Showing papers in "International Journal of Theoretical Physics in 1976"
TL;DR: In this article, the conditions that a Killing tensor of order 2 be the contracted product of a Killing-Yano tensor with itself with respect to itself were given. And the conditions for admission of all the Killing tensors in order 2 in empty space-times were obtained.
Abstract: The conditions that a Killing tensor of order 2 be the contracted product of a Killing-Yano tensor of order 2 with itself are found. All Killing-Yano tensors of order 2 admitted in empty space-times are obtained
67 citations
TL;DR: In this article, a double slit is used to construct lines of constant amplitude, constant phase and energy flow, showing how the electromagnetic boundary conditions necessitate a particular undulation in the path of light energy and that the consequent redistribution of energy corresponds with a diffraction or interference pattern.
Abstract: Solutions to Maxwell's equations at a semi-infinite plane and a double slit are used to construct lines of constant amplitude, constant phase and energy flow. The lines of energy flow show how the electromagnetic boundary conditions necessitate a particular undulation in the path of the light energy and that the consequent redistribution of energy corresponds with a diffraction or interference pattern. This interpretation complements the interpretation in terms of the interaction of secondary wavelets due to Huygens.
63 citations
TL;DR: In this article, the Poynting vector of a plane electromagnetic wave diffracted by the gravitational field of a large spherical body (large compared to its Schwarzschild radius) is given.
Abstract: This paper gives the Poynting vector of a plane electromagnetic wave diffracted by the gravitational field of a large spherical body (large compared to its Schwarzschild radius) and shows in detail how this body works as a gravitational lens. The most interesting results are (1) an extreme amplification of intensity near to the axis of symmetry in the far field behind the body, with a factor of 10 times the Schwarzschild radius divided by the wavelength of the light, and (2) the appearance of double images, differing in shape and position from the predictions of geometrical optics.
32 citations
TL;DR: In this paper, it is shown that many of the difficulties associated with the Copenhagen interpretation of quantum theory are resolved by a new interpretation of interference derived from solutions to Maxwell's equations, and an infinite wave model of the photon based on these solutions is described and used to explain the interference of single photons as well as the corpuscular behavior evident in Compton and photoelectric effects.
Abstract: It is shown that many of the difficulties associated with the Copenhagen interpretation of quantum theory are resolved by a new interpretation of interference derived from solutions to Maxwell's equations. An infinite wave model of the photon based on these solutions is described and used to explain the interference of single photons as well as the corpuscular behavior evident in the Compton and photoelectric effects. The wave-particle duality and the uncertainty relations are also discussed. According to the new interpretation of interference in a Young's double-slit experiment, photons which pass through the left-hand slit always arrive in the left-hand part of the screen and no photons pass into this area via the right-hand slit. This conclusion is compared with the viewpoint of the Copenhagen school and an experiment to distinguish between them is suggested.
30 citations
TL;DR: In this article, the authors give an elementary discussion of the localization concept of relativistic particles and prove the so-called Hegerfeldt theorem, which says that localization of a one-particle state in a finite space-time volume is inconsistent with causality, in two different ways.
Abstract: In this paper we give an elementary discussion of the localization concept of relativistic particles. We prove the so-called Hegerfeldt theorem, which says that localization of a one-particle state in a finite space(-time) volume is inconsistent with causality, in two different ways. The proofs are elementary and use on the one hand the same type of arguments as used in the proof of the well-known theorem of Reeh-Schlieder and on the other a remark due to Borchers.
29 citations
TL;DR: In this paper, a Bargmann-Segal type quantization of space-time via the vector and spinor structures of the tangent space is used to formulates the theory of measurement as a quantum theory.
Abstract: Gravity is treated geometrically in terms of nonlinear realizations ofGL(4, ℝ) with particular reference to almost complex structures. This approach is used to carry out a Bargmann-Segal type quantization of space-time via the vector and spinor structures of the tangent space that formulates the theory of measurement as a quantum theory quantized in terms of a basic unit of length that appears in a new uncertainty relation. The theory is also used to discuss the gauge conditions for quantum gravity and the Kostant theory of quantization applied using a line bundle with structure groupGL(2, ℂ)/SL(2, ℂ).
