A new interpretation of Bell's inequalities

Bell's inequalities are always derived assuming that local hidden-variable theories give a set of positive-definite probabilities for detecting a particle with a given spin orientation. The usual claim is that quantum mechanics, by its very nature, cannot produce a set of such probabilities. We show that this is not the case if one allows for generalized (nonpositive-definite) master probability distributions. The master distributions give the usual quantum mechanical violation of Bell's inequalities. Consequences for the interpretation of quantum mechanics are discussed.     

Nonlocality and Gleason's lemma. Part I. Deterministic theories

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker paradox in quantum mechanics.     

The chaotic ball: An intuitive analogy for EPR experiments

Actual realisations of EPR experiments donot demonstrate non-locality. A model is presented that should enable non-specialists as well as specialists to understand how easy it is to find realistic explanations for the observations. The model also suggests new areas where realistic (hidden-variable) models can give valid predictions whilst quantum mechanics fails. It offers straightforward explanations for some anomalies that Aspect was unable to account for, providing perhaps the first experimental evidence that a hidden-variable theory can besuperior to quantum mechanics. The apparent success of quantum mechanics in predicting results is shown to be largely due to the use of unjustifiable and biased analysis of the data. Data that has been discarded because it did not lead to a valid Bell's test may give further evidence that hidden variables exist.     

Realism in quantum mechanics

We first present a realistic framework for quantum probability theory based on the path integral formalism of quantum mechanics and illustrate this framework by constructing a model that describes a quantum particle evolving in a discrete space-time lattice. We then present a finite model for describing the internal dynamics of elementary particles and show that this model gives the standard particle classification scheme and successfully predicts particle masses.     

On measurement and irreversible processes

The nature of physical measurements performed on microscopic systems is discussed, and it is suggested that the procedures which are conventionally referred to as measurements fall into at least three different categories. The connection between observation processes and irreversible processes is stressed. The customary quantum mechanical treatment of irreversible processes is discussed, and its deficiencies from the philosophical point of view are criticized. The standpoint that quantum mechanics should not be considered as a basic philosophical system but rather as an immensely useful tool is defended. Some attempts at developing a more basic theory are discussed, and a hypothesis is put forward concerning the role of entropy within some possible future nonlocal hidden-variable theory.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Some Thought-Experiments Involving Macrosystems as Illustrations of Various Interpretations of Quantum Mechanics

I consider various experiments related to the so-called macroscopic quantum coherence experiment, which are probably at present in the class of thought experiment but are likely to become realistic in the next few decades. I explore the way in which outcomes consistent with the predictions of quantum mechanics would be interpreted by an adherent of, respectively, the Copenhagen, statistical, and Bohmian interpretations of the formalism.     

Coherent quantum oscillation trajectories

We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examples for both a superposition of position states, and a superposition of momentum states.     

Path integral and transactional interpretation

The concept of transaction, introduced by Cramer in his realistic nonlocal interpretation of quantum mechanics (QM), is herein reformulated in the language of the Feynman graphs' technique.     

Reconstruction of abstract quantum theory

Understanding quantum theory as a general theory of prediction, we reconstruct abstract quantum theory. Abstract means the general frame of quantum theory, without reference to a three-dimensional position space, to concepts like particle or field, or to special laws of dynamics. Reconstruction is the attempt to do this by formulating simple and plausible postulates on prediction in order to derive the basic concepts of quantum theory from them. Thereby no law of classical physics is presupposed which would then have to be quantized. We briefly discuss the relationship of theory and interpretation in physics and the fundamental role of time as a basic concept for physics. Then a number ofassertions are given, formulated as succinctly as possible in order to make them easily quotable and comparable. The assertions are arranged in four groups: heuristic principles, verbal definitions of some terms, three basic postulates, and consequences. The three postulates of separable alternatives, indeterminism, and kinematics are the central points of this work. These brief assertions are commented upon, and their relationship with the interpretation of quantum theory is discussed. Also given are an outlook on the further development into concrete quantum theory and some philosophical reflections.     

Relative compatibility and joint distributions of observables

The notion of relative compatibility of observables is treated and its relation to the existence of joint distributions is obtained. The case of conventional quantum mechanics is studied and a generalization to the case of the quantum logic approach to quantum mechanics is given. It is shown that relative compatibility is equivalent to the existence of so-called type 1 joint distributions.     

Observable consequences from second-type state vectors of quantum mechanics

Starting from a singlet state vector for two correlated systems we find an observable whose expectation is 3 according to quantum mechanics, while it has a maximum value of 1 if only state vectors of the first type are considered. This allows a much easier experimental check of the hitherto unobserved state vectors of the second type than suggested by Bell's inequality.     

