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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 Simulation-Hypothesis  black-hole  graviton  quantum-gravity  gravitational-orbital  Planck-gravity  Planck-unit  mathematical electron  mathematical universe
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.Nick Bostrom & Julian Savulescu - 2009 - Oxford University Press.

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