24 citations
TL;DR: In this article, a relational and objectivistic theory of space is proposed, based on the assumption that the physical world is constituted by changing things, and the notion of interposition between two things is defined as the set of things interposed between them.
Abstract: Our problem is to build a relational theory of space, i.e., one according to which space is a sort of network of relations among things. We take the notions of concrete thing and of action of one thing upon another as undefined, or rather as defined in another context. We define the notion of interposition between things in terms of the previous notions. We then define the separation between two things as the set of things interposed between them. The collection of things equipped with the separation function is called thething space—a representation of ordinary space sufficient for philosophical purposes but not for physics. The next step is to define a topology for the thing space: This is done with the help of the separation function. The set of things together with this topology is called thephysical space. We then define the family of balls lying between any two things and postulate that it satisfies Huntington's axioms for solid geometry. By adding a few more natural assumptions we render physical space a three-dimensional manifold, which is what current physical theories require. We abstain from any metrical considerations, not only because these would require building space-time, but also because our problem was not to describe space but to explain how it comes about. Nevertheless our construction of space involves the notions of event and of event composition, and the latter allows one to define a time order of events, which in turn is required to define the notion of action of one thing upon another. The upshot is a full-fledged relational and objectivistic theory of space based on the assumption that the physical world is constituted by changing things.
22 citations
TL;DR: In this article, the authors derived a Bell type inequality, involving average values of physical quantities whose quantum mechanical operators need not be two-valued, under the hypothesis that composite systems are described by statistical mixtures.
Abstract: Bell's inequality, as it is generally understood, is a relation involving average values over the readings of the apparatuses when dicotomic observables are measured, which can be derived on the basis of local hidden variables and can be violated by quantum mechanics. We derive a Bell type inequality, involving average values of physical quantities whose quantum mechanical operators need not be two-valued, under the hypothesis that composite systems are described by “proper” mixtures (i.e., statistical mixtures in the ordinary sense). This inequality is analyzed in detail for the case of aJ=M=0 state decaying into subsystems I, II with anyj and when average values of the quantity\((\overrightarrow J \cdot \hat a)_I \otimes (\overrightarrow J \cdot \hat b)_{II}\) are considered; it is then found that it cannot be violated ifj>1/2 by the quantum mechanical description of the composite system in terms of a “second-kind state.” A theorem is, however, established proving that in the general case suitable observables can be introduced for which a violation by quantum mechanics could be observed. This encourages the work in progress on more general situations and observables.
18 citations
TL;DR: The second-order generally invariant Lagrangians for the metric fields on any n-dimensional manifold are studied as certain special coordinate functions on a space of jets in this paper.
Abstract: The second-order generally invariant Lagrangians for the metric fields on anyn-dimensional manifold are studied as certain special coordinate functions on a space of jets. The number of independent Lagrangians of this type is determined. The dimensionsn=3 andn=4 are examined in detail with the help of a computer.
12 citations
TL;DR: The generators of the Lie algebra of the symplectic groupsp(2n, R) are, recurrently, realized by means of polynomials in the quantum canonical variablesp ≥ 0 andq ≥ 0.
Abstract: The generators of the Lie algebra of the symplectic groupsp(2n, R) are, recurrently, realized by means of polynomials in the quantum canonical variablesp
i andq
i. These realizations are skew-Hermitian, the Casimir operators are realized by constant multiples of identity elements, and, depending on the number of the canonical pairs used, they depend ond, d=1, 2, ...,n free real parameters.
11 citations
TL;DR: In this paper, it was shown that in the absence of superselection rules, there are quantum mechanical observables whose expectation value depends on the type of state vector (first type or second type) describing the system.
