Causal Budget Framework, Part 3: How C = T + M Unifies Physics

This work demonstrates how the Causal Budget Framework's fundamental constraint C = T + M unifies diverse areas of physics through a single computational principle. The budget law divides finite computational effort between translation (T) and maintenance (M), revealing deep connections between seemingly unrelated physical phenomena.

Key contributions include: (1) Geometric interpretation of C = T + M as a right triangle that reproduces the mathematical structure of special relativity, energy-momentum relations, and spacetime intervals, (2) Derivation of electromagnetic phenomena as pure translation processes with Maxwell's equations emerging from T-budget evolution, (3) Explanation of particle physics through maintenance requirements, showing how photons (M = 0) and matter particles (M > 0) arise from different budget allocations, (4) Unified treatment of wave behavior, interference, diffraction, and spin as computational processes within the T/M framework.

The work reveals that the triangular identity T² + M² = 1 encodes the same mathematical relationships underlying the Lorentz factor, relativistic energy-momentum equations, and Minkowski spacetime structure. Rather than being separate physical laws, these phenomena emerge naturally from computational budget allocation constraints.

Specific applications include: relativistic time dilation as reduced maintenance cycles, electromagnetic waves as pure T-evolution with no internal upkeep, photon creation through T+M emission stamps in local fields, spin as persistent maintenance-side bookkeeping, and quantum interference as phase relationships within translation pathways.

This is Part 3 in a series establishing CBF as a computational foundation for fundamental physics. The framework suggests that major physical theories of special relativity, electromagnetism, quantum mechanics, and particle physics, represent different manifestations of a single underlying computational constraint governing how the universe allocates processing resources between motion and internal state preservation.

The work serves as a "Rosetta Stone" for interpreting diverse physical phenomena through the lens of computational budget allocation, preparing the foundation for understanding global event coordination mechanisms in subsequent installments.