We consider the special and general relativistic extensions of the action principle behind the Schrödinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the classical Einstein equation we identify the conformal content of the above action and obtain classical gravitation for massive particles, but with a cosmological term representing off-mass-shell contribution to the energy–momentum tensor. In this scenario the—on the Planck scale surprisingly small—cosmological constant stems from quantum bound states having (...) a Bohr radius a as being \. (shrink)

This paper is motivated by the desire to formulate a relativistically covariant hidden-variable particle trajectory interpretation of the quantum theory of the vector field that is formulated in such a way as to allow the inclusion of gravity. We present a methodology for calculating the flows of rest energy and a conserved density for the massive vector field using the time-like eigenvectors and eigenvalues of the stress-energy-momentum tensor. Such flows may be used to define particle trajectories which follow the (...) flow. This work extends our previous work which used a similar procedure for the scalar field. The massive, spin-one, complex vector field is discussed in detail and the flows of energy-momentum are illustrated in a simple example of standing waves in a plane. (shrink)

The energy-momentum tensor for a particular matter component summarises its local energy-momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy-momentum tensor, whose statement and proof we recall. In the first half of this paper we do this within the realm of Special Relativity and in (...) the traditional mathematical language using components with respect to affine charts, thereby focusing on the intended physical content and interpretation. In the second half we show how to do all this in a proper differential-geometric fashion and on arbitrary space-time manifolds, this time focusing on the group-theoretic and geometric hypotheses underlying these results. Based on this we give a proper geometric statement and proof of Laue's theorem, which is shown to generalise from Minkowski space to space-times with significantly less symmetries. This result, which seems to be new, not only generalises but also clarifies the geometric content and hypotheses of Laue's theorem. A series of three appendices lists our conventions and notation and summarises some of the conceptual and mathematical background needed in the main text. (shrink)

We compute the energy tensor and the energy-momentum tensor for electrodynamics coupled to the current of a charged scalar field and for electrodynamics coupled tothe current of a Dirac spinor field, without using the equations of motion.

The notions of ``motion'' and ``conserved quantities'', if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions that underlie these concepts, which we will review in some detail. Next to the prerequisites from Special Relativity, like Minkowski space and its automorphism group, this will include the notion of a body in Minkowski space, the momentum map, a characterisation of the habitat of globally conserved (...) quantities associated with Poincare symmetry -- so called Poincare charges --, the frame-dependent decomposition of global angular momentum into Spin and an orbital part, and, last not least, the likewise frame-dependent notion of centre of mass together with a geometric description of the Moeller Radius, of which we also list some typical values. (shrink)

two dimensions, quantum radiation production is incompatible with a conserved and traceless T„,. We therefore resolve an ambiguity in our expression for Tr„, regularized by a geodesic point-separation procedure.

In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{0,1}$\end{document}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be (...) completely characterised by algebraic invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum, the quantum potential and the relativistic time evolution of its spin for the first time. (shrink)

We address to the Poynting theorem for the bound electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \ and bound electric field \ are generated by the same (...) source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way, we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (...) (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)

I describe how relativistic field theory generalizes the paradigm property of material systems, the possession of mass, to the requirement that they have a mass–energy–momentum density tensor T µ associated with them. I argue that T µ does not represent an intrinsic property of matter. For it will become evident that the definition of T µ depends on the metric field g µ in a variety of ways. Accordingly, since g µ represents the geometry of spacetime itself, the (...) properties of mass, stress, energy, and momentum should not be seen as intrinsic properties of matter, but as relational properties that material systems have only in virtue of their relation to spacetime structure. (shrink)

By means of a Clebsch representation which differs from that previously applied to electromagnetic field theory it is shown that Maxwell's equations are derivable from a variational principle. In contrast to the standard approach, the Hamiltonian complex associated with this principle is identical with the generally accepted energy-momentum tensor of the fields. In addition, the Clebsch representation of a contravariant vector field makes it possible to consistently construct a field theory based upon a direction-dependent Lagrangian density (it is this (...) kind of Lagrangian density that may arise when developing the Finslerian extension of general relativity). The corresponding field equations are proved to be independent of any gauge of Clebsch potentials. The law of energy-momentum conservation of the field appears to be covariant and integrable in a rather wide class of direction-dependent Lagrangian densities. (shrink)

