arXiv subjects

Gustavo R. Gonzalez-Martin

Publications and source records attributed to Gustavo R. Gonzalez-Martin.

15 recordsLinked to original sources

arXiv2014

Geometric gravitational origin of neutrino oscillations and mass-energy

A mass-energy scale for neutrinos was calculated from the null cone curvature using geometric concepts. The scale is variable depending on the gravitational potential and the trajectory inclination with respect to the field direction. The proposed neutrino covariant equation provides the adequate curvature. The mass-energy at the Earth surface varies from a horizontal value 0.402 eV to a vertical value 0.569 eV. Earth spinor waves with winding numbers n show squared energy differences within ranges from 2.05 x 10*(-3) to 4.10 x 10*(-3) eV*2 for n=0,1 neutrinos and from 3.89 x 10*(-5) to 7.79 x 10*(-5) eV*2 for n=1,2 neutrinos. These waves interfere and the different phase velocities produce neutrino-like oscillations. The experimental results for atmospheric and solar neutrino oscillation mass parameters respectivelly fall within these theoretical ranges. Neutrinos in outer space, where interactions may be neglected, appear as particles travelling with zero mass on null geodesics. These gravitational curvature energies are consistent with neutrino oscillations, zero neutrino rest masses and Einstein's General Relativity and energy mass equivalence principle. When analyzing or averaging experimental neutrino mass-energy results of different experiments on the Earth it is of interest to consider the possible influence of the trajectory inclination angle.

physics.gen-ph↗

arXiv2011

Slow photon delay and the neutrino velocity

Starting from the coordinate system used by Einstein to find the bending of light rays by gravitational fields we calculate the effect of the Earth gravitational energy along a hypothetical photon null path on the geoid non inertial system. There is an energy term, relative to an inertial system, which may be interpreted as a small time-relative "dressed" physical rest mass correction to the photon null mass. This relative gravitational potential energy determines a proper time delay proportional to the laboratory non inertial flying time interval along the trajectory with a small factor 5.276x10-5. We also use a geometric technique based on Ehresmann connections to compare the parallel transport of the photon vector and the neutrino spinor on null trajectories. The result is that there is a theoretical neutrino time delay from its inertial path which is half the delay of the photon. Applying these delays to a hypothetical particle trajectory from the CERN SPS/CNGS target to the LNGS OPERA detector we find that the difference between the experimental and theoretical results falls within the reported experimental errors. The delayed neutrino is faster than the delayed photon but its speed is smaller than the fundamental constant c. The results also indicate that neutrino trajectories, as photon trajectories, are affected by gravitational fields but with smaller effects.

physics.gen-ph↗

arXiv2009

The G Gravitational Parameter and the Concepts of Mass and Dark Matter

The gravitational coupling parameter G is determined by a non riemannian curvature scalar of a background substratum. This substratum represents an inertial solution to the nonlinear equations of a geometric unified theory and provides a limit solution to general solutions in the theory. When a solution approaches the substratum solution as a limit we physically obtain a newtonian limit of the gravitational sector of the unified theory. The curvature scalar is determined by the interaction mass-energy content of the solution. In the limit the equation reduces to Poisson equation and the curvature scalar reduces to the constant substratum curvature scalar which determines Newton gravitational constant G. Outside the limit the curvature parameter replaces the newtonian constant G as the coupling parameter of Einstein equation of gravitation. This new parameter may be approximately constant in certain physical conditions but, in general should be considered a variable which depends on the matter and energy on space-time. This effect and the geometric structure of matter and fields may be interpreted as dark matter effects. The substratum also determines a constant mass parameter for field excitations which obey the Dirac equation and behave as particles. Physically we consider that the substratum provides two related mass scales: the gravitational constant G characterizes a macroscopic mass scale and a fundamental particle mass m characterizes a microscopic mass scale. The substratum geometrically represents the physical concept of inertial system.

physics.gen-ph↗

arXiv2008

Binding Energies of the Alpha Particle and the A=3 Isobars from a Theoretical Geometric Model

We assume a triple geometric structure for the electromagnetic nuclear interaction. This nuclear electromagnetism is used to calculate the binding energies of the alpha particle and the A=3 isobar nuclides. The approximation for the resultant wave equation which lead to the deuteron binding energy from the modified Mathieu equation for the radial eigenvalue equation also establishes proton-electron-proton magnetic bonds in these nuclides and determines their binding energies. Completely theoretical calculations give 28.5 Mev., 7.64 Mev. and 8.42 Mev. for the binding energies of the alpha particle, the helium 3 isotope and tritium respectively. These values admit correction factors due to the approximations made.

physics.gen-ph↗

arXiv2008

Binding Energies of the Deuteron, the Neutron and the Alpha Particle from a Theoretical Geometric Model

