Gedanken Experiment for Refining the Unruh Metric Tensor Uncertainty Principle via Schwarzschild Geometry and Planckian Space-Time with Initial Nonzero Entropy and Applying the Riemannian-Penrose Inequality and Initial Kinetic Energy for a Lower Bound to Graviton Mass (Massive Gravity)

This paper is with the permission of Stepan Moskaliuk similar to what he will put in the confer-ence proceedings of the summer teaching school and workshop for Ukrainian PhD physics stu-dents as given in Bratislava, as of summer 2015. With his permission, this paper will be in part reproduced here for this journal. 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 δg_tt. The metric tensor variations given by δg_rr, and are negligible, as compared to the variation δg_tt. Afterwards, what is referred to by Barbour as emergent duration of time is from the Heisenberg Uncertainty principle (HUP) applied to δg_tt in such a way as to give, in the Planckian space-time regime a nonzero minimum non zero lower ground to a massive graviton, m_graviton. The lower bound to the massive graviton is influenced by δg_tt and kinetic energy which is in the Planckian emergent duration of time δt as (E-V)？. We find from δg_tt version of the Heisenberg Uncertainty Principle (HUP), that the quantum value of the Δt·ΔE Heisenberg Uncertainty Principle (HUP) is likely not recoverable due to δg_tt ≠ Ο(1)~g_tt ≡ 1.？i.e. δg_tt≠ Ο(1) . i.e. is consistent with non-curved space, so Δt · ΔE ≥ no longer holds. This even if we take the stress energy tensor approximation