Generalized Uncertainty Principle in Quantum Cosmology

  • V. E. Kuzmichev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • V. V. Kuzmichev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
Keywords: quantum gravity, quantum geometrodynamics, cosmology, uncertainty principle

Abstract

The effects of gravity which manifest themselves when performing the simultaneous measurement of two non-commuting observables in the quantum theory are discussed. Matter and gravity are considered as quantum fields. The Schr¨odinger-type time equation is given for the case of a finite number of degrees of freedom: one for the matter field and one for geometry. For a spatially closed system filled with dust and radiation being in definite quantum states, the solutions to the quantum equations are found, and the existence of the minimum measurable length and the minimum momentum is shown. It appears that the simultaneous measurement of fluctuations of the intrinsic and extrinsic curvatures of the spacelike hypersurface in spacetime cannot be performed with an accuracy exceeding the Planck constant. Unruh’s and Bronstein’s uncertainty relations are discussed.

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Published
2019-11-25
How to Cite
Kuzmichev, V., & Kuzmichev, V. (2019). Generalized Uncertainty Principle in Quantum Cosmology. Ukrainian Journal of Physics, 64(11), 1050. https://doi.org/10.15407/ujpe64.11.1050
Section
Fields and elementary particles