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.     

Quantum measurements,sequential and latent

The results of a hypothetical experiment requiring a sequence of quantum measurements are obtained retrospectively, after the experiment has been completed, from a single reading of an apparatus register. The experiment is carried out reversibly and Schrödinger's equation is satisfied until the terminal reading of the register. The technique is illustrated using a feasible method of measuring photon spin as the quantum object observable and using the photon energy as the apparatus register. The technique is used to discuss the watchdog effect, the effect of repeated measurements inhibiting quantum jumps.     

Squeezed “atomic” states,pseudo-Hermitian operators and Wigner D-matrices

The states of N two-level atoms can be mapped onto the eigenvectors of angular momentum (with j=N/2) and this system in interaction with a radiation field constitutes a fundamental model in Quantum Optics. There from one may construct atomic coherent states and minimum uncertainty packets. The squeezing of such states is of considerable contemporary interest. We show that the properties of squeezed atomic states are most elegantly and economically expressed in terms of pseudo-Hermitian operators and through Wigner D-matrices and their analytical continuation.     

The preparation of “perfect” dendritic germanium crystals

Perfect germanium crystals with the required resistivity and small dislocation density are reproducibly prepared in the Popov Research Institute of Radiocommunications. Perfect dendrites are suitable for use, for example, in the preparation of alloy diffused transistors. The shape, pulling apparatus and actual preparation of perfect germanium dendrites are described. Some of the parameters influencing the growth of a perfect dendrite are analyzed and the optimum conditions for its growth are determined.     

Lorentz matrices: A review

This is an expository review of the Lorentz transformation, which is a change of coordinates used by one inertial observer to those used by another one. The transformation can be represented by a four-by-four matrix, the Lorentz matrix or the Minkowski-Lorentz matrix. The most familiar, or special, case has thex axis of both observers parallel to their relative velocity. A more general transformation drops this constraint. But then a seeming paradox arises when there are three observers, and this has led to a challenge to the self-consistency of the special theory of relativity. It is shown here that this challenge is based on a misunderstanding. The properties of the more general Lorentz transformation are reviewed consistently in terms of the matrix approach, which the author believes is now the easiest approach to understand. The spectral analysis of the Lorentz matrix is also discussed. Several checks are included to make assurance double sure.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

Evolutionary drive: The effect of microscopic diversity,error making,and noise

In order to model any macroscopic system, it is necessary to aggregate both spatially and taxonomically. If average processes are assumed, then kinetic equations of population dynamics can be derived. Much effort has gone into showing the important effects introduced by non-average effects (fluctuations) in generating symmetry-breaking transitions and creating structure and form. However, the effects of microscopic diversity have been largely neglected. We show that evolution will select for populations which retain variability, even though this is, at any given time, loss-making, predicting that we shall not observe populations with optimal behavior, but populations which can learn. This lesser short-term efficiency may be why natural diversity is so great. Evolution is seen to be driven by the noise to which it leads.     

A phase cell approach to Yang-Mills theory

Variables are chosen to describe the continuum Yang-Mills fields, a discrete set of group valued variables. These are group elements associated to the sequence of lattice field theory configurations realizing the continuum field. The field is laid down inductively. At each inductive step one of three types of field excitations makes its contribution to the total field. These are either pure modes, averaging correction modes, or chunks. The pure modes are small field excitations, as studied in previous papers in this series [2,3]. The averaging correction modes are small excitations added to make sure the block spin transformation is satisfied at each edge. The chunks, encompassing most of our difficulties, are large field excitations. Topological obstructions in ₃(G) must be dealt with in defining a gauge choice for each chunk. The laying down process is complex, but fiendishly clever, ensuring a principle of gauge invariant coupling. Each group valued variable is either the amplitude of a pure mode or an internal variable in a chunk. The amplitude of an averaging correction mode is a dependent variable, a function of the (independent) variables used to describe the field. The (independent) variables herein defined are those whose mutual interaction will later be inductively decoupled in defining the phase cell cluster expansion (of course treating the variables of each chunk as a unit).This work was supported in part by the National Science Foundation under Grant No. PHY-85-02074     

Analysis of conformal-invariant scattering amplitudes for the two-dimensional world model

The explicit form of the conformal-invariant phase shift analysis in thes-channel for a scattering process involving two incoming and two outgoing particles is derived for the two-dimensional world model. The high energy behaviour of the scattering amplitudes is determined completely (up to a constant factor) by the requirement of conformal invariance. It is not possible to obtain this high energy limit by neglecting the masses right from the beginning. The main mathematical problem is the determination of the Clebsch-Gordan coefficients forSU ₀(1, 1) in the momentum basis.     

