Thermodynamic unification of emergent gravity: entropy and the quantum floor of spacetime. The stoney limit as a solution to Big Bang singularities and gravitational collapse.

Abstract

This document presents the definitive mathematical framework of Scalar Dissipation Theory (TDE-137). It demonstrates that the fine-structure constant (1/137) governs the geometric packing of spacetime through a Minimum Dissipation Area, derived directly from quantum entropy equilibrium at the event horizon. Using the original 1899 formulation of the Planck mass (based on the original constant *h*), a quantum gravity equation is derived at the vacuum "pixel" scale; this equation absolutely cancels out Newton's gravitational constant (G), thereby demonstrating the non-existence of the graviton. The model establishes a dynamic boundary law regulated by a Stoney mass, reformulates Hawking evaporation thermodynamics, and structures the Einstein metric with a quantum floor, ensuring the center of a black hole does not blow up to infinity.

The most significant milestone of this model lies in the perfect and explicit unification of classical Newtonian gravity and quantum gravity upon reaching the Stoney mass scale. While contemporary physics keeps these two forms of gravity separated by an insurmountable mathematical barrier, this development demonstrates that when a black hole's mass shrinks to microscopically match the Stoney mass, the system undergoes a phase transition where macroscopic and quantum laws converge at a single equilibrium point.

This algebraic approach not only preserves numerical consistency with the macroscopic models of classical general relativity—yielding identical predictions for stellar-mass bodies—but also naturally resolves the mathematical divergence toward infinity (the terminal singularity) that plagues standard theory during its final quantum stages.