Abstract: Let Σ be a physical system consisting of two subsystems,S andT: We prove that there are, in the absence of superselection rules, quantum mechanical observables (called “sensitive”), whose expectation value depends on the type of state vector (first type or second type) describing Σ. This result generalizes a previous one obtained under the restriction that the Hilbert spaces ofS andT are two dimensional.
TL;DR: In this paper, it is assumed that our world is being examined from a similar world which is moving relative to us with a velocity greater than that of light, and the two worlds are supposed to be similar in that the particles in each appear to any observer in that world to have real measurable properties.
Abstract: It is imagined that our world is being examined from a similar world which is moving relative to us with a velocity greater than that of light. The two worlds are supposed to be similar in that the particles in each appear to any observer in that world to have real measurable properties. However, the enormous relative velocity so distorts the observations that each world makes on the other that the squares of certain real quantities appear to the other observer to be negative. Neglect of this fact has led to the erroneous belief that a free charged tachyon would emit Cerenkov radiation and that the existence of tachyons would lead to logical paradoxes.
TL;DR: In this article, it was shown that the basic concepts of special relativity can be formulated and the basic properties deduced using only arithmetic, including velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space.
Abstract: Under relatively general particle and rocket frame motions, it is shown that, for special relativity, the basic concepts can be formulated and the basic properties deduced using only arithmetic. Particular attention is directed toward velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space, and to relativistic generalizations of Newton's second law. The resulting mathematical simplification is not only completely compatible with modern computer technology, but it yields dynamical equations that can be solved directly by such computers. Particular applications of the numerical equations, which are either Lorentz invariant or are directly related to Lorentz-invariant formulas, are made to the study of a relativistic harmonic oscillator and to the motion of an electric particle in a magnetic field.
TL;DR: In this article, a new realization of the conformal group in the classical phase space of a positive mass relativistic scalar particle is obtained, and a physical interpretation in the spirit of conformal relativity is discussed.
Abstract: A new realization of the conformal group in the classical phase space of a positive mass relativistic scalar particle is obtained. A physical interpretation in the spirit of conformal relativity is discussed.
TL;DR: In this article, the functional differential equation which describes the one-dimensional symmetric motion of two charged particles in the framework of classical electrodynamics is considered, and it is proved that the global solution exists and can be specified uniquely by the instantaneous initial data, if the classical energy at the initial moment is sufficiently small.
Abstract: The functional-differential equation which describes the one-dimensional symmetric motion of two charged particles in the framework of classical electrodynamics is considered. In the case of the charges of a like sign it is proved that the global solution exists and it is specified uniquely by the instantaneous initial data, if the classical energy at the initial moment is sufficiently small. In the case of the charges of opposite sign there are additional restrictions on the initial data. The estimates are given which allow one to obtain an approximate description of motion.
TL;DR: In this article, a necessary and sufficient criterion of inertia for the flat space-time theory of general frames of reference is presented, in terms of the vanishing of some typical components of the affine connection pertaining to curvilinear coordinate systems.
Abstract: A necessary and sufficient criterion of inertia is presented, for the flat space-time theory of general frames of reference, in terms of the vanishing of some typical components of the affine connection pertaining to curvilinear coordinate systems. The physical identification of inertial forces thus arises in the context of the special theory of relativity.
TL;DR: In this article, it was proved that canonical realizations of the Lie algebra in the quotient division ring are related to the standard minimal one in 2n − 2 quantum canonical pairs.
Abstract: It is proved that canonical realizations of the Lie algebraC
n in the quotient division ringD
2(2n−2) of the Weyl algebraW
2(22−2) in 2n − 2 quantum canonical pairs are, in a definite sense, related to the standard minimal one inD
2n
⊂D
2(2n−2). Further, in any realization ofC
n inW
2(2n-1) all Casimir operators are realized by multiples of identity element.
TL;DR: In this article, two kinds of structurological generalizations of our nonlocal field (i.e., the (x, ψ) field) are considered physicogeometrically.
