Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

Authors

  • G. Gómez Institut de Matematica Multidisciplinaria, Universitat Politecnica de Valencia, Camı de Vera s/n 46022 Valµencia, SPAIN,
  • I. Kotsireas Dept. of Physics and Computer Science, Wilfrid Laurier University Science Building, Room N2078, 75 University Ave. W. Waterloo, ON, N2L 3C5, CANADA
  • I. Gkigkitzis Departments of Mathematics, East Carolina University 124 Austin Building, East Fifth Street Greenville NC 27858-4353, USA.
  • I. Haranas Dept. of Physics and Computer Science, Wilfrid Laurier University Science Building, Room N2078, 75 University Ave. W. Waterloo, ON, N2L 3C5, CANADA.
  • M.J. Fullana Institut de Matematica Multidisciplinaria, Universitat Politecnica de Valencia, Camı de Vera s/n 46022 Valencia, SPAIN,

DOI:

https://doi.org/10.31349/RevMexFis.64.18

Keywords:

De Broglie Bohm, curvature of space time, metric tensor, general relativity, hydrogen-like atoms, electron trajectory, quantum potential, wave function, numerical methods, geodesics, Lorenz geometry.

Abstract

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

Downloads

Additional Files

Published

2018-01-30

How to Cite

[1]
G. Gómez, I. Kotsireas, I. Gkigkitzis, I. Haranas, and M. Fullana, “Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics”, Rev. Mex. Fís., vol. 64, no. 1 Jan-Feb, pp. 18–29, Jan. 2018.

Issue

Vol. 64 No. 1 Jan-Feb (2018): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.