In the energy–momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid (...) with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy–momentum density, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell’s stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural solution for the notorious, more than a century old but thought by many as still unresolved, 4/3 problem in the electromagnetic mass. (shrink)

Stemming from our energy localization hypothesis that energy in general relativity is localized in the regions of the energy-momentum tensor, we had devised a test with the classic Eddington spinning rod. Consistent with the localization hypothesis, we found that the Tolman energy integral did not change in the course of the motion. This implied that gravitational waves do not carry energy in vacuum, bringing into question the demand for the quantization of gravity. Also if information is conveyed by the (...) waves, the traditional view that information transfer demands energy is challenged. Later, we showed that the “body” angular momentum changed at a rate indicating that the moment of inertia increased to higher order, contrary to traditional expectations. We consider the challenges facing the development of a localized expression for the total angular momentum of the body including the contribution from gravity. We find that Komar's expression does not lead to an adequate formulation of localized angular momentum. (shrink)

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of (...) this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined. (shrink)

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work (...) relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

We develop a geometro-dynamical approach to the cosmological constant problem (CCP) by invoking a geometry induced by the energy-momentum tensor of vacuum, matter and radiation. The construction, which utilizes the dual role of the metric tensor that it structures both the spacetime manifold and energy-momentum tensor of the vacuum, gives rise to a framework in which the vacuum energy induced by matter and radiation, instead of gravitating, facilitates the generation of the gravitational constant. The non-vacuum sources comprising (...) matter and radiation gravitate normally. At the level of classical gravitation, the mechanism deadens the CCP yet quantum gravitational effects, if strong, can keep it existent. (shrink)

In the recent literature, it has been shown that the wave function in the de Broglie–Bohm theory can be regarded as a new kind of field, i.e., a "multi-field", in three-dimensional space. In this paper, I argue that the natural framework for the multi-field is the original second-order Bohm’s theory. In this context, it is possible: i) to construe the multi-field as a real-valued scalar field; ii) to explain the physical interaction between the multi-field and the Bohmian particles; and iii) (...) to clarify the status of the energy-momentum conservation and the dynamics of the theory. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called 4/3-problem (...) without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

The existence of current–time universe’s acceleration is usually modeled by means of two main strategies. The first makes use of a dark energy barotropic fluid entering by hand the energy–momentum tensor of Einstein’s theory. The second lies on extending the Hilbert–Einstein action giving rise to the class of extended theories of gravity. In this work, we propose a third approach, derived as an intrinsic geometrical effect of space–time, which provides repulsive regions under certain circumstances. We demonstrate that the (...) effects of repulsive gravity naturally emerge in the field of a homogeneous and isotropic universe. To this end, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. Moreover, we show that repulsive gravity counterbalances the standard gravitational attraction influencing both late and early times of the universe evolution. This phenomenon leads to the present speed up and to the fast expansion due to the inflationary epoch. In so doing, we are able to unify both dark energy and inflation in a single scheme, showing that the universe changes its dynamics when \, at the repulsion onset time where this condition is satisfied. Further, we argue that the spatial scalar curvature can be taken as vanishing because it does not affect at all the emergence of repulsive gravity. We check the goodness of our approach through two cosmological fits involving the most recent union 2.1 supernova compilation. (shrink)

A new hypothesis for energy localization in general relativity is introduced which is based upon the fact that the energy-momentum conservation laws are devoid of content in vacuum. The vanishing of pseudotensor components forms the basis of coordinate conditions consistent with the above. The implication is that energy is localized where the energy-momentum tensor is nonvanishing. As a consequence, gravitational waves are not carriers of energy in vacuum. A detailed analysis of a Feynman detector interacting with a plane gravitational (...) wave is consistent with the hypothesis. The fact that there has never been a confirmed direct energy transfer to a detector via gravitational radiation is also consistent with the hypothesis. (shrink)

In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) (...) one with a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained. (shrink)

