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Current issue   Ukr. J. Phys. 2017, Vol. 62, N 8, p.727-740


Beckwith A.W.1, Moskaliuk S.S.2

1 Physics Department, Chongqing University, College of Physics, Chongqing University Huxi Campus
(No. 44 Daxuechen Nanlu, Shapinba District, Chongqing 401331,people’s Republic of China; e-mail: abeckwith@uh.edu)
2 Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14-b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: mss@bitp.kiev.ua)

Generalized Heisenberg Uncertainty Principle in Quantum Geometrodynamics and General Relativity

Section: General Problems of Theoretical Physics
Original Author's Text:  English

Abstract: We focus on the energy fows in the Universe as a simple quantum system and are concentrating on the nonlinear Hamilton–Jacobi equation, which appears in the standard quantum formalism
based on the Schr¨odinger equation. The cases of the domination of radiation, barotropic fuid,
and the quantum matter-energy are considered too. As a result, the generalized Heisenberg
uncertainty principle (GHUP) is formulated for a metric tensor. We also use the Kuzmichev–Kuzmichev geometrodynamics as a way to quantify the interrelationship between the GHUP
for a metric tensor and conditions postulated as to a barotropic fuid, i.e. a dust for the early
Universe conditions.

Key words: generalized Heisenberg uncertainty principle, general relativity, Universe, cos-
mology, quantum geometrodynamics.