De Broglie-Bohm Interpretatin for Wave Function of the Wheeler-DeWitt Equation in Spherically Symmetric Spacetime

Bobo Wang

Vera Matarese

Ch’ng Han Siong, Shahidan Radiman

The Einstein's general relativity is formulated in the Hamiltonian form for a spatially Bat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler—DeWitt equation. Solving the Wheeler—DeWitt equation and employing the de Broglie—Bohm interpretation to the wave function of the universe, we obtain a new version of spatially Bat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufficiently small.

Michel Gondran, Alexandre Gondran

Chrsquo, Ch’ng Han Siong, Shahidan Radiman

Friedmann equations play a central role in cosmology for describing the evolution of the universe. Initially, the Friedmann equations were derived by Alexander Friedmann in 1922. He derived the equations from Einstein’s field equations for a universe which is spatially homogeneous and isotropic. The equations were again derived from Newtonian mechanics by Milne. However in this paper, we derive the spatially flat Friedmann equation from Wheeler-DeWitt equation. We apply the Bohm-de Broglie interpretation to the wave function of universe. In addition, we also set a condition to the wave function, where a large scale factor of the universe is needed.   Key words: Canonical quantum cosmology, Friedmann equations, Wheeler-DeWitt equation.

Eduardo Sergio Santini

In this thesis the Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum gravity. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-De Witt equation yields a generate four-geometry compatible with the strong gravity limit of General Relativity and the Carroll group. We prove that quantum geometrodynamics in the Bohm-de Broglie interpretation is consistent for any quantum potential. As a previous step to introduce our metodology, we study the quantum theory of fields in Minkowski spacetime in the Bohm-de Broglie interpretation and exhibit a concrete example where Lorentz invariance of individual events is broken.