We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle's dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle's elementary magnetic dipole moment. As consistency checks, we calculate (...) the overall system's energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system's Belinfante-Rosenfeld energy-momentum tensor. (shrink)

A massless Weyl-invariant dynamics of a scalar, a Dirac spinor, and electromagnetic fields is formulated in a Weyl space, W4, allowing for conformal rescalings of the metric and of all fields with nontrivial Weyl weight together with the associated transformations of the Weyl vector fields κμ, representing the D(1) gauge fields, with D(1) denoting the dilatation group. To study the appearance of nonzero masses in the theory the Weyl symmetry is broken explicitly and the corresponding reduction of the Weyl space (...) W4 to a pseudo-Riemannian space V4 is investigated assuming the breaking to be determined by an expression involving the curvature scalar R of the W4 and the mass of the scalar, selfinteracting field. Thereby also the spinor field acquires a mass proportional to the modulus Φ of the scalar field in a Higgs-type mechanism formulated here in a Weyl-geometric setting with Φ providing a potential for the Weyl vector fields κμ. After the Weyl-symmetry breaking, one obtains generally covariant and U(1) gauge covariant field equations coupled to the metric of the underlying V4. This metric is determined by Einstein's equations, with a gravitational coupling constant depending on Φ, coupled to the energy momentum tensors of the now massive fields involved together with the (massless) radiation fields. (shrink)

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I (...) conclude by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter. (shrink)

In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly filfilled for the energy-momentum and for the angular (...) momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just “flat.” This suggests that in the universe a “missing mass” should exist in a form of matter. (shrink)

Time arises in the theory of gravity through the semiclassical approximation of the gravitational part of the solution of the Wheeler-De Witt equation in the manner shown by Banks (SCAG). We generalize Banks' procedure by grafting a Born-Oppenheimer type approximation onto SCAG. This allows for the feedback of matter onto gravity, wherein the latter is driven by the (quantum) mean energy-momentum tensor of matter. The wave function is nonvanishing in classically forbidden configurations of gravity. In SCAG this is described (...) by the evolution of matter in imaginary time. This is interpreted as an inverse temperature, and the norm of the matter wave function, no longer conserved for these gravitational configurations, is a partition function. A simple cosmological model is worked out to illustrate these ideas. In this model it is shown that the temperature of the matter which emerges into the classically permitted region is the inverse bounce time of the bounce executed by the system in the forbidden region (behind the horizon).Time present and time past are both perhaps present in time future. And time future contained in time past. If all time is eternally present All time is unredeemable.—T. S. Eliot, “Burnt Norton,”Four Quartets, 1943. (shrink)

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, e.g., (...) the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)

If we live on the weak brane with zero effective cosmological constant in a warped 5D bulk spacetime, gravitational waves and brane fluctuations can be generated by a part of the 5D Weyl tensor and carries information of the gravitational field outside the brane. We consider on a cylindrical symmetric warped FLRW background a U self-gravitating scalar field coupled to a gauge field without bulk matter. It turns out that brane fluctuations can be formed dynamically, due to the modified (...) energy–momentum tensor components of the scalar-gauge field. As a result, we find that the late-time behavior could significantly deviate from the standard evolution of the universe. The effect is triggered by the time-dependent warpfactor with two branches of the form \}\) constants) and the modified brane equations comparable with a dark energy effect. This is a brane-world mechanism, not present in standard 4D FLRW, where the large disturbances are rapidly damped as the expansion proceed. Because gravity can propagate in the bulk, the cosmic string can build up a huge angle deficit by the warpfactor and can induce massive KK-modes felt on the brane. Disturbances in the spatial components of the stress-energy tensor cause cylindrical symmetric waves, amplified due to the presence of the bulk space and warpfactor. They could survive the natural damping due to the expansion of the universe. It turns out that one of the metric components becomes singular at the moment the warp factor develops an extremum. This behavior could have influence on the possibility of a transition from acceleration to deceleration or vice versa. (shrink)

