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Multiway Systems and Quantum Mechanics vs Relativistic and Gravitational Properties

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	Multiway Systems and Quantum Mechanics Fringe	Relativistic and Gravitational Properties Fringe
Proposed	2020	2020
Key figures	Jonathan Gorard	Jonathan Gorard
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.	Gorard's companion arXiv paper derived Lorentzian-signature geodesics, the Schwarzschild metric around a dense hyperedge cluster, and the vacuum Einstein equations from the geodesic ball volume formula of the causal graphs produced by causal-invariant hypergraph rules.
Predictions	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	A dense hyperedge cluster in the rewriting rule's graph produces a causal structure identical to the Schwarzschild spacetime in the continuum limit, with an event horizon at the correct radius for the effective mass Gravitational waves correspond to propagating disturbances in the geodesic structure of the causal graph; their speed is the speed of light, the maximum hyperedge propagation rate The coupling constant in the Einstein equations, Newton's constant, is determined by the combinatorics of the rewriting rule; different rules give different effective values of the gravitational coupling The Penrose-Hawking singularity theorems, the results in general relativity showing that collapsing matter is forced to form singularities once gravity has positive energy and a well-defined cause-and-effect ordering, should have counterparts in the hypergraph framework that follow from how its causal graph links earlier events to later ones
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 mathematical machinery of quantum mechanics (Hilbert space, the abstract space of quantum states, along with the inner products, hermitian operators, and spectral theorem built on top of it) is described as an analogy rather than derived with the rigor needed to match experiment 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	The derivation fills in multiple steps heuristically; going from geodesic volume scaling to the full Einstein equations with the correct energy-momentum source term requires the identification of what plays the role of the stress-energy tensor, which has not been rigorously carried out The Schwarzschild derivation holds in the pure-gravity case of an empty background with one dense patch; extending to matter coupling and non-vacuum spacetimes has not been demonstrated with the same precision The derivation assumes a specific continuum limit procedure that is not derived from the discrete rules themselves; different choices of continuum limit could give different equations, and the correct procedure has not been uniquely specified Renate Loll and others have noted that the Wolfram causal graph has not been formally connected to causal dynamical triangulations, a rival quantum gravity approach that also builds spacetime from tiny discrete pieces and then adds up all possible geometries, so it is not clear whether the two programs agree or contradict each other
Key unresolved problem	The probability problem: no one has shown how the familiar odds of quantum measurements (the Born rule) arise from the branching structure of the multiway system.	The no-matter problem: the derivation