Introduction to Wolfram's Theory of Everything

• Stephen Wolfram: computer scientist/mathematician, creator of Mathematica
• Theory attempts to explain everything using computer code
• Basic premise: simulation hypothesis on solid mathematical foundation
• Goal: find code producing fundamental physics (gravity, standard model particles)
• Physicists largely ignore his work despite mathematical competence

Core Concept: Universe as Computation

• Universe operates like computer program with simple rules
• Laws of physics emerge from basic computational rules
• Similar to cellular automata but in 4 dimensions
• Cellular automata: produce 2D patterns line by line from simple code
• Idea: extend to 4D to explain entire universe

Initial Problems with Computational Approach

• Fundamental incompatibility with Einstein's General Relativity
• Computation requires discrete steps in time/space
• Any computation needs update rules (step-by-step progression)
• Introduces increments of time and space that conflict with relativity

Wolfram's 2002 Approach: Networks/Graphs

• "A New Kind of Science" book describes space as network/graph
• Graph: dots connected by lines (mathematicians call same thing)
• Laws of physics = rules to update network connections
• Can describe both space and matter
• Problem: gaps in graphs and time steps always observable

Relativity Incompatibility Problem

• Photon energy example demonstrates core issue
• Photon wavelength inversely proportional to energy
• Energy depends on observer's motion (Doppler effect)
  • Observer moving toward: blue shift (higher energy)
  • Observer moving away: red shift (lower energy)
• No "real" energy exists - all energies equally valid
• Energy can be arbitrarily high/low, wavelength arbitrarily small/large

Mathematical Proof Against Discrete Approaches

• Author wrote paper proving network approaches impossible
• For any discrete structure at Planck length scale
• Some observer exists for whom structure appears sub-Planck
• Cannot approximate general relativity with graphs while respecting symmetries
• Departure from symmetries always large for some observer

Experimental Testing Issues

• Small deviations from Lorentz symmetry claimed as simulation tests
• Makes catchy headlines but fundamentally flawed
• Quantum mechanics: smallest symmetry deviations spill into observable particle physics
• Such deviations long ruled out experimentally
• Explains why experiments never find Lorentz symmetry violations

2020 Breakthrough: Hypergraphs Approach

• Wolfram addressed Lorentz symmetry criticism
• Published follow-up work with collaborators
• Coincided with COVID lockdowns
• Used PR team/press release instead of standard academic paper
• Claimed "path to fundamental Theory of physics"

Hypergraphs Technical Details

• Uses hypergraphs instead of simple graphs
• Hypergraph: collection of multiple graphs
• Points describe spacetime and matter based on properties
• Key innovation: links have no physical length
• Links only quantify relations between points
• No problem with length changes for different observers
• Author calls this "clever idea"

Connection to Causal Sets Theory

• Author's 2020 exchange with Jonathan Gorard (Wolfram researcher)
• Realized approach identical to existing "causal sets" theory
• Causal sets: Rafael Sorkin's approach
• Spacetime = set of points with causal relations (arrows)
• Already respects Einstein's theory symmetries
• Wolfram's work essentially rediscovered existing approach

Current Research Status

• Post-2020 work focuses on hypergraphs-causal sets relationship
• Jonathan Gorard leads most research
• Studied general relativity applications
• Addresses singularity prevention (unsolved in causal sets)
• Progress on discretized differential equations on graphs

Remaining Challenges

• Quantum physics treatment unclear/nonsensical
• Problems with non-quantum algorithms for quantum physics
• No specifics on reproducing standard model
• No details on elementary particles
• However: causal sets papers show discretization possible

Author's Current Assessment

• Research program progressing well
• Physicists should pay more attention
• Acknowledges initial skepticism was justified
• Now sees potential in refined approach