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.     

On the electromagnetic structure of elementary particles

Using modern similarity and dimensionality methods, criteria of similarity are derived and used as transformations, which effect the conversion from one natural system of units to another. The exclusion principles thus defined are used to determine the powers of the similarity criteria in quantitative relations.Systems of units of the fermion and boson types are used in the simplest identification of the parameters corresponding to elementary particles.A set of electric and magnetic physical constants with dimensionality length, area, and volume, is obtained and successfully unified within the limits of a vortex ring, the maximum dimensions of which are defined by the Compton wavelength, and the minimum by the classical radius of the particle. The vortex ring model is in accordance with the latest experimental data, and it enables the behavior of the incident and target particles in the scattering process to be predicted.In modern theoretical physics the elementary particles are still considered as essentially structureless point formations, and hence it is impossible to give a purely theoretical treatment of the structure of the particles. Thus the various attempts in this direction (Hofstadter, Blokhintsev) have a polyphenomenological character and are internally inconsistent. (The search for the structure of an elementary particle is carried out on the assumption that it is not elementary, since truly elementary particles are defined as point size.) The author recognizes the need for an original approach to the structure of elementary particles, based on a method of study adequate for the problem. Such a method is the theory of dimensionality and similarity (Sedov, Gukhman, and Kirpichev), which serves as a scientific basis of a physical experiment (Kirpichev), or as the scientific basis for a model of the phenomena, insofar as the criteria of similarity are a reflection of the physical model of the process (Gukhman).It is a pleasure to thank Academician L. I. Sedov and Professor K. A. Putilov for valuable criticism and advice, and Professor A. S. Irisov and V. V. Lokhin for useful discussions.     

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.     

Semi-classical asymptotics in solid state physics

This article studies the Schrödinger equation for an electron in a lattice of ions with an external magnetic field. In a suitable physical scaling the ionic potential becomes rapidly oscillating, and one can build asymptotic solutions for the limit of zero magnetic field by multiple scale methods from homogenization. For the time-dependent Schrödinger equation this construction yields wave packets which follow the trajectories of the semiclassical model. For the time-independent equation one gets asymptotic eigenfunctions (or quasimodes) for the energy levels predicted by Onsager's relation.     

Anti-photon

It should be apparent from the title of this article that the author does not like the use of the word photon, which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the aether or vacuum to stand for empty space, even if no such thing existed. There are very good substitute words for photon, (e.g., radiation or light), and for photonics (e.g., optics or quantum optics). Similar objections are possible to use of the word phonon, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics.It is a pleasure to join in the 60th birthday celebration of the Director, Herbert Walther, of the Max-Planck-Institute for Quantum Optics at Garching, and wish him much happiness and many more years of his very great scientific creativity.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

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.     

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.     

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     

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.     

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.     

On “surface currents” of a tubular beam having helical electron trajectories in the field of a fast wave

The causes of the noncoincides of the results of the hydrodynamic and corpuscular methods of analyzing the interaction of a rotating electron beam in a fast wave, which have been presented in published papers, are investigated. Consideration of the pulsations of the beam boundaries in the hydrodynamic analysis by introducing equivalent surface currents leads to the relativistic dispersion equation derived by Gaponov [1] in the case of a small thickness of the beam walls.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 136–143, January, 1972.     

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.     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.     

Information theory and the problem of molecular structure

Recently it has been shown that the classical stick and ball viewpoint of molecules is inconsistent with quantum theory (QT). We suggest an unusual reconciliation: The QT state is not a physical property, but instead reflects our state of knowledge about observable aspects of reality. We show how this perspective is nevertheless objective. Applied to molecules, the view permits structure to exist only when observable evidence is compatible with this feature. Typically one must replace the a priori model (in particular, the dynamical generator) with one consistent with the evidence. We show that such structure is stable in the context of first-order perturbation theory. We also indicate how dynamics can be inferred from scattering data—a process alternative to postulating (field-theoretic) models for environment.     

Comparison of the structure of island deposits of gold on NaCl produced by thermal vaporization and by cathode sputtering

A comparison was made of island deposits of gold on NaCl, produced by thermal vaporization (thermal Au/NaClid) and cathode sputtering (cathode Au/NaClid). In thermal Au/NaClid, two orientations of the gold microcrystals with respect to the NaCl (100) shear face were observed; multiply twinned particles were formed. In cathode Au/NaClid, only one orientation is present and the formation of complex particles is not observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 46–50, November, 1971.     

Cosmological surrealism: More than “eternal reality” is needed

Inflationary cosmology makes the universe eternal and provides for recurrent universe creation, ad infinitum — making it also plausible to assume that our Big Bang was also preceeded by others, etc.. However, GR tells us that in the parent universe's reference frame, the newborn universe's expansion will never start. Our picture of reality in spacetime has to be enlarged.Wolfson Distinguished Chair in Theoretical Physics.Also on leave from the University of Texas, Center for Particle Physics, Austin, Texas.     

Quantum formalism via signal analysis

The general properties of signals permit a nonaxiomatic reconstruction of the quantum probability formalism independent of the standard Copenhagen interpretation of quantum mechanics. Performance standards are specified for candidate clock, signaller, and reflector devices, and it is shown that the resulting formalism forces identification of a probability- or intensity-like structure as the absolute square of an amplitude, the relative phases of amplitudes appearing explicitly in the probability composition law. Inequalities are produced which on one interpretation reduce to the Heisenberg relations, but it is pointed out that this reconstruction disqualifies position as an observable property of a signal.     

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.