The quantum mass (QM) is expressed using the expectation value of the kinetic energy derived from the Schrödinger equation (SE). The mass‐energy equation (ME) is expressed using the kinetic energy of a body in Newtonian mechanics. The SE is modified using the QM and ME. The Adams‐Williamson equation adeptly characterizes the density distribution within Earth's interior, highlighting the role of pressure in storing elastic energy. This stored energy forms the basis for deriving the Newtonian gravitational field. Intriguingly, the eigenvalue of electron's energy in the hydrogen-like atom derived from the modified SE exhibits variation in response to gravitational field strength.
This is the first in a two-part series in which we extend non-relativistic stochastic mechanics, in the ZSM formulation [1, 2], to semiclassical Newtonian gravity (ZSM-Newton) and semiclassical Newtonian electrodynamics (ZSM-Coulomb), under the assumption that the gravitational and electromagnetic fields are fundamentally classical (i.e., not independently quantized fields). Our key findings are: (1) a derivation of the usual
N-particle Schr{ö}dinger equation for many particles interacting through operator-valued gravitational or Coulomb potentials, and (2) recovery of the `single-body' Schr{ö}dinger-Newton and Schr{ö}dinger-Coulomb equations as mean-field equations valid for systems of gravitationally and electrostatically interacting identical particles, respectively, in the weak-coupling large N limit. We also compare ZSM-Newton/Coulomb to semiclassical Newtonian gravity/electrodynamics approaches based on standard quantum theory, dynamical collapse theories, and the de Broglie-Bohm theory.