Information, Quantum Mechanics, and Gravity

Abstract

This is a basically expository article, with some new observations, tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.

Remarks on Osmosis, Quantum Mechanics, and Gravity

“…We begin with some features of Weyl geometry and the Dirac-Weyl theory following [54,55,56,84] (cf. also [1,2,3,4,8,12,15,16,17,19,20,23,24,25,29,77,81,85,86,87,95]). Note that the paper is in part an expansion of some ideas in [24] and we correct some notational confusion from [17,24].…”

Metric fluctuations, entropy, and the Wheeler-deWitt equation

“…[6], [20]). A deeper understanding of this situation can be gained based on the results in [9] if the Weyl geometry and the SE is used (also see [6], [21]- [24]). Theorem 2.1.…”

“…Another context involving the SE with a statistical geometry and a Weyl space produces a Weyl vector φ i = −∂ i log(ρ) related to an osmotic velocity field [6], [9], [21], [22]. Hence, the relation u = −cφ = c∇ log(ρ) can be envisioned with ρ = P ∼ R 2 , and we are consequently motivated to consider…”

Флуктуации Метрики, Энтропия И Уравнение Уилера - Де Витта

“…Более глубокого понимания этой ситуации можно достичь на основе результатов работы [9], если использовать вейлевскую геометрию и УШ (см. так-же [6], [21]- [24]). Теорема 2.1.…”

“…В другом контексте, включающем УШ со статистической геометрией, а также пространство Вейля, получается вектор Вейля φ i = −∂ i ln(ρ), связанный с осмотическим полем скоростей [6], [9], [21], [22]. Таким образом, соотношение u = −cφ = c∇ ln(ρ) можно представить себе с ρ = P ∼ R 2 так, что вместо того чтобы рассматривать δS/δh ij = π ij − (1/P )(δP/δh ij ), мы имеем повод рассмотреть…”