The Computational Universe as Physics' Foundation

After decades of development, Stephen Wolfram's Physics Project proposes that the universe operates on elementary rules transforming abstract relations between points. These rules evolve hypergraphs - structures of interconnected nodes - which spontaneously generate the fabric of spacetime and everything within it.

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Core Discoveries

  1. Space as Evolving Hypergraphs: Simple rules like {{x,y},{x,z}} → {{x,z},{x,w},{y,w},{z,w}} generate increasingly complex structures resembling multidimensional space
  2. Causal Invariance Unifies Physics: The property that different rule application sequences yield consistent causal relationships explains both:
    • Relativity through reference frame independence
    • Quantum mechanics via multiway system consistency
  3. Energy and Mass Emerge: Energy corresponds to causal edge flux through spatial surfaces, while mass relates to temporal flux, deriving $E=mc^2$
  4. Einstein's Equations: Hypergraph curvature from rule evolution matches general relativity's predictions

Quantum-Classical Bridge

Quantum behavior emerges when observers sample specific paths through the multiway system. Measurement constitutes "freezing" branchial space - the dimension tracking quantum states - creating an effect analogous to black hole event horizons.

"What we're seeing is that relativity and quantum mechanics are actually the same idea... both theories are consequences of causal invariance" - Wolfram

Finding Our Universe's Rule

The team has launched an open Registry of Notable Universes cataloging nearly 1,000 rules. While computational irreducibility challenges direct simulation of our universe (estimated at 10500 rule applications), pockets of reducibility allow verification against known physics.

Experimental Pathways

Surprisingly, testable predictions may emerge before identifying our exact rule:
- Oligons: Hypothetical lightweight particles from sparse hypergraphs could explain dark matter
- Early Universe Signatures: Anisotropies in cosmic background radiation may reflect primordial hypergraph structure

Implications and Next Steps

This framework suggests:
- Single Universe: All possible rules coexist in one rulial space
- Observer-Centric Physics: Description languages determine apparent rule simplicity
- New Fundamental Constants: Beyond lightspeed (c), maximum entanglement speed (ζ) and rule-emulation speed (ρ)

The project now invites global collaboration through open tools and livestreamed research to identify our universe's specific rule.

Source: Wolfram Physics Project Technical Introduction, Stephen Wolfram (April 2020)