Spacetime curvature, a potential result of the quantum mass/energy Information Entropy
Résumé
This work proposes a possible proof on how the spacetime curvature is created by any object (mass/energy) and suggests a mathematical model that may conciliate quantum mechanics and general relativity. As each elementary particle is a fluctuation in its particular field in Quantum Fiel Theory and follows quantum mechanics properties, the wave function of each elementary particle of an object is deformed at each spacetime point in the presence of another massive object (set of particles). This comes from the fact that the wave functions of the particles of the two massive objects in their respective quantum fields may be aggregated and hence modifies in time and space the wave functions values. This could subsequently change the location of the object less massive as the probabilities of the presence of the elementary particles are getting higher next to the highly massive objects: the less massive objects are correlated to the highly massive one. In this study we suppose that between two nearest spatial points Nx and N2 there is an infinity of quantum-mechanically possible Time paths in quantum vacuum (or what we will call Time paths) as assumed in path integrals theory. Using a modified Information Entropy of Shannon into the complex probabilities on the Time paths arriving to N2 from any Nx, we prove in this paper that this entropy on the trajectories is equivalent to the Hilbert-Einstein Lagrangian density which leads to the Einstein general relativity equation by minimizing this entropy or in other words by applying the principle of least action.his work proposes a possible proof on how the spacetime curvature is created by any object (mass/energy) and suggests a mathematical model that may conciliate quantum mechanics and general relativity. As each elementary particle is a fluctuation in its particular field in Quantum Fiel Theory and follows quantum mechanics properties, the wave function of each elementary particle of an object is deformed at each spacetime point in the presence of another massive object (set of particles). This comes from the fact that the wave functions of the particles of the two massive objects in their respective quantum fields may be aggregated and hence modifies in time and space the wave functions values. This could subsequently change the location of the object less massive as the probabilities of the presence of the elementary particles are getting higher next to the highly massive objects: the less massive objects are correlated to the highly massive one. In this study we suppose that between two nearest spatial points Nx and N2 there is an infinity of quantum-mechanically possible Time paths in quantum vacuum (or what we will call Time paths) as assumed in path integrals theory. Using a modified Information Entropy of Shannon into the complex probabilities on the Time paths arriving to N2 from any Nx, we prove in this paper that this entropy on the trajectories is equivalent to the Hilbert-Einstein Lagrangian density which leads to the Einstein general relativity equation by minimizing this entropy or in other words by applying the principle of least action.
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