Bohr's discussion of the fourth uncertainty relation revisited

Bohr's 1930 derivation of the uncertainty relation c ² m th bears a close relationship to Einstein's 1913 derivation of the gravitational redshift via the equivalence principle. A rewording of Bohr's argument is presented here, not taking the last step of acceleration as equivalent to a uniform gravity field, thus yielding a derivation of the formula c ² m th, avoiding Treder's 1971 objection.     

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.     

Fluctuation Dissipation Equation for Lattice Gas with Energy

In this paper we introduce a lattice gas with energy, and obtain the fluctuation dissipation equation for it. The system has two conserved quantities, the number of particles and the total energy. Once the fluctuation dissipation equation is established, the hydrodynamic limit is easily deduced from it by using the methods found in ref. 1 for this model.     

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.     

Recent hypernuclear research at the Brookhaven AGS

Recent AGS experiments contributing to our knowledge of hypernuclei are reviewed. These experiments have suggested new areas of research on hypernuclei. With the proper beam line facilities, the AGS will be able to perform experiments in these areas and provide a transition to the future era of kaon factories.Invited contribution to the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

New two-color dimer models with critical ground states

We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.     

The metric in a static cylindrical elastic medium and in an empty rotating frame as solutions of Einstein's field equations

Using the Weyl-type canonical coordinates, an integration of Einstein's field equations in the cylindrosymmetric case considered by Kurunolu is reexamined. It is made clear that the resulting metric is not describing the spacetime in a rotating frame, but in astatic cylindrical elastic medium. The conclusion of Kurunolu that for an observer on a rotating disk there is no way of escape from a curved spacetime is therefore not valid. The metric in an empty rotating frame is found as a solution of Einstein's field equations, and is not orthogonal. It is shown that the corresponding orthogonal solution represents spacetime in an inertial frame expressed in cylindrical coordinates. Introducing a noncoordinate basis, the metric in a rotating frame is given the static form of Kurunolu's solution. The essential role played by the nonvanishing structure coefficients in this case is made clear.     

Statistical thermodynamic formalism in the solution of information theory problems

This is the first of several papers dealing with the application of statistical thermodynamic methodology to the solution of coding and communication theory problems. Emphasis is placed on the various ensemble techniques of statistical mechanics, the words or samples of a message taking the place of molecules in the prototype physical system. Analogs of temperature, internal energy, pressure, chemical potential, volume, entropy, etc., are developed. The isomorphism with thermodynamics is complete and these quantities transform (for example, by partial differentiation) in exactly the same way as the prototype physical quantities. The methods are nicely applicable to coding cases involving sources with memory, in which case, correlation can be discussed in terms of analog coupling energies between signals or words so that the store of many-body-problem techniques can be used. In addition, the manipulative freedom stemming from the possibility of choosing from a multiplicity of ensembles constrained by intensive parameters proves a distinct advantage. A concrete example dealing with the choice of a compact code for a nonextended source with memory is presented. The compact code is derived, and some discussion is given concerning the breadth of its power spectrum. In a following paper, its autocorrelation function within the framework of pulse code modulation is derived and transformed by Wiener theory so that the power spectrum is directly exhibited (along with the spectra for several other cases).Research supported under AFOSR Grant No. 70-1877. The present work is contribution No. 2643 of the Department of Chemistry, University of California-Los Angeles.     

Stationary non-equilibrium states of infinite harmonic systems

We investigate the existence, properties and approach to stationary non-equilibrium states of infinite harmonic crystals. For classical systems these stationary states are, like the Gibbs states, Gaussian measures on the phase space of the infinite system (analogues results are true for quantum systems). Their ergodic properties are the same as those of the equilibrium states: e.g. for ordered periodic crystals they are Bernoulli. Unlike the equilibrium states however they are not stable towards perturbations in the potential.We are particularly concerned here with states in which there is a non-vanishing steady heat flux passing through every point of the infinite system. Such superheat-conducting states are of course only possible in systems in which Fourier's law does not hold: the perfect harmonic crystal being an example of such a system. For a one dimensional system, we find such states (explicitely) as limits, whent, of time evolved initial states _i in which the left and right parts of the infinite crystal are in equilibrium at different temperatures, _L ^–L _R ^–1 , and the middle part is in an arbitrary state. We also investigate the limit of these stationary (t) states as the coupling strength between the system and the reservoirs goes to zero. In this limit we obtain a product state, where the reservoirs are in equilibrium at temperatures _L ^–1 and _R ^–1 and the system is in the unique stationary state of the reduced dynamics in the weak coupling limit.On leave of absence from the Fachbereich Physik der Universität München. Work supported by a Max Kade Foundation FellowshipResearch supported in part by NSF Grant MPS75-20638     

Action-angle variables in quantum statistical mechanics

Utilizing the facts (i) that the number of particles in the many-boson system is conserved and (ii) that the Hamiltonian is Hermitian, a new set of variables comprising action and angle variables has been introduced. These variables are conjugate in the mean and provide a rigorous approach to introducing phase variables for total-number-conserving many-boson systems.Lecture given at the Saha Institute of Nuclear Physics, Calcutta, June 1971.     

Hierarchy structure in integrable systems of gauge fields and underlying Lie algebras

An improved version of Nakamura's self-dual Yang-Mills hierarchy is presentd and its symmetry contents are studied. The new hierarchy as well as the previous one represents a set of commuting dynamical flows in an infinite dimensional manifolds of loop type, but includes a large set of dependent variables. Because of new degrees of freedom the theory acquires a more symmetric form with richer structures. For example it allows a large symmetry algebra of Riemann-Hilbert type, which is actually a direct sum of two subalgebras (left and right). This phenomenon is basically the same as observed recently by Avan and Bellon on the case of principal chiral models. In addition to these rather familiar symmeties, a new type of symmetries referred to as coordinate transformation type are also introduced. Generators of the above dynamical flows are all included therein. These two types of symmetries altogether form a big Lie algebra, which lead to more satisfactory understanding of symmetry properties of integrable systems of guage fields.     