We assume a triple geometric structure for the electromagnetic nuclear interaction. This nuclear electromagnetism is used to calculate the binding energies of the deuteron and the neutron. The corresponding Pauli quantum wave equation in a geometric theory, with the SU(2) electromagnetic coupling instead of the standard "minimal" coupling, contains a 1/r to-the-fourth-power, short-range attractive magnetic potential term. This term, produced by the odd part of the electromagnetic potential, may be responsible for a strong nuclear interaction. An approximation for the resultant wave equation leads to the modified Mathieu equation. Completely theoretical calculations give 2.205 Mev, 0.782 Mev and 27.6 Mev for the binding energies of the deuteron, the neutron and the alpha particle respectively. These values admit correction factors due to the approximations made.

physics.gen-ph↗

arXiv2007

Massive Connection Bosons

It is shown that geometric connection field excitations acquire mass terms from a geometric background substratum related to the structure of space-time. Commutation relations in the electromagnetic su(2) sector of the connection limit the number of possible masses. Calculated results, within corrections of order alpha, are very close to the experimental masses of the intermediate W, Z bosons.

physics.gen-ph↗

arXiv2004

Lepton and meson masses

The lepton mass ratios are calculated using a geometric unified theory, taking the leptons as the only three possible families of topological excitations of the electron or the neutrino. The theoretical results give 107.5916 Mev for the muon mass and 1770.3 Mev for the tau mass using the mass ratios. Using the additional geometric interaction energy in a muon-neutrino system, the main leptonic mass contribution to the pion and kaon mass is calculated to be, respectively, 140.88 Mev and 494.76 Mev. The necessary first order corrections, due to the interaction of the excitations, should be of the order of the discrepancies with experimental values. The three geometric families of leptonic excitations may be related to a quark structure.

physics.gen-ph↗

arXiv2004

Magnetic moment of the proton

The magnetic moment of the proton is calculated using a geometric unified theory. The geometry determines a generalized Pauli equation showing anomalous terms due to the triplet proton structure. The theoretical result gives a bare anomalous Lande gyromagnetic g-factor close to the experimental value. The necessary radiative corrections should be included in the actual theoretical dressed value. The first order correction raises the value to 2(2.7796). Similarly we obtain for the neutron gyromagnetic g-factor the value 2(1.9267).

physics.gen-ph↗

arXiv2000

p/e Geometric Mass Ratio

A previously proposed geometric definition of mass in terms of energy, in a geometrical unified theory, is used to obtain a numerical expression for a ratio of masses of geometrical excitations. The resultant geometric ratio is approximately equal the ratio of the proton to electron physical masses.

physics.gen-ph↗

arXiv2000

The Alpha Constant from Relativistic Groups

The value of the alpha constant, known to be equal to an algebraic expression in terms of pi and entire numbers related to certain group volumes, is derived from the relativistic structure group of a geometric unified theory, its subgroups and corresponding symmetric space quotients.

physics.gen-ph↗

arXiv2000

A Program for the Geometric Classification of Particles and Relativistic Interactions

Geometric relativistc interactions in a new geometric unified theory are classified using the dynamic holonomy groups of the connection. Physical meaning may be given to these interactions if the frame excitations represent particles. These excitations have algebraic and topological quantum numbers. The proton, electron and neutrino may be associated to the frame excitations of the three dynamical holonomy subgroups. In particular, the proton excitation has a dual mathematical structure of a triplet of subexcitations. Hadronic, leptonic and gravitational interactions correspond to the same subgroups. The background geometry determines non trivial fiber bundles where excitations live, introducing topological quantum numbers that classify families of excitations. From these three particles, the only stable ones, it may be possible, as suggested by Barut, to build the rest of the particles. The combinations of the three fundamental excitations display SU(3)xSU(2)xU(1) symmetries.

physics.gen-ph↗

arXiv2000

Relativistic Geometry and Quantum Electrodynamics

Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field operator. Because of the inherent geometric algebraic structure these operators obey the standard commutation rules of QED. If we work with excitations, we need to use statistical theory when considering the evolution of microscopic subsystems. The use of classical statistics, in particular techniques of irreversible thermodynamics, determine that the probability of absorption or emission of a geometric excitation is a function of the classical energy density. Emission and absorption of geometric excitations imply discrete changes of certain physical variables, but with a probability determined by its wave energy density. Hence, this geometric theory, without contradicting the fundamental aspects of quantum physics, provides a geometric foundation for the theory.

physics.gen-ph↗

arXiv2000

Relativistic Geometry and Weak Interactions

Geometric interactions in a new relativistic geometric unified theory include interactions other than gravitation and electromagnetism. In a low energy limit one of these interactions leads essentially to a Fermi type theory of weak interactions including the Hamiltonian and coupling constant.

physics.gen-ph↗

arXiv2000

Charge to Magnetic Flux Ratios

It is shown that if the carriers in the fractional quantum Hall effect are taken as geometrical excitations with quanta of charge e and magnetic flux h/2e, as proposed in a previous publication, the calculated results are compatible with the series of fractions obtained experimentally.

cond-mat.mes-hall↗

arXiv2000

The Geometric Gravitational Internal Problem

In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian limit where we obtain Poisson's equation.

gr-qc↗