Must quantum spacetimes be Euclidean?

Abstract

The Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum cosmology. 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 Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

“…This means that Lorentz invariance is broken. A similar situation is shown in quantum geometrodynamics where the quantum potential determine the quantum evolution of Universe [1] [10]. Now we will show that already the ground state of the free scalar field produces a quantum potential that breaks the Dirac's algebra.…”

“…We then use this approach to rederive, in a concrete example, the well known break of Lorentz invariance of individual events in BdB theory in terms of the break of the Dirac's algebra of the constraints. In section IV we consider quantum geometrodynamics in the BdB interpretation following the approach of our previous work and prove the consistency of the theory, completing the possible scenarios for the BdB view of quantum cosmology presented in [1]. Section V is for discussion and conclussions.…”

“…It has been sucessfully applied to quantum minisuperspace models [4][5][6][7][8][9] and even to full superspace models [1] [10]. In the first case it was discussed the classical limit, the singularity problem, the cosmological constant problem, and the time issue.…”

“…In our previus work [1] we left open the possibility of an inconsistent evolution: a complicated non-local quantum potential would avoid the closure of the algebra whatever it would be (Dirac-Teitelboim or another alternative algebra). In the present work we show that this is not the case: we prove that for any quantum potential the theory is consistent, and the algebra is closed when restricted to the bohmian trajectories.…”

“…In the present work we show that this is not the case: we prove that for any quantum potential the theory is consistent, and the algebra is closed when restricted to the bohmian trajectories. In order to make the present paper self contained, we present the formalism developped in [1] applied to parametrized quantum field theory in flat background. We obtain analogous results as in quantum geometrodynamics, namely, the break of Dirac's algebra and the consistency of the theory for any quantum potential.…”