Showing papers on "Four-force published in 1971"
01 Jan 1971
TL;DR: Galilean transformation laws were but an approximation to the more exact Lorentz formulas, and one could distinguish the abstract principle of relativity from its concrete expressions, as various possible theories of relativity as mentioned in this paper.
Abstract: Publisher Summary Galileo Galilei explicitly introduced the principle of relativity in physics. He was the first one to recognize the existence of inertial transformations, connecting various frames of reference in which the laws of physics take the same form. Starting with the recognition that the Galilean transformation laws were but an approximation to the more exact Lorentz formulas, one could distinguish the abstract principle of relativity from its concrete expressions, as various possible theories of relativity. At the same time, one could begin to see the basic role played by the relevant theory of relativity in structuring a given physical theory—Galilean relativity for classical mechanics, Einstein relativity for “relativistic” mechanics, and electromagnetism. Applications of the Galilei group are described for classical physics and for quantum physics. A “super-Galilei group” has been defined in relation to non-relativistic cosmology. This is a sixteen-parameter group acting on the five-dimensional manifold of space-time and gravitational potential.
245 citations
TL;DR: In this paper, a boundary is attached on which incomplete geodesics terminate as well as inextensible timelike curves of finite length and bounded acceleration, and the construction is free ofad hoc assumptions concerning the topology of the boundary and the identification of curves defining the same boundary point.
Abstract: To any space time a boundary is attached on which incomplete geodesics terminate as well as inextensible timelike curves of finite length and bounded acceleration. The construction is free ofad hoc assumptions concerning the topology of the boundary and the identification of curves defining the same boundary point. Moreover it is a direct generalization of the Cauchy completion of positive definite Riemannian spaces.
221 citations
TL;DR: In this paper, the cosmological constant λ appears as an unavoidable Lagrange multiplier, belonging to a constraint expressing the existence of a fundamental element of space-time hypervolume at every point.
Abstract: In usual formulations of general relativity, the cosmological constant λ appears as an inelegant ambiguity in the fundamental action principle. With a slight reformulation, λ appears as an unavoidable Lagrange multiplier, belonging to a constraint. The constraint expresses the existence of a fundamental element of space-time hypervolume at every point. The fundamental scale of length in atomic physics provides such a hypervolume element. In this sense, the presence in relativity of an undetermined cosmological length is a direct consequence of the existence of a fundamental atomic length.
196 citations
TL;DR: In this article, a test particle with spin possessing a canonical energy-momentum tensor with a nonvanishing antisymmetric part is used to measure torsion.
134 citations
TL;DR: In this article, it was shown that a relativistic formulation of thermodynamics or statistical mechanics has as its aim to provide a unique correspondence between the descriptions which different observers in uniform relative motion will give of a thermodynamic system.
68 citations
56 citations
TL;DR: In this paper, the problem of non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case.
Abstract: The problem tackled by B. K. Datta, [1] in a recent paper concerning non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case. A full classification of the possible motions is given.
46 citations
Journal Article•
TL;DR: In this article, the authors develop from a variational formulation the field equations, jump conditions across a discontinuity surface and nonlinear constitutive equations for a magnetized elastic medium with finite deformations in the frame of the general theory of relativity.
Abstract: In this article, we develop from a variational formulation the field equations, jump conditions across a discontinuity surface and nonlinear constitutive equations for a magnetized elastic medium with finite deformations in the frame of the general theory of relativity. RESUME. Dans le present article, nous généralisons dans le cadre de la relativité générale, la théorie des milieux continus déformables en interaction avec le champ magnétique donnée precedemment dans le cadre de la relativité restreinte [6][25]-[27]. Le milieu continu considéré est un milieu solide élastique sujet a des deformations finies et en interaction avec les champs gravifique et magnétique. Un principe variationnel qui suit la formulation que Taub [12] a donnée pour le schema fluide parfait est employe. Toutes les equations du champ (equations d’Einstein, conservation de 1’impulsion-energie, equations de Maxwell dans un milieu matériel, conservation du flux d’entropie) en découlent ainsi que les conditions de saut a travers une surface de discontinuité. Comme dans le travail de Taub, il est montré que cette derniere ne peut etre variée indépendamment du parametre thermodynamique. Les lois non-linéaires de comportement sont également obtenues a partir d’un potentiel, l’énergie libre de Helmholtz qui est écrite sous forme invariante, ceci généralisant la contrainte habituellement imposée par le principe d’indifference matérielle en mécanique classique des milieux continus. ANN. INST. POINCARÉ, A-X V-4 20 276 G~RARD A. MAUGIN
25 citations
TL;DR: By a new choice of the arbitrarily given quantities on an initial 3-manifold, the authors reduced the system of constraints in General Relativity to an elliptic system of four equations.
Abstract: By a new choice of the arbitrarily given quantities on an initial 3-manifold we reduce the system of constraints, in General Relativity, to an elliptic system of four equations, the coefficients of which have a simple geometric interpretation on the 3-manifold. The system seems well suited for a global study and some results are given in this direction.
