Nonunitary higher derivative gravity classically equivalent to Einstein gravity and its Newtonian limit

Abstract

Runaway solutions can be avoided in fourth order gravity by doubling the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with a change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its nonunitary Newtonian limit is shown to lead to a sharp transition, around 10 11 proton masses, from the wavelike properties of microscopic particles to the classical behavior of macroscopic bodies, as well as to a trans-Planckian regularization of collapse singularities. A unified reading of ordinary and black hole entropy emerges as entanglement entropy with hidden degrees of freedom. The emergent picture gives substantial agreement with Bekenstein-Hawking entropy and the Hawking temperature.

Relativistic generalizations of gravity-induced localization models

“…(12) in Ref. [23]. Secondly we should stress that, even though the obstruction to the formulation of consistent relativistic localization models is removed within a unified theory of localization and gravity, this does not mean that our special relativistic extensions may include a relativistic theory of gravity.…”

“…(5) one replaces the scalar field with a positive energy one, by changing the sign in the exponent of the first exponential, one gets a model still with a vanishing net force, but without localization properties, as the interaction between physical and hidden degrees of freedom is repulsive. Although our aim was the introduction of a well-defined relativistic theory, on a heuristic level one can introduce another relativistic model where both positive and negative energy fields are present, with the further bonus of Pauli-Villars-like cancellations, like in the general covariant theory [20,22,23]. In fact, if we consider a relativistic action…”

“…In order to do that, consider that the Newtonian model gives a localization length Λ ∼ (h 2 R 3 /GM 3 ) 1/4 for a body whose linear dimension is R and whose mass M is above the threshold, which for ordinary densities is ∼ 10 11 proton masses (m p ) [15,23]. The localization process implies a localization energy E Λ ∼h 2 /(MΛ 2 ) ∼hG 1/2 ρ 1/2 , depending only on the body density ρ, which, for ordinary densities is E Λ ∼ 10 −20 eV.…”

“…The localization process implies a localization energy E Λ ∼h 2 /(MΛ 2 ) ∼hG 1/2 ρ 1/2 , depending only on the body density ρ, which, for ordinary densities is E Λ ∼ 10 −20 eV. This process takes a time T G ∼ 10 20 (M/m p ) −5/3 s [17,23] and consists of the transformation of potential into kinetic meta-energy, corresponding to twice the physical kinetic energy.…”

“…As the observable algebra is identified with the ψ operator algebra, expectation values can be evaluated by preliminarily tracing out theψ operators. It was shown that the ensuing nonunitary dynamics, while embodying the ordinary Newton interaction, gives rise to a dynamical localization that is compatible both with the wavelike behavior of microscopic particles and the emergence of classicality for macroscopic bodies [15][16][17]23,24].…”