Foundations of quantum theory. Part I

The first part of a new axiomatization for quantum mechanics is described. An expression is derived for the probability associated with a particular value of a variable for a given system at some time.     

Spacetime and future quantum theory

Space and time are discussed in connection with the future of quantum theory.     

Calculating the probabilities of quantum processes in external gravitational fields. I.

A method is proposed for calculating the amplitudes of quantum processes for a synchronous and sealer field in warped space-time. It is shown that these amplitudes can be expressed in terms of the matrix elements of the Green functions of the field equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 90–95, March, 1979.The authors thank V. P. Frolov for stimulating discussions on the problems referred to in the paper.     

A unified quantum theory of mechanics and thermodynamics. Part I. Postulates

A unified axiomatic theory that embraces both mechanics and thermodynamics is presented in three parts. It is based on four postulates; three are taken from quantum mechanics, and the fourth is the new disclosure of the existence of quantum states that are stable (Part I). For nonequilibrium and equilibrium states, the theory provides general original results, such as the relation between irreducible density operators and the maximum work that can be extracted adiabatically (Part IIa). For stable equilibrium states, it shows for the first time that the canonical and grand canonical distributions are the only stable distributions (Part IIb). The theory discloses the incompleteness of the equation of motion of quantum mechanics not only for irreversible processes but, more significantly, for reversible processes (Part IIb). It establishes the operational meaning of an irreducible density operator and irreducible dispersions associated with any state, and reveals the relationship between such dispersions and the second law (Part III).     

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.     

The foundation of quantum theory and noncommutative spectral theory. Part I

The present paper is the first part of a work which follows up on H. Kummer: A constructive approach to the foundations of quantum mechanics,Found. Phys. 17, 1–63 (1987). In that paper we deduced the JB-algebra structure of the space of observables (=detector space) of quantum mechanics within an axiomatic theory which uses the concept of a filter as primitive under the restrictive assumption that the detector space is finite-dimensional. This additional hypothesis will be dropped in the present paper.It turns out that the relevant mathematics for our approach to a quantum mechanical system with infinite-dimensional detector space is the noncommutative spectral theory of Alfsen and Shultz.We start off with the same situation as in the previous paper (cf. Sects. 1 and 2 of the present paper). By postulating four axioms (Axioms S, DP, R, and SP of Sec. 3), we arrive in a natural way at the mathematical setting of Alfsen and Shultz, which consists of a dual pair of real ordered linear spaces Y, M: A base norm space, called the strong source space (which, however, in slight contrast to the setting of Alfsen and Shultz, is not 1-additive) and an order unit space, called the weak detector space, which is the norm and order dual space of Y. The last section of part I contains the guiding example suggested by orthodox quantum mechanics. We observe that our axioms are satisfied in this example. In the second part of this work (which will appear in the next issue of this journal) we shall postulate three further axioms and derive the JB-algebra structure of quantum mechanics.     

Toward a micro realistic version of quantum mechanics. Part I

This paper investigates the possibility of developing a fully micro realistic version of elementary quantum mechanics. I argue that it is highly desirable to develop such a version of quantum mechanics, and that the failure of all current versions and interpretations of quantum mechanics to constitute micro realistic theories is at the root of many of the interpretative problems associated with quantum mechanics, in particular the problem of measurement. I put forward a propensity micro realistic version of quantum mechanics, and suggest how it might be possible to discriminate, on experimental grounds, between this theory and other versions of quantum mechanics.     

Generalized Borel law and quantum probabilities

A version of the Borel law of large numbers is found which remains valid for nonclassical (Mackey-type) probability theories. Its relation to a frequency interpretation of quantum probabilities is discussed.Supported by the Polish Ministry of Science, Higher Education and Technology, Program MRI7.     

Spacetime Topology from the Tomographic Histories Approach: Part II

As an inverse problem, we recover the topology of the effective spacetime that a system lies in, in an operational way. This means that from a series of experiments we get a set of points corresponding to events. This continues the previous work done by the authors. Here the relativistic case is considered. The existence of upper bound in the speed of transfer of matter and information induces a partial order on the set of events. While the actual partial order is not known in our operational set up, the grouping of events to (unordered) subsets corresponding to possible histories, is given. From this we recover the partial order up to certain ambiguities that are then classified. Finally two different ways to recover the topology are sketched and their interpretation is discussed.     

Weak objectification,joint probabilities,and Bell inequalities in quantum mechanics

The weak objectification of physical properties is shown to yield the same probabilistic implications as strong objectification and can therefore be refuted on the basis of suitable interference experiments. An alternative test of hypothetical objectification statements, as they occur in the EPR experiment, is based on joint probabilities and the ensuing Bell inequalities. Quantum mechanics turns out to be partially compatible with Bell's inequalities even in cases where weak objectification is excluded by interference.     

Superselection rules in quantum theory: Part I. A new proposal for state restriction violation

It is argued that preparation of a quantum state characterized by density operator not commuting with a superselection operatorQ does not by itself constitute an instance of superselection rule violation. It would, however, be an instance of state restriction violation. It is held that superselection rule violation is only possible with simultaneous observable and state restriction violations. It is shown that it is a priori conceivable to subdivide an ensemble whose satisfies[, Q] = 0 into subensembles whose density operators violate the state restrictions. The dynamics of the subdivision process is not considered.     

On the connection between quantum and classical descriptions

The review paper presents generalization of d??Alembert??s variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum force ?j, ??. Spatial attention is dedicated to the systems with (hidden) symmetries. It is shown how the symmetry reduces the number of quantum degrees of freedom down to the independent ones. The sin-Gordon model is considered as an example of such field theory with symmetry. It is shown why the particles S-matrix is trivial in that model.     

Quantum probabilities,Kolmogorov probabilities,and informational probabilities

The relations between quantum probabilities, Kolmogorov probabilities, and informational probabilities are studied against the background offered by the concept of a quantum mechanical probability tree built in previous work. It is shown that the quantum mechanical transformation theory goes beyond the Kolmogorov concept of probabilities. It is furthermore shown that the quantum mechanical concept of probability is of the same essence as the informational one. The analyses that produce these conclusions bring forth the first lines of a general mathematical representation of the emergence and circulation of patterns of any kind.     

The Bohm approach to cavity quantum scalar field dynamics. Part I: The free field

Bohm 's approach to quantum field theory is illustrated through its application to cavity quantum scalar field dynamics. Specific calculations demonstrate how the evolution of the well-defined scalar field is governed by the nature of its quantum state. The implications of the nonlocality inherent in quantum mechanics and the meaning of the classical limit are discussed in this context.