The traditional Standard Quantum Mechanics is unable to solve the Spin-Statistics problem, i.e. to justify the utterly important Pauli Exclusion Principle. We show that this is due to the non completeness of the standard theory due to an arguable con
ception of the spin as a vector characterizing the rotational properties of the elementary particles. The present Article presents a complete and straightforward solution of the Spin-Statistics problem on the basis of the Conformal Quantum Geometrodynamics, a theory that has been proved to reproduce successfully all relevant processes of the Standard Quantum Mechanics based on the Dirac or Schrodinger equations, including Heisenberg uncertainty relations and nonlocal EPR correlations. When applied to a system made of many identical particles, an additional property of all elementary particles enters naturally into play: the intrinsic helicity. This property determines the correct Spin-Statistics connection observed in Nature.
The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyls differential geometry are presented. The theory applied to the case of the relativistic single quantum spin 1/2 leads a novel and unconventional derivation
of Diracs equation. The further extension of the theory to the case of two spins 1/2 in EPR entangled state and to the related violation of Bells inequalities leads, by an exact albeit non relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.
Since the 1935 proposal by Einstein Podolsky and Rosen the riddle of nonlocality, today demonstrated by innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper
tackles the problem by a non relativistic approach based on the Weyls conformal differential geometry applied to the Hamilton-Jacobi solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the nonlocality rests on the entanglement of the spin internal variables, playing the role of hidden variables. At the end, the violation of the Bell inequalities is demonstrated without recourse to the common nonlocality paradigm. A discussion over the role of the % textit{internal space} of any entangled dynamical system involves deep conceptual issues, such the textit{indeterminism} of quantum mechanics and explores the in principle limitations to any exact dynamical theory when truly hidden variables are present. Because of the underlying geometrical foundations linking necessarily gravitation and quantum mechanics, the theory presented in this work may be considered to belong to the unifying quantum gravity scenario.
A rigorous textit{ab initio} derivation of the (square of) Diracs equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyls conformal geometry is found to be
linearized, exactly and in closed form, by an textit{ansatz} solution that can be straightforwardly interpreted as the quantum wave function $psi_4$ of the 4-spinor Diracs equation. In particular, all quantum features of the model arise from a subtle interplay between the conformal curvature of the configuration space acting as a potential and Weyls pre-potential, closely related to $psi_4$, which acts on the particle trajectory. The theory, carried out here by assuming a Minkowsky 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, referred to as Affine Quantum Mechanics, 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.
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of the mater
ial interior, as it only uses knowledge of the reflection amplitudes for its surface. Therefore, our results are valid for all homogeneous surfaces, including layered systems and metamaterials, at all temperatures. In particular, we obtain new formulae for the near-field region, which are important for interpreting the numerous current experiments probing proximity effects for macroscopic and/or microscopic bodies separated by small empty gaps. By use of Onsagers reciprocity relations, we obtain also the general symmetry properties that must be satisfied by the reflection matrix of any material.
