Richard Andrew Healey

I offer an account of how the quantum theory we have helps us explain so much. The account depends on a pragmatist interpretation of the theory: this takes a quantum state to serve as a source of sound advice to physically situated agents on the content and appropriate degree of belief about matters concerning which they are currently inevitably ignorant. The general account of how to use quantum states and probabilities to explain otherwise puzzling regularities is then illustrated by showing how we can explain single-particle interference phenomena, the stability of matter, and interference of Bose–Einstein condensates. Finally, I note some open problems and relate this account to alternative approaches to explanation that emphasize the importance of causation, of unification, and of structure. 1 Introduction2 Two Requirements on Explanations in Physics3 What We Can use Quantum Theory to Explain4 The Function of Quantum States and Born Probabilities5 How These Functions Contribute to the Explanatory Task6 Example One: Single-Particle Interference7 Example Two: Explanation of the Stability of Matter8 Example Three: Bose Condensation9 Conclusion

Is there a vacuum in nature? This is a question which preoccupied natural philosophers for millennia. Great thinkers including Democritus and Newton maintained the existence of a vacuum, while Aristotle, Descartes and Leibniz argued strongly that there was not, and perhaps could not be, any such thing. A casual glance at the literature of contemporary physics may leave the impression that scientific progress has produced a definitive positive answer, so that the philosophers' debates are now of only historical interest. Not only is the attainment of high vacua a multimillion dollar industry, but almost every text and research paper in theoretical high energy or condensed matter physics or cosmology includes multiple references to the vacuum and its often surprising properties. And yet we have it on the authority of no less a scientist than Einstein himself that his general theory of relativity vindicates Descartes' conclusion that there could be no vacuum since the idea of space without matter is unintelligible! Does this mean that there is after all no scientific consensus on this issue, and that the ancient philosophical debate should simply be resumed with renewed vigor? I shall argue that it does not. The progress of physics has given rise to such a proliferation of different uses of the word 'vacuum' as to irretrievably alter the terms of that debate. Rather than asking whether there is a vacuum in nature, one should ask how well what counts as the vacuum in some physical theory represents reality. This in turn splits up into a semantic question and an empirical question I shall focus mainly on the prior, semantic question here

It has sometimes been suggested that quantum phenomena exhibit a characteristic holism or nonseparability, and that this distinguishes quantum from classical physics. One puzzling quantum phenomenon arises when one performs measurements of spin or polarization on certain separated quantum systems. The results of these measurements exhibit patterns of statistical correlation that resist traditional causal explanation. Some have held that it is possible to understand these patterns as instances or consequences of quantum holism or nonseparability. Just what holism and nonseparability are supposed to be has not always been made clear, though, and each of these notions has been understood in different ways. Moreover, while some have taken holism and nonseparability to come to the same thing, others have thought it important to distinguish the two. Any evaluation of the significance of quantum holism and/or nonseparability must rest on a careful analysis of these notions.

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations, an agent may assign a quantum state to form expectations about other possible physical situations. Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.

In his recent work, Michael Redhead (1986, 1987, 1989, 1990) has introduced a condition he calls robustness which, he argues, a relation must satisfy in order to be causal. He has used this condition to argue further that EPR-type correlations are neither the result of a direct causal connection between the correlated events, nor the result of a common cause associated with the source of the particle pairs which feature in these events. Andrew Elby (1992) has used this same condition as a premise in an independent argument for the conclusion that EPR-type correlations cannot be causally explained (except, perhaps, by a nonlocal hidden variable theory). I wish to argue here that robustness is itself too fragile a notion to support such conclusions

Quantum mechanics predicted the Aharonov-Bohm effect and violations of Bell inequalities before either phenomenon was experimentally verified. It is now commonly taken to explain both phenomena. Maudlin has pointed out significant disanalogies between these phenomena. But he has failed to appreciate the striking analogy that emerges when one examines the structure of their quantum mechanical explanations. The fact that each may be explained quantum mechanically in terms of a locally-acting, but nonseparable process suggests that the lesson of quantum nonlocality may be that while there is no action at a distance, the world is nonseparable

