[Paper Review] Cosmological constant, semiclassical gravity, and foundations of quantum mechanics

Hrvoje Nikolić|ArXiv.org|Nov 6, 2006

Quantum Mechanics and Applications3 references3 citations

TL;DR

This paper proposes a reformulation of semiclassical gravity using Bohmian mechanics to resolve the old and new cosmological constant problems and the discontinuous wave-function collapse issue. By treating particles as deterministic trajectories guided by a wave function, the theory avoids vacuum energy divergences and nonlocal collapses, yielding a smooth, continuous energy-momentum tensor that conserves locally and naturally incorporates a cosmological constant via the quantum potential.

ABSTRACT

The old cosmological-constant (CC) problem indicates an inconsistency of the usual formulation of semiclassical gravity. The usual formulation of semiclassical gravity also seems to be inconsistent with the conventional interpretation of quantum mechanics based on the discontinuous wave-function collapse. By reformulating semiclassical gravity in terms of Bohmian deterministic particle trajectories, the resulting semiclassical theory avoids both the old CC problem and the discontinuous collapse problem of the usual semiclassical theory. The relevance to the new CC problem and to particle creation by classical gravitational fields is also discussed.

Motivation & Objective

• To resolve the old cosmological constant problem, where vacuum energy contributions in standard semiclassical gravity are vastly larger than observed.
• To address the discontinuous wave-function collapse problem in standard semiclassical gravity, which violates local energy-momentum conservation.
• To provide a consistent semiclassical framework that avoids inconsistencies between quantum mechanics and gravity.
• To explore connections between the quantum potential and the cosmological constant, potentially linking to the new CC problem and dark energy.
• To propose a mechanism for backreaction in particle creation processes, such as Hawking radiation, via a continuous energy-momentum contribution U^{\mu\nu}.

Proposed method

• Replaces the standard semiclassical Einstein equation with a formulation based on Bohmian trajectories for particles, where particle positions evolve deterministically under the influence of the wave function.
• Introduces a quantum potential Q derived from the wave function's amplitude R, which contributes to the effective energy-momentum tensor as g^{\mu\nu}Q.
• Uses the de Broglie-Bohm guidance equation to define particle trajectories, ensuring continuity and determinism, avoiding instantaneous wave-function collapse.
• Derives the energy-momentum tensor as a sum of particle contributions and a non-particle contribution U^{\mu\nu} arising from time-varying particle effectivities e_n.
• Applies the formalism to the nonrelativistic limit, showing that particle mass m contributes to the cosmological constant via |Q| ~ m, suggesting a link to the coincidence problem.
• Analyzes particle creation processes, showing that U^{\mu\nu} arises only when effectivities e_n change over time, providing a transient but physically meaningful backreaction mechanism.

Experimental results

Research questions

• RQ1 Can a Bohmian formulation of quantum matter in semiclassical gravity eliminate the old cosmological constant problem by avoiding vacuum energy divergences?
• RQ2 Does replacing wave-function collapse with continuous Bohmian trajectories resolve the inconsistency between local energy-momentum conservation and the standard semiclassical equation?
• RQ3 Can the quantum potential Q in the Bohmian framework naturally generate a cosmological constant term proportional to g^{\mu\nu}Q, offering a mechanism for dark energy?
• RQ4 How does the non-particle energy-momentum contribution U^{\mu\nu} emerge from time-varying particle effectivities, and what is its role in backreaction during particle creation?
• RQ5 Can this formalism provide new insights into the new cosmological constant problem and the nature of dark energy as arising from nontrivial wave functions with large spatial extent?

Key findings

• The quantum potential Q contributes a term proportional to g^{\mu\nu}Q in the energy-momentum tensor, which acts as a cosmological constant and is of order m in the nonrelativistic limit.
• The energy-momentum tensor derived from Bohmian trajectories satisfies local conservation ∇^μ⟨T_μν⟩ = 0, resolving the discontinuous collapse problem of standard semiclassical gravity.
• The non-particle contribution U^{\mu\nu} arises only when particle effectivities e_n change over time, representing a transient but physically meaningful backreaction during particle creation.
• In processes like Hawking radiation, where particles are created from vacuum, U^{\mu\nu} can remain nonzero in the final state, providing a mechanism for backreaction.
• The formalism suggests that dark energy could arise from particles described by wave functions with large spatial width, leading to nontrivial Q and preventing structure formation.
• The theory avoids the old CC problem by treating particles as fundamental with deterministic trajectories, so vacuum contributions do not appear as divergent energy densities in the same way as in standard QFT.