TITLE:
Unruh Metric Tensor HUP via Planckian Space-Time Compared to HUP Based Complexity of Measured System Results to Obtain Inflaton Potential Magnitude
AUTHORS:
Andrew Walcott Beckwith
KEYWORDS:
Massive Gravitons, Heisenberg Uncertainty Principle (HUP)
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.10 No.4,
October
10,
2024
ABSTRACT: 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
δ
g
tt
. The metric tensor variations given by
δ
g
rr
,
δ
g
θθ
and
δ
g
ϕϕ
are negligible, as compared to the variation
δ
g
tt
. Afterwards, what is referred to by Barbour as emergent duration of time
δt
is from the Heisenberg Uncertainty principle (HUP) applied to
δ
g
tt
in such a way as to be compared with
ΔxΔp≥
ℏ
2
+
γ
˜
∂C
∂V
with V here a volume spatial term and
γ
˜
a complexification strength term and
∂C
∂V
influence of complexity of physical system being measured in order to obtain a parameterized value for the initial value of an inflaton which we call
V
0
.