In the context of a covariant mechanics with Poincaré-invariant evolution parameter τ, Sa'ad, Horwitz, and Arshansky have argued that for the electromagnetic interaction to be well posed, the local gauge function of the field should include dependence on τ, as well as on the spacetime coordinates. This requirement of full gauge covariance leads to a theory of five τ-dependent gauge compensation fields, which differs in significant aspects from conventional electrodynamics, but whose zero modes coincide with the Maxwell theory. The pre-Maxwell (...) fields may exchange mass with charged particles, permitting pair annihilation even at the classical level. The total mass-energy-momentum tensor of the fields and particles is conserved. The Green's functions for the fields provide spacelike and timelike support for correlations, as well as lightlike propagation. A τ-integration of the fields—singling out the massless photons—recovers the standard Maxwell theory, which then has the character of an equilibrium limit of the underlying microscopic dynamics. The pre-Maxwell theory also turns out to be the solution of the inverse problem in variational mechanics: it is shown to be the most general local gauge theory consistent with unconstrained commutation relations in four dimensions. Posed in this framework, the extension to n-dimensions, curved background space, and non-abelian gauge symmetry becomes straightforward. (shrink)

We envisage a black hole perturbed by a force-free magnetic field outside and attempt to determine its structure. We suppose the metric that describes this black hole is of the static spherical type, that is Schwarzschild, and the energy–momentum tensor emanating from an FFMF source perturbs this background metric, in this regard one can imagine a magnetic accretion disk around the black hole. By solving the equations for such a configuration, we will show that in addition to modifying (...) the diagonal elements of the background metric, we will also see the non-zeroing of the off-diagonal elements of the general metric, one of the immediate consequences of which will be a static to stationary transition. (shrink)

This paper is part II of a trilogy on the transition from classical particle mechanics to relativistic continuum mechanics that one of the authors is working on. The first part, on the Trouton experiment, was published in the Stachel festschrift (Janssen 2003). This paper focuses on the Lorentz-Poincaré electron, and, in particular, on the "Poincaré pressure" or "Poincaré stresses" introduced to stabilize the electron. It covers both the original argument by Poincaré (1906) and a modern relativistic argument for adding a (...) negative pressure term to the system's energy-momentum tensor inspired by the work of Laue (1911a, b). It highlights the importance of a paper by Lorentz (1899) in this context and of the "electromagnetic mechanics" of Abraham (1903). (shrink)

The parametrized post-Newtonian (PPN) approximation is generalized to accommodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum (...) and angularmomentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories. (shrink)

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion Ωμ of spacetime. This conjecture is made feasible by the natural separation of the connection ω μ v into “gravitational” and “electromagnetic” parts α μ v and β μ v , respectively, related to the metric and to the torsion. When α μ v is neglected in front of β μ v , the affine geodesics are shown to become the equations of motion of charged (...) particles with Lorentz force, for an appropriate choice of Ωμ. Since β μ v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if Ωμ were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when β μ v 《 α μ v ).In addition to the factor q/m, the velocity of the test particle appears in Ωμ. This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor. (shrink)

We show that the spread of momentum can be broken up into two terms, one that depends only on the change in amplitude and the other which depends only on the deviations of current from the average momentum. We present a method for measuring the relative contributions of each and interpret each contribution in terms of local quantities. A generalization for arbitrary operators is given. For the case of the Hamiltonian, the local value of energy is shown to yield the (...) quantum potential as defined by Bohm. (shrink)

Gravitomagnetic equations result from applying quaternionic differential operators to the energy–momentum tensor. These equations are similar to the Maxwell’s EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; the Hamilton–Jacobi equation loaded by the quantum potential. (...) This equation in pair with the continuity equation leads to getting the Schrödinger equation describing a state of the superfluid quantum medium ; gravitomagnetic wave equations loaded by forces acting on the outer space. These waves obey to the Planck’s law of radiation. (shrink)

Maxwell's equations are established for the free electromagnetic field in two-dimensional space-times. In Minkowski space they are solved under the boundary conditions set by a pair of uniformly accelerated “plates.” With the help of these solutions we determine the regularized energy-momentum tensor of the canonically quantized electromagnetic field at the position of one of the “plates.” Thereby (as a new result) we arrive at a Casimir effect in an accelerated reference frame.

