Showing papers in "International Journal of Theoretical Physics in 1978"
46 citations
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23 citations
TL;DR: In this paper, the authors consider a quantum logic with a sufficiently large collection of states (probability measures) and show the connections of this theory to the well-known models of quantum mechanics and classical measure theory.
Abstract: Let II be a quantum logic; by this we mean an orthocomplemented, orthomodular, partially ordered set. We assume that II carries a sufficiently large collection Δ of states (probability measures). Then, Δ is embedded as a base for the cone of a partially ordered normed spaceL and II is also embedded in the dual order-unit Banach spaceL*. We consider conditions on the pairs (Δ, II) and (L,L*) that guarantee that II is a dense subset of the extreme points of the positive part of the unit ball ofL*. We demonstrate a connection of these conditions in noncommutative measure theory. The assumptions made here are far weaker than the assumptions of the traditional quantum mechanical formalisms and also apply to situations quite different from quantum mechanics. Finally, we show the connections of this theory to the well-known models of quantum mechanics and classical measure theory.
23 citations
TL;DR: In this article, the notion of the invariance group of a function on the Φ algebra is described, and all functions having a given invariance groups are canonically deduced in what is here called Φ theorem.
Abstract: The algebra of physical (dimension-carrying) quantities is axiomatized in a scheme called a Φ algebra. Systems of units (gauges) are readily described in this algebra, and the set of transformation of units (the gauge group) is discussed. The notion of the (gauge) invariance group of a function on the Φ algebra is described, and all functions having a given invariance group are canonically deduced in what is here called the Φ theorem. The scheme is applied to classical mechanics in order to understand better in what sense mass, length, and time are “irreducible” physical quantities. The latter two are found to be so, but the former is not. Other theories, relativity and quantum mechanics, are also briefly discussed and are shown to reduce this fundamental set of units even further.
13 citations
TL;DR: In this paper, a number operator based on the binary presentation of numbers is introduced, and operators for differentiation and integration of operator functions are defined, which take the usual form in the classical limit.
Abstract: A number operator has been introduced based upon the binary (p-nary) presentation of numbers. This operator acts upon a numerical state vector. Generally the numerical state vector describes numbers that are not precise but smeared in a quantum sense. These states are interpreted in wave logic terms, according to which concepts may exist within the inner language of a phenomenon that in principle cannot be translated into the language of the investigator. In particular, states may exist where mean values of a quantity, continuous in classical limits, take only discrete values. Operators for differentiation and integration of operator functions are defined, which take the usual form in the classical limit.
11 citations
TL;DR: In this paper, it was shown that the 4-dimensional equations δR2/δgij=0 can be rewritten as 5-dimensional problems which are linear in the components of the Riemann tensor.
Abstract: It is shown that the 4-dimensional equationsδR2/δgij=0 may be rewritten as 5-dimensional equations which are linear in the components of the Riemann tensor.
10 citations
TL;DR: In this article, it was shown that the entropy with respect to an observable describing "simultaneous" measurement of position and momentum is greater than the von Neumann entropy for the fuzzy and sharp positions.
Abstract: We investigateA-entropy with respect to certain semispectral measures in a given state. It is shown that the entropy with respect to an observable describing “simultaneous” measurement of position and momentum is greater than the von Neumann entropy. Similar results are obtained for the fuzzy and sharp positions. The continuity properties of this entropy are also examined.
10 citations
TL;DR: In this article, the assumption of the original Einstein-Podolsky-Rosen argument is formally stated as axioms and non-logical rules of inference, making explicit the assumptions, logical structure, and conclusions involved.
Abstract: Assumptions of the original Einstein-Podolsky-Rosen argument are formally stated as axioms and nonlogical rules of inference. Then the argument is formally stated, making explicit the assumptions, logical structure, and conclusions involved. In turn several interpretative disputes are resolved. One frequent objection to the argument and a prevalent response to that objection as well are shown to be misguided.
9 citations
TL;DR: Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect-fluid spheres are generalized in this article.
Abstract: Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect-fluid spheres are generalized. Solutions are spherically symmetric and conformally flat.
8 citations
TL;DR: In this paper, the mass relation was derived and the propagators obtained in the framework of the present theory have the same types as those with a simple cutoff, however, the tildon field with indefinite metric is always confined in the virtual state and never appears in real processes as a physical entity.
