Quantum Gravity and the Holographic Mass

Abstract

We find an exact quantized expression of the Schwarzschild solution to Einstein’s field equations utilizing spherical Planck units in a generalized holographic approach.  We consider vacuum fluctuations within volumes as well as on horizon surfaces, generating a discrete spacetime quantization and a novel quantized approach to gravitation.  When applied at the quantum scale, utilizing the charge radius of the proton, we find values for the rest mass of the proton within  of the CODATA value and when the 2010 muonic proton charge radius measurement is utilized we find a deviation of    from the proton rest mass. We identify a fundamental mass ratio between the vacuum oscillations on the surface horizon and the oscillations within the volume of a proton and find a solution for the gravitational coupling constant to the strong interaction.  We derive the energy, angular frequency, and period for such a system and determine its gravitational potential considering mass dilation.  We find the force range to be closely correlated with the Yukawa potential typically utilized to illustrate the exponential drop-off of the confining force.  Zero free parameters or hidden variables are utilized.