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.
The present work reports on an extended research endeavor focused on the theoretical and experimental realization of a macroscopic quantum superposition (MQS) made up with photons. As it is well known, this intriguing, fundamental quantum condition i
s at the core of a famous argument conceived by Erwin Schroedinger, back in 1935. The main experimental challenge to the actual realization of this object resides generally on the unavoidable and uncontrolled interactions with the environment, i.e. the decoherence leading to the cancellation of any evidence of the quantum features associated with the macroscopic system. The present scheme is based on a nonlinear process, the quantum injected optical parametric amplification, that maps by a linearized cloning process the quantum coherence of a single - particle state, i.e. a Micro - qubit, into a Macro - qubit, consisting in a large number M of photons in quantum superposition. Since the adopted scheme was found resilient to decoherence, the MQS demonstration was carried out experimentally at room temperature with $Mgeq $ $10^{4}$. This result elicited an extended study on quantum cloning, quantum amplification and quantum decoherence. The related theory is outlined in the article where several experiments are reviewed such as the test on the no-signaling theorem and the dynamical interaction of the photon MQS with a Bose-Einstein condensate. In addition, the consideration of the Micro - Macro entanglement regime is extended into the Macro - Macro condition. The MQS interference patterns for large M were revealed in the experiment and the bipartite Micro-Macro entanglement was also demonstrated for a limited number of generated particles: $Mprecsim 12$. At last, the perspectives opened by this new method are considered in the view of further studies on quantum foundations and quantum measurement.
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 present the proposition of an experiment in which the multiphoton quantum superposition consisting of N= 10^5 particles generated by a quantum-injected optical parametric amplifier (QI-OPA), seeded by a single-photon belonging to an EPR entangled
pair, is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize a Macroscopic Quantum Superposition (MQS) involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in space-like separated distant places.
We believe that a recent, unconventional theoretical work published in Physical Review Letters 103, 113601 (2009) by Sekatsky, Brunner, Branciard, Gisin, Simon, albeit appealing at fist sight, is highly questionable. Furthermore, the criticism raised
by these Authors against a real experiment on Micro - Macro entanglement recently published in Physical Review Letters (100, 253601, 2008) is found misleading and to miss its target.
The optical spin-orbit coupling occurring in a suitably patterned nonuniform birefringent plate known as `q-plate allows entangling the polarization of a single photon with its orbital angular momentum (OAM). This process, in turn, can be exploited f
or building a bidirectional spin-OAM interface, capable of transposing the quantum information from the spin to the OAM degree of freedom of photons and textit{vice versa}. Here, we experimentally demonstrate this process by single-photon quantum tomographic analysis. Moreover, we show that two-photon quantum correlations such as those resulting from coalescence interference can be successfully transferred into the OAM degree of freedom.
We show that all Macroscopic Quantum Superpositions (MQS) based on phase-covariant quantum cloning are characterized by an anomalous high resilence to the de-coherence processes. The analysis supports the results of recent MQS experiments and leads t
o conceive a useful conjecture regarding the realization of complex decoherence - free structures for quantum information, such as the quantum computer.
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 M
acro - Macro paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N=10^5 particles. Crucial experimental issues as the violation of Bells inequalities by the Macro - Macro system are considered.
