Showing papers in "International Journal of Theoretical Physics in 1968"

Comments on the scalar-tensor theory

Abstract: Scalar-tensor theories are discussed as encompassing three classical long-range fields, including the electromagnetic field. In order to shed additional light on the restrictive assumptions made by Dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws. The integrals are extended over two- and three-dimensional domains that lie entirely in empty space but surround the regions containing matter; as for the latter, the vacuum field equations are not required to hold, but no further assumptions are made. It turns out that the gradient of the incident scalar field will contribute to the rate of change of the mass and linear momentum of a ‘particle’ an amount proportional to that particle's scalar-field source strength, which in turn is an arbitrary function of time, unless Dicke's special restriction is imposed. To this extent the motion of a test particle is indeterminate, contrary to experience.

Twistor quantisation and curved space-time

Abstract: The formalism of twistors [the ‘spinors’ for the group O(2,4)] is employed to give a concise expression for the solution of the zero rest-mass field equations, for each spin (s=0, 1/2, 1, ...), in terms of an arbitrary complex analytic functionf(Zα) (homogeneous of degree −2s −2). The four complex variablesZα are the components of a twistor. In terms of twistor space (C-picture) it is analytic structure which takes the place of field equations in ordinary Minkowski space-time (M-picture). By requiring that the singularities off(Zα) form a disconnected pair of regions in the upper half of twistor space, fields of positive frequency are generated.

Simultaneous measurability in quantum theory

Abstract: This paper presents a study of what is sometimes regarded as the conceptual heart of quantum theory, namely, the orthodox ‘physical’ interpretation of non-commuting operators as representatives of incompatible (non-simultaneously-measurable) observables. To provide a firm foundation for the analysis, a definite statement of the essentials of modern quantum theory is given briefly in the form of a mathematical axiomatization together with a review of the two measurement constructs introduced elsewhere (Park, 1967b). Contrary to custom in discussions on simultaneous measurability, the uncertainty principle is not dwelt upon but simply stated carefully in order to establish its actual irrelevance to the problem at hand. It is then demonstrated that the much quoted ‘principle’ of incompatibility of noncommuting observables is false. The axiomatic root of all incompatibility arguments is next identified; and it is shown that, with a slight modification of the basic postulates which affects neither useful theorems nor practical calculations, quantum physics no longer entails illogical restrictions on measurability. Among the related topics touched upon are the problem of joint probability distributions, the ‘logical’ approach to quantum mathematics (wherein noncommutativity becomes incompatibility within a propositional calculus), and the field theoretic attempt to unify quantal and relativistic physics through a postulated connection between incompatibility and space-like intervals.

Spectral theory in quantum logics

Abstract: If one supposes a quantum logicL to be a σ-orthocomplete, orthomodular partially ordered set admitting a set of σ-orthoadditive functions (called states) fromL to the unit intervals [0, 1] such that these states distinguish the ordering and orthocomplement onL, then the observables onL are identified withL-valued measures defined on the Borel subsets of the real line. In this structure (and without the aid of Hilbert space formalism) the author shows that (1) the spectrum of an observable can be completely characterised by studying the observable (A−λ)−1, and (2) corresponding to every observableA there is a spectral resolution uniquely determined byA and uniquely determiningA.

Fundamental limitations on the detectability of electromagnetic signals

Abstract: The detection of signals in an ideal receiver is considered as a decision between quantum-mechanical density operators describing the field in the receiver, respectively when thermal radiation alone is present and when besides this background there is a signal field present. The detectability of the signal is assessed by the minimum probability of error attainable in such a decision. Coherent signals of known and unknown phase are treated. The theory is shown to reduce to conventional detection theory in the classical limit.

On the simplicity of Haag fields

Abstract: It is shown that the simplicity of the C* -algebra of quasilooal observables of a Haag field caa be deduced from a postulate which seems to be plausible from a physical point of view.

