Towards a Resolution of Dilemma: Nonlocality or Nonobjectivity?

This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell’s assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr’s view.     

p-Adic valued quantization

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ? _p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ? _p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.     

p-Adic orthogonal wavelet bases

We describe all MRA-based p-adic compactly supported wavelet systems forming an orthogonal basis for L ²(ℚ _p ). The text was submitted by the authors in English.     

On the p-adic Navier–Stokes equation

ABSTRACT

We prove the local solvability of the p-adic analog of the Navier–Stokes equation. This equation describes, within the p-adic model of porous medium, the flow of a fluid in capillaries.     

Pseudo-topological commutative superalgebras with nilpotent ghosts

Translated from Matematicheskie Zametki, Vol. 48, No. 2, pp. 114–122, August, 1990.     

p-Adic stochastics and Dirac quantization with negative probabilities

A new mathematical apparatus, ap-adic theory of probability, is applied to realize the hypothetical world based on negative probability distributions created by Dirac for the relativistic quantization of photons. Within thep-adic theory of probability, negative probability distributions are well defined (in the language of limits of relative frequencies, but with respect to ap-adic metric). We propose that the negative Gibbs distributions arising in relativistic quantization are described byp-adic Stochastics.on leave from Moscow Institute of Electronic Engineering, Moscow, Russia.     

Gaussian quantization of the Klein-Gordon equation in variational derivatives and secondary quantization of a Boson string

A Klein-Gordon equation in variational derivatives is proposed for the quantum theory of a Boson string in a fixed gauge. By using this equation a secondary quantization is constructed for a Boson string in the functional space of string functionals that are square summable in a countable additive Gaussian measure.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 32–36, January, 1990.The author is grateful to V. S. Vladimirov and I. V. Volovich for useful discussions of the quantum and field theories of a boson string.     

The theory of non-archimedean generalized functions and its applications to quantum mechanics and field theory

The work was supported by the Russian Fundamental Sciences Foundation, project N 93-011-16114.