Showing papers in "International Journal of Theoretical Physics in 1971"

A Problem of Information Gain by Quantal Measurements

Abstract: For the average information gain by a quantal measurement of the first kind, an expression is suggested for a lower bound, which turns out to be non-negative.

Energy--momentum quanta in fresnel's evanescent wave.

Abstract: Fresnel's theory of the evanescent wave in total reflection entails that the propagation vectork and the momentum quantaħ k have an imaginary component and, thus, a projection on the reflecting plane that is larger (in units such thatc=1) than the angular frequencyω and the energy quantaħω. We discuss the ‘tachyon properties’ of these energy-momentum quanta and propose an experimental test using absorption or stimulated emission by an atomic or ionic beam. We then show that the Maxwell-Minkowski tensor (although certainly appropriate to discuss the macroscopic energy-momentum exchange between wave and diopter) does not describe adequately the energy-momentum density of the quanta in the evanescent wave, this stemming from its too remote connection with the generator ∂i of space-time displacements. On the other hand de Broglie's energy-momentum tensorA k[∂i]B jk is the density canonically associated with the generator of space-time displacements; we show that it describes quite satisfactorily both the energy fluxes (as measured through the longitudinal Goos-Hanchen and our new transverse shifts of the reflected beam in total reflection) and the momentum densities of the quanta inside the evanescent wave. Finally, we show that it is the gauge which is transverse in the diopter's rest frame that directly yields the physically measured energy fluxes. We take this fact as a new argument, strongly supported by experimental evidence, in favour of the physical reality of electromagnetic potentials.

Derivation of Schrödinger's equation from stochastic electrodynamics

Abstract: Using exclusively classical arguments, an equation similar to Schrodinger's equation is derived within the framework of stochastic electrodynamics.

Generalized Vaidya Metrics

Abstract: We investigate criteria under which one may construct the energy tensor of a null radiation field from an algebraically special vacuum metric. The field bears the same relationship to the original metric as does Vaidya's to Schwarzschild's. As an example we generate a class of null radiation fields from a class of vacuum metrics without symmetry discovered by Robinson and Robinson.

A new theory of elementary matter. part i. philosophical approach and general implications.

Abstract: This is the first of a series of articles that reviews and expands upon a new theory of elementary matter. This paper presents an exposition of the philosophical approach and its general implications. The ensuing explicit form of the mathematical expression of the theory and several applications in the atomic and elementary particle domains will be developed in the succeeding parts of this series.

Power series of the free field as operator-valued functional on spaces of type S

Abstract: Infinite series of Wick powers of the free, massive Bose field are analysed in terms of test function spaces of typeS for arbitrary space dimension. By direct estimates of the smeared phase space integrals sufficiency conditions for the existence of the vacuum expectation values are derived. These conditions are shown to be precise. The field-operators are defined on a dense invariant domain in Fock space, where they satisfy the Wightman axioms with the possible exception of locality. Localisable and nonlocalisable fields are dealt within the same frame. The behaviour of spectral functions and the strength of singularities are discussed.

Particle-like objects in a nonlinear field theory.

Abstract: We further discuss the field theory which we introduced in a previous paper. We find that it is possible for a component of the field to have a minimum at an arbitrary origin point as a consequence of the field equations.

Classical effects from a factorized spinor representation of Maxwell's equations

Abstract: It was demonstrated in earlier work that the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations (Sachs & Schwebel, 1962). The latter is a generalization of the usual formalism, in the sense that in addition to predicting all of the effects that are implied by the vector theory, it predicts additional observable effects that are out of the domain of prediction of the Maxwell formalism. The latter extra predictions were derived in previous publications (Sachs & Schwebel, 1961, 1963; Sachs, 1968a, b). In this paper, the spinor formalism is applied to effects that are expected to agree with the predictions of the standard formalism—the Coulomb force between point charges and the measured speed of a charged particle which moves in an electric potential. While there are no vector or tensor variables involved in this formalism, the results are found, as expected, to be in agreement with the conventional representation of electromagnetic theory. The analysis serves the role of demonstrating that in the appropriate limiting case, the factorized spinor formulation of electromagnetism does predict the explicit classical effects that are also predicted by Maxwell's field equations. The paper also presents a derivation of the general form of the solutions of the spinor field equations.

