TITLE:
How 5 Dimensions May Fix a Deterministic Background Spatially as to Be Inserted for HUP in 3 + 1 Dimensions, and Its Relevance to the Early Universe? Criteria for Massive Graviton Detection from Relic Conditions Mentioned
AUTHORS:
Andrew Walcott Beckwith
KEYWORDS:
Massive Gravitons, Heisenberg Uncertainty Principle (HUP), Riemannian-Penrose Inequality
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.9 No.1,
January
13,
2023
ABSTRACT: We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter included in an integration of momentum over space which equals a ration of L divided by small l (length) and all these times a constant. The ratio of L over small l is a way of making deterministic inputs from 5 dimensions into the 3 + 1 dimensional HUP. In doing so, we come up with a very small radial component for reasons which due to an argument from Wesson is a way to deterministically fix one of the variables placed into the 3 + 1 HUP. This is a deterministic input into a derivation which is then, first of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining is variation in δgtt. We state that the metric tensor variations are given by δgrr, δgθθ and δgφφ are negligible contributions, as compared to the variation δgtt. From there the expression for the HUP and its applications into certain cases in the early universe are strictly affected after we take into consideration a vanishingly small r spatial value in how we define δgtt.