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Fundamental theories of physics

Locality

Gerard ’t Hooft

Published Jan 1, 2016• 0 citations
Publisher

Abstract

The usual ‘proofs’ that deterministic hidden variable models for quantum mechanics cannot be completely local, are based on rather indirect arguments, using thought experiments, free will, and the like. In this chapter we show how difficulties emerge when we wish to construct mathematical models. We also show how, in principle, the problem can be addressed at the level of model building. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-319-41285-6_14

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The usual ‘proofs’ that deterministic hidden variable models for quantum mechanics cannot be completely local, are based on rather indirect arguments, using thought experiments, free will, and the like. In this chapter we show how difficulties emerge when we wish to construct mathematical models. We also show how, in principle, the problem can be addressed at the level of model building. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Even if the underlying deterministic model may be assumed to obey decent locality requirements, a systematic procedure to define a quantum Hilbert space starting from its ontological states, would in general lead to a quantum system without manifest locality at all. Instead, what we are really after is a procedure that generates a local, relativistic quantum field theory. In this chapter we describe a procedure that follows the construction of relativistic quantum field theory more closely. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The world of atoms and molecules is described by exactly the same expressions as the determinisric world described in the previous chapter, yet here, a world consisting of ‘real things’, seems to be missing. As soon as one makes some very basic assumptions about locality and causality, it seems to be possible to prove that such a world cannot exist at all. Have other assumptions been made? Can deterministic theories exist that generate strong correlations in space-like directions? What does free will mean? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The conclusion of Part I, the non-technical (or somewhat less technical) part of this book, is that a completely convincing model of our universe is lacking. This should be a model that shows how quantum mechanical behaviour, with all its mysteries and paradoxes, can emerge from a local, deterministic theory. Yet we also find that one can assume its existence to arrive at a picture of our quantum mechanical universe that makes perfect sense. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure subject. Whereas to most physicists the possibility of a classical reinterpretation of quantum mechanics remains remote and perhaps irrelevant to current problems, a minority have kept the issue alive throughout this period. (See Freistadt [5] for a review of the problem and a comprehensive bibliography up to 1957.) As far as results are concerned there are on the one hand purported proofs of the non-existence of hidden variables, most notably von Neumann’s proof, and on the other, various attempts to introduce hidden variables such as de Broglie [4] and Bohm [1] and [2]. One of the difficulties in evaluating these contradictory results is that no exact mathematical criterion is given to enable one to judge the degree of success of these proposals. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This chapter gives an introduction to a chain of results attempting to exclude deeper layers underneath quantum mechanics that restore some form of classical physics: ‘[Such results] more or less illustrate the ways along which some opponents might hope to escape Bohr’s reasonings and von Neumann’s proof and the places where they are dangerously near breaking their necks.’ (Groenewold, 1946, p. 454). In so far as they are mathematically precise, such no-go results have their roots in von Neumann’s 1932 book, which gave rise to two traditions that were often in polemical opposition to each other. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
An outline is given of the interpretation of quantum mechanical expressions if one assumes that what is called Quantum Mechanics today, refers to an underlying reality as in Chap. 2 , even if many authors claim to have evidence to the contrary, as is usually brought forward. If there exists a sub-microscopic classical world of real things, is that the same classical world as the world of large things such as planets, rocks and people? How does the notion of probability enter into quantum mechanics? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.