%0 Journal Article %T 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) %A Andrew Walcott Beckwith %J Journal of High Energy Physics, Gravitation and Cosmology %P 106-124 %@ 2380-4335 %D 2016 %I Scientific Research Publishing %R 10.4236/jhepgc.2016.21012 %X 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 汛g_tt. The metric tensor variations given by 汛g_rr, $\"\"$ and $\"\"$ are negligible, as compared to the variation 汛g_tt. Afterwards, what is referred to by Barbour as emergent duration of time is from the Heisenberg Uncertainty principle (HUP) applied to 汛g_ttin 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 汛g_ttand kinetic energy which is in the Planckian emergent duration of time 汛t as (E-V) . We find from 汛g_ttversion of the Heisenberg Uncertainty Principle (HUP), that the quantum value of the 忖t﹞忖E Heisenberg Uncertainty Principle (HUP) is likely not recoverable due to 汛g_tt≧ 旬(1)~g_tt √ 1. i.e. 汛g_tt≧ 旬(1) . i.e. is consistent with non-curved space, so 忖t ﹞ 忖E ≡ $\"\"$ no longer holds. This even if we take the stress energy tensor approximation