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.     

Bell-type inequalities in the nonideal case: Proof of a conjecture of bell

Recently Bell has conjectured that, with epsilonics, one should be able to argue, à la EPR, from almost ideal correlations (in parallel Bohm-Bell pair experiments) to almost determinism, and that this should suffice to derive an approximate Bell-type inequality. Here we prove that this is indeed the case. Such an inequality—in principle testable—is derived employing only weak locality conditions, imperfect correlation, and a propensity interpretation of certain conditional probabilities. Outcome-independence (Jarrett's completeness condition), hence factorability of joint probabilities, is not assumed, but rather an approximate form of this is derived. An alternative proof to the original one of Bell [1971] constraining stochastic, contextual hidden-variables theories is thus provided.     

The evaluation map in field theory,sigma-models and strings I

The rôle of the evaluation map in anomaly calculations for field theory, sigma-models and strings is investigated. In this paper, anomalies in field theory (with and without a backgrounds connection), are obtained as pull-backs of suitable forms via evaluation maps. The cohomology of the group of gauge transformations is computed in terms of the cohomology of the base manifold and of the cohomology of the structure group. This allows us to clarify the different topological significance of gauge and gravitational anomalies. The relation between locality and universality is discussed and local cohomology is linked to the cohomology of classifying spaces. The problem of combining the locality requirement and the index theorem approach to anomalies is also examined. Anomaly cancellation in field theories derived from superstrings is analyzed and the relevant geometrical constraints are discussed.On leave of absence from Dipartimento di Fisica dell'Universitá di Padova and Istituto Nazionale di Fisica Nucleare, Sezione di PadovaWork supported in part by: Ministero Pubblica Istruzione (research project on Geometry and Physics)On leave of absence from Department of Mathematics, University of North Carolina, Chapel Hill, N.C. 27514. Work supported in part by N.S.F.     

Gravity and Signature Change

The use of proper time to describe classical spacetimes which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.     

Variational formulation of general relativity from 1915 to 1925 “Palatini's method” discovered by Einstein in 1925

Among the three basic variational approaches to general relativity, the metric-affine variational principle, according to which the metric and the affine connection are varied independently, is commonly known as the Palatini method. In this paper we revisit the history of the golden age of general relativity, through a discussion of the papers involving a variational formulation of the field problem. In particular we find that the original Palatini paper of 1919 was rather far from what is usually meant by Palatini's method, which was instead formulated, to our knowledge, by Einstein in 1925.     

Hypernuclear physics

The contributed papers submitted to the session C Hypernuclear and kaon physics and not presented orally at the Conference are briefly reviewed here.Rapporteur talk at the symposium Mesons and Light Nuclei IV, Bechyn, Czechoslovakia September 5–10, 1988.     

High energy electrons in the earth's radiation belts

Special experiments performed aboard the space stations Salyut-6-SoyuzProgress, Salyut-7-Soyuz T-13-Kosmos-1669, and the artificial earth satellite IK Bolgariya-1300 discovered, significant electron and positron fluxes with energies of more than decades of MeV in the earth's radiation belts. Spatial and angular characteristics of these fluxes have been studied. Study of the charge ratio of the electron-positron component has shown that it is electron-based. This indicates that in outer space near the earth some efficient mechanism capable of accelerating electrons to energies of more than decades of MeV exists.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 38–43, September, 1986.The authors consider it their pleasant duty to express gratitude to V. M. Gracev, S. V. Koldashov, A. V. Popov, and S. E. Ulin for their preparation of the equipment and conduct of the experiments.     

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.     

Quasigroups Connected with Clifford Groups

In Clifford groups, a nonassociative product is defined which leads to the definition of nonassociative groups. These nonassociative groups have matrix representations on the condition that the row by column product of two matrices is replaced by the column by column product. A nonassociative group of transformations connected with the Lorentz group is determined, together with its irreducible, double-valued matrix representation, whose matrices undergo the column by column product.     

Einstein,Gödel,Bohr

Linear combinations of elements of reality, as defined by Einstein, Podolsky, and Rosen, may not be themselves elements of reality. There are questions which can be formulated (and unambiguously answered) in the ordinary language of experimental physics, but cannot be represented in the mathematical framework of quantum theory in a nontrivial way.     

Strengthening of some spinodal binary and pseudobinary copper alloys

Age hardening and microstructure (TEM) in the Cu-Ni-Sn and Cu-Ti alloys is studied. The annealing curves with a plateau and a double peak are discussed with respect to the structure development.