The Law of Probability Inertia within Emergent Quantum Gravity: Resolving the Preferred Basis Problem and the Dynamical Cosmological Constant

This paper presents an emergent physical model bridging information physics and quantum gravity by reformulating the "Law of Probability Inertia". We hypothesize that the spacetime fabric exhibits a physical resistance (inertia) exclusively during the collapse of the wave function within the Position Basis, thereby resolving the preferred basis problem. The mathematical formulation is regularized utilizing the maximum Planck limit to avoid energy infinities at zero probabilities. Furthermore, the local spacetime's effective quantum temperature is linked to the self-gravitational energy of spatial superpositions, in alignment with the Di'osi-Penrose model. To secure thermodynamic and relativistic consistency, we introduce a hidden U1 gauge field formulation characterized by zero kinetic mixing and strict local covariant conservation of the stress-energy tensor. This completely resolves microcausality concerns and accounts for the absence of spontaneous continuous radiation in the Gran Sasso experiments. Finally, we demonstrate how this model provides a dynamical explanation for the cosmological constant (dark energy) problem, casting it as an informational bulk viscosity of spacetime that resists quantum superpositions throughout cosmic history.