Quantum particles from classical statistics

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being “classical” or “quantum” ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross‐fertilization between classical statistics and quantum physics.     

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall （QH） effect on a noncommutative phase space （NCPS）. By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.     

Comment on “A local realist model for correlations of the singlet state” by K. De Raedt,K. Keimpema,H. De Raedt,K. Michielsen and S. Miyashita

De Raedt et al. [Eur. Phys. J. B 53, 139 (2006)] have claimed to provide a local realist model for correlations of the singlet state in the familiar Einstein-Podolsky-Rosen-Bohm (EPRB) experiment when time-coincidence is used to decide which detection events should count in the analysis, and furthermore that this suggests that it is possible to construct local realistic models that can reproduce the quantum mechanical expectation values. In this letter we show that these conclusions cannot be upheld since their model exploits the so-called coincidence-time loophole. When this is properly taken into account no startling conclusions can be drawn about local realist modelling of quantum mechanics.     

Time reversal of pseudo-spin 1/2 degrees of freedom

We show that pseudo-spin 1/2 degrees of freedom can be categorized in two types according to their behavior under time reversal. One type exhibits the properties of ordinary spin whose three Cartesian components are all odd under time reversal. For the second type, only one of the components is odd while the other two are even. We discuss several physical examples for this second type of pseudo-spin and highlight observable consequences that can be used to distinguish it from ordinary spin.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall (QH) effect on a noncommutative phase space (NCPS). By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and \bar{θ}, respectively. In our calculation, we assume that these parameters vary from layer to layer.     

Generalized Quantum Mechanics for Separated Systems

We give seven necessary physical conditions on a property lattice for to describe two quantum systems when they are separated.     

Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities

We reformulate the separated quantum entities theorem, i.e., the theorem that proves that two separated quantum entities cannot be described by means of standard quantum mechanics, within the fully elaborated operational Geneva–Brussels approach to quantum axiomatics, where the basic mathematical structure is that of a State Property System. We give arguments that show that the core of this result indicates a failure of standard quantum mechanics, and not just some peculiar shortcoming due to the axiomatic approach to quantum mechanics itself.     

GR-Friendly Description of Quantum Systems

We present an axiomatic modification of quantum mechanics with a possible worlds semantics capable of predicting essential “nonquantum” features of an observable universe model—the topology and dimensionality of spacetime, the existence, the signature and a specific form of a metric on it, and a set of naturally preferred directions (vistas) in spacetime unrelated to its metric properties.     

Lyapunov exponents from quantum dynamics

We extract classical Lyapunov exponents from the time dependence of quantum mechanical expectation values. Classical chaos is revealed as a quantum transient with a liftetime ～? ln ?. Our strategy is shown to work for the example of a periodically kicked top.     

A Continuous Transition Between Quantum and Classical Mechanics. II

Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.     

A local realist model for correlations of the singlet state

Can quantum correlations of the singlet state be produced by two separate subsystems which have interacted in the past but do not communicate? We show that, using a locally causal realist model of the Einstein-Podolsky-Rosen-Bohm experiment, the answer is affirmative if coincidence in time is used to decide which detection events are stemming from a single two-particle system, the criterion employed in all experimental realizations of the Einstein-Podolsky-Rosen-Bohm gedanken experiment.     

Transitions to the Continuum: Three Different Approaches

We present three different derivations of the transition probabilities to the continuum. It is shown that calculations, performed as a direct application of the postulates of orthodox quantum mechanics (OQM), do not yield results consistent with experiments. Traditional treatments are summarized and criticized. The relation of the transitions to the continuum with the traditional quantum measurement problem is pointed out; we sum up and comment some contributions concerning this issue. It is shown that an approach based on the notion of spontaneous projections yields expressions of the transition probabilities similar to those obtained in the traditional way and new predictions which could be submitted to experimental tests.     

Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.     

Reconsidering Mermin’s “In Praise of Measurement”

We critically analyze a recent paper by D. Mermin and we compare his statements with Bell’s position on the problems he is discussing. It is a pleasure for me to dedicate this paper to Prof. Pekka Lathi on the occasion of his 60th birthday.