FROM ENERGY ALONE: A Unified Ontological and Physical Framework דו טורי

From Energy Alone: A Unified Scalar Framework for Physics The theory proposes that all physical structure emerges from a single scalar energetic field E:X→RE : X \to \mathbb{R}E:X→R, defined on a smooth manifold equipped with a fixed Euclidean differentiable scaffold used only to define derivatives. This background structure is non-dynamical and carries no physical meaning; all physical geometry arises from the energetic field itself. The physical metric is defined as a functional of the scalar field and its first derivatives: gij=∂iE∂jE+λ(E) δij,g_{ij} = \partial_i E \partial_j E + \lambda(E)\,\delta_{ij},gij=∂iE∂jE+λ(E)δij, so spacetime geometry is emergent rather than assumed. Dynamics are derived from an energetic action depending on EEE and its derivatives. Variation of this action yields effective gravitational field equations, and in the low-curvature (infrared) limit the equations reduce to the Einstein field equations with an emergent gravitational constant. Gauge structures arise from degeneracy properties of energetic level sets, and particle masses emerge from the spectral properties of the fluctuation operator around energetic backgrounds. Quantum behavior is described through spectral and heat-kernel analysis of these fluctuations. No spacetime metric, gauge field, or quantum field is taken as fundamental. All physical structures—geometry, gravity, gauge symmetry, and mass—are emergent manifestations of a single scalar energetic ontology.