What are the principles of quantum mechanics? Since 1925, proponents of various interpretations have championed theirs, while doubters have searched for new ones. Principles, therefore, are important Am but what do we mean by a “principle” when talking about a scientific theory?
KeywordsQuantum Mechanic Quantum Logic Quantum Geometry Pure Wave Bright Student
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- [p. 190]Einstein’s principles: from Lorentz et al. (1923). For the Hilbert-Einstein episode, see Pais (1982) and J. Earman and C. Glymour in Archiv. His. Exact Sciences 19 (1978), pp. 291–308. A fair judgment might be: it was Einstein’s theory, but the Einstein-Hilbert equations of gravity.Google Scholar
- [p 193]“Against ‘measurement’” was based on a talk Bell gave in Erice, Sicily, in August 1989. See A. Miller (ed.), 62 Years of Uncertainty (1990), p. 19, reprinted in Physics World (August 1990). N. G. van Kampen (one of the three authors mentioned by Bell) angrily replied in that journal in October; Rudolf Peierls (Bell’s thesis advisor many years before) in January 1991; and Kurt Gottfried (another author) in October 1991. Bell’s criticisms whizzed by these establishment physicists, who repeat old arguments as if unable to hear the dead physicist’s voice. For example, Peierls claimed “it is easy to give an acceptable account” of quantum measurements (meaning an account FAPP), and asserted that the wave function represents merely “our knowledge” of the particle. When criticized by a letter writer (May 1991) for ignoring Bell’s concerns, he replied “concepts like ‘reality’ cannot be given any meaning at the quantum level.” That may put deluded realists in their place, but it misses Bell’s point that physicists never found a precise account of atoms.Google Scholar
- [p 195]Quantum logic: see Jammer (1974). Quantum probability: see Accardi and Weldenfels (eds.) (1989). Many worlds: see H. Everett, Rev. Mod. Phys. 29 (1957), pp. 454–462, reprinted in Wheeler and Zurek. Another remark about these theories is that, when one gets to the details, one discovers that assumptions no more plausible than those of conventional theory are needed to derive a Hilbert space.MathSciNetADSCrossRefGoogle Scholar
- [p 196]Wallstrom first published his observations in Found. Phys. Lett. 5, no. 2 (1989), p. 113, a journal so obscure that he might have done better in Stamp Collecting News. He wrote a more comprehensive account for Phys. Rev., 49, no. 3 (1994), pp. 1613–1617. While preparing the latter, Wallstrom discovered that his discovery had been made earlier, by Takehiko Takabayasi from Nagoya, Japan, in a paper on the hydrodynamical interpretation that appeared in—you guessed it—1952. (See Prog. Theor. Phys. 8 (1952), p. 143.) Although Takabayasi did not quite make the connection with topology, he noted the line-integral condition (math)(where m denotes the particle’s mass, v the velocity, h Planck’s constant, n an integer, and the line-integral is taken around any closed curve y not intersecting the zero-set of the probability density) and remarked At any rate we are led to a new postulate… which is so to speak the ‘quantum condition’ for fluidal motion and of ad hoc and compromising character for our formulation, just as [Bohr’s angular momentum condition of Chapter 2] was for the old quantum theory. Wallstrom’s observation was that it is equally compromising for stochastic mechanics.Google Scholar
- [p. 198]Cartan’s book: E. Cartan (1931). Axioms for quantum geometry: manuscript of the author (1991, unpublished).Google Scholar
- [p. 200]Wootters’ information principle appears in A. Marlow (ed.) Quantum Theory and Gravitation (1980), pp. 13–26; see also Phys. Rev. 23 (1981), pp. 357–362. The observation that minimizing the error in estimating a parameter leads to the rule “probability equals the square of a projection” dates back to a paper of R. A. Fisher, one of the founders of modern statistics; see Proc. Royal Soc. Edinburgh 62 (1922), pp. 321–341.Google Scholar
- [p. 202]Böhm and Bub: Rev. Mod. Phys. 38 (1966), p. 447. C. Papaliolios, Phys. Rev. Lett. 18, no. 15 (1967), tested one consequence of the model, with negative results. K. Hepp, Helv. Acta. 45 (1972), p. 237, proposed that in the limit of infinitely large systems quantum mechanics can resolve a dichotomy. See Bell (1987), paper six, for a criticism. When Arthur Wightman advertised Hepp’s result in a seminar at Princeton, Eugene Wigner is said to have remarked, “You’re a great man, Arthur, but you are not infinite.”Google Scholar
- [p. 204]The GRW scheme: see Phys. Rev. D 34, no. 2 (1986), p. 470, and Miller, 62 Years of Uncertainty (1990). Solution to the exercise: The equations are the classical ones associated with the Hamiltonian H. The dynamical laws of this type are precisely the classical, linear Hamiltonian flows that commute as flows with the maximally symmetric case (Hi,j = δi,j).Google Scholar