Discrete Causal Model
A theoretical physics research program proposing that the universe is a discrete matrix algebra operating on a growing index space. There is no fundamental “space” — only indices in a matrix. What we call space is the index structure of a Fock space; time is a sequence of unitary matrix multiplications; and physics is the rule for constructing the evolution operator U(t).
Every analytical result is backed by Python numerical verification and, where applicable, formal proofs in Lean 4.
Central Equation
The state of the universe at time T is given by:
|Ψ(T)⟩ = U(T−1) · U(T−2) · … · U(1) · U(0) · |Ψ(0)⟩
where U(t) is the unitary evolution operator at each Planck-scale time step and the orbital index space N(t) grows — encoding the expansion of the universe.
Key Ideas
Running Alpha
The fine-structure constant α(t) evolves in the ultra-early universe and freezes after charged-particle threshold crossing. Late-time acceleration is modeled by a separate vacuum-like channel.
Causal Gravity
Gravity emerges as a retarded potential from the past light cone — a non-Markovian delta-kernel construction. No background spacetime is assumed.
Holographic Bounds
Entropy is bounded by the index space (S ≤ N ln 2 for fermions). The vacuum expansion rate HΛ is derived from holographic entropy bounds.
Research Topics
- Quantum Gravity / Foundations of Physics — discrete causal substrate, Planck-scale time updates, growing orbital index space
- Cosmology — redshift from growing N(t), dark energy from index space expansion, CMB predictions
- Decoherence — novel α-mismatch mechanism (no consciousness or observer required)
- Holographic Principle — 3D universe from a fundamentally 2D boundary description, explicit implementation in the data structure
- Initial State — T₀ uniqueness theorem (for N ≤ 4), no fine-tuning needed
Verification Approach
Results are verified through two complementary methods:
- Python numerical simulations — Fock space evolution, gravity, light cones, parameter scans, and alpha-history simulations using NumPy and SciPy.
- Lean 4 formal proofs — Machine-checked proofs covering holographic entropy bounds, T₀ uniqueness, conservation laws, and causal structure properties.
Every claim in the research is tagged with its epistemic status: established physics, derived, assumption, numerically verified, Lean-proved, or open question.
Status
The Discrete Causal Model is an active research program with 13+ papers covering foundations, gravity, conservation laws, cosmology, quantum mechanics, holography, and particle ontology. The papers are not yet published.