Quantum entanglement is widely believed to be a feature of physical reality with undoubted metaphysical implications. But Schrödinger introduced entanglement as a theoretical relation between representatives of the quantum states of two systems. Entanglement represents a physical relation only if quantum states are elements of physical reality. So arguments for metaphysical holism or nonseparability from entanglement rest on a questionable view of quantum theory. Assignment of entangled quantum states predicts experimentally confirmed violation of Bell inequalities. Can one use these experimental results to argue directly for metaphysical conclusions? No. Quantum theory itself gives us our best explanation of violations of Bell inequalities, with no superluminal causal influences and no metaphysical holism or nonseparability—but only if quantum states are understood as objective and relational, though prescriptive rather than ontic. Correct quantum state assignments are backed by true physical magnitude claims: but backing is not grounding. Quantum theory supports no general metaphysical holism or nonseparability; though a claim about a compound physical system may be significant and true while similar claims about its components are neither. Entanglement may well have have few, if any, first-order metaphysical implications. But the quantum theory of entanglement has much to teach the metaphysician about the roles of chance, causation, modality and explanation in the epistemic and practical concerns of a physically situated agent.

If physical reality is nonseparable, as quantum mechanics suggests, then it may contain processes of a quite novel kind. Such nonseparable processes could connect space-like separated events without violating relativity theory or any defensible locality condition. Appeal to nonseparable processes could ground theoretical explanations of such otherwise puzzling phenomena as the two-slit experiment, and EPR- type correlations. We find such phenomena puzzling because they threaten cherished conceptions of how causes operate to produce their effects. But nonseparable processes offer us an alternative deal of natural order, conformity to which makes such phenomena seem quite normal and not at all unexpected. Attempts to answer the further question, as to whether an appeal to a nonseparable process provides a genuine "causal" explanation, have something to teach us about our concept of causation, but do not threaten to undermine the value of the explanation itself

I offer an account of how the quantum theory we have helps us explain the enormous variety of phenomena it is generally taken to explain. The account depends on what I have elsewhere called a pragmatist interpretation of the theory. This rejects views according to which a quantum state describes or represents a physical system, holding instead that it functions as a source of sound advice to physically situated agents like us on the content and appropriate degree of belief about matters concerning which they are currently inevitably ignorant. So while the account given here is incompatible with some views of structural explanation in quantum theory it is nevertheless able to incorporate what I take to be their valuable insights.

Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum “particles”, it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis of a supposed gravitational analog to the Aharonov-Bohm effect. By contrast with electromagnetism in the original Aharonov-Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of non-gravitational interactions is associated with holism depends on what counts as the relevant part-whole relation. Loop representations of quantized gauge theories of non- gravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields.

On a pragmatist view of quantum theory, a quantum state has the role of advising physically situated agents rather than representing the condition of physical systems. The advice concerns the cognitive significance of a magnitude claim S: σ has, locating the value of magnitude Q on system σ in set Δ of real numbers. The quantum state offers advice both on the content of a magnitude claim S and on its credibility, provided it has enough content. The advice is authoritative—anyone who both accepts quantum theory and agrees on the correct quantum state is bound to heed it. On this view, the content of a magnitude claim is a function of its place in a web of material inferences connecting it to other claims, and hence to perception and action. A quantum state offers advice on the content of a magnitude claim by controlling its place in this inferential web. It thereby adds a contextual element to the content even of claims about the properties of familiar objects like gross experimental apparatus and the moon. But by modeling the behavior of quantum states, quantum theory itself reassures us that only for claims about currently unfamiliar objects does the consequent modification of content amount to anything

Classically, a gauge potential was merely a convenient device for generating a corresponding gauge field. Quantum-mechanically, a gauge potential lays claim to independent status as a further feature of the physical situation. But whether this is a local or a global feature is not made any clearer by the variety of mathematical structures used to represent it. I argue that in the theory of electromagnetism (or a non-Abelian generalization) that describes quantum particles subject to a classical interaction, the gauge potential is best understood as a feature of the physical situation whose global character is most naturally represented by the holonomies of closed curves in space-time.

