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Fundamental theories of physics

Deterministic Quantum Mechanics

Gerard ’t Hooft

Published Jan 1, 2016• 11 citations
Publisher

Abstract

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.

DOI
10.1007/978-3-319-41285-6_4

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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.
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 source of inspiration for doing quantum probability lies in the ingenious methods adopted by physicists to compute probabilities of events concerning the subatomic world of elementary particles where the laws of classical mechanics break down and the distinction between a particle and a wave becomes vague. These methods lead to a generalisation of classical probability which may be described as a study of observable quantities concerning any system subject to chance and exhibiting the following basic features: (i) each observable quantity behaves like a classical real valued random variable on a probability space and hence has a probability distribution on the real line; (ii) it may be impossible to measure simultaneously two individually observable quantities in the sense that measurement of one may interfere with and destroy already existing information about the value of the other; (iii) bounded observable quantities constitute a real linear space in which the vectorial sum of two individually observable quantities interfering with each other is different from the arithmetic sum of their actual values. 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 previous chapter addressed the challenge of making sense of the notion of a quantum state assignment being performed correctly without thereby acknowledging the notion of a quantum state a quantum system ‘is in’. The present chapter discusses what interpretation of quantum probabilities goes best with the account that I have called the ‘Rule Perspective’ and started to develop in the previous chapter. The first section considers what quantum probabilities should be taken to be probabilities of in the Rule Perspective; the second investigates what philosophical interpretation of probabilities applies best to quantum probabilities thus conceived. The third section considers two objections to the resulting account of quantum probabilities. 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.
We mentioned in Chapter 1 that many people believe that science deals in facts, laws and certainties that resolve the mysteries, superstitions and fantasies of religion, but Huxley asserts that science has explained nothing. His claim is exaggerated but as we enter the quantum world and hear about imaginary time, the difficulty of predicting how the smallest units of matter behave, black holes and various views of reality we will understand his bewilderment. 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.