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Fundamental theories of physics

The Problem of Quantum Locality

Gerard ’t Hooft

Published Jan 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1007/978-3-319-41285-6_22

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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.
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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 therapeutic approach to quantum theory developed here is meant to be applicable not only to non-relativistic quantum mechanics, but to more advanced quantum theories as well. More specifically, it is meant to be applicable to the quantum theories of systems with infinitely many degrees of freedom, quantum field theories in particular. However, the quantum theories of systems with infinitely many degrees of freedom harbour additional philosophical challenges besides those that are already present in non-relativistic quantum mechanics, and it is to be hoped that the approach suggested here may help to clarify and address those challenges as well. The present chapter turns to some aspects of the interpretation of quantum field theory and assesses them in the light of the Rule Perspective. 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.
In this chapter we introduce the Hilbert space which plays the central role in quantum mechanics. For a more detailed discussion of this subject we refer to the books of Balakrishnan [5], Richtmyer [137], Sewell [146], Stakgold [152], Steeb [163], Weidmann [181], Yosida [185]. Moreover the proofs of the theorems given in this chapter can be found in these books. We assume that the reader is familiar with the notation of a linear space. First we introduce the pre-Hilbert space. 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.