While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of the meaning of quantum theory continue to proliferate . In this article I offer a diagnosis of this situation and outline a pragmatist solution to the problem it poses, leaving further details for subsequent articles.

In papers published in the 25 years following his famous 1964 proof John Bell refined and reformulated his views on locality and causality. Although his formulations of local causality were in terms of probability, he had little to say about that notion. But assumptions about probability are implicit in his arguments and conclusions. Probability does not conform to these assumptions when quantum mechanics is applied to account for the particular correlations Bell argues are locally inexplicable. This account involves no superluminal action and there is even a sense in which it is local, but it is in tension with the requirement that the direct causes and effects of events are nearby.

This is one of the most important books on quantum mechanics to have appeared in recent years. It offers a dramatically new interpretation that resolves puzzles and paradoxes associated with the measurement problem and the behavior of coupled systems. A crucial feature of this interpretation is that a quantum mechanical measurement can be certain to have a particular outcome even when the observed system fails to have the property corresponding to that outcome just prior to the measurement interaction.

A quantum state represents neither properties of a physical system nor anyone's knowledge of its properties. The important question is not what quantum states represent but how they are used as informational bridges. Knowing about some physical situations, an agent may assign a quantum state to form expectations about other possible physical situations. Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.

All change involves temporal variation of properties. There is change in the physical world only if genuine physical magnitudes take on different values at different times. I defend the possibility of change in a general relativistic world against two skeptical arguments recently presented by John Earman. Each argument imposes severe restrictions on what may count as a genuine physical magnitude in general relativity. These restrictions seem justified only as long as one ignores the fact that genuine change in a relativistic world is frame-dependent. I argue on the contrary that there are genuine physical magnitudes whose values typically vary with the time of some frame, and that these include most familiar measurable quantities. Frame-dependent temporal variation in these magnitudes nevertheless supervenes on the unchanging values of more basic physical magnitudes in a general relativistic world. Basic magnitudes include those that realize an observer's occupation of a frame. Change is a significant and observable feature of a general relativistic world only because our situation in such a world naturally picks out a relevant class of frames, even if we lack the descriptive resources to say how they are realized by the values of basic underlying physical magnitudes.

The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inferences. This promises a better treatment of meaning than that offered by Bohr. Quantum theory models physical systems with no mention of measurement: it is decoherence, not measurement, that licenses application of Born’s probability rule. So quantum theory also offers advice on its own application. I show how this works in a simple model of decoherence, and then in applications to both laboratory experiments and natural systems. Applications to quantum field theory and the measurement problem will be discussed elsewhere

The paradox of Wigner’s friend challenges the objectivity of quantum theory. A pragmatist interpretation can meet this challenge by judicious appeal to decoherence. Quantum theory provides situated agents with resources for predicting and explaining what happens in the physical world—not conscious observations of it. Even in bizarre Wigner’s friend scenarios, differently situated agents agree on the objective content of physical magnitude statements while, normally, quantum Darwinism permits agents equal observational access to their truth. Quantum theory has nothing to say about conscious experiences. But it does prompt us to reexamine the significance of everyday claims about the physical world.

Although there has been some discussion in the literature of Bas van Fraassen's modal interpretation of Quantum Mechanics, it has for the most part been concentrated on difficulties that van Fraassen's viewpoint shares with those of some other authors, including Kochen, Dieks, and Healey. van Fraassen's approach has, however, some problems of its own; in this note we want to focus on what seems to us to be one of the most serious of these. The difficulty concerns immediately repeated non-disturbing measurements of the same observable on a single system. As is well known, von Neumann's Projection Postulate guarantees that such measurements will always give the same outcome; likewise, in the approaches of the “modalists” mentioned above, such ‘consilience of repeated measurements’ is in one way or another built into the formalism. By contrast, we shall argue, van Fraassen's modal interpretation neither guarantees this result nor adequately explains why it is unnecessary to do so.