Wolfram Physics Notes

A personal, evolving notebook on the Wolfram Physics Project — hypergraphs and rewriting rules, causal and multiway graphs, the Ruliad, and how space, time, relativity, and quantum mechanics might emerge from simple computational rules. Concepts are explored with interactive diagrams you can poke at.

Concepts

• Hypergraphs & Rewriting

  The starting point of the Wolfram model — structureless collections of relations, updated by a single rewriting rule.

  foundationshypergraphsrewriting

• Causal Graphs

  Once things start happening, some happenings depend on others. That web of "what had to happen before what" is the causal graph — and it's where time comes from.

  foundationscausal-graphstime

• Multiway Systems

  The rule can usually fire in more than one place. Instead of choosing, follow every choice at once — and you get a branching tree of all possible histories.

  foundationsmultiwaybranchialquantum

• Causal Invariance

  Run the rule in any order you like, take any branch you like — and the same causal graph comes out the other end. That stubborn agreement is what lets one shared reality exist at all.

  foundationscausal-graphsrelativity

• Computational Irreducibility

  The universe runs on a simple rule — yet to know what it does, there's no shortcut but to let it run, step by relentless step.

  foundationscomputationtime

• The Principle of Computational Equivalence

  A single audacious bet — that almost anything not obviously simple is, deep down, as computationally sophisticated as anything else, our universe included.

  foundationscomputation

• Space from a Hypergraph

  Space isn't a stage the universe sits on — it's the large-scale shape of the hypergraph itself, the same web that everything else is made of.

  spacedimensionemergence

• Curvature & Gravity

  Curvature shows up as a tiny discrepancy in how fast a ball fills out as it grows — and from that discrepancy, gravity is argued to follow.

  spacegravityrelativity

• Time, Foliations & Reference Frames

  There's no master clock in the universe — only the order the causal graph forces; slice that order into "moments of now" and you've chosen a reference frame.

  timerelativitycausal-graphs

• Special Relativity

  A moving observer slices the causal graph at a tilt — and that single geometric tweak is enough to make clocks run slow and pin a universal speed limit.

  relativitytimespace

• General Relativity & Gravity

  Put special relativity and hypergraph curvature side by side and a tantalising road opens up — one that is argued to lead all the way to Einstein's equations.

  relativitygravityspace

• Energy, Momentum & Matter

  If space is woven from activity, then energy might just be how much of that activity flows through a slice of it — and matter, a knot in the weave that refuses to dissolve.

  energymatterfoundations

• Branchial Space

  Take all the histories that coexist at one instant of the multiway system, link the ones that just split apart, and zoom out — you get a second emergent space, proposed as the arena where quantum mechanics lives.

  quantumbranchialmultiway

• Quantum Mechanics from Branching

  Refuse to pick a single history and the multiway system keeps them all at once — and from that thicket of co-existing branches, the project argues, the shape of quantum mechanics is supposed to fall out.

  quantummultiwaybranchial

• Entanglement & Branchial Distance

  If two quantum states are "close" in the branching tree of histories, the model proposes they are entangled — so a map of who-shares-an-ancestor becomes a map of entanglement itself.

  quantumentanglementbranchial