On pair annihilation and the Einstein-Podolsky-Rosen paradox

Abstract: Discussion is given to the experimental facts that are associated with ‘pair annihilation’, as a real example, rather than a gedanken experiment, to illustrate the Einstein-Podolsky-Rosen paradox. It is shown how the paradox disappears in a nonlinear relativistically covariant spinor field theory of this author, which takes thesingle interaction, rather thanmany free particles, as the elementary entity. In this theory there is no actual annihilation of matter. Rather, the observed facts that are conventionally interpreted as ‘pair annihilation’ arederived from an exact solution of the nonlinear field equations for the interacting pair in a particular deeply bound state. This solution reveals the observed facts, including the energy separation of 2m from the asymptotic state where the particles can be assumed to be (almost) free, and the prediction of two distinguishable currents whose phases are correlated by a 90° difference and are polarized in a common plane that is perpendicular to the direction of propagation of interaction with a detecting apparatus. The paradox disappears essentially because of the rejection by this theory (in principle and in the exact mathematical formalism) of anyphysical description in terms of truly uncoupled partial systems.

Scalar radiation from a point source

Abstract: We consider a classical scalar field, obeying the inhomogeneous Klein-Gordon equation, in the case of a single point source. We propose a definition for the radiated energy-momentum and give an expression for it in terms of the prescribed world line of the source where we assume that the acceleration vanishes outside a finite interval. We find that only the part of the world line with non-vanishing acceleration contributes to the radiation, which travels at all speeds less than but not equal to the speed of light. We briefly discuss the case with more than one point source.

Theory of resonance pressure broadening: Resolvent operator formalism and classical path approximation

Abstract: The problem of resonance pressure broadening of spectral lines in monatomic gases is discussed using a resolvent operator formalism. A differential equation is developed to determine the resolvent, and it is shown how its solution for a limiting case yields the familiar classical path approximation for the translational motion of the atoms, and how quantum corrections may be systematically studied. Commonly used limiting cases within the classical path approximation (two-body static and impact approximations) are also exhibited as limiting cases, with methods for systematic evaluation of corrections. Closed form solutions are obtained for the two-body static and impact cases. The results are compared with available experimental data, and generally satisfactory agreement is obtained. Of some theoretical interest is the formalism, which embraces all the usual approximations and permits them to be studied together with corrections to them from a unified point of view. New results of more practical interest are the closed form solutions for the limiting cases, and the estimation of the lowest-order quantum corrections, which are appreciable under some experimental conditions.

Conjunction, succession, determination and causation

Abstract: The principles of regular (invariable or stochastic) conjunction, of retarded action, determination, and causality, are stated exactly and analyzed. To this end, the concepts of system, property, state, and event, as well as those of conjunction (of events and of properties) are first elucidated. Four types of determination are distinguished and analyzed and it is shown that only one of them qualifies as a causal nexus, the others being deterministic (in the large sense) but noncausal. The overall conclusion is that, while the principles of regular conjunction, retarded action and determination are both distinct and universal, the causal principle is just a restricted version of the principle of determinacy.

Astronomical implications of a cosmological theory of light propagation

Abstract: It is shown that a simple Cosmological model of light propagation permits the existence and observation of recession velocities greater thanc, though the Einstein measure of these velocities remains less thanc in accordance with relativistic theory.

Some relationships between representation systems and physics. I: Representation systems

Abstract: A representation system developed by Smullyan is discussed briefly. Additional notation is introduced to make it suitable for problems concerned with physical systems. Rules for the formation of a concatenation operation called the product, are introduced.

Exploding spheres of dust

Abstract: In this paper, we extend the work of Oppenheimer & Snyder (1939) who treated the zero curvature case in the gravitational collapse of spheres of dust intended to represent collapsing stars. A solution is given which is valid for all space and is characterized by negative curvature of the space within a sphere of dust. This solution is obtained by matching the negative curvature interior solution (as well as, for completeness, zero and positive curvatures interior solutions) to an exterior Schwarzschild geometry. In this solution, corresponding to the case of a Newtonian system with positive total energy, the mass as seen by an observer at infinity is found to be positive definite. Also, in each case, the positive definite massm is related to the densityν and radiusr [defined as the square root of the (surface area/4π)] of the dust cloud viam=(4π/3)pr3. The methods employed here for matching interior and exterior solutions are applicable to the construction of cosmological models in which the sign of the curvature and/or expansion rate differ in two or more regions, e.g. a universe expanding in one region and contracting in another.