Abstract: In this paper, continued from the last paper (Ikeda, 1974), two kinds of structurological generalizations of our nonlocal field (i.e., the (x, ψ) field) are considered physicogeometrically. One is a Finslerian generalization, where the base field [i.e., the (x) field] is extended to a Finslerian field and Weyl's gauge field (i.e., the electromagnetic potential) is physically identified with the directional vector adopted as the internal variable in the ordinary nonlocal field theory. Another is a generalization by which the spinor (ψ) itself is taken as an independent variable, where some inherent characteristics ofψ are fused into the spatial structure. The latter is regarded as a “nonlocalization” of the (x) field accomplished by attachingψ to each point, in the true sense of the word. Particularly, the spatial structures of these generalized nonlocal fields are described in detail.
TL;DR: In this paper, a simple application of the Newman-Penrose spin coefficient formalism, useful for beginners, was proposed to find the vacuum spherical symmetry (Schwarzschild) solution.
Abstract: As a simple application of the Newman-Penrose spin coefficient formalism, useful for beginners, we find the vacuum spherical symmetry (Schwarzschild) solution. The calculations also show that all spherically symmetric metrics are Petrov typeD.
TL;DR: In this article, the covariance of relativistic mechanics and electrodynamics under the inhomogeneous Lorentz group is studied under the assumption that the physical magnitudes derived from the space-time coordinates should take rational values.
Abstract: Following recent developments in the hypothesis of a discrete space-time lattice, some assumptions are postulated that seem necessary to work out this model in the theory of special relativity. In particular, the assumption of space-time coordinates with integer values requires the translation of relativistic mechanics and electrodynamics into the language of finite difference equations. A special study of the covariance of these equations under the inhomogeneous Lorentz group is carried out. Finally, a stronger assumption is postulated, by which the physical magnitudes derived from the space-time coordinates should take rational values.
TL;DR: In this article, the extremal technique to define the photon form factors of the nonlocal quantum electrodynamics needs some extensions, and the use of form factors that are not entire analytical functions does not have to be rejected from the very beginning.
Abstract: Proofs have been given that the extremal technique to define the photon form factors of the nonlocal quantum electrodynamics needs some extensions. There is evidence that the use of form factors that are not entire analytical functions does not have to be rejected from the very beginning. In this respect several mutually connected form factors have been calculated and discussed. The short-distance behavior of the electrostatic potential is then established.
TL;DR: In this article, the mapping of axioms into transfinite number fields provides a method whereby the magnitudes of experimental values can be distinguished in a clear manner, and it is shown also to result in a logical interpretation for the presence of exponential forms and for their imaginary arguments.
Abstract: The mapping of axioms into transfinite number fields provides a method whereby axioms and the magnitudes of experimental values can be distinguished in a clear manner. This procedure is shown also to result in a logical interpretation for the presence of exponential forms and for their imaginary arguments.
TL;DR: In this article, the Hartree-Fock method is expressed in terms of repeated unitary transformations and shown to be applicable to the general SCF (self-consistent field) equations.
Abstract: The traditional Hartree method of solving the Hartree-Fock equations, by repeated diagonalization and recalculation of the single-particle Hamiltonian, is expressed in terms of repeated unitary transformations and shown to be applicable to the general SCF (self-consistent field) equations. The necessary and sufficient conditions for convergence to a unique local SCF solution are derived and it is shown that only a small class of solutions are obtainable by this method.
TL;DR: In this article, the existence of nonlinear reversible dynamical evolutions for isolated quantum systems is investigated within the Hilbert model with the aid of the superposition principle and the law of entropy.
Abstract: Some considerations on the existence of nonlinear reversible dynamical evolutions for isolated quantum systems are developed within the Hilbert model with the aid of the superposition principle and the law of entropy.
TL;DR: In this paper, a hierarchy of isolated systems of finite radii whose associated charges form a geometric series with enormous imaginary common ratio is proposed, and the content of an infinite cosmos within a Hubble radius of an observer, an electron, and a neutrino as three consecutive members of the hierarchy.
