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The British Journal for the Philosophy of Science

Reconstruction of Quantum Theory

Alexei Grinbaum

Published Aug 1, 2007• 107 citations
Publisher

Abstract

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction. 1. What is Wrong with Interpreting Quantum Mechanics2. Reconstruction of Physical Theory2.1. Schema2.2. Selection of the first principles2.3. Status of the first principles3. Examples of Reconstruction3.1. Early examples of reconstruction3.2. Hardy's reconstruction3.3. Rovelli's reconstruction3.4. The CBH reconstruction3.5. Intentionally incomplete reconstructions4. Conclusion

DOI
10.1093/bjps/axm028

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What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction. 1. What is Wrong with Interpreting Quantum Mechanics2. Reconstruction of Physical Theory2.1. Schema2.2. Selection of the first principles2.3. Status of the first principles3. Examples of Reconstruction3.1. Early examples of reconstruction3.2. Hardy's reconstruction3.3. Rovelli's reconstruction3.4. The CBH reconstruction3.5. Intentionally incomplete reconstructions4. Conclusion
We give a condensed and accessible summary of a recent derivation of quantum theory from information-theoretic principles, and use it to study the consequences of this and other reconstructions for our conceptual understanding of the quantum world. Since these principles are to a large extent expressed in computational terminology, we argue that the hypothesis of "physics as computation", if suitably interpreted, attains surprising explanatory power. Similarly as Jeffrey Bub and others, we conclude that quantum theory should be understood as a "principle theory of information", and we regard this view as a partial interpretation of quantum theory. We outline three options for completion into a full-fledged interpretation of quantum theory, but argue that, despite their interpretational agnosticism, the principled reconstructions pose a challenge for existing psi-ontic interpretations. We also argue that continuous reversible time evolution can be understood as a characteristic property of quantum theory, offering a possible answer to Chris Fuchs' search for a "glimpse of quantum reality".
This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein-Podolsky-Rosen argument, Bell's theorem, and Hardy's paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie-Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.
Abstract The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra‐mathematical content. Here, a representative series of specifically information‐based treatments—from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems—is reviewed.
One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably takes the quantum formalism as the starting point for philosophical reflection and analysis. I argue that this methodology is particularly inappropriate, for it invariably marginalizes much of the theory's content, both that implicit in modelling heuristics and experimental practices, and that encapsulated in the mathematical structures of its formalism. In addition, the prevailing methodology offers little protection against undue influence by metaphysically-laden language which invariably accompanies the formalism. Here, I summarize an alternative methodology whose goal is to ensure that an interpretational project take into account all forms of theoretic content. The methodology harnesses the recent results of the quantum reconstruction program. These results distil the mathematical content of the quantum formalism into physical principles and assumptions, which are more readily philosophically digestible than the formalism itself, and bracket much of its metaphysically-laden language. As a case study of reconstruction-based interpretation, I describe the reconstruction of the identical particle formalism, and its step-by-step interpretation, highlighting the key questions that drive the interpretation forwards and the techniques and stances that are employed in each step. The interpretation yields a novel metaphysical profile for systems of identical particles as potential parts of a whole, which can be traced step-by-step to elementary experimental data and the reconstruction's physical postulates and assumptions. I also describe some of the pitfalls that one faces in any attempt to directly interpret the identical particle formalism.