arXiv subjects
Publications and source records attributed to Miguel Socolovsky.
We show that when the proper description of the behaviour of individual photons or spin 1/2 particles in a spherically symmetric entangled pair is done through the use of the density matrix, the Leggett's inequality is not violated by quantum mechanics.
We show that the collapse of the wave function of an entangled state of two spin 1/2 particles or two photons in the singlet state can be geometrically understood as a change of fibre bundles.
We consider the so called Legget inequalities which are deduced from the assumption of general (local or non-local) realism plus the arrow of time preservation. Then, instead of assuming cryto-nonlocal hidden variables, we assume any (local or non-local) realism compatible with the joint and non-joint expected values dictated by quantum mwechaanics. Hence, we prove that this double assumption is not consistent, since the corresponding general Leggett inequalities are violated by quantum mechanics. Thus, realism plus arrow of time preservation and quntum mechanics are not compatible. In other words, quantum mechanics cannot be completed with any (local or non-local) hidden variables, provide we assume the common sense of the arrow of time. The result would deserve to be experimentally tested and we discuss why it is not invalidated by hidden variable theories as the one from Bohm.
Strictly working in the framework of the nonrelativistic quantum mechanics of a spin 1/2 particle coupled to an external electromagnetic field, we show, by explicit construction, the existence of a charge conjugation operator matrix which defines the corresponding antiparticle wave function and leads to the galilean and gauge invariant Schroedinger-Pauli equation satisfied by it.
We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.
Using the standard representation of the Dirac equation we show that, up to signs, there exist only TWO SETS of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T). In both cases, P^2=-1, and then two succesive applications of the parity transformation to spin 1/2 fields NECESSARILY amounts to a 2πrotation. Each of these sets generates a non abelian group of sixteen elements, G_1 and G_2, which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to C. It turns out that G_1 is isomorphic to D_8 x Z_2, where D_8 is the dihedral group of eight elements (the symmetries of the square) and Z_2 is isomorphic to S^0 (the 0-sphere); while G_2 is isomorphic to a certain semidirect product of D_8 and Z_2. Instead, the corresponding quantum operators for C, P, and T generate a UNIQUE group G, which we call THE CPT GROUP OF THE DIRAC FIELD, and which is isomorphic to Q x Z_2, where Q is the quaternion group. This group, however, is compatible only with the second of the above two matrix solutions, namely with G_2, which is then called THE MATRIX CPT GROUP. It is interesting to remark that G_1, G_2, and G are the only non abelian groups of sixteen elements with three generators. Finally, the matrix groups are also given in the Weyl and Majorana representations, suitable for taking the massless limit and for describing self-conjugate fields.