Abstract: Under the hypothesis of a fundamental lengthl0, the Bopp equation is considered as a basic equation of motion instead of the Klein-Gordon equation. Assuming that the mass is a function of0, we derive a mass relationm≥(ħ/2l0c). The propagators obtained in the framework of the present theory have the same types as those with a simple cutoff. However, because of the mass relation, the tildon field with indefinite metric is always confined in the virtual state and never appears in real processes as a physical entity. Thus, our new version leads to a finite theory of quantum electrodynamics.
8 citations
TL;DR: Barbour and Bertotti as mentioned in this paper proposed a prerelativistic Machian theory of gravitation in a relative configuration space, which fulfils the principle of equivalence in a natural way.
Abstract: A prerelativistic Machian theory of gravitation in a relative configuration space of the type developed in Barbour and Bertotti (1977) is proposed, which fulfils the principle of equivalence in a natural way. This is accomplished by assuming that the basic interactions with which the dynamical Lagrangian is constructed are three-body and velocity dependent. Gravity arises between two bodies when other masses move-in particular when the universe expands (or contracts). The properties and physical consequences of this theory are very similar to the previous one; in particular the two-body problem has a small post-Newtonian correction leading to an advance of the periastron, and to the determination of the velocity of expansion of the universe. We find that the motion of test particles introduces naturally into the theory the restricted covariance group, in which any space transformation that preserves simultaneity is allowed. This permits us to define an inertial frame of reference, and to obtain the analog of the equation of geodesic deviation. Finally, we discuss the effect of the anisotropy of the universe on the mass.
TL;DR: In this paper, the authors describe magnetic kinks with one axis of rotational invariance analytically and graphically, and examine their relevance to the puzzle of the origin of galaxies.
Abstract: Three-dimensional magnetic kinks in nonresistive plasmas may be created and annihilated in pairs and conserve their homotopy properties during their lifetime. Such kinks could prove relevant to astrophysical, geophysical, or laboratory plasma problems. We describe magnetic kinks with one axis of rotational invariance analytically and graphically. As an example, we examine their relevance to the puzzle of the origin of galaxies.
TL;DR: In this article, the Poynting vector of a plane electromagnetic wave diffracted by the gravitational field of a Schwarzschild black hole was given in a suitable approximation, and the relation between the approximation procedure and the concept of rays was established.
Abstract: This paper gives (in a suitable approximation) the Poynting vector of a plane electromagnetic wave diffracted by the gravitational field of a Schwarzschild black hole. The relation between the approximation procedure and the concept of rays is established. The main results are as follows: (1) On the focal line an extreme amplification of intensity takes place. (2) In the whole space off this focal line a double image is to be seen. (3) Rays having revolved around the black hole repeatedly give small corrections only. (4) The phase differences (transit-time differences) along the different rays are computed.
TL;DR: In this paper, a solution of the gravitational field equations is found by using an axially symmetric metric which is asymptotically a de Sitter space metric, and the conditions for the existence of gravitational radiation in this metric are investigated.
Abstract: A solution of the gravitational field equations is found by using an axially symmetric metric which is asymptotically a de Sitter space metric. We use the general approach of Bondi, van der Burg, and Metzner as applied to the asymptotic flat-space case and search for the necessary conditions for gravitational radiation in asymptotic de Sitter space. We find that the character of the gravitational radiation, if it exists at all, is considerably different from that obtained in the case of asymptotic flat space.
TL;DR: The electron mass valuem=9.093 × 10−28 g is obtained from the QED self-energy formula amended to include gravitational selfenergy and restricted by the space-time equipartition lawm/n0=4/3.
Abstract: The electron mass valuem=9.093 × 10−28 g is shown to be obtainable from the QED self-energy formula amended to include gravitational selfenergy and restricted by the space-time equipartition lawm/n0=4/3. Held together by gravity, the electron has a radiusre=8πħGm/9e2c=2.588 × 10−53 cm. An extension of the analysis yields the theoretical muon-electron mass ratio of 206.241 and predicts heavier charged leptons with mass values of 1.915 GeV, 15.67 GeV, and above.
TL;DR: In this paper, a discussion of the possible relevance of magnetic monopoles in strong interaction models and their role in quark confinement schemes is given, and extensions of these ideas are illustrated.
Abstract: We review some properties of magnetic monopoles in non-Abelian gauge theories. Removal of Dirac string singularities and generalizations of the Wu-Yang solution that follow from this procedure are described. A discussion of the possible relevance of monopoles in strong interaction models and their role in quark confinement schemes is given. The magnetic monopole soliton discovered by 't Hooft and Polyakov, the first order formalism developed by Bogomolny, and extensions of these ideas are illustrated.
