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. (shrink)

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. (shrink)

Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space-like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel “Macro-Macro” paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N≈105 particles. Crucial experimental issues as the violation of Bell’s inequalities by the Macro-Macro system are considered.

In this paper we analyze the resilience to decoherence of the Macroscopic Quantum Superpositions (MQS) generated by optimal phase-covariant quantum cloning according to two coherence criteria, both based on the concept of Bures distance in Hilbert spaces. We show that all MQS generated by this system are characterized by a high resilience to decoherence processes. This analysis is supported by the results of recent MQS experiments of N=3.5×104 particles.

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. (shrink)

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. (shrink)