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arXiv:quant-ph/0407025 · International Journal of Quantum Information

CONTEXTUAL OBJECTIVITY AND THE QUANTUM FORMALISM

Philippe Grangier

Published Dec 17, 2004• 18 citations
arXivHTMLPDF

Abstract

The "new orthodoxy" of quantum mechanics (QM) based on the decoherence approach requires many-worlds as an essential ingredient for logical consistency, and one may wonder what status to give to all these "other worlds." Here we advocate that it is possible to build a consistent approach to QM where no other worlds are needed, and where the quantum formalism appears as a consequence of requiring the enumerability of physical properties. Such a quantization hypothesis is closely related to indistinguishability, and is deeply inconsistent with classical physics.

DOI
10.1142/s0219749905000396

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The "new orthodoxy" of quantum mechanics (QM) based on the decoherence approach requires many-worlds as an essential ingredient for logical consistency, and one may wonder what status to give to all these "other worlds." Here we advocate that it is possible to build a consistent approach to QM where no other worlds are needed, and where the quantum formalism appears as a consequence of requiring the enumerability of physical properties. Such a quantization hypothesis is closely related to indistinguishability, and is deeply inconsistent with classical physics.
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.
The quasi-classical world of modern physics is a class of classical worlds superposed, literally a 'metaworld'. The measurement problem is itself evidence for the two different types of world, at the different levels of logical type. The enactment of linear dynamics in the classical worlds alters the class invariant, and thus induces physical collapse of the metaworld to a subclass. No new physics is required. The complex formalism that seems deeply counterintuitive is class arithmetic. Superposition and interference: properties of classes of worlds. Measurement: set-selection of a subclass compatible with the observed outcome. The uncertainty principle: incompatible set-selections. Fourier transforms: switching set-selection. Operators: enactment of set-selection. Decoherence: loss of coherence between worlds. Normalisation is required because all worlds are equally real, thus the probability of an outcome is essentially the proportion of worlds that instantiate it. True probability arises through phase, which is the degree to which the rest of each world aligns internally with this outcome. This is the second-logical-type phenomenon of interference: the degree to which worlds cohere in the classical actions that give rise to the outcome.This transforms the familiar structures of the formalism from postulates to inherent attributes of the class structure. The Born rule, unitary evolution, the complex structure of amplitudes, the probabilistic character of prediction, and the wave-mechanical form of the theory emerge as outputs of the ontology rather than independent axioms. The wavefunction is real. It is the ontological architecture of the metaworld and the reality of the quasi-classical world: this is the quantum realm. The classical world, quantum mechanics and relativistic physics are unified in logical types.
Orthodox quantum mechanics, or at least some extreme interpretations of it, adopts a nonrealistic stance by assuming, in its fifth, or reduction postulate, that Reality is, in last instance, a making of the observer consciousness. The enormous empirical success of orthodox quantum mechanics lead most of the scientific community to accept without reserve this highly idealistic posture even without fully realizing its deep implications. Now, almost a century after its formulation, a return to a realistic view of Physics seems possible.