Abstract: A theorem concerning fermion interaction is postulated and applied to the problems of atomic (electronic) and nuclear physics. Model building basedsolely upon the postulate thatadjacent like fermions must be singlet paired accounts for the closed shells ofboth nuclear and atomic structure. The implied antiferromagnetic FCC lattice of protons and neutrons in alternating layers has been found previously to be the lowest-energy solid configuration of nuclear matter (N=P) (Canuto and Chitre, 1974). The buildup of the FCC lattice from a central tetrahedron reproduces all of the shells and subshells of the isotropic harmonic oscillator, which of course is the basis for the shell model. In atomic structure, the singlet pairing of adjacent electrons implies closed-shell structures uniquely at the six noble gases and the three noble metals, Ni, Pd, and Pt. The basis for the postulate concerning fermions is found in terms of classical electrodynamics; it is a microscopic corollary of Biot-Savart's law that parallel currents attract whereas antiparallel currents repel.
TL;DR: In this paper, the authors briefly answer the comments in "Information Flow, Causality and the Classical Theory of Tachyons" by Basano and answer the questions raised by the reader.
Abstract: We briefly answer the comments in “Information Flow, Causality and the Classical Theory of Tachyons” by Basano.
TL;DR: In this article, it was shown that baryons exhibit features that we had come to recognize as the hallmark of the ordered SM, such as quark structure (qqq), the OZ[ rule (e.g., p/~ is strongly suppressed), Regge pole dominance, exchange degeneracy for many trajectories, etc.
Abstract: The sequentially ordered SM, and the DTU scheme based on it, were seen to describe from a unified point of view a wide range of phenomena in the meson sector; indeed, it appears to have the potential of becoming a quantitative theory of mesons (of course a strong-interaction theory cannot be complete without including all hadrons, but to the extent that baryons do not affect the calculations too strongly, it appears to be a good approximation for mesons). Given this state of affairs, we found it hard to believe that the ordered SM idea would remain limited to mesons, particularly since baryons, too, exhibit features that we had come to recognize as the hallmark of the ordered SM, such as quark structure (qqq), the OZ[ rule (e.g., ~--~ p/~ etc. is strongly suppressed), Regge pole dominance, exchange degeneracy for many trajectories, etc. In fact, the need to extend duality and particularly the DTU program to baryons had been felt acutely for quite a while, and had given rise to numerous attempts to accomplish this, none of them really successful. One of the more persistent obstacles was the problem posed by the
TL;DR: In this article, a joint distribution of a set of observables on a quantum logic in a statem is defined and its properties are derived, and it is shown that if the joint distribution exists, then the observables can be represented in the statem by the set of commuting operators on a Hilbert space.
Abstract: A joint distribution of a set of observables on a quantum logic in a statem is defined and its properties are derived. It is shown that if the joint distribution exists, then the observables can be represented in the statem by a set of commuting operators on a Hilbert space.
TL;DR: In this article, a new theory of gravitational, electromagnetic, and nuclear fields was proposed, which is based on the assumption that the motion of a particle is determined from a variational principle of the form δ ∫ A B dτ = 0.
Abstract: Through an examination of neutron lifetimes we shall propose a new theory of gravitational, electromagnetic, and nuclear fields. The fundamental assumption of our theory is that the motion of a particle in a combination of gravitational, electromagnetic, and nuclear fields is determined from a variational principle of the form δ ∫ A B dτ=0. The form of the physical time is determined from an examination of classical equations of motion. The field equations are determined from an examination of Maxwell-Einstein theory and Yukawa theory. Utilizing the standard elementary model of the deuteron, the theory predicts that at a proton-neutron separationr ∼ 10−13 cm the neutron lifetime is infinite and that nucleons have a repulsive core. These predictions have been experimentally verified.
TL;DR: The Dirac relativistic equation for the hydrogen atom as augmented by dual interaction terms is solved exactly and the eigenvalues for the bound states are determined as discussed by the authors, where En =μ[1 +κ2/ (n + s)2]−1/2, withs2 =k2−κ2(1±Λ)2, where Λ is a constant which is a measure of the strength of the dual interaction relative to the standard interactionγµAµ.
Abstract: The Dirac relativistic equation for the hydrogen atom as augmented by dual interaction terms is solved exactly and the eigenvalues for the bound states are determined. These areEn =μ[1 +κ2/ (n + s)2]−1/2, withs2=k2−κ2(1±Λ)2, where Λ is a constant which is a measure of the strength of the dual interaction relative to the standard interactionγµAµ. It is shown that the ratios of the experimental values for the Lamb shifts of various energy levels in hydrogen and singly ionized helium are correctly given by the theory. The origin of the anomalous magnetic moment and, in fact, the operator for the total magnetic moment is given.
