# Planck unit quantum gravity (gravitons) for Simulation Hypothesis modeling

5 Pages Posted: 18 Sep 2019 Last revised: 20 Mar 2020

Date Written: August 7, 2019

### Abstract

Defined are gravitational formulas in terms of Planck units and units of \hbar c. Mass is not assigned as a constant property but is instead treated as a discrete event defined by units of Planck mass with gravity as an interaction between these units, the gravitational orbit as the sum of these mass-mass interactions and the gravitational coupling constant as a measure of the frequency of these interactions and not the magnitude of the gravitational force itself. Each particle that is in the mass-state (defined by a unit of Planck mass) per unit of Planck time is directly linked to every other particle also in the mass-state by a discrete unit of m_P v^2 r = \hbar c, the velocity of a gravitational orbit is summed from these individual v^2. As this approach presumes a digital time, it is suitable for use in programming Simulation Hypothesis models. As this link is responsible for the particle-particle interaction it is analogous to the graviton. Orbital angular momentum of the planetary orbits derives from the sum of the planet-sun particle-particle orbital angular momentum irrespective of the angular momentum of the sun itself and the rotational angular momentum of a planet includes particle-particle rotational angular momentum.

**Keywords:** graviton, gravity, quantum gravity, Planck constant, ħc, gravitational, orbital, momentum, simulation hypothesis, mathematical universe, Planck mass, black-hole, Matrix

**JEL Classification:** C60

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