Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

Role of time in the sum-over-histories framework for gravity

I sketch a self-contained framework for quantum mechanics based on its path-integral or sum-over-histories formulation. The framework is very close to that for classical stochastic processes like Brownian motion, and its interpretation requires neither measurement nor state-vector as a basic notion. The rules for forming probabilities are nonclassical in two ways: they use complex amplitudes, and they (apparently unavoidably) require one to truncate the histories at a collapse time, which can be chosen arbitrarily far into the future. Adapting this framework to gravity yields a formulation of quantum gravity with a fully spacetime character, thereby overcoming the frozen nature of the canonical formalism. Within the proposed adaptation, the value of the collapse time is identified with total elapsed spacetime four-volume. Interestingly, this turns the cosmological constant into an essentially classical constant of integration, removing the need for microscopic fine tuning to obtain an experimentally viable value for it. Some implications of the V = T rule for quantum cosmology are also discussed.     

Piron's axioms for quantum mechanics: A reply to Foulis and Randall

In their paper A note on Misunderstandings of Piron's Axioms for Quantum Mechanics, Foulis and Randall undertake a reply to our critique of Piron's question-proposition system (qp-s) which appeared in previous issues of this journal. In the present paper, we want briefly to refute the points of criticism raised by Foulis and Randall (FR). We argue that the misunderstandings are not ours, and we prove it.     

Correlation inequalities for multicomponent rotators

A recent approach to G.H.S. and Lebowitz inequalities is used to prove Griffiths' second inequality for 3 and 4 component models (e.g. Classical Heisenberg model, ||⁴ Euclidean fields). Applications include monotonicity of the mass gap in the external field, and two-sided inequalities between parallel and transverse correlations.     

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.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

The meaning of the terms “phase” and “phase transition”

Various meanings of the terms phase and phase transition encountered in scientific literature are discussed. These terms supplement each other and cover only together all the macroscopic situations which are now denoted by this term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1988.     

Can particle creation by a black hole be described in terms of more familiar laboratory processes?

Particle creation by a black hole is described in terms of temperature corrections to the Casimir effect. The results of Levin, Polevoy, and Ritov for spectral and total Poynting vector for a fluctuating electromagnetic field in a plane vacuum gap between two arbitrary media with different temperatures in flat spacetime are applied to clarify the situation that exists between the horizon of a nonrotating black hole and spatial infinity. This helps to reveal the mechanism of particle creation. The Hawking radiation is born inside the bell formed by a potential barrier of a black hole in all the region [2M, ]. Its blackbody spectrum is due to the interaction of field fluctuations with the surface of the bell. The particles between the walls are virtual ones. They can become real after passing through the [3M, ] tail, appearing to an observer at future infinityJ ⁺ as real ones. The arguments for and against the present standpoint are discussed.     

Electronic “phase” transition of hydrogen molecules in the electron density functional method

Using the electronic density functional method (EDFM), it is shown that as hydrogen atoms approach to interatomic distance of 2.4a ₀ a bond charge forms in the spin polarized (antiferromagnetic) biradical state, after which there is a jump-like electronic phase transition to the spincompensated (covalent) state typical for a chemical bond. The electronic phase transition is calculated in two approximations for the electronic density: superposition of atomic densities and bond charge. The formation of a bond charge stabilizes the hydrogen molecule due to the decrease in the nonelectrostatic (quantum) energy of electrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 24–27, October, 1982.     

Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a state-event-probability (SEVP) structure, using a quite standard fuzzification procedure, a set of unsharp events (or effects) is constructed and the corresponding state-effect-probability (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are interpreted in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied.     

Dark body and black hole horizons

The formula for the horizon of a Newtonian dark body is given and compared to that of a relativistic black hole: a Newtonian dark body has at least one hair.     