Mach's principle and the reciprocal symmetry of nature

This article develops the postulate that spacetime-charge inversion invariance reflects a fundamental reciprocal symmetry in nature between the two long range forces, from which the derivation of Mach's principle (i.e., the principle that the fundamental parameters of the electromagnetically elementary charged particle are related to those describing the electromagnetically observable universe) follows quite easily. Interpreting this result, it is argued that relativity and quantum mechanics can be made conceptually compatible and mathematically consistent by this reciprocal symmetry if one realizes that relativity isboth a macroscopic, semiclassical theory (i.e., the global half of relativity, described by Eq. (1.1), including special and general relativity) and a microscopic theory (i.e., the local half of relativity, described by Eq. (2.1), including relativistic quantum mechanics and field theory). The reciprocal symmetry of nature, then, promises unique (differential and/or integral) relationships between the coordinate variables of the observers of these tworeciprocally related theories, which implies unique, consistent numerical values for the scalar curvatureR, the massM, and the critical density for closure, _c, of the observable universe [derived from the elementary particle parameters (i.e., the electron mass and Coulomb radius)]. With this symmetry we also postulate a plausible mechanism for spontaneous generation of matter from the ubiquitous (zero-mass ether) nothingness of the Dirac sea of filled negative energy states, and can consistently interpret both the positive and negative-energy state solutions of Dirac's equation for massive, spin-1/2 (i.e., fermion) particles and both the advanced and retarded potential solutions of electromagnetic field equations. It is pointed out that, with this interpretation of the advanced potential solutions from electromagnetic field theory, one can actuallyderive causality from electromagnetic theory.     

Intersubjectivity,relativistic covariance,and conditionals: response to C. I. J. M. Stuart

A misunderstanding persists between Stuart and me, which I do my best to clarify. Bayesian inverse subjectivities versus relativistic covariance and physical intersubjectivity are discussed. A joint number of chances formalism taking care of the propagation of the probability of causes is proposed.     

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.     

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.     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part I. Fundamental concepts

A method is proposed that should facilitate the construction of theories of submicroscopic particles (denoted as theories of microchannels) in a way similar to the use of group-theoretical methods. The conceptual analysis (CA) method is based on the analysis of the basic concepts of a theory; it permits a determination of necessary conditions imposed on the mathematical apparatus (of the theory) which then appear as a mathematical representation of the structures obtained in a formal scheme of a theory. A pertinent conceptual analysis leads to a new definition (relativization) of the concept empirical implication. The approach may be characterized as realistic and operational. The application of the CA method is illustrated on the example of quantum theory. In Part I the algebraic structure of a partially ordered, up-ward directed, bounded set is deduced from the rudimentary concepts. In Parts II and III, we shall deduce the Hilbert-space structure (well established in quantum mechanics) from postulates on some essential idealizations accepted in the theory. Whereas Part II is concerned with the idealizations of existing quantum theories based on the Hilbert-space formalism, Part I may be considered as a general basis for a wider class of theories.Dedicated to Prof. G. Ludwig on the occasion of his 60th birthday.     

Some remarks on braided group reconstruction and braided doubles

The cross coproduct braided group AutC)B is obtained by Tannaka-Krein reconstruction from C ^B C for a braided group B in braided category C. We apply this construction to obtain partial solutions to two problems in braided group theory, namely the tensor problem and the braided double. We obtain AutC) Aut(C) Aut(C) Aut(C) and higher braided group spin chains. The example B(R) B(R) ... B(R) is described explicitly by R-matrix relations. We also obtain Aut(C) Aut(C)* as a dual quasitriangular codouble braided group by reconstruction from the dual category C° C. General braided double crossproducts B C are also considered.     

Magnetic charge as a “hidden” gauge symmetry

A theory containing both electric and magnetic charges is formulated using two vectors potentials,A andC . This has the aesthetic advantage of treating electric and magnetic charges both as gauge symmetries, but it has the experimental disadvantage of introducing a second massless gauge boson (the magnetic photon) which is not observed. This problem is dealt with by using the Higgs mechanism to give a mass to one of the gauge bosons while the other remains massless. This effectively hides the magnetic charge, and the symmetry associated with it, when one is at an energy scale far enough removed from the scale of the symmetry breaking.This paper is dedicated to my grandparents Herbert and Anneliese Schmidt.     

Quantization of fields on principal bundles

A constructive method of quantization of free gauge fields is presented. In particular, by using a geometric approach (classical gauge fields as connections on principal fibre bundles) and the Borchers-Uhlmann method, an algebraic quantum field theory of gauge fields is constructed. Thus, a linearized version of a quantum field theory of non-Abelian gauge fields is obtained generalizing Bongaarts' results for the Abelian U(1)-theory.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Formation of F-centers in Kcl-Rbcl solid solutions with Sr2+ and OH− impurities

The kinetics of F-center formation are studied in crystals of KCl-RbCl. solid solutions, both in the pure state and with Sr²⁺ and OH^– impurities. The crystals were irradiated by electrons at 1.2 MeV at room temperature. The initial stage of coloration in crystals that have been purified of divalent cation impurities is the same as that of pure crystals; only when Sr²⁺ is introduced is this stage sharply accelerated. The efficiency of F-center formation in the second stage of coloration is significantly smaller in purified crystals than in pure crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 38–41, July, 1971.