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S. Antoci

Publications and source records attributed to S. Antoci.

At least 19 recordsLinked to original sources
arXiv2012

Confinement in Einstein's unified field theory

After recalling the mathematical structure of Einstein's Hermitian extension of the gravitational theory of 1915, the problem, whether its field equations should admit of phenomenological sources at their right-hand sides, and how this addition should be done, is expounded by relying on a thread of essential insights and achievements by Schrödinger, Kursunoglu, Lichnerowicz, Hély and Borchsenius. When sources are appended to all the field equations, from the latter and from the contracted Bianchi identities a sort of gravoelectrodynamics appears, that totally departs from the so called Einstein-Maxwell theory, since its constitutive equation, that rules the link between inductions and fields, is a very complicated differential relation that allows for a much wider, still practically unexplored range of possible occurrences. In this sort of theory one can allow for both an electric and a magnetic four-current, which are not a physically wrong replica of each other, like it would occur if both these currents were allowed in Maxwell's vacuum. Particular static exact solutions show that, due to the peculiar constitutive equation, while electric charges with a pole structure behave according to Coulomb's law, magnetic charges with a pole structure interact with forces not depending on their mutual distance. The latter behaviour was already discovered by Treder in 1957 with an approximate calculation, while looking for ordinary electromagnetism in the theory. He also showed that in the Hermitian theory magnetic charges of unlike sign mutually attract, hence they are permanently confined entities. The exact solutions confirm this finding, already interpreted in 1980 by Treder in a chromodynamic sense.

gr-qc↗
arXiv2007

The issue of photons in dielectrics: Hamiltonian viewpoint

The definition of the photon in the vacuum of general relativity provided by Kermack et al. and by Synge is extended to nondispersive, nonhomogeneous, isotropic dielectrics in arbitrary motion by Hamiltonian methods that rely on Gordon's effective metric. By these methods the old dilemma, whether the momentum-energy vector of the photon in dielectrics is timelike or spacelike in character, is shown to reappear under a novel guise.

gr-qc↗
arXiv2007

Hans-Juergen Treder and the discovery of confinement in Einstein's unified field theory

In the year 1957, when interest in Einstein's unified field theory was fading away for lack of understanding of its physical content, Treder performed a momentous critical analysis of the possible definitions of the electric four-current in the theory. As an outcome of this scrutiny he was able to prove by the E.I.H. method that properly defined point charges, appended at the right-hand side of the field equation $R_{[[μν],λ]}=0$, interact mutually with Coulomb-like forces, provided that a mutual force independent of distance is present too. This unwanted, but unavoidable addition, could not but lay further disbelief on the efforts initiated by Einstein and Schroedinger one decade earlier. However in 1980 Treder himself recalled that the potential $ϕ=a/r+cr$, found by him in 1957, was the one used by particle physicists to account phenomenologically for the spectrum of bound quark systems like mesons. Exact solutions have later confirmed beyond any doubt that Einstein's unified field theory does account in a simple way, already in classical form, for the confinement of pole charges defined by the four-current first availed of by Treder. In the present paper it is proposed, ad memoriam, a thorough recollection of the article published by Treder in 1957, showing the way kept by him to find what would have been later recognized as confinement in Einstein's unified field theory.

physics.hist-ph↗
arXiv2005

The topology of Schwarzschild's solution and the Kruskal metric

Kruskal's extension solves the problem of the arrow of time of the ``Schwarzschild solution'' through combining two Hilbert manifolds by a singular coordinate transformation. We discuss the implications for the singularity problem and the definition of the mass point. The analogy set by Rindler between the Kruskal metric and the Minkowski spacetime is investigated anew. The question is answered, whether this analogy is limited to a similarity of the chosen "Bildräume'', or can be given a deeper, intrinsic meaning. The conclusion is reached by observing a usually neglected difference: the left and right quadrants of Kruskal's metric are endowed with worldlines of absolute rest, uniquely defined through each event by the manifold itself, while such worldlines obviously do not exist in the Minkowski spacetime.

gr-qc↗
arXiv2005

The physical meaning of the "boost-rotation symmetric" solutions within the general interpretation of Einstein's theory of gravitation

The answer to the question, what physical meaning should be attributed to the so-called boost-rotation symmetric exact solutions to the field equations of general relativity, is provided within the general interpretation scheme for the ``theories of relativity'', based on group theoretical arguments, and set forth by Erich Kretschmann already in the year 1917.

gr-qc↗
arXiv2005

The Electrostatics of Einstein's Unified Field Theory

When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély's physically correct metric is adopted.

gr-qc↗
arXiv2004

The Origin of the Electromagnetic Interaction in Einstein's Unified Field Theory with Sources

Einstein's unified field theory is extended by the addition of matter terms in the form of a symmetric energy tensor and of two conserved currents. From the field equations and from the conservation identities emerges the picture of a gravoelectrodynamics in a dynamically polarizable Riemannian continuum. Through an approximate calculation exploiting this dynamical polarizability it is argued that ordinary electromagnetism may be contained in the theory.

