The modal interpretation of quantum mechanics has two variants: the Copenhagen variant (CV) and the anti-Copenhagen variant (ACV). Healey uses the Bell-Wigner locality condition to criticize the latter, which I do not advocate. 2 The conclusions of Healey's admirably written article are therefore welcome to me. But if I had wished to advocate the ACV, I do not think that his arguments would have dissuaded me. Specifically, as I shall explain, we should distinguish between Physical Locality and Metaphysical Locality. The (...) first principle is unexceptionable, but Healey needs the second for his reductio. At the end I shall briefly indicate why I reject the ACV and advocate instead the Copenhagen variant. (shrink)

Recent discussions of experimental tests of the Sum Rule have been carried out in the context of the special circumstances attending the Cross-Ramsey experiment. A more general analysis of possible tests is presented. A technical mistake of Fine and Glymour concerned with a misunderstanding of the physics of the Cross-Ramsey experiment is explained and a detailed analysis of a thought experiment based on the Einstein-Podolsky-Rosen wave function is given. It is concluded, in agreement with Fine, that scattering experiments do not (...) test the Sum Rule as a principle which supplements standard quantum mechanics. (shrink)

In 1924, Bohr, Kramers and Slater tried to introduce into microphysics conservation principles that hold only on the average. This attempt was abandoned in the light of the Compton-Simon experiment. Since that time, except for a moment of doubt in 1936, it has been thought that the classical conservation laws hold in quantum theory for each individual interaction, in a way that yields the classical exchange-and-balance of momentum familiar from the laws of elastic collisions. It has been thought, that is, (...) that in each individual “collision” what one part of the total system loses in linear momentum another part gains, so as to maintain the same total amount afterwards as before. To those familiar with discussions of the interpretation of quantum theory, however, it will be apparent that the very concepts needed to express this idea of an elastic collision are generally not admitted in the theory. For one needs the idea that both before and after collision the total system has a well-defined value for the conserved quantity and, moreover, that the various component parts of the system have well-defined values for those quantities out of which the conserved one is composed. But in the case of spin, for example, it is customary to say that although total spin may be conserved in certain interactions one cannot attribute values to the separate components of spin because the associated operators do not commute. Moreover, one does not generally refer to the values of quantities except in eigenstates. Hence, in general, one would not refer to the value of the conserved quantity before and after interaction, except for interactions initiated in eigenstates. (shrink)

Bell's problem of the possibility of a local hidden variable theory of quantum phenomena is considered in the context of the general problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space, and Bell's result is presented as a generalization of Maczynski's theorem for maximal magnitudes. The proof of this generalization is shown to depend on the impossibility of recovering the quantum statistics for sequential probabilities in a classical representation without introducing a (...) randomization process for the hidden variables. Hidden variable theories that exclude such a randomization process are termed “strict,” and it is shown that the class of local hidden variable theories is included in the class of strict theories. A counterargument by Freedman and Wigner is evaluated with reference to Clauser's extension of a hidden variable model proposed by Bell. (shrink)

Existing "no hidden variable proofs" for quantum mechanics deal exclusively with observables with discrete spectra. This note shows that similar results hold for observables with continuous spectra.