Conventional formulations of Noether's theorem in classical field theory

Abstract: The role of invariance considerations in conventional formulations of Noether's theorem in classical field theory is investigated and found weaker than is usually supposed. It is shown how nonfulfilment of the conventional assumptions going into Noether's theorem brings about nonconservation.

On the motion of a charged particle in a uniform electric field with radiation reaction

Abstract: It is shown that the motion of a charged particle in a uniform electric field, obeying Dirac-Lorentz relativistic equation of motion with radiation reaction, is confined in a plane. Further, the component of velocity normal to the lines of force continuously decreases to zero. Thus, the motion asymptotically tends to a rectilinear motion along the line of force. The motion is completely described up to a correcting factor 1+0[(e 3 F/m 2 c 4)2]e 3 F/m 2 c 4≃5.10−14 F for electrons,F in volts cm−1.

Synchrotron motion with radiation reaction.

Abstract: It is shown that the longitudinal velocity of a charged particle moving in a uniform magnetic field, and obeying Dirac-Lorentz relativistic equation of motion with radiation reaction is constant. Suitable approximate methods, which give fairly accurate results, are used to obtain the expression for velocity and displacement along the transverse section. They describe the motion completely up to a correcting factor $$1 + 0\left\{ {\left( {\frac{{e^3 B}}{{m^3 c^4 }}} \right)^2 } \right\}; \frac{{e^3 B}}{{m^3 c^4 }} \simeq 10^{ - 16} B$$ for electrons,B inG.

Newtonian gravitational field theory: Two-body problem

Abstract: The effects of a dual force which appears in a consistent field theory of Newtonian gravitation are explored by a study of the motion of two bodies which interact with each other through the gravitational field. The equations of motion are solved exactly. Among the results obtained, we find that the present theory formulated in accordance with the Special Theory of Relativity leads to the same analytical result for the precession of the perihelion of the orbit as does Einstein's General Theory of Relativity. Another result is that classical particles are endowed with an intrinsic angular momentum of constant magnitude—a helicity of classical origin. Other results, such as the period of revolution, are similar to Kepler's law, except for relativistic corrections. A slight deviation from the planar orbit of classical theory results, and may be observable. This deviation is related to the magnitude of the precession of the perihelion of the orbit. The significance of these results for charged particles, viewed classically or quantum mechanically, are discussed.

Dynamics of Probability Distributions Over Classical Fields

Abstract: It is shown that the original Hopf formulation for the time evolution of probability distributions over classical fields follows deductively from the space-time version of the theory.

Atomicity and Determinism in Boolean Systems

Abstract: The logic of a Boolean system of finite degrees of freedom is shown to be atomic if and only if the system obeys a deterministic theory. This is, therefore, the physical meaning of atomicity. Furthermore, it is proved that nondeterminacy of such a system implies the nonexistence of phase space.

Space-time structure and measurement theory

Abstract: The present paper is a naive operational approach to measurement theory in a truly relativistic framework. Both experiments and states exist in finite regions of space-time. The causality structure of the underlying Minkowski space is described in terms of these.

Inertial reference frames in einstein's theory of gravitation.

Abstract: A physical definition of the inertial reference frame (IRF) is given, and the properties of solutions of the Einstein equation (with cosmological constantΛ), which admit an IRF (IRF solutions) are investigated Their Petrov type is uniquely determined by the viscous stress tensor Only the typesI, D or 0 are possible The unique vacuum IRF solution is the Minkowski space-time The unique IRF solution belonging to a perfect fluid is the Einstein universeΛ is of special importance ForΛ=0, the only physically admissible IRF solution is the Minkowski space-time ForΛ≠0, only interior solutions with strong restrictions for density and pressure are possible

A new theory of elementary matter. part ii. electromagnetic and inertial manifestations.

