Toward a Dimensional Expansion Theory: Unifying Fundamental Interactions via the Walking Droplet Formalism

This article proposes a theoretical framework for a model based on the hypothesis of dimensional expansion as a constituent process of spacetime. Utilizing the walking droplets formalism as a hydrodynamic analogue of wave-particle duality, a coherent description of elementary particles and their fundamental interactions is derived. This model not only recovers the phenomenology of quantum entanglement and vacuum energy through medium fluctuations but also provides a natural explanation for dark matter, dark energy, and the acceleration of cosmic expansion without the need for ad hoc constants. Crucially, a unified mathematical formulation is presented that integrates electromagnetism and gravity, allowing for the analytical derivation of the speed of light (c), the fine-structure constant (α), the universal gravitational constant (G), and the elementary charge (e) from a single set of geometric and dynamic principles. Finally, the implications of this model regarding black hole singularities and the convergence of general relativity and quantum mechanics under a dimensional emergence paradigm are discussed.