scholarly journals On geometro dynamics in atomic stationary states

2019 ◽  
Vol 65 (2) ◽  
pp. 148
Author(s):  
G. Gómez i Blanch ◽  
And M.J. Fullana i Alfonso
Keyword(s):  
Wave Function ◽  
Lorentzian Manifold ◽  
Momentum Tensor ◽  
Stationary States ◽  
Dynamic Approach ◽  
Metric Tensor ◽  
Lorentzian Metric ◽  
Non Local ◽  
Bohm Model ◽  
De Broglie Bohm

In a previous paper [G.Gomez Blanch and M.J.Fullana, 2017] we dened, in the frame of a geometro-dynamic approach, a metric corresponding to a lorentzian spacetime were the electron stationary trajectories in an hydrogenoid atom, derived from the de Broglie-Bohm model, are geodesics. In this paper we want to complete this purpose: we will determinate the remaining relevant geometrical elements of that approach and we will calculate the energetic density component of the energy-momentum tensor. We will discuss the meaning of the obtained results and their relationship with other geometro-dynamic approaches.Furthermore, we will derive a more general relationship between the lorentzian metric tensor and the wave function for general stationary states. The electron description by the wave function ψ in the Euclidean space and time is shown equivalent to the description by a metric tensor in an lorentzian manifold. In our approach, the particle acquires a determining role over thewave function, in a similar manner as the wave function determines the movement of the particle. This dialectic approach overcomes the de Broglie-Bohm model. And furthermore, a non local element (the quantum potential) is introduced in the model, that therefore goes beyond the relativistic locality.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

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.

Gravity, stability and cosmological models

2017 ◽  
Vol 26 (12) ◽  
pp. 1743026
Author(s):  
Asher Yahalom
Keyword(s):  
Stability Analysis ◽  
Cosmological Model ◽  
Cosmological Constant ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Lorentzian Metric ◽  
Standard Cosmological Model ◽  
Flat Spacetimes ◽  
Stable Solutions ◽  
The Universe

Stability analysis plays a major rule in our understanding of nature. For example it was shown that among empty flat spacetimes only those with a Lorentzian metric are stable [A. Yahalom, Found Phys. 38 (2008) 489–497; Int. J. Mod. Phys. D 18(4) (2009) 2155–2158]. However, the universe is not empty and the energy momentum tensor is metric dependent an thus effects stability. In this essay we concentrate on simple perturbations of the standard cosmological model with and without cosmological constant which is based on a uniform mass distribution. The results suggest that while Euclidean, open or closed section models are valid solutions, the choice of stable solutions is limited. In particular, the popular Lambda-CDM model is unstable.

Phase space generalization of the de Broglie-Bohm model

1997 ◽  
Vol 27 (6) ◽  
pp. 845-863 ◽  
Author(s):  
Roderick I. Sutherland
Keyword(s):  
Phase Space ◽  
Bohm Model ◽  
De Broglie Bohm

Geometric phase, quantum measurements, and the de Broglie–Bohm model

1997 ◽  
Vol 56 (2) ◽  
pp. 1638-1641 ◽  
Author(s):  
Erik Sjöqvist ◽  
Henrik Carlsen
Keyword(s):  
Geometric Phase ◽  
Quantum Measurements ◽  
Bohm Model ◽  
De Broglie Bohm

scholarly journals Partly non-local potentials in the model triton

1977 ◽  
Vol 55 (10) ◽  
pp. 884-897 ◽  
Author(s):  
Dale D. Ellis
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Deuteron Wave Function ◽  
Form Factors ◽  
Zero Energy ◽  
Normalization Constant ◽  
Separable Potentials ◽  
Non Local ◽  
Local Potentials ◽  
Asymptotic Normalization Constant

Binding energy, ET, wave function, form factor, and asymptotic normalization constant, CT, have been calculated for the model triton using two classes of phase equivalent potentials: partly non-local (PNL) potentials, and rank-two separable potentials. The results are compared with those of Fiedeldey. The binding energy is sensitive to the deuteron wave function and zero-energy wound integral. The triton form factors depend on ET and the deuteron wave function. CT is almost insensitive to variations in the PNL potentials, but increases with ET for the separable potentials.

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