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arXiv:1308.1007

The Fate of the Quantum

Gerard ’t Hooft

Published Aug 5, 2013• 1 citation
arXivHTMLPDF

Abstract

Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other conceptual obstacles. Here, it is shown how mappings can be formulated that relate quantum systems to classical systems. By generalizing these ideas, one gets quite general models in which quantum mechanics and classical mechanics can merge. It is helpful to have some good model examples such as string theory. It is suggested that notions such as 'super determinism' and 'conspiracy' should be looked at much more carefully than in the, by now, standard arguments.

DOI
10.48550/arxiv.1308.1007

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Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other conceptual obstacles. Here, it is shown how mappings can be formulated that relate quantum systems to classical systems. By generalizing these ideas, one gets quite general models in which quantum mechanics and classical mechanics can merge. It is helpful to have some good model examples such as string theory. It is suggested that notions such as 'super determinism' and 'conspiracy' should be looked at much more carefully than in the, by now, standard arguments.
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This paper reviews some of our understanding of general quantum mechanics. It starts with the exposition of an abstract algebraic formalism useful to formulate classical and quantum-mechanical models of physical systems. It then highlights the essential differences between classical models (commutative algebra) and quantum-mechanical models (non-commutative algebra) of physical systems. It is explained in which sense classical models are “realistic” and deterministic, while quantum-mechanical models are intrinsically probabilistic – in spite of the fact that the Heisenberg time-evolution of operators representing physical quantities is “deterministic”. The quantum theory of time-ordered sequences of measurements is developed in some detail, and the crucial role of “decoherence” in the emergence of facts – or “(almost) consistent histories” – is explained. Some technical matters (Bell inequalities, quantum marginal problem) are discussed in appendices.
Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.
Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?