Logical anomalies of quantum objects. A survey

We discuss some aspects of the concept of object and objectuation as suggested by the articulation of modern physics. In particular we analyze the new ontological thickness of the notion ofobject in quantum mechanics and in relativistic quantum mechanics.At the end we try to formulate some modifications of the logical approach to quantum theory in order to grasp the new situation connected with relativistic quantum theory.     

К ТЕОРИИ ГРАВИТАЦИОННОГО ИЗЛУЧЕНИЯ

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On the theory of gravitational radiation

The equations of motion of weakly radiating particles are investigated in a linear approximation in which the pseudo-Euclidian metric remains valid but energy changes caused by gravitational radiation are considered. The classical relativistic equations of motion with variable rest mass are applied. An elementary theory of the gravitational radiation of a rotator is formulated. The results are applied for particles in circular accelerators. It is found that a rotator with non-zero rest mass cannot exist for an unlimited period and that it cannot exceed the velocity of light. This explains why particles with non-zero rest mass cannot attain the velocity of light in circular accelerators; it is also shown that the gravitational radiation of particles in circular accelerators does not exist in practice.

     

Mysteries Without Mysticism and Correlations Without Correlata: On Quantum Knowledge and Knowledge in General

Following Niels Bohr's interpretation of quantum mechanics as complementarity, this article argues that quantum mechanics may be seen as a theory of, in N. David Mermin's words, correlations without correlata, understood here as the correlations between certain physical events in the classical macro world that at the same time disallow us to ascertain their quantum-level correlata.     

Fuzzy quantum logic II. The logics of unsharp quantum mechanics

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operatorsF on a Hilbert space such that, 0¦F²) the role played by orthomodular posets with respect to orthogonal projections (corresponding to sharp effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (afuzzy-like and anintuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ^* posets, and BZ³ posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.     

Hidden variables and Bell's theorem in quantum mechanics

In the present paper we give a precise definition of a hidden-variable theory for quantum mechanics, whereby we adopt the weakest possible definition of a hidden-variable theory, which is compatible with the assumption that the bounded observables of a quantum mechanical system are represented by the elements of the real part A_r of a W^*-algebra A (of the most general type) and the states are represented by the normal states (in the mathematical sense) of A. We then go on to show that an example put forward by Bell in 1966 satisfies our definition (Sec. 2). Finally we make use of Bell's famous theorem to show that for a sufficiently non-commutative W^*-algebra A no hidden-variable theory in our sense exists (Theorem 3.3 and its corollaries).     

A local realistic explanation of EPR correlations

The reality of physical properties is divided into two types: relatively and absolutely real. Concerning the reality of spatial observables, it is proposed to drop the concept of an absolute reality of spatial observables. The resulting relative reality then isnot the observer-dependent reality of the standard interpretation of quantum mechanics, but rather the reference frame-dependent reality implied by the principle of relativity. Within the frame of this relative reality, it is then shown that a local explanation for the existence of EPR correlations can be found when two-valued discrete spatially directed observables (like the spin-1/2 components of electrons, or the polarization states of photons) are assumed. The new explanation is formally analogous to the standard explanation of classical correlations at a distance. Sufficient assumptions to obtain this result are the isotropy of space and the existence of two-valued discrete spatially directed observables. Thus, the possibility to find a both local and realistic explanation of correlations at a distance is extended to quantum variables violating Bell's inequality.     

On the Role of Spin in Quantum Mechanics

From the invariance properties of the Schrödinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an external motion, which can be interpreted as the motion of the centre of mass, and an internal one, whose presence disappears in the classical limit. The latter is caused by the spin of the particle, whatever is its actual value (different from zero). The quantum potential in the Schrödinger equation, which is responsible of the quantum effects of the system, is then completely determined from the properties of the internal motion, and its unusual properties have a simple and physical explanation in the present context. From the impossibility to fix the initial conditions relevant for the internal motion follows, finally, the need of a probabilistic interpretation of quantum mechanics.     

On the zigzagging causility model of EPR correlations and on the interpretation of quantum mechanics

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B B|. An exact correspondence exists between the Born-Jordan-Dirac wavelike algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations |B) (B| were over real hidden states. While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes A|C = C|A*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |A|C|². CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is | U | = | U = U|, with | denoting a preparation, | a measurement, and U the evolution operator. The transformation | = |U or | = |U^–1 exchanges the preparation representation and the measurement representation of a system and is ancillary in the formalization of the quantum chance game by the wavelike algebra of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude A|C = A|BB|C between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility A|C = C|A* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of blind statistical retrodiction—that is, of final cause.Dedicated to Professor David Bohm, proponent of the EPRB version of nonseparability.