The Gravity of the Classical Klein-Gordon field

The work shows that the evolution of the field of the free Klein-Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been covariantly extended to the curved space-time, the gravity equation (GE), determining the geometry of the space-time, is obtained by minimizing the overall action comprehending the gravitational field. The derived Einstein-like gravity for the KGE field shows an energy-impulse tensor density (EITD) that is a function of the field with the spontaneous emergence of the cosmological pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant(CC). The energy-impulse tensor of the theory shows analogies with the modified Brans-Dick gravity with an effective gravity constant G divided by the field squared. Even if the classical cosmological constant is set to zero, the model shows the emergence of a theory-derived quantum CPTD that, in principle, allows to have a stable quantum vacuum (out of the collapsed branched polymer phase) without postulating a non-zero classical CC. In the classical macroscopic limit, the gravity equation of the KGE field leads to the Einstein equation. Moreover, if the boson field of the photon is considered, the EITD correctly leads to its electromagnetic energy-impulse tensor density. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it tends to zero as the space-time approaches to the flat vacuum, leading to an overall cosmological effect on the motion of the galaxies that may possibly be compatible with the astronomical observations.Comment: Published paper www.mdpi.com/journal/symmetr

The Non-Euclidean Hydrodynamic Klein-Gordon Equation with Perturbative Self-Interacting Field

In this paper the quantum hydrodynamic approach for the KGE owning a perturbative self-interaction term is developed. The generalized model to non-Euclidean space-time allows to determine the quantum energy impulse tensor density of mesons for the gravitational equation of quantum mechanical systems.Comment: 11 page

The Uncertainty Principle derived by the finite transmission of light and information

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows that the measurement process performed in the large scale classical limit of stochastic QHA (SQHA), cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.Comment: submitted for pubblicatio