Dispersion in momentum space and the existence of U( t,t')

Abstract: The operatorU(t,t') giving transition probabilities between finite times or connecting free and interacting fields does not exist (apart from the ultraviolet divergence problem) because of the 3-translation invariance of current quantum field theory. To remedy this, the idealization that one has an infinite timeT = ∞ to prepare initial, or measure final,n-particle momentum eigenstates is discarded here. It is shown that random space-time (which itself eliminates ultraviolet divergences from field theory) implies and fixes uniquely a random momentum space if free particle momentaK are determined by time-of-flight measurements withT < ∞. In particular, the dispersion ofK ∞ mλ/T, whereλ is the space-time dispersion andm is the particle mass. Stochastic momentum space is incorporated into field theory in a preliminary way; because 3-translation form-invariance is slightly violated, the unitaryU-operator expressed as the usualT-exponential exists and the limitU → S ast → ∞,t' → −∞ is welldefined withoutad hoc tricks like the adiabatic cut-off. A frame-dependence is necessarily introduced into fields andU-operator, and the transformation properties expressing Lorentz covariance are of the same more general type encountered in previous work on quantum field theory over stochastic spacetime.

Symmetry and composite particles

Abstract: The description of systems with internal structure evident only in the presence of operators other thanP u andM uv defined on the spaceS of the relativistic states is explored. The assumption is made that there must be dennedone operator of this kind, namely µ≡limP 0 /c. The individual particle variables of a composite are eliminated and a special kind of ‘composite particle representation’ is introduced. The nonrelativistic composite (an isolated molecule) is described by a single value of the Galilei invariantμ and many values of the other two Casimir operatorsC 1 andC 2, and it is this direct sum structure which is sought as the contracted limit of a relativistic composite particle with all its bound state levels. The internal energy operatorh 0 arises as the contraction of (M−μ)c 2, and the correct nonrelativistic Hamiltonian of the composite is shown to be given byH=H 0+P 2/2μ. As an application of these ideas, our previous results (compare Fleischman & Roman, 1967) concerning the nonrelativistic limit of theSU 3 commutator structure are rederived in a simple manner. Throughout the paper, comparison is made with, and ramificational remarks are proferred on the extensive related literature.

Quantenmechanik, Beobachtung und Deutung

Abstract: The doctrine of wave-particle duality and complementarity has been regarded since the late 1920's as the only possible interpretation of observations such as electron diffraction through crystals and screens with two slits as well as other coherence phenomena. Physicists have been unaware that those apparent wave features can be accounted for, without supernatural dual manifestations made palatable by semi-philosophical 'renunciation', by the unitary quantum mechanics of matter particles alone if one only is consistent enough to admit that there are three (rather than only two) conservation laws of mechanics, hence ~here are three (rather than two) corresponding selection rules, for E, P~0 and also for the linear momentum p, restricting the mechanical activity of time-, angular-periodic, and also of space-periodic systems. This clears up the mystery of dualism in a physical manner without philosophical subtleties and leads to a great simplification of the quantum ideology. 1. Das Problem der Dualiti~t W/ihrend der nicht-relativistische Quantenformalism us keinem Zweifel unterliegt, bestehen nach vierzig Jahren immer noch Fragen fiber seine Dcutung. Dabei nimmt der Kopenhagener Dualismus eine so vorherrschende Stellung ein, dass abwcichende Ansichten sich meistens nur auf Einzelheitcn beziehen (siehe die Ubersicht in Kap. III dicses Aufsatzes). Im scharfen Gegensatz zu allen diesen Meinungen, die stets eine Dualit/~t in dieser oder jener Form als unvermeidlich betrachten, steht die um 1955 vorgeschlagene einheitliche Deutung der Quantenerscheinu ngen, fiber die hier kurz berichtet werden soll. Dies ist natfirlich nur im Zusammenhang mit eincr Kritik der Dualit~tslehre mSglich. Letztere begann schon 1905 beim lichtelektrischen Effekt und wiederholte sich in sch~rferem Masse bei der Materienbeugung (1926). Hier trat die Frage auf, wie man die diskreten Reflektionswinkel yon Elektronen an Krystallen anders erkl/~ren kann als auf Grund yon Wellen entsprechend der Bragg'schen Interferenzbezie hung 2L. sin 0 n = n~

Some relationships between representation systems and physics. II: Non-relativistic quantum theory

Abstract: Using Bunge's procedures, non-relativistic quantum mechanics is discussed. It is shown that if a certain carefully defined idea of determinism is included in the presentation, operators which are not Hermitian need to be used to describe physical processes. An absolute time scale is suggested.