TL;DR: In this article, a theory of gravitation is considered which resembles the general theory of relativity in being based on the equivalence principle, but is without the covariance principle, leading to the same results as general relativity in the three crucial tests.
Abstract: Since there seems to exist a preferred frame of reference in the universe, determined by the large-scale distribution of matter, a theory of gravitation is considered which resembles the general theory of relativity in being based on the equivalence principle, but is without the covariance principle. This theory leads to the same results as general relativity in the three crucial tests. The formalism can be modified to take into account the solar oblateness observed by Dicke and Goldenberg.
TL;DR: In this paper, the concept of spinors which transform according to the unimodular group is analyzed on the basis of Riemann-Cartan geometry, and conservation laws are derived by considering the invariance of the action function under infinitesimal co-ordinate and spin transformations.
Abstract: The concept of spinors which transform according to the unimodular group is analysed on the basis of Riemann-Cartan geometry. Using the principle of minimal coupling, we obtain a matter Lagrangian, which differs from the Lagrangian of the conventional theory of general relativity in that it is also a function of torsion. Conservation laws are derived by considering the invariance of the action function under infinitesimal co-ordinate and spin transformations. These conservation laws or identities lead to the definition of an asymmetric energy-momentum tensor, the antisymmetric part of which is related to the spin angular momentum. It is also shown that the force acting on the material system depends on the spin of the material and on the curvature.
TL;DR: In this paper, the Hamiltonian of general relativity can be made homogeneous in the momenta by means of a canonical transformation, and the corresponding Hamilton-Jacobi equations yield functionals of the configuration-space variables which are constant over equivalence classes generated by the constraints.
Abstract: By means of a canonical transformation, the Hamiltonian of general relativity can be made homogeneous in the momenta. Solutions of the corresponding Hamilton-Jacobi equations yield functionals of the configuration-space variables which are constant over equivalence classes generated by the constraints. The constancy of such solutions of the Hamilton-Jacobi equations is also a sufficient condition for infinitesimally neighboring sets of configuration variables to lie within the same four-dimensional space-time of the given family of Ricciflat manifolds.
TL;DR: For instance, this paper argued that the Mach's principle as frequently described may be illusory, but attempts at deeper formulations are difficult to interpret and therefore cannot be interpreted correctly.
Abstract: Mach's principle as frequently described may be illusory, but attempts at deeper formulations are difficult to interpret.
TL;DR: In this article, it was shown that if the theory is quantized, then the quantum mechanical states corresponding to 1-particle systems in the unquantized theory may have properties similar to fermions.
Abstract: When general relativity is examined from the point of view of algebraic topology, it is found that the theory exhibits conserved particlelike structures. The number of such particles associated with a given metric is determined by the homotopy class of the metric. This paper is concerned with showing that if the theory is quantized, then the quantum mechanical states corresponding to 1‐particle systems in the unquantized theory may have properties similar to fermions. In particular, it is proved that it is possible for wavefunctionals to exist which are double‐valued under 2π rotation.
TL;DR: In this article, the authors extended the study of uniformly polytropes with axial symmetry to include all rotational terms of order Ω4, where Ω is the angular velocity, consistently within the first post-Newtonian approximation to general relativity.
Abstract: The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order Ω4, where Ω is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter υ = Ω2/2πGϱ
c
and a relativity parameter, σ =p
c
/ϱ
c
C
2
, wherep
c
and ϱc are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of orderσυ
2. The critical rotation parameterv
c
, which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of σ. Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.
01 Jan 1971
TL;DR: In this paper, the Dirac field equations are derived with the help of the usual variational formalism, which show the correspondence between the canonical energy momentum and Einstein's tensor as well as the corresponding correspondence between spin angular momentum and contorsion.
Abstract: SummaryThis is the continuation of the previous paper. The action function of matter is supplemented by the action function of a free field. With the help of the usual variational formalism we derive the field equations, which show the correspondence between the canonical energy momentum and Einstein’s tensor as well as the correspondence between the canonical spin angular momentum and contorsion. It is shown that these equations are consistent with the conservation laws as derived in the previous paper. As a simple example we consider the Dirac field in this formalism. We show that spin angular momentum in this case is completely antisymmetric and that the additional terms in the action function arising from torsion express a spin-spin contact interaction. The generalized Dirac equation is shown to be equivalent to a nonlinear spinor equation of Heisenberg-Pauli type in which the nonlinear term is induced by torsion.RiassuntoQuesto è il seguito dell’articolo precedente. La funzione di azione della materia è completata con la funzione di azione di un campo libero. Con l’aiuto dell’usuale formalismo Tariazionale si deducono le equazioni di campo che mostrano la corrispondenza fra l’energia-impulso canonica ed il tensore di Einstein ed anche la corrispondenza fra il momento angolare di spin canonico e la contorsione. Si mostra che queste equazioni sono consistenti con le leggi di conservazione dedotte nell’articolo precedente. Come semplice esempio si considera in questo formalismo il campo di Dirac. Si dimostra che in questo caso il momento angolare dello spin è completamente antisimmetrico e che i termini addizionali nella funzione di azione derivanti dalla torsione esprimono un’interazione di contattp spin-spin. Si dimostra che l’equazione di Dirae generalizzata è equivalente ad un’equazione spinoriale non lineare del tipo di Heisenberg-Pauli in cui il termine non lineare è introdotto dalla torsione.РезюмеЭта работа представляет продолжение предыдущей статьи. Функция действия вещества дополняется функцией действия свободного поля. С помощью обычного вариационного формализма мы выводим уравнения поля, которые обнаруживают соответствие между каноническим тензором энергии-импульса и тензором Эйнштейна, а также соответствие между каноническим спиново-орбитальным моментом и искажением. Показывается, что эти уравнения не противоречат законам сохранения, выведенным в предыдущей статье. В качестве примера мы рассматриваем поле Дирака в этом формализме. Мы показываем, что спиново-орбитальный момент в этом случае является полностью антисимметричным, и дополнительные члены в функции действия, возникающие из закручивания, выражают спин-спиновое контактное взаимодействие. Показывается, что обобщенное уравнение Дирака эквивалентно нелинейному спинорному уравнению типа Гайзенберга-Паули, в котором нелинейный член обусловлен закручиванием.
TL;DR: In this paper, the equivalence of the Euclidean and the Lorentz-covariant representations of the physical laws of the metric tetradrithm has been established.
Abstract: We define a derivation operation working on hybrid objects which are tensors under theEinstein group of coordinate transformations and under theLorentz group of transformations of reference systems. With these general covariant derivations we formulate the principle of the equivalence of theEinstein- and of theLorentz-covariant representations of the physical laws. This principle means the general covariant constance of the metric tetradsh
i
A
(Weyl's lemma).
TL;DR: In this article, a weak field low velocity (EIH) approximation to general relativity is used to measure the forces between spinning cylinders and disks, which is based on the potential theory in electrodynamics.
Abstract: BECAUSE of the widespread interest in measuring forces between spinning cylinders and disks1,2 and the speculative nature of the conclusions reached in previous discussions, we have made a quantitative calculation of the magnitude of the forces. As in earlier calculations3, our approach is based on a weak field low velocity (EIH) approximation to general relativity. By methods familiar from potential theory in electrodynamics we first compute the first order corrections to a fiat space metric due to the presence of a spinning cylinder.
TL;DR: In this article, the field equations of Yilmaz's new approach to general relativity are extended to the case when matter is present and used to find cosmological models.
Abstract: The field equations of Yilmaz’ new approach to general relativity are extended to the case when matter is present and are used to find cosmological models It is shown that the theory includes both steady-state and Robertson-Walker type models which are not the same as those found in the usual relativistic cosmology
TL;DR: In this article, action principles using the Eulerian description are proposed for the elastic solid and perfect fluid in general relativity, taking into account the constraints on the independent variables appearing in the Lagrangian density.
Abstract: Action principles using the Eulerian description are proposed for the elastic solid and perfect fluid in general relativity. By taking into account the constraints on the independent variables appearing in the Lagrangian density, it is shown that these action principles are equivalent to those using the Lagrangian description, which have been given previously.
TL;DR: The ether-wave theory of light, suitably modified, is fully supported by all known evidence as mentioned in this paper, and further observation and analysis will be required to determine which of its several forms accurately represents reality.
Abstract: The ether-wave theory of light, suitably modified, is fully supported by all known evidence. Further observation and analysis will be required to determine which of its several forms accurately represents reality. On the other hand, the tactile theory, the Newtonian corpuscular theory, the Ritz extinction theory, and the Special Theory of Relativity are not supported by the evidence.
TL;DR: In this article, a new theory of gravitation is proposed which uses the world picture of general relativity but is not covariant, which is in contradiction to the principle of covariance on which the general relativity theory is based.
Abstract: Homogeneous isotropic models of the universe, based on the general theory of relativity, lead to the existence of a preferred frame of reference, which is similar to the absolute space of, Newton, and a preferred time coordinate, which resembles the absolute time of Newton These concepts seem to be in contradiction to the principle of covariance on which the general relativity theory is based A theory of gravitation is therefore proposed which uses the world picture of general relativity but is not covariant In the three crucial tests, the proposed theory gives the same results as the general relativity theory However, in contrast to general relativity, the present theory predicts the emission of gravitational waves by spherically symmetric systems, and gravitational waves are found, in general, to have both transverse and longitudinal components
TL;DR: In this article, a mathematical axiom system for general affine kinematics is proposed, and then the relativistic case is separated from the classical one by means of a single axiom.
Abstract: In this paper a mathematical axiom system for general affine kinematics is proposed, and then the relativistic case is separated from the classical one by means of a single axiom. A "characteristic" k is introduced, which allows to classify naturally three distinct types of affine kinematics. It is shown that, once the classical point of view is abandoned, there are essentially two types of relativistic affine kinematics: one of them is characterised by the existence of a limit velocity, and the other by the existence of time reversal. Physical axioms are later introduced and the concept of model is studied in connection with transfor mation groups. A general epistemological discussion closes the paper.