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

By F. J. Belinfante

A Survey of Hidden-Variables Theories is a three-part ebook at the hidden-variable theories, referred during this e-book as ""theories of the 1st kind"". half I experiences the causes in constructing forms of hidden-variables theories. the search for determinism ended in theories of the 1st style; the hunt for theories that appear like causal theories whilst utilized to spatially separated platforms that interacted long ago ended in theories of the second one style. components II and III additional describe the theories of the 1st variety and moment type, respectively.
This publication is written to make the literature on hidden variables understandable to those that are stressed by way of the unique papers with their controversies, and to usual reader of physics papers.

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Since ( — Jn)2 = J2, points on the sphere that are each other's antipodes will have the same color. Any point P and its antipode are the poles of a great circle C representing all directions perpendicular to n. According to (60c) this circle C for any red point P must be a completely blue circle. Since, thus, each red point introduces many more blue points, we find that it is impossible to get enough red color onto the sphere so as to make one-third of the sphere red, as condition (60b) suggests we would need.

We have already told in general terms that the inequality (28), for observ­ ables A, B, and (A+B) that are not simultaneously measurable, is not only unavoidable, but also is desirable (see footnote 13), and that the validity of (30) or (32) for quantum theory is not something that should be postulated as if it were an a priori obvious triviality, but that it is a happenstance which follows from more elementary parts of the theory which von Neumann unfortunately did not choose to be his fundamental axioms.

By the application of a small electric field of rhombic symmetry, the energy of the helium atom is perturbed by Hs = aS2 + bS2+cS2. (58) Here, S = J. The eigenstates of this perturbation are the same as mentioned above, and the perturbation energy is (b+c)h2 or (c+a)ft2 or (a+b)h2 depending on which of the three J2 operators has the value zero. So by measuring the energy of the atom we can determine, for the three orthogonal coordinate axes determined by the rhombic electric field, along which of these three axes is J2 = 0, and then J2 = h2 along the other two axes.

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