Photons uncertainty removes Einstein-Podolsky-Rosen paradox

Einstein, Podolsky and Rosen (EPR) argued that the quantum-mechanical probabilistic description of physical reality had to be incomplete, in order to avoid an instantaneous action between distant measurements. This suggested the need for additional "hidden variables", allowing for the recovery of determinism and locality, but such a solution has been disproved experimentally. Here, I present an opposite solution, based on the greater indeterminism of the modern quantum theory of Particle Physics, predicting that the number of photons is always uncertain. No violation of locality is allowed for the physical reality, and the theory can fulfill the EPR criterion of completeness.Comment: 12 pages, 2 figure

New Neutral Gauge Bosons and New Heavy Fermions in the Light of the New LEP Data

We derive limits on a class of new physics effects that are naturally present in grand unified theories based on extended gauge groups, and in particular in $E_6$ and $SO(10)$ models. We concentrate on $i$) the effects of the mixing of new neutral gauge bosons with the standard $Z_0$; $ii$) the effects of a mixing of the known fermions with new heavy states. We perform a global analysis including all the LEP data on the $Z$ decay widths and asymmetries collected until 1993, the SLC measurement of the left--right asymmetry, the measurement of the $W$ boson mass, various charged current constraints, and the low energy neutral current experiments. We use a top mass value in the range announced by CDF. We derive limits on the $Z_0$--$Z_1$ mixing, which are always \lsim 0.01 and are at the level of a few {\it per mille} if some specific model is assumed. Model-dependent theoretical relations between the mixing and the mass of the new gauge boson in most cases require $M_{Z'} > 1\,$TeV. Limits on light--heavy fermion mixings are also largely improved with respect to previous analyses, and are particularly relevant for a class of models that we discuss.Comment: 12 pages (including two tables), revised version, accepted for publication in Phys. Lett. B. Includes a discussion of the m_t and alpha_s dependence of the bounds on the Z' mass and the fermion mixing

Bivariate Infinite Series Solution of Kepler's Equations

A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on an iterative procedure for the analytical computation of all the higher-order partial derivatives of the eccentric anomaly with respect to the eccentricity $e$ and mean anomaly $M$ in a given base point $(e_c,M_c)$ of the $(e,M)$ plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of $(e_c,M_c)$, and their convergence is studied numerically. In particular, the polynomials that are obtained by truncating the infinite series up to the fifth degree reach high levels of accuracy in significantly large regions of the parameter space $(e,M)$. Besides their theoretical interest, these series can be used for designing 2-D spline numerical algorithms for efficiently solving Kepler's equations for all values of the eccentricity and mean anomaly