According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor $\hat \Theta _{ik}$ satisfying the relation $\hat \Theta _{i;k}^k = 0$ . The tensor $\hat \Theta _{ik}$ is formed from the Einstein-Cartan torsion field given by the (...) anholonomy objects, FAik=2hA[i,k], and appears together with Hilbert’s energy-momentum tensor T* ik and Poincaré’s pressure λgik on the right-hand side of Einstein’s equations so that one has $$R_{ik} - (1/2)g_{ik} R = - \kappa T*_{ik} - \lambda g_{ik} - \hat \Theta _{ik}$$ According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincaré and Einstein-Cartan terms to exist. The torsion field FAik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics. (shrink)

Curved multi-dimensional space-times (5D and higher) are constructed by embedding them in one higher-dimensional flat space. The condition that the embedding coordinates have a separable form, plus the demand of an orthogonal resulting space-time, implies that the curved multi-dimensional space-time has 4D de-Sitter subspaces (for constant extra-dimensions) in which the 3D subspace has an accelerated expansion. A complete determination of the curved multi-dimensional spacetime geometry is obtained provided we impose a new type of “equivalence principle”, meaning that there is a (...) geodesic which from the embedding space has a rectliniar motion. According to this new equivalence principle, we can find the extra-dimensions metric components, each curved multi-dimensional spacetime surface’s equation, the energy-momentum tensors and the extra-dimensions as functions of a scalar field. The generic geodesic in each 5D spacetime are studied: they include solutions where particle’s motion along the extra-dimension is periodic and the 3D expansion factor is inflationary (accelerated expansion). Thus, the 3D subspace has an accelerated expansion. (shrink)

The considerations of the two former articles concerning the special and general theories of relativity are extended. The question of the physical reality of the ether and the interpretation of some cosmological problems are discussed. A view is expanded according to which the metric tensor g is taken as the energy momentum tensor of the ether. The gravitational equation of Einstein is considered to represent the equations of motion of the ether. The cosmological red shift is also interpreted (...) in such terms. (shrink)

In this work, a Clifford algebra approach is used to introduce a charge-current wave structure governed by a Maxwell-like set of equations. A known spinor representation of the electromagnetic field intensities is utilized to recast the equations governing the charge-current densities in a Dirac-like spinor form. Energy-momentum considerations lead to a generalization of the Maxwell electromagnetic symmetric energy-momentum tensor. The generalized tensor includes new terms that represent contributions from the charge-current densities. Stationary spherical modal solutions representing the charge-current (...) densities and the associated self-fields are derived. The use of a Clifford type dependence on time results in a distinct symmetry between the magnetic and electric components. It is shown that, for such spherical modes, the components of the force density deduced from the generalized energy-momentum tensor can vanish under certain conditions. (shrink)

It is shown, in a large variety of manifestations, that the Aharonov—Bohm effect has classical counterparts in aspects concerning energy and momentum balance. No counterexamples are found in the cases considered, although whenever image charges shield the magnetic field region from the electric field of the passing electron the classical momentum effects, while present, would not be observable. Similarly, if the magnetic flux is maintained by superconductors, magnetic shielding will also render the classical energy effect unobservable. Partial shieldings of either (...) type will reduce but not totally eliminate the corresponding observable classical manifestations of these effects. (shrink)

Fibre suspension has garnered considerable attention in turbulent flows that are used in many industries. Solid particles, such as dust particles, notably affect the turbulent flow field in a rotational frame. In assessing their impacts, the dusty turbulent flow for fibre suspensions needs to be studied in a frame of rotation that can be substantially applied in many industries. This study, therefore, aims to build a theoretical model for the energy motion of dusty turbulent flow of fibre suspensions in a (...) rotational frame. The turbulence momentum equation was considered to formulate the model in presence of dusty fluid rotating flow of fibre suspensions. The newly derived equation was derived in second-order correlation tensors Fi,j, Wi,j, Gi,j, Si,j, Xi,j, Yi,j, Qi,j, and Ri,j at any two points in the flow domain, where the tensors were expressed as space, time, and distance functions. The developed model is a considerable improvement because it takes into account all of the potential influential parameters that could affect the motion of turbulent energy, such as dust particles, suspending particles, and rotating frame. However, the impact of these parameters on turbulence energy motion must be evaluated in order to assess the performance of turbulence systems utilized in a variety of industries, such as paper manufacturing. The present theoretical development will contribute to open up experimental and numerical research opportunities for the advancement of the industry, science, and technology. (shrink)