Abstract: In accordance with the philosophical approach and its mathematical implications that were derived in Part I of this series (see p. 433), this paper deals explicitly with the manifestations of matter that are concerned with its electromagnetic and inertial properties. It is demonstrated that a logically and mathematically generalized version of electromagnetism emerges from extending the Faraday-Maxwell field approach, so as to fully unify these features of matter with the field description of matter itself. It is then shown how the most general expression of matter (according to the axioms of this theory), in terms of two-component spinor fields in a Riemannian space, leads to a derivation of the inertial properties of matter. The mass field so-derived (1) is a positive-definite of the (global) coordinates--implying that gravitational forces can only be attractive; (2) approaches a discrete spectrum of values as the mutual coupling among the matter components of the closed system becomes arbitrarily weak; (3) predicts mass doublets in this approximation; and (4) approaches zero as the closed system becomes depleted of all other matter (in accordance with the Mach principle). It is also proven, as a consequence of the same field theory, that electromagnetic forces can be attractive or repulsive, depending on certain features of the geometrical fields of the Riemannian space. 1. Electromagnetic Theory In view of the logical implication of the generalized Mach principle regarding the elementarity of the interaction rather than the free particle, there follows an interpretation of the Maxwell field equations that differs from the usual one. The interaction is described here in terms of the coupling of field variables which are associated with the components of a closed material system. Electromagnetic phenomena are expressible in terms of two types of field variables. One set relates to the field intensity that is conventionally associated with the electric and magnetic field variables. The other set relates to the 'source fields' that are conventionally identified with the charge density and its motion. According to the interpretation that is advocated here, Maxwell's equations are not more than a covariant prescription for determining one of these types of electromagnetic field variables in terms of the other. Thus, Maxwell's equations

Reference systems and gravitation

Abstract: It is shown how the formalism of the tetrad theory of gravitation used by Treder (1967a, b, 1970) follows from the more general fibre bundle formalism. This is of interest in the study of the relations between tetrad theories and the general theory of relativity. In particular, the breaking of the principle of general relativity and the interpretation of tetrad fields as reference systems are considered in greater detail.

Hamilton-Jacobi functional theory for the integration of classical field equations

Abstract: By employing the terminology of functional differential calculus, Hamilton-Jacobi theory is extended to apply to classical field equations. It is shown that an asymptotic solution to the Hamilton-Jacobi functional differential equation provides an asymptotic general solution to the associated nonlinear classical field equations.

Energy-momentum-stress tensor and gravitational field of uniformly rotating masses

Abstract: Beginning with a general ansatz for the energy-momentum-stress tensor of masses in uniform rotation we determine uniquely the energy tensor and the gravitational field of two particular systems; namely, a thin, rotating, hollow cylinder and a spinning rod (dumb-bell). All calculations are made within the framework of linearised theory, but no restriction is made upon angular velocity, except that given by the velocity of light.

Remark on general Lorentz-covariance

Abstract: The present paper is a mathematical comment on a paper by Treder (Treder, 1970). The metric tensorg reduces the tangent bundleT of a space-time to the tangent Lorentz bundleL. The Levi-Civita connection inT induces in a natural way connections inL, and in the tensor product bundles ofT, L, and the spinor bundleS. These connections are ‘the general Lorentz-covariant connection’ by Treder. It is possible to treat the local tetrad field components as local components of a global cross-section of L⊗T, with vanishing general Lorentz-covariant derivative.

Scalar-tensor theories and the principle of equivalence

Abstract: We investigate the restrictions on scalar-tensor theories of gravitation implied by the assumptions: (i) the field equations are derivable from an action principle, (ii) units of mass length and time are defined by atomic standards, and (iii) the principle of equivalence holds whenever gravitational self-energy can be neglected. We show that in all these theories the presence of gravitational energy in a system leads to violations of the principle of equivalence.

Group deformations and relativity

Abstract: A theory of deformation (homcomorphism but non-isomorphism) of topological groups is developed. In particular, a theory of deformation of subgroups structure is considered. The whole formalism is based on conceptions of holonomicity and relative geometry.

