The Mass–Wave Continuum: An Informational Substrate for Emergent Gravity and Quantum Localization

This work proposes a unified conceptual framework in which mass, energy, inertia, and spacetime curvature arise from a single underlying entity: a continuous mass–wave spectrum defined on an informational vacuum substrate. In this picture, “mass-like” (M) and “wave-like” (W) behaviors are not separate categories but limiting cases of a single localization parameter. The degree of localization determines both a particle’s inertial response and its gravitational influence.

The central hypothesis is that the quantum vacuum functions as a medium with finite informational throughput, characterized by a universal conduction speed identified with the speed of light. Localized (M-dominant) excitations require continual reconfiguration of this substrate, giving a natural physical interpretation to inertia, relativistic kinetic effects, and the divergence in energetic cost as v \to c. Wave-like (W-dominant) excitations propagate freely at the throughput limit and do not source curvature.

In this approach, proper time corresponds to the amount of information the substrate must process along a worldline. Both gravitational time dilation and special-relativistic time dilation emerge as consequences of increased informational load rather than modifications to an underlying geometric clock rate.

A localization-dependent effective stress–energy tensor is constructed, leading to an emergent metric response consistent with the weak-field limit of General Relativity. Quantum-mechanical superposition is reinterpreted as reduced localization cost rather than simultaneous occupancy of multiple geometric states. The framework is explicitly designed not to modify observed quantum predictions, but to provide a unified narrative in which GR and QM can be described using a common substrate language.

The manuscript includes:

• a formal definition of the mass–wave localization functional

• an informational reinterpretation of relativistic inertia and proper time

• an emergent-gravity stress tensor derived from localization gradients

• a reconstruction of gravitational lensing via effective refractive index

• a discussion of gravitational waves as substrate excitations

• experimentally accessible falsifiability conditions

• conceptual links to prior work (Verlinde, Penrose, Wheeler, analog gravity)

This version refines the earlier draft (Zenodo v1) by reorganizing the structure, adding mathematical development, clarifying physical assumptions, and expanding the discussion of observable consequences and experimental discriminants.