Transformation Capacity Framework (TCF)

Abstract

This manuscript introduces the Transformation Capacity Framework (TCF), an axiomatic proposal deriving special relativity, quantum mechanics, and general relativity from a single discrete substrate. Rather than quantizing classical spacetime or embedding quantum fields onto a pre-existing geometric background, we model the physical universe as a locally finite, reversible causal graph governed by a conserved transformation capacity budget. Crucially, within this architecture, macroscopic time is not a fundamental background dimension; rather, it emerges purely as a thermodynamic receipt, a measurable accumulation of discrete, microscopic physical transformations. We establish that a conserved variance partition between internal state updates and external spatial diffusion uniquely generates a macroscopic Lorentzian metric in the continuum limit, resolving the Minkowski signature without prior geometric assumptions. Because time is the accumulated length of change, relativistic time dilation arises mechanically as a capacity trade-off: external spatial routing exhausts the localized capacity available for internal state updates. Primitive operation symmetry implies universal Hamiltonian scaling, recovering the equivalence principle. Microscopic information preservation forces the emergence of complex Hilbert space structure, unitary time evolution via Stone's theorem, and the Born rule via Gleason's theorem. Finally, the macroscopic thermodynamic limit of the network yields the Einstein field equations as the unique low-energy effective theory, where mathematical singularities are resolved via finite queue saturation. This framework demonstrates that spacetime geometry and quantum mechanics are complementary macroscopic manifestations of a resource-constrained, information-preserving computational network.