A Unified Energy-Based Framework for Space, Gravity, and Quantum Dynamics
Author: Gregory GoossensDate: May 2025
Abstract
We propose a fundamental framework where energy is constant and primary, while space, geometry, and apparent forces are derived phenomena. By treating geometry as a dynamic response to local energy distribution, and allowing the speed of light to vary with spatial compression, we derive modified versions of the Schrödinger equation and gravitational dynamics. The resulting model offers an integrated explanation for quantum behavior, gravitational attraction, and cosmological expansion without invoking singularities or dark matter. The paper culminates in a single universal formula uniting energy, geometry, and wave dynamics.
1. Introduction
Current physical theories - general relativity and quantum mechanics - successfully describe macroscopic and microscopic phenomena, yet remain fundamentally incompatible. General relativity treats geometry as a smooth manifold influenced by mass-energy, while quantum mechanics models reality as probabilistic wavefunctions on a fixed geometric backdrop.We present a unifying hypothesis: energy exists in continuous wave form and remains constant, while space and geometry are emergent, adaptive structures governed by the distribution and gradients of that energy.
2. Fundamental Assumptions
Total energy is locally conserved: E_mass + E_space = constant
3. Modified Quantum Dynamics
From the assumption that space compresses to preserve energy, we derive a modified Schrödinger equation:
iħ ∂ψ/∂t = -ψ · ∇a(E) - (ħ² / [2m₀ · a(E)²]) ∇²ψ
Here, the Laplacian and potential terms are modulated by the spatial compression factor a(E), itself derived from the energy distribution.
4. Energy-Driven Geometry
Instead of treating spacetime curvature as fundamental, we model it as an outcome of the local second derivatives of energy:
□E(x, t) = 0
This wave equation ensures the preservation of total energy while defining the geometric backdrop through spatial gradients.
5. The Universal Energy Law
The following expression encapsulates the entire model:
iħ ∂ψ/∂t = -ψ · ∇a(E) - (ħ² / [2m₀ · a(E)²]) ∇²ψ
Space compression around massive bodies is modeled as:
a(x) = 1 + k/r
Here, r is the radial distance from an energy-dense region (e.g., a mass), and k is a proportionality constant reflecting how strongly the local energy distribution affects spatial geometry. This term ensures that space compresses more strongly closer to energetic sources, and flattens at larger distances.
Where:- ψ(x,t) is the energy wavefunction- ħ is the reduced Planck constant- m₀ is a reference mass constant- a(E) is the space compression factor derived from energy- ∇a(E) is the spatial gradient of compression (like a force)- ∇²ψ is the spatial curvature (Laplacian) of the wave
Where:- E_mass represents the energy concentrated in mass-like forms (particles, matter)- E_space is the distributed energy in the geometric structure of space itself- The total energy remains conserved and balanced between both forms