mechanics is then that the development of a scientific theory may constitute great progress even though that theory offers no novel representation of a reality capable of producing measurement outcomes. Quantum measurements have outcomes whose probabilities the theory correctly predicts through its Born rule as applied to the quantum state of the measured system(s). If it is to explain how these outcomes are produced, it must represent them within its models. The only available candidate is the mathematical object (vector or density operator) the theory uses to represent the quantum state of a system. So any description the theory offers of the physical correlate of the measurement outcome must be provided by such a representation of the quantum state of the apparatus at the conclusion of its interaction with the measured system. The theory does have the resources to model a suitable interaction satisfying the Criterion for the Physical Correlate of Measurement. But this is not enough to show how any individual measurement outcome is produced. To do that one would have to use the theory to show, for each of a wide range of initial quantum states of a single quantum system, that this interaction would put the apparatus into a correlated quantum state representing the outcome of the measurement. The problem is that can’t be done: for most initial quantum states of the measured object, the final quantum state of the apparatus after an otherwise suitable interaction fails to represent the measurement as having any determinate outcome. Van Fraassen argues that this is not a problem when the theory is seen through empiricist eyes: … [N]one of this entails that what happens in the actual situation must be displayed as entirely identifiable in the theoretical model. The most stringent demand that can be made here is that the relative frequencies of certain events in this sort of situation must have a good fit to probability functions, extrapolated from them in surface models, which are identifiable as parts of corresponding probability functions in the theoretical models. (305) This demand is met by observed frequencies of measurement outcomes, as classified in accordance with standard laboratory practice, and that is enough – for Copenhagen physicists, and for van Fraassen’s philosophy of science. A further demand, to explain how each individual measurement outcome is produced by representing its production within the theory, is not met in quantum mechanics. So the Appearance from Reality Criterion has been rightly rejected in the development of our most successful scientific theory. But Van Fraassen’s dismissal of the measurement problem is premature. To see why, focus on the event spaces of the relevant probabilities, in quantum mechanics on the one hand and in the surface model of the experimental frequencies on the other. The surface models will provide probability functions for events that are classified as outcomes in situations classified as measurements of given observables. Those probability functions need to be parts of the theoretically specified Born probabilities for the same situation as theoretically represented in terms of possible states and evolutions. (305) It is precisely because he assumes quantum states (are used to) represent reality in quantum mechanics that van Fraassen has not yet succeeded in dismissing the measurement problem. By dropping this assumption, we can put the problem behind us and come to a better appreciation of how the development of the theory should change our view of science. The developers of quantum mechanics did not agree on the nature of the quantum state, and the topic remains controversial to this day.8 To deny that assigning a quantum state to a system is a way of describing or representing (some of) that system’s properties is to take a position in this controversy held by some, but not all, of the theory’s Copenhagen founders. But the lack of consensus on this issue contrasts strikingly with the overwhelming consensus on how to apply the theory, and the wholly successful results of all such applications. This is strong evidence that one can consistently accept quantum mechanics while denying a descriptive or representative role to the quantum state. One distinct advantage of doing so is that this permits a simple response to the quantum measurement problem. If quantum states neither describe nor represent any reality according to the theory, then a fortiori the theory cannot represent the outcome of a measurement interaction by any quantum state of the apparatus. (So the denial commits one to supposition 1 as stated by van Fraassen on page 298.) This makes the theory descriptively incomplete (as Einstein famously argued it was). But, as Bohr insisted, no predictive incompleteness follows. Given a full specification of any situation in which one wishes to apply quantum mechanics, including a description of the various measurement outcomes in terms available independently of quantum mechanics, an assignment of a quantum state to the target system always generates a well-defined probability function over these outcomes. There is no tension between the dynamics of the quantum state and the Born rule, since that dynamics represents no physical process while the latter concerns events not represented by any quantum state. If the role of the quantum state is to generate probabilities for various measurement outcomes, doesn’t playing this role entail describing or representing something after all, namely these probabilities? That depends on the status of quantum probabilities. According to one popular view, quantum indeterminism is a locus for objective chance: at least some quantum state assignments can then be understood to describe such objective chances. David Lewis developed an influential account of objective chance and connected it to subjective credence through his Principal Principle. This account does not mesh well with the way quantum states generate probabilities.9 According to self-styled quantum Bayesians, there is no such thing as objective chance: the quantum state generates subjective/personal probabilities. They readily infer that quantum state assignments are equally subjective. Interestingly, I think van Fraassen’s own view of a theory’s use of probability is to be preferred to either of these alternatives. He reviews this in an Appendix to Chapter 13. The background to this view is van Fraassen’s abandonment of any objective notion of probability and move towards something like Richard Jeffrey’s radical probabilism in epistemology. The move did not make him a quantum Bayesian, however, in part because he does not regard of a theory as just a of of prior of What is in of a probabilistic theory like quantum mechanics is rather of that theory’s probabilities as own of So if of the Born rule in a situation that is in terms available independently of quantum mechanics generates a probability function for outcomes of a quantum measurement, then one quantum mechanics will take these probabilities as his by them as his own of for these outcomes. a constructive quantum mechanics will doing this only when the outcomes are In this means taking Born rule probabilities as functions for the relevant set of I find Van Fraassen’s view of quantum probabilities its because it their peculiar status as neither wholly subjective nor wholly I to of quantum probabilities since their role is not to state but rather to On this view, quantum states do not generate probabilities that describe or represent they generate as to how one should form These are not about probabilities, and nor are they about any property of the quantum system whose state generates them. They are about outcomes of measurements on that system, in terms available independently of quantum I common ground with van Fraassen in denying that probabilities in quantum mechanics are used to represent anything in that theory. It that the quantum state does not any descriptive or representative role by them. The quantum state is and a for to a in a specific physical situation on how to form about results of or measurements of whose outcome he is If one then neither quantum probabilities nor the quantum state that generates them to represent according to the theory that them. of quantum measurements are but not by anything by quantum they are represented by or mathematical objects that come from way of it was to of by of Quantum mechanics does new such as spin and the between and But even here one can such terms as in the theory – as the kinds of quantum state that it makes available rather describing or representing for is a form of – a magnitude previously by Quantum mechanics it by outcomes of spin measurements on systems like silver atoms that cannot be understood as values of that So van Fraassen is right that the development of quantum mechanics shows that science is not bound by the Appearance from Reality but not for the he The enormous scientific progress about by the development of quantum mechanics shows that even our most fundamental scientific theory need not its by representing anything that science could not represent without Quantum mechanics cannot explain how measurement outcomes are produced since to apply the theory one must that they It is a great theory because it provides such a in over an enormous range of such applications physics provides a better of this constructive constructive our to what the quantum state and the probabilities it generates are used to do rather to what they Quantum mechanics is a more physics that may be used in situations the latter In such this may be used for predictive and even though it no new descriptive or resources of its the constructive measurement outcomes are the development of quantum mechanics does not the function of the used to describe or represent them. This is something the pragmatist will because of the of quantum mechanics in situations theories he will be to the in how the of theories functions, even as it to be used in describing or representing quantum measurement outcomes in to apply quantum mechanics. But this disagreement between constructive empiricist and pragmatist is a to the that van Fraassen and from science for an description of the fundamental of the physical world as a for their own Scientific Representation should be required reading for contemporary and analytic It is an important to a of work in philosophy of science by like and as well as including and to with science as it is rather how they it to

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