On the Derivation of Quantum Mechanics from the Non-Local Geometrodynamics Model

Tomer Shushi

In this paper, we discuss a geometrodynamical approach to particle physics, in which quantum mechanics is no more than an approximated model of nature in the microscopic scale. We derive quantum mechanics from the concept of non-local geometrodynamics. Using the concept of superoscillations, we obtain the metric of the particles, which allows mapping this metric into the quantum wavefunction representation.

Ivano Tavernelli

T. W. B. Kibble

Davide Fiscaletti

The de Broglie–Bohm theory allows us to have got a satisfactory geometrodynamic interpretation of quantum mechanics. The fundamental element, which creates a geometrodynamic picture of the quantum world in the non-relativistic domain, a relativistic curved space-time background, and the quantum gravity domain, is the quantum potential. It is shown that, in the non-relativistic domain, the geometrodynamic nature of the quantum potential followsfrom the fact that it is an information potential containing a space-like active information on the environment; the geometric properties of the space expressed by the quantum potential determine non-local correlations between subatomic particles. Moreover, in the de Broglie–Bohm theory in a curved space-time, it is shown that the quantum, as well as the gravitational, effects of matter have geometric nature and are highly related: the quantum potential can be interpreted as the conformal degree of freedom of the space-time metric, and its presence is equivalent to the curved space-time. It is shown on the basis of some recent research that, in quantum gravity, we have a generalized geometric unification of gravitational and quantum effects of matter; Bohm's interpretation shows that the form of a quantum potential and its relation to the conformal degree of freedom of the space-time metric can be derived from the equations of motion.

V.E. Kuzmichev, V. V. Kuzmichev

An analogy between non-relativistic quantum mechanics in the Madelung formulation and quantum geometrodynamics in the case of the maximally symmetric space is drawn. The equations equivalent to the continuity equation and the hydrodynamic Euler equation describing the evolution of the velocity introduced for the case of hypothetical fluid flow characterizing the cosmological system are obtained. It is shown that the perfect nature of the fluid is broken by the quantum Bohm potential. The quantum potential is calculated in the semi-classical approximation for different forces acting in the system both in standard quantum mechanics and in the minisuperspace model of quantum geometrodynamics. The explicit dependences of the cosmic scale factor on the conformal time, which account for the quantum additive, are found for the empty space with spatial curvature and for a spatially flat universe with dust and radiation.

F. De Martini, Enrico Santamato