"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.Comment: 7 pages, 2 eps figure

A four-dimensional Hooke's law can encompass linear elasticity and inertia

The question is examined, whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke's law is found able to account for the inertia of matter; in the flat space, slow motion approximation the field equations for the ``displacement'' four-vector field can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity.Comment: AMS LaTeX, 8 pages, Nuovo Cimento B (in press

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.Comment: 12 pages, one figure; text to appear in Nuovo Cimento

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.Comment: 13 pages, 1 figure. Text to appear in Nuovo Cimento

A forgotten argument by Gordon uniquely selects Abraham's tensor as the energy-momentum tensor for the electromagnetic field in homogeneous, isotropic matter

Given the present status of the problem of the electromagnetic energy tensor in matter, there is perhaps use in recalling a forgotten argument given in 1923 by W. Gordon. Let us consider a material medium which is homogeneous and isotropic when viewed in its rest frame. For such a medium, Gordon's argument allows to reduce the above mentioned problem to an analogous one, defined in a general relativistic vacuum, in presence of a suitably determined effective metric. For the latter problem the form of the Lagrangian is known already, hence the determination of the energy tensor is a straightforward matter. One just performs the Hamiltonian derivative of the Lagrangian chosen in this way with respect to the true metric. Abraham's tensor is thus selected as the electromagnetic energy tensor for a medium which is homogeneous and isotropic in its rest frame.Comment: Plain TeX, 9 pages, no figures, to appear in Nuovo Cimento

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.Comment: 12 pages, one figure; text to appear in Nuovo Cimento

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.Comment: 8 pages; text accepted for publication by Astronomische Nachrichte

Electrostatics and confinement in Einstein's unified field theory

A way for appending sources at the right-hand sides of the field equations of Einstein's unified field theory is recalled. Two exact solutions endowed with point sources in equilibrium are shown, and their physical meaning is discussed.Comment: 4 pages, talk given at MG11, Berlin, July 200