Hidden assumptions in the derivation of the Theorem of Bell

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance

Corpuscular Event-by-Event Simulation of Quantum Optics Experiments: Application to a Quantum-Controlled Delayed-Choice Experiment

A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is discussed. The event-based corpuscular model gives a unified description of multiple-beam fringes of a plane parallel plate and single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum eraser, two-beam interference, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments. The approach is illustrated by application to a recent proposal for a quantum-controlled delayed choice experiment, demonstrating that also this thought experiment can be understood in terms of particle processes only.Comment: Invited paper presented at FQMT11. Accepted for publication in Physica Scripta 27 June 201

Explanation of the Gibbs paradox within the framework of quantum thermodynamics

The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally looses its dominant place and the target of the paradox is naturally shifted to the decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of ``difference between the gases'' gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counter-intuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases, or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.Comment: Published version. New title. 17 pages Revte

Chaos, decoherence and quantum cosmology

In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler - DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the Wave function of the Universe adopting a Wentzel - Kramers - Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet.Comment: 40 page