Multiway Systems and Quantum Mechanics
The branching structure of all possible rule applications, the multiway system, is proposed to reproduce quantum mechanical superposition, interference, and the Feynman path integral, with branches playing the role of paths.
Placeholder for a 3D visualisation of Wolfram Physics Project. The interactive scene will land in Phase 3. The Wolfram Physics Project, announced by Stephen Wolfram in April 2020, proposes that all of fundamental physics emerges from the iterated application of a simple substitution rule to an abstract hypergraph, a network of relations among abstract elements with no pre-assigned meaning. Wolfram, Jonathan Gorard, and collaborators showed that for certain classes of rules the large-scale limit of hypergraph evolution displays properties resembling a Lorentzian [[spacetime]] satisfying [[general relativity]]; separately, the branching structure of the multiway system, the record of all possible rule applications rather than just one, reproduces features of quantum mechanics including non-commutativity and a version of the Feynman path integral over branches rather than paths. The project has produced an extensive technical literature on its own website and in Wolfram Research publications, but has received limited engagement from mainstream theoretical physicists, who have raised concerns about whether the claimed derivations are precise derivations of the known laws or structural analogies.
§1 · The claim, in one sentence
Gorard's 2020 Complex Systems paper showed that the causal structure of the multiway system, the graph tracking all possible orders of rule applications, reproduces several formal features of quantum mechanics including a version of non-commutativity and a path-integral-like formulation over branches.
§2 · Why it might be true
In the primary Wolfram model, one sequence of rule applications is chosen and followed, producing a single evolving hypergraph. But many hyperedges overlap with multiple applicable rule patterns simultaneously. The multiway system instead follows all possible application sequences in parallel, building a branching tree of possible hypergraph evolutions. Gorard's claim is that this branching structure is the origin of quantum superposition: each branch represents a possible history, and the branchial graph connecting branches that share recent common ancestors plays the role of Hilbert space.
Gorard demonstrates that quantum-mechanical interference arises from branches that reconverge in the multiway system, producing a formal structure resembling the Feynman path integral where paths are replaced by branches and interference is a graph-theoretic convergence. He also shows that the algebra of operators on branches satisfies a non-commutativity property: applying rule A followed by B is not the same as applying B followed by A, analogous to the non-commutativity of quantum operators in the canonical formalism.
The paper was published in Complex Systems, Wolfram's own journal, rather than in Physical Review or the Journal of High Energy Physics. This is a concrete limitation on the external review the work has received. The formal structures identified are suggestive, but whether the branchial graph genuinely reproduces quantum mechanics quantitatively, including Born-rule statistics, Hilbert space inner products, and unitary evolution, has not been established to a precision that mainstream quantum foundations researchers have found convincing.
The family stance
Physics is substrate-independent and computational: the specific hypergraph and rewriting rule are accidents, while the emergent large-scale laws, relativity and quantum mechanics, follow from universal properties of rule systems that are causally invariant. Finding the correct rule would in principle specify all of physics from a single discrete combinatorial object.
§2.5 · Evidence
- Gorard's paper shows that the multiway evolution of specific simple rules produces formal structures satisfying non-commutativity relations analogous to those in quantum mechanics
- The path-integral-like formulation over branches is internally consistent with the causal structure of the multiway graph and reproduces the formal superposition principle
- The derivation does not require the identification of any specific correct rule and applies to a wide class of causal-invariant rewriting systems, suggesting robustness of the structural claim
§3 · What you'd need to test it
- Quantum superposition and interference emerge from the causal convergence of branches in the multiway system without additional postulates about wave functions or measurement
- The non-commutativity of quantum operators corresponds to the non-commutativity of rule applications in overlapping hyperedge patterns, with Planck's constant related to the characteristic scale of branching in the underlying rule
- Decoherence corresponds to the geometric separation of branches in the branchial graph; macroscopic classical behavior arises when branch convergences become rare on the relevant scale
- Quantum entanglement corresponds to shared ancestry of two branches in the multiway causal graph, with the entanglement entropy related to the number of shared ancestral events
§4 · Where it breaks
- The derivation does not produce the Born rule for measurement probabilities from first principles; how probabilities over branches are to be defined and why they obey Born-rule statistics is not addressed
- The paper appeared in Complex Systems, Wolfram's own journal, and has not been subjected to the peer-review process of mainstream quantum foundations or quantum gravity journals; the formal structures need independent verification
- The connection to the standard Hilbert space formulation of quantum mechanics, including inner products, hermitian operators, and the spectral theorem, is described analogically rather than established with mathematical rigor
- Scott Aaronson and others have pointed out that producing a formal non-commutativity is not sufficient to recover the specific predictions of quantum mechanics, including interference fringe patterns and entanglement correlations violating Bell inequalities
Go deeper
Branchial graph: a graph connecting pairs of branches in the multiway system that share a common ancestor within a recent time window. Two branches are branchially adjacent if they can be reached from a common parent by a single rule application. The branchial graph changes with each time step and is proposed to play the role of the projective Hilbert space of the quantum system.
Non-commutativity in the multiway system: two rule applications A and B are non-commutative if applying A to a hyperedge pattern and then B gives a different result than applying B first and then A. This happens whenever the two rules have overlapping patterns. Gorard maps this to the non-commutativity of quantum operators, with the commutator [A,B] corresponding to the topological difference between the two application-order graphs in the branchial structure.
Born rule problem: the most serious technical gap in the quantum mechanics derivation is the absence of a derivation of Born-rule statistics. Ordinary branches in the multiway system are discrete objects; assigning probabilities proportional to the squared amplitudes requires a measure on the branching space that is not naturally provided by the combinatorics of the rewriting rules alone.
Connection to many-worlds interpretation: Gorard's framework has a structural similarity to the Everett many-worlds interpretation, where all branches exist and interference is interference between branches of the wavefunction. The branchial graph plays the role of the branching world structure, and Gorard notes this connection explicitly in the paper.
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▸§5 · Who built it, and when(1 source, 1 established)
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