By F. J. Belinfante

ISBN-10: 0080170323

ISBN-13: 9780080170329

A Survey of Hidden-Variables Theories is a three-part publication at the hidden-variable theories, referred during this e-book as ""theories of the 1st kind"". half I studies the reasons in constructing types of hidden-variables theories. the hunt for determinism resulted in theories of the 1st style; the hunt for theories that appear like causal theories while utilized to spatially separated structures that interacted long ago ended in theories of the second one type. components II and III extra describe the theories of the 1st sort and moment style, respectively.

This e-book is written to make the literature on hidden variables understandable to people who are pressured through the unique papers with their controversies, and to commonplace reader of physics papers.

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**Additional resources for A Survey of Hidden-Variables Theories**

**Sample text**

44 A SURVEY OF HIDDEN-VARIABLES THEORIES Gleason's proof of existence of a density matrix for quantum-mechanical states In the discussion of Gleason's work, we do not talk about truth values vn9 but about the quantum-theoretical probabilities wn = νν(φΛ) for finding experimentally that a state φη is realized. "25 He defines a frame function of weight W as a real function/(φ) of normalized vectors φ in φ such that, if {(/>,·} is any orthonormal basis of φ, then £/(/) = fF. Gleason's postulates thus make ' £ νν(φ,) = 1 for any complete orthonormal {φ,}, (67a) 0 ^ H # „ ) ^ 1.

Also, if ψ 5* φ^ in any explicit hidden-variables theory the algorithm determining n(y>, I, {Φί}) enables us to calculate the selection n(ip, |, {φ^) for given φ, | and {φ,}. Our principal worry, however, is whether a given experimental arrangement for making a measurement will enable us to tell with sufficient precision what set {φ^ describes the possible results of the measurement. There are many cases where there can be doubts. Manipulating the choice ο/{φί) If we measure an observable A and want to find out whether A = Αχ or A = A2, but An happens to be a threefold-degenerate eigenvalue with infinitely many possible sets {017>m} with m = 1, 2, 3 spanning the Hilbert subspace corresponding to An, how do we know which of these sets describes possible results of our measurement?

This subspace may be a single Hilbert vector or it could be a more-dimensional subspace spanned by several Hilbert vectors. An example of the latter would be the Hilbert subspace corresponding to a degenerate eigenvalue of some operator. We shall discuss propositions corresponding to more-dimensional subspaces of Hilbert space in Chapter 4 in a discussion of some of the work of Jauch and Piron. " That is, according to them it should be possible, for any given hidden-variables state (ψ, |), to assign to every Hilbert vector φη a "truth value" v such that v = 1 would mean that the proposition mentioned above con cerning the system being in state φη would be true, while v = 0 would mean that this propo sition would be a false statement.

### A Survey of Hidden-Variables Theories by F. J. Belinfante

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