Francesco Martini

A novel and versatile polarization-entanglement scheme is adopted to investigate the violation of the EPR local realism for a non-maximally entangled two-photon system according to the recent “nonlocality proof” by Lucien Hardy. In this context the adoption of a sophisticated detection method allows direct determination of any “element of physical reality” (viz., determined “with probability equal to unity” in the words of Einstein, Podolsky and Rosen) for the pair system within complete measurements that are largely insensitive to the detector quantum-efficiencies and noise

The traditional standard theory of quantum mechanics is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper :858–873, 2015) we presented a proof of the spin–statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics”. In the present paper, by the same theory the proof of the spin–statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin–statistics connection observed in Nature :858–873, 2015). The present proof of the spin–statistics theorem is simpler than the one presented in Santamato and De Martini :858–873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

The traditional standard quantum mechanics theory is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle”. A complete and straightforward solution of the spin–statistics problem is presented on the basis of the “conformal quantum geometrodynamics” theory. This theory provides a Weyl-gauge invariant formulation of the standard quantum mechanics and reproduces successfully all relevant quantum processes including the formulation of Dirac’s or Schrödinger’s equation, of Heisenberg’s uncertainty relations and of the nonlocal EPR correlations. When the conformal quantum geometrodynamics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the “intrinsic helicity”. This property, not considered in the Standard Quantum Mechanics, determines the correct spin–statistics connection observed in Nature

A rigorous ab initio derivation of the (square of) Dirac’s equation for a particle with spin is presented. The Lagrangian of the classical relativistic spherical top is modified so to render it invariant with respect conformal changes of the metric of the top configuration space. The conformal invariance is achieved by replacing the particle mass in the Lagrangian with the conformal Weyl scalar curvature. The Hamilton-Jacobi equation for the particle is found to be linearized, exactly and in closed form, by an ansatz solution that can be straightforwardly interpreted as the “quantum wave function” of the 4-spinor solution of Dirac’s equation. All quantum features arise from the subtle interplay between the conformal curvature acting on the particle as a potential and the particle motion which affects the geometric “pre-potential” associated to the conformal curvature itself. The theory, carried out here by assuming a Minkowski metric, can be easily extended to arbitrary space-time Riemann metric, e.g. the one adopted in the context of General Relativity. This novel theoretical scenario appears to be of general application and is expected to open a promising perspective in the modern endeavor aimed at the unification of the natural forces with gravitation

Hearsay or indirect testimony receives little discussion even today in epistemology, and yet it represents one of the cardinal modes for the transmission of knowledge and for human cognitive development. It suffices to think of school education whereby a student listens to teachers reporting knowledge acquired, often indirectly, from the most varied sources such as text books, newspapers, personal memory, television, etc… Or let us consider the importance of oral tradition in the social and cultural development of civilisations. Or even let us call to mind the learning process of infants who, only thanks to the knowledge learned from others, succeed in learning the language. Finally, with the emerging digital technology, the information gleaned from third parties is influencing the creation of knowledge in a full gamut of fields, in a quasi-comprehensive manner. This leads us to claim that hearsay, despite the reductionist conceptual scheme to which epistemology has confined it in that indirect testimony, is in any case quintessential in the dissemination of knowledge. This work fully expounds upon the basic mechanism of indirect testimonial transmission and provides an epistemologically founded explanation of the cognitive possibilities of hearsay by investigating, in the light of the anti-reductionist paradigm, three mutually connected epistemic properties, namely trust, reputation and coherence, that are key in the epistemic justification of the truth acquired via an indirect testimony