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Birkhäuser Boston eBooks

Bell’s Theorem

David Wick

Published Jan 1, 1995• 0 citations
Publisher

Abstract

In the early 1950s, a physics student in Northern Ireland of unusual critical ability noticed a puzzling situation. Einstein, the student knew, had claimed quantum mechanics gave an inadequate account of atoms, and he had read about von Neumann’s “impossibility proof” in a popular book. 94 But then was not one of these geniuses wrong? 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
10.1007/978-1-4612-5361-7_11

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In the early 1950s, a physics student in Northern Ireland of unusual critical ability noticed a puzzling situation. Einstein, the student knew, had claimed quantum mechanics gave an inadequate account of atoms, and he had read about von Neumann’s “impossibility proof” in a popular book. 94 But then was not one of these geniuses wrong? 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.
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.