Raman effect of light on argon atoms

Scalar scattering of light on the 3p and 3s subshells of the argon atom (Stokes scattering) and anti-Stokes scattering on the excited 4p and 4s states of argon are examined in the Hartree-Fock approximation. The calculation is made in a velocity form and in a length form. It is shown that the value in the r form is 1.5–2 times greater than in the form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–42, January, 1977.     

On a “structure intermediate between quasiperiodic and random”

This paper proves rigorously that the structure factor of the structure intermediate between quasiperiodic and random introduced by Aubry. Godréche, and Luck is purely singluar continuous apart from a delta function at zero for most choices of the parameters. The result is based on a proof that a flow under a steep function over an irrational circle rotation is weakly mixing for most parameters, and on the wonderland Theorem.     

Correlation functions for quasi-linear response theory

A quasi-linear regression formula is derived by an expansion around quasi-static equilibrium. It relates the relaxation of thermodynamic forces to the regression of correlations of thermodynamic coordinates in quasi-static equilibrium. Correlation functions and memory kernels can be introduced in almost complete analogy to linear response theory. A non-linear, non-Markovian kinetic equation is derived. The kinetic coefficients are given in terms of correlation functions of stochastic forces in quasi-static equilibrium similar to the linear theory.     

Stiff magnetic field lines. I. A geometrical foundation

It is shown that the foliation of a space-time manifold of codimension 2 provides a basis for the study of the deformation of magnetic field lines. It is found that the fluid flow vector and the curvature vector of a nongeodesic stiff magnetic field line are always orthogonal. Further, it is shown that the metric tensor of the 2-space orthogonal to the Maxwellian string is Lie-transported along the magnetic field lines when the magnetic field lines are stiff. If there exists a spacelike Killing vector field parallel to the magnetic field, then the magnetic field lines must be stiff.     

On some frequent but controversial statements concerning the Einstein-Podolsky-Rosen correlations

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.     

Electromagnetic-gravitational energy systems

Two methods axe considered to tap the earths' rotational energy. This ancient collapsed gravitational energy exceeds the earth-lunar binding energy. One involves an orbiting electromagnetic-gravitational coupling system whereby the earth's rotation, with its nonuniform mass distribution, first uses gravity to add orbital energy to a satellite, similar to a planetary flyby.rd The second stage involves enhanced satellite drag as current-carrying coils withdraw the added orbital energy as they pass through the earth's nonuniform magnetic field. A second more direct method couples the earth's rotational motion using conducting wires moving through the noncorotating part (ionospheric current systems) of the geomagnetic field. These methods, although not immediately feasible, are considerably more efficient than using pure gravitational coupling to earth-moon tides.     

Economic demography in fuzzy spatial dilemmas and power laws

Adaptive agents, playing the iterated Prisoners Dilemma (IPD) in a two-dimensional spatial setting and governed by Pavlovian strategies (higher success-higher chance to stay), are used to approach the problem of cooperation between self-interested individuals from a novel angle: We investigate the effect of different possible measures of success (MS) used by players to asses their performance in the game. These MS involve quantities such as: the players utilities U, his cumulative score (or capital) W, his neighborhood welfare, etc. To handle an imprecise concept like success the agents use fuzzy logic. The degree of cooperation, the economic demography and the efficiency attained by the system depend dramatically on the MS. Specifically, patterns of segregation or exploitation are observed for some MS. On the other hand, power laws, that may be interpreted as signatures of critical self-organization (SOC), constitute a common feature for all the MS.     

A new procedure for thin-film deposition by solution spraying

The major reasons for the low photovoltaic efficiency of Cu₂S/CdS cells, in which the CdS film is deposited by spraying, are due to small film thicknesses which do not exceed 4 m and the small average grain size which ranges from 0.1 to 0.5 m.A new experimental solution spraying procedure is described that prevents both restrictions by controlling the substrate temperature. Average grain sizes of more than 1 m are obtained.Work supported by Ministere Pubblica Istruzione and Centro Regionale Ricerche Nucleari e di Struttura della Materia