Vibrational Dynamics I: Foundations and the Standing Wave Model

This paper introduces Vibrational Dynamics, a foundational framework for quantum gravity in which quantum fluctuations generate fundamental vibrational fields. These vibrations encode mass-energy information and interact with the quantum foam structure of spacetime, resulting in standing wave patterns. These standing waves are proposed as the geometric origin of gravitational fields, offering a new perspective on how classical spacetime emerges from quantum behaviour. Two constants arise naturally from first principles: the Vibrational constant αv ∼ ℏG/c3, which aligns with the square of the Planck length, and the Phishia constant ξ ∼ ℏc5/G2, corresponding to the Planck-scale energy density. Their product encodes the coupling between vibrational energy and spacetime curvature. A curvature-dependent suppression mechanism governs the emergence of classicality by modulating coherence, refined via numerical simulations from exponential to logarithmic decay for physical accuracy. A central consequence of this framework is the emergence of the Quantum Equivalence Principle, which states that just as gravitational and inertial frames are locally indistinguishable, classical and quantum behaviours are locally indistinguishable when considered through curvature-dependent vibrationalgeometry. This principle offers a novel pathway to unify quantum mechanics and general relativity without requiring higher-dimensional constructs. This framework also yields several specific testable predictions. This first paper establishes the core equations, suppression dynamics, and standing wave interpretation within Vibrational Dynamics. Future work will extend this model.