Abstract: Why attraction and repulsion between likes should not enjoy equal status in nature is considered. By postulating a hierarchy of isolated systems of finite radii whose associated charges form a geometric series with enormous imaginary common ratio, and by identifying a “universe” (the content of an infinite cosmos within a Hubble radius of an observer), an electron, and a neutrino as three consecutive members of the hierarchy (in fact the only three observable because of the uncertainty principle), it is possible to treat gravitational and electromagnetic phenomena as perfectly analogous and complementary for the overall structure of the cosmos. An isolated system behaves, from an external viewpoint, as an elementary particle, and from an internal viewpoint, as a universe. Remarkable relationships between physical constants emerge.
TL;DR: In this paper, the authors draw a straight line between the representation theory of SU(3) and the classification schemes in particle physics, drawing an important part of particle physics into line with two contemporary accounts of compact Lie groups.
Abstract: In this Note, we draw a straight line between the representation theory of SU(3) and the SU(3)-classification schemes in particle physics. Our approach is based on that of Weyl, but we have in mind the versions which appear, “in modern dress,” in Adams and Bott. Our formulation brings an important part of particle physics into line with two contemporary accounts of compact Lie groups.
TL;DR: In this article, a general formalism is set up to evaluate the Casimir operators of the Lie algebra of the group in terms of the degrees of homogeneity of the functions (which are eigenfunctions of the operators) in then variables.
Abstract: I have presented a means of getting a representation space of a general linear group ofn dimensions in terms of homogeneous functions ofn,n-dimensional vectors. Except in particular cases, the representation is of the Lie algebra, rather than the group. A general formalism is set up to evaluate the Casimir operators of the Lie algebra of the group in terms of the degrees of homogeneity of the functions (which are eigenfunctions of the Casimir operators) in then variables. It is noticed that the Casimir operators exhibit certain symmetries in these degrees of homogeneity which relate different representations having the same eigenvalues for the Casimir operators. Contour integral formulas that enable one to pass from one such representation to another are presented. An expression for the eigenvalues of a general Casimir operator in terms of the degree of homogeneity is presented.
TL;DR: In this article, the intimate connection between global integrability conditions and equilibrium conditions for stationary Einstein-Maxwell fields is described, and regularity conditions are deduced for all the presently known classes of solutions.
Abstract: This paper describes the intimate connection between global integrability conditions and equilibrium conditions for stationary Einstein-Maxwell fields. Regularity conditions are deduced for all the presently known classes of solutions.
TL;DR: In this paper, it is shown that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance, and that massless particles like photons and neutrinos will appear only as point particles in the physical world.
Abstract: From the point of view that the charge and mass of an electron is of dynamical origin and quantization of charge in units ofe is related to the space-time quantization as developed in an earlier paper, we here show that it is possible to consider that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance. This helps us to develop a consistent theory of nonlocal fields for extended particles where the infinite mass degeneracy is avoided. Moreover, this ensures the convergence of nonlocal field theories and suggests that massless particles like photons and neutrinos, though they may be taken to be of extended structure, will appear only as point particles in the physical world. In this picture, Lorentz invariance appears to be a consequence of the distribution of matter and energy in the Universe, and this may be taken to be another interpretation of Mach's principle.
TL;DR: In this paper, a set of nonlinear partial differential equations covariant in a non-Euclidean space is reduced to the Dirac equation for the electron and the Maxwell-Lorentz equations of electromagnetic fields under certain assumptions.
Abstract: A set of nonlinear partial differential equations covariant in a non-Euclidean space is reduced to the Dirac equation for the electron and the Maxwell-Lorentz equations of electromagnetic fields under certain assumptions. In the course of reduction, we have opportunities for understanding the relationship between the Dirac equation and the Maxwell-Lorentz equations, and also for visualizing conditions which limit feasible applications of those known equations in physics.