gr-qc↗
arXiv2003

Gravitational singularities via acceleration: the case of the Schwarzschild solution and Bach's gamma metric

The so called gamma metric corresponds to a two-parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that rules a deviation from spherical symmetry. It is shown that there is invariantly definable singular behaviour beyond the one displayed by the Kretschmann scalar when a unique, hypersurface orthogonal, timelike Killing vector exists. In this case, a particle can be defined to be at rest when its world-line is a corresponding Killing orbit. The norm of the acceleration on such an orbit proves to be singular not only for metrics that deviate from Schwarzschild's metric, but also on approaching the horizon of Schwarzschild metric itself, in contrast to the discontinuous behaviour of the curvature scalar.

gr-qc↗
arXiv2001

A Rule for the Equilibrium of Forces in the Hermitian Theory of Relativity

When the behaviour of the singularities, which are used to represent masses, charges or currents in exact solutions to the field equations of the Hermitian theory of relativity, is restricted by a no-jump rule, conditions are obtained, which determine the relative positions of masses, charges and currents. Due to these conditions the Hermitian theory of relativity appears to provide a unified description of gravitational, colour and electromagnetic forces.

gr-qc↗
arXiv2001

One thing that general relativity says about photons in matter

Let us abandon for a moment the strict epistemological standpoint of quantum field theory, that eventually comes to declare nonsensical any question about the photon posed outside the quantum theoretical framework. We can then avail of the works by Whittaker et al. and by Synge about the particle and the wave model of the photon in the vacuum of general relativity. We can also rely on important results found by Gordon and by Pham Mau Quan: thanks to Gordon's discovery of an effective metric these authors have been able to reduce to the vacuum case several problems of the electromagnetic theory of dielectrics. The joint use of these old findings allows one to conclude that a quantum theoretical photon in an isotropic dielectric has a classical simile only if the dielectric is also homogeneous.

gr-qc↗
arXiv2001

Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force four-vector. The norm of this force is calculated for Bach's two-body solution, that is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l' is made to vanish. In the limit when, say, l' goes to zero, the norm of the force divided by l' and calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms happen thus to grow without limit when the test body (respectively the vanishing mass l') is kept at rest in a position closer and closer to Schwarzschild's two-surface.

gr-qc↗
arXiv2001

Reconsidering Schwarzschild's original solution

We analyse the Schwarzschild solution in the context of the historical development of its present use, and explain the invariant definition of a singular surface at the Schwarzschild's radius, that can be applied to the Kerr-Newman solution too.

gr-qc↗
arXiv2000

Hermitian extension of the four-dimensional Hooke's law

It has been shown recently that the classical law of elasticity, expressed in terms of the displacement three-vector and of the symmetric deformation three-tensor, can be extended to the four dimensions of special and of general relativity with a physically meaningful outcome. In fact, the resulting stress- momentum-energy tensor can provide a unified account of both the elastic and the inertial properties of uncharged matter. The extension of the displacement vector to the four dimensions of spacetime allows a further possibility. If the real displacement four-vector is complemented with an imaginary part, the resulting complex ``displacement'' four-vector allows for a complex, Hermitian generalisation of the four-dimensional Hooke's law. Let the complex, Hermitian ``stress-momentum-energy'' tensor density built in this way be subjected to the usual conservation condition. It turns out that, while the real part of the latter equation is able to account for the motion of electrically charged, elastic matter, the imaginary part of the same equation can describe the evolution of the electromagnetic field and of its sources. The Hermitian extension of Hooke's law is performed by availing of the postulate of ``transposition invariance'', introduced in 1945 by A. Einstein for finding the nonsymmetric generalisation of his theory of gravitation of 1915.

gr-qc↗
arXiv2000

"Violating'' Clauser-Horne inequalities within classical mechanics

Some authors have raised the question whether the probabilities stemming from a quantum mechanical computation are entitled to enter the Bell and the Clauser-Horne inequalities. They have remarked that if the quantum probabilities are given the status of conditional ones and the statistics for the various settings of the detectors in a given experiment is properly kept into account, the inequalities happen to be no longer violated. In the present paper a classical simile modeled after the quantum mechanical instances is closely scrutinised. It is shown that the neglect of the conditional character of the probabilities in the classical model leads not only to ``violate'' the Clauser-Horne inequalities, but also to contradict the very axioms of classical probability theory.

quant-ph↗
arXiv1999

Electrodynamic forces in elastic matter

A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon's general relativistic derivation of Abraham's electromagnetic energy tensor as starting point. The necessary description of the elastic and of the inertial behaviour of matter is provided through a four dimensional generalisation of Hooke's law, made possible by the introduction of a four dimensional ``displacement'' vector. As intimated by Nordstroem, the physical origin of electrostriction and of magnetostriction is attributed to the change in the constitutive equation of electromagnetism caused by the deformation of matter. The part of the electromagnetic Lagrangian that depends on that deformation is given explicitly for the case of an isotropic medium and the resulting expression of the electrostrictive force is derived, thus showing how more realistic equations of motion for matter subjected to electromagnetic fields can be constructed.

physics.class-ph↗