Classical spin variables and classical counterpart of the Dirac-Feynman-Gell-Mann equation

Abstract: In an extended relativistic fluid droplet, it is possible to define new internal variables which correspond to the classical counterpart of spin. If we introduce a new constraint, different from Weysenhoff's, we obtain by quantisation the Feynman-Gell-Mann wave equation. This also yields a theoretical connection between mass and spin which can be compared with the observed baryon boson mass spectrum.

Phase space, fibre bundles and current algebras

Abstract: The purpose of this paper is to extend into phase space the cellular description introduced by Bohmet al. (1970) and to show how this may help to give an understanding of the current algebra approach to elementary particle phenomena. We investigate this cellular structure in phase space in some detail and show how certain features of the structure may be described in terms of the mathematics of fibre bundle theory. The frame bundle is discussed and compared with the Yang-Mills theory. As a result of this discussion we are able to introduce generalised currents which are related to the duals of the curvature forms, and these are shown to span the Lie algebra of a sub-group of the structure group of the frame bundle. We then discuss the implications of these results in terms of our cell structure. By assuming that the de Rahm cohomology, defined by the curvature forms and their duals, reflect a cohomology on the integers defined on the original cell structure, we show that the currents and ‘curvature’ can be given a meaning in terms of a discrete structure. In this case the currents only span a Lie algebra in some suitable limit, implying that a description using Lie algebras is only an approximation.

On structure preserving quantisations

Abstract: Maps of functions on classical phase space to quantum operators do not preserve the algebraic structure. After locating the algebraic reasons for it, the problem of quantisation is redefined and the Moyal bracket is discussed for its structure preservation. This quantisation entails the inclusion of Schwartz distributions to the space of classical functions.

Local Quantum Entropy

Abstract: It is shown that it is possible to define ‘true local entropy’ in velocity space, in an approximate version of the two-fluid formulation of quantum theory introduced by the present author in earlier papers. Using this definition, it is then shown that it is possible to define finite forms for total entropy at all points in configuration space. This important step is achieved by the introduction of a ‘responding’ velocity space. The use of a basis system which responds to occupation number density, makes possible a clear separation of the statistics and the dynamics of the underlying quantum process, and also makes possible the unambiguous use of certain divergent and oscillatory integrals.

Photons, neutrinos, electrons and baryons in a unified spinor field theory of relativity

Abstract: A mathematically precise model may be constructed by considering a distribution of basic spinors in a Kaluza 5-space, such that (1) The basic spinors W satisfy curl5 W=0 (2) The four-dimensional curvature is in accordance with Einstein's General Theory, taking the energy-momentum-tension tensor as TIJ = k1, Qi Qj + k2PiPj + k3gij(PkkPk) where\(Q_i = \widetilde{\bar W}TX_i W,{\text{ }}P_2 = \widetilde{\bar W}T\phi X_i W\), and the ratiosk1:k2:k3 are adjustable to give the best fit. (3) The five-dimensional curvature associated with the electromagnetic field is determined by the concomitant $$F_{ij} = \widetilde{\bar W}TX_i X_j W$$ In this model there can exist wave packets which behave in exactly the same way as the physical properties of photons, neutrinos, electrons and baryons.

Probability Interpretation of Particle(s) along Classical Trajectories

Abstract: The theory of divergent series is used to show that the probability density of a wavemechanical state becomes classical trajectories (for a single particle or many interacting particles) in the limit ħ→0. The probability interpretation is claimed to be valid even if a ‘classical particle’ idea is inserted into the theory. The idea ‘particle’ is claimed as a classical entity valid for ħ→0. Finally, the double slit experiment is illustrated as an example and interpreted by the above theory. The interpretation is that the interaction between the incident and interference beams and the double slit is approximately described by the wave theory (interference mechanism).

A new interpretation of Vaidya radiation

Abstract: If Vaidya radiation is taken to be a combination of an electromagnetic energy flux together with that of a null fluid it is shown that the singularity in the current density along an axis, which arises in the absence of a null field, is removed.