TL;DR: In this article, a solution of the Einstein equations corresponding to a thin shell of dust under rigid rotation solution is obtained, where the region interior to the shell is flat and the exterior vacuum region is chosen as a Lewis manifold.
Abstract: Following the method developed by Papapetrou and Hamoui, a solution of the Einstein equations corresponding to a thin shell of dust under rigid rotation solution is obtained. The region interior to the shell is flat and the exterior vacuum region is chosen as a Lewis manifold. An essential limitation of this type of shell is that it does not allow the limitM1 andL1→ 0, whereM1 andL1 are the mass and the angular momentum per unit length. It is shown that the limitation is a consequence of the fact that the Lewis metric does not contain the Minkowski metric as a special case.
TL;DR: In this article, the Krupka and Trautman method for the description of all generally invariant functions of the components of geometrical object fields is applied to the invariants of second degree of the metrical field and other tensor fields.
Abstract: The Krupka and Trautman method for the description of all generally invariant functions of the components of geometrical object fields is applied to the invariants of second degree of the metrical field and other tensor fields. The complete system of differential identities fulfilled by the invariants mentioned is found and it is proved that these invariants depend on the tensor quantities only.
TL;DR: In this article, the problem of finding all functionally independent Lagrangians of first-order invariant Einstein-Cartan structures is discussed. But it is shown that each Lagrangian of these structures depends only on certain tensors constructed from the metric and the connection fields.
Abstract: A first-order invariant Einstein-Cartan structure is a Lagrangian structure on a differential manifold defined by a generally invariant Lagrangian depending on a metric field, a connection field, and the first derivatives of these fields. Moreover, it is assumed that the metric and connection fields satisfy the so-called compatibility condition. In this paper the problem of finding all such invariant Einstein-Cartan structures is discussed. It is shown that each Lagrangian of these structures depends only on certain tensors constructed from the metric and the connection fields, which means that all the Lagrangians can be described within the framework of the classical theory of invariants. The maximal number of functionally independent Lagrangians is determined as a function of the dimension of the underlying manifold.
TL;DR: In this paper, the Weinberg-Salam theory is applied to the case where a pair of magnetic poles are bound by a flux string of the Z 0 field, with an energy scale in the TeV range.
Abstract: A Higgs vacuum field φ is characterized by the set of conditionsDμφ=0, which lead to a generalized Meissner effect and partially determine the vector potentialAμ in terms of φ. Applying this method to the Weinberg-Salam theory, we assert that there exist stringlike configurations in which a pair of magnetic poles are bound by a flux string of theZ0 field, with an energy scale in the TeV range. We also point out that pure gauges in non-Abelian gauge theories are not well-defined due to topological singularities. In order to be meaningful, they must be enlarged to a class of almost pure gauges which include the various known topological configurations.
TL;DR: In this article, the authors start from the primitive concepts of preparticle and membership relation e of set theory to obtain the derivative concepts of particle (already introduced in a previous work), field, and the interaction between systems of particles.
Abstract: We start from the primitive concepts of preparticle and membership relation e of set theory to obtain the derivative concepts of particle (already introduced in a previous work), field, and the interaction between systems of particles. We have explicitly stated, in addition, what the relationship between a system of particles and the field it produces is in the present model of physical systems. In order to discuss the motion of particles we have analyzed one of the possible definitions of a reference frame.
TL;DR: In this article, a systematic algorithm is presented that generates a sequence of monotonically increasing values for the square variance function of a finite-dimensional Hamiltonian H obeys a maximum principle that leads to the determination of its maximum and minimum eigenvalues.
Abstract: The square variance function of a finite-dimensional Hamiltonian H obeys a maximum principle that leads to the determination of its maximum and minimum eigenvalues. A systematic algorithm is presented that generates a sequence of monotonically increasing values for the square variance. It is shown that the method converges to the exact two-dimensional eigenvalue problem determined by the lowest and highest eigenvalues. Preliminary numerical results are briefly outlined.
TL;DR: In this article, the authors construct a mathematical model which proves that the set of axioms for the theoretical description of single microsystems developed by Ludwig is free of contradictions and admits of nontrivial solutions.
Abstract: Starting with the usual Hubert space formulation of quantum mechanics we construct a mathematical model which proves that the set of axioms for the theoretical description of single microsystems developed by Ludwig is free of contradictions and admits of nontrivial solutions.