The significance of the de Broglie/Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the single-particle Newton–Wigner position. The effect of non-positive excursions of the ensemble density for extreme cases of positive-energy waves is easily computed using an integral of the equations of motion developed here for free spin-0 particles in 1 + 1 dimensions and is interpreted in terms of virtual-like pair creation and annihilation beneath the Compton wavelength. A Bohm-theoretic description of the acausal explosion of (...) a specific Newton–Wigner-localized state is presented in detail. The presence of virtual pairs found is interpreted as the Bohm picture of the spatial extension beyond single point particles proposed in the 1960s as to why space-like hyperplane dependence of the Newton–Wigner wavefunctions may be needed to achieve Lorentz covariance. For spin-1/2 particles the convective current is speculatively utilized for achieving parity with the spin-0 theory. The spin-0 improper quantum potential is generalized to an improper stress tensor for spin-1/2 particles. (shrink)

In this work, we explore modeling of wormholes in framework of f(R, T) gravity with the functional form f(R,T)=R+αR2+λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R, T)= R+\alpha R^2 +\lambda T$$\end{document}, where R and T are the Ricci scalar and trace of energy-momentum tensor respectively, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} are arbitrary constants. Using the equation of state (EoS) pr=ωρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_r=\omega \rho$$\end{document} and shape function b(r)=r0arar0,(0shrink)

Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v 2 /c 2 analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that a treatment (...) exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift. (shrink)

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2 , does reveal a connection between (...) the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c 2 , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems. (shrink)

We study a Weyl geometric scalar tensor theory of gravity with scalar field \ and scale invariant “aquadratic” kinematical Lagrange density. The Weylian scale connection in Einstein gauge induces an additional acceleration. In the weak field, static, low velocity limit it acquires the deep MOND form of Milgrom/Bekenstein’s gravity. The energy momentum of \ leads to another add on to Newton acceleration. Both additional accelerations together imply a MOND-ian phenomenology of the model. It has unusual transition functions \, \nu (...) _w\). They imply higher phantom energy density than in the case of the more common MOND models with transition functions \, \, \mu _2\). A considerable part of it is due to the scalar field’s energy density which, in our model, gives a scale and generally covariant expression for the self-energy of the gravitational field. (shrink)

The determination of inertia by matter is looked at in general relativity, where inertia can be represented by affine or projective structure. The matter tensor T seems to underdetermine affine structure by ten degrees of freedom, eight of which can be eliminated by gauge choices, leaving two. Their physical meaning---which is bound up with that of gravitational waves and the pseudotensor t, and with the conservation of energy-momentum---is considered, along with the dependence of reality on invariance and of causal (...) explanation on conservation. (shrink)

A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and (...) vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, our reformulation retains the potentially important antisymmetric contribution. (shrink)

En este artículo pretendo desmantelar la opinión generalizada según la cual una interpretación relacional del espaciotiempo no es posible. Centro mi atención en el hecho de que las variables dinámicas usualmente están asociadas a objetos materiales en las teorías físicas. El tensor métrico de la Teoría General de la Relatividad (TGR) es un objeto dinámico así que —sostengo— este debe ser mejor entendido como un campo material en toda regla. Este argumento me lleva a vincular la naturaleza relacional del (...) espaciotiempo a las dificultades para formular una genuina ley de conservación de energía-momento en la TGR.I will try to dismantle the widespread impression that a relational account of spacetime is not possible. I concentrate on the fact that dynamical variables are usually linked to material objects in physical theories. The metric tensor field of GR is a dynamical object so, I claim, it should be viewed as a matter field. The argument links the relational ontological status of spacetime to the failure to provide a genuine law of energy-momentum conservation within General Relativity. (shrink)