Non-Deterministic Gravity

This article explores the application of conditional probability theory within the framework of General Relativity. It reveals that uncertainties in particle momentum and position induce corresponding uncertainties in spacetime metric. The findings demonstrate an energy-dependent transition from deterministic spacetime to a probabilistic regime, occurring at scales defined by the particle’s wavelength, as distances approach Gℏ/c^3 λ. The study also provides a methodology for determining wavefunction evolution in regimes where quantum particles induce significant uncertainty in the spacetime geometry.