Propensity and probability in quantum mechanics

We give in this letter an operational definition of quantum mechanical propensity based on a realistic measuring process. We show that such a propensity can be defined by a state to be measured, a filter or a reference state and a group of possible “motions” of such filter. Such a propensity exhibits the tendency of the measured state to take up certain states of the filter accessible by its “motion”. We give two examples of such propensities for space-momentum and spin-orientation measurements.     

Realistic quantum probability

A mathemetical framework for a realistic quantum probability theory is presented. The basic elements of this framework are measurements and amplitudes. Definitions of the various concepts are motivated by guidelines from the path integral formalism for quantum mechanics. The operational meaning of these concepts is discussed. Superpositions of amplitude functions are investigated and superselection sectors are shown to occur in a natural way. It is shown that this framework includes traditional nonrelativistic quantum mechanics as a special case. Proofs of most of the theorems will appear elsewhere.     

Local quantum physics and models

The problem of characterizing a specific model within the frame of local quantum physics is addressed.Dedicated to Huzihiro Araki     

Classical physics and quantum loops

The standard picture of the loop expansion associates a factor of variant Planck's over 2pi with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss counterexamples wherein classical effects arise from loop diagrams and display the relationship between the classical terms and the long range effects of massless particles.     

Einstein's relativity and quantum physics

There are reasons to reject the idea that a field in empty space is a real physical entity. The nonexistence of the electromagnetic field and the gravitational field as physical entities leads to far-reaching consequences. The basic equations sufficient to constructclassical electrodynamics (the Maxwell equations and the Lorentz force equation) are obtained by combining quantum considerations with two premises: (a) there exists a subatomic particle, theemon, each concrete emon having a specific electric property described by aspacelike four-vector; (b) every concrete charged particle possesses a specific electric property described by atimelike four-vector. Some other points of interest are also discussed, in particular, ones related to Einstein's gravitational field as well as the action-at-a-distance versus local-action issue. Einstein's second postulate of special relativity is also shown to need some revision of principle.     

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.     

Environment-assisted invariance,entanglement, and probabilities in quantum physics

I introduce environment-assisted invariance or envariance-a symmetry exhibited by correlated quantum systems and related to causality-and describe how it can be used to understand the nature of ignorance and, hence, the origin and interpretation of Born's rule for quantum probabilities.     

Inference in quantum physics

In quantum physics all experimental information is discrete and stochastic. But the values of physical quantities are considered to depict definite properties of the physical world. Thus physical quantities should be identified with mathematical variables which are derived from the experimental data, but which exhibit as little randomness as possible. We look for such variables in two examples by investigating how it is possible to arrive at a value of a physical quantity from intrinsically stochastic data. With the aid of standard probability calculus and elementary information theory, we are necessarily led to the quantum theoretical phases and state vectors as the first candidates for physical quantities.     

Free probability and quantum electrodynamics

The stochastic limit of a free particle coupled to the quantum electromagnetic field without dipole approximation leads to many new features such as: interacting Fock space, Hilbert module commutation relations, disappearance of the crossing diagrams, etc. In the present paper we begin to study how the situation is modified if a free particle is replaced by a particle in a potential which is the Fourier transform of a bounded measure.We prove that the stochastic limit procedure converges and that the overall picture is similar to the free case with the important difference that the structure of the limit Hilbert module is strongly dependent on the wave operator of the particle.     

Novel quantum phases and mesoscopic physics in quantum gases

Among many notable jubilees brought by the year 2012, the one of a special importance for the community of statistical physicists was the 140th birth anniversary of Marian Smoluchowski (Maryan Ritter von Smolan Smoluchowski, 28.05.1872 - 5.09.1917), who was one of the pioneers of statistical physics and, on a larger scale, one of those who shaped modern physical science as a whole. The present issue of EPJ ST entitled From Brownian motion to self-avoiding walks and Lévy flights aims to reflect the evolution of Smoluchowski’s ideas in the field of statistics of interacting random and self-avoiding walks, stochastic equations for many-particle systems, physics of glass-forming and noise driven systems. Majority of papers in this issue were presented at the international conference in statistical physics that took place in Lviv (Ukraine) on July 3-6, 2012.     

Relationships between quantum physics and biology

The known facts of quantum physics and biology strongly suggest the following hypotheses: atoms and the fundamental particles have a rudimentary degree of consciousness, volition, or self-activity; the basic features of quantum mechanics are a result of this fact; the quantum mechanical wave properties of matter are actually the conscious properties of matter; and living organisms are a direct result of these properties of matter. These hypotheses are tested by using them to make detailed predictions of new facts, and then by showing that the predictions can be verified. The hypotheses are used to predict successfully that the quantum wave properties of matter are strongly predominant in proteins, to explain the presence and relative abundance of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur in proteins, and to explain diffraction phenomena, the behavior of helium II, the exclusion principle, and causality and determinism in modern science, thus closely relating physics and biology.This article is an outgrowth of the author's thesis work in the Graduate School (Physics Department) of the University of Missouri—Rolla.     

Foundations of quantum probability

This paper presents an overview of the foundations of quantum probability. The main concepts in this theory are measurements and generalized actions. These concepts correspond to the usual quantum observables and states. Probabilities are computed by means of a universal influence function. We first derive the form of the universal influence function and then construct the amplitude and probability of a measurement with respect to a given generalized action. It is shown that traditional quantum mechanics can be derived as a special case of this theory and moreover the theory gives a complete realistic interpretation of quantum mechanics. It is demonstrated that spins of any order can be described within this framework and a realistic solution to the EPR problem can be achieved.     

Preparation and measurement in quantum physics

To honor Henry Margenau on the occasion of his 90th birthday, we attempt in this essay to integrate certain aspects of the physics, philosophy, and pedagogy of quantum mechanics in a manner very much inspired by Margenau's idealist scientific epistemology. Over half a century ago, Margenau was perhaps the first philosopher of science to recognize and elaborate upon the essential distinction between thepreparation of a quantum state and themeasurement of an observable associated with a system in that state; yet in contemporary quantum texts that distinction rarely receives adequate emphasis even though, as we demonstrate, it may be explicated through a series of simple illustrations.     

新型超导量子比特及量子物理问题的研究

近年来,超导量子计算的研究有了很大的进展.本文首先介绍了nSQUID新型超导量子比特的制备和研究进展,包括器件的平面多层膜制备工艺和量子相干性的研究.这类器件在量子态的传输速度和二维势系统的基础物理问题研究方面有着很大的优越性.其次,国际上新近发展的平面形式的transmon和Xmon超导量子比特具有更长的量子相干时间,在器件的设计和耦合方面也有相当的灵活性.本文介绍了我们和浙江大学与中国科学技术大学等单位合作逐步完善的这种形式的Xmon器件的制备工艺、制备出的多种耦合量子比特芯片,以及参与合作,在国际上首次完成的多达10个超导量子比特的量子态纠缠、线性方程组量子算法的实现和多体局域态等固体物理问题的量子模拟.最后介绍了基于这些超导量子比特器件开展的大量的量子物理、非线性物理和量子光学方面的研究,包括在Autler-Townes劈裂、电磁诱导透明、受激拉曼绝热通道、循环跃迁和关联激光等方面形成的一整套系统和独特的研究成果.     

Selection rules,causality, and unitarity in statistical and quantum physics

The integrodifferential equations satisfied by the statistical frequency functions for physical systems undergoing stochastic transitions are derived by application of a causality principle and selection rules to the Markov chain equations. The result equations can be viewed as generalizations of the diffusion equation, but, unlike the latter, they have a direct bearing onactive transport problems in biophysics andcondensation aggregation problems of astrophysics and phase transition theory. Simple specific examples of the effects of severe selection rules, such as the relaxational Boltzmann transport equation and the diffusion equation, are also given. Finally, partial differential equations for the probability amplitudes of quantum mechanics are derived, usingunitarity instead of causality, and a selection rule is applied directly to obtain ageneralization of the Dirac equation in which infinite transitions between states arenot allowed.     

Semantic incompleteness of quantum physics

We discuss the completeness of quantum physics (QP) from a nonrealistic viewpoint. To this end we make use of the formalized languageL for QP that we introduced in a recent paper and show that QP is incomplete both in an intuitive sense and in a more formal logical sense. We also show that a pure state is not physically equivalent to the physical property which characterizes it in QP, and that the set of all properties whose truth value can be predicted for a physical object in the stateS coincides with the set of all properties which are certainly true or certainly false inS. These results lead us to introduce a notion of compatibility between states which can be applied to the EPR experiment, in order to prove that no quantum paradox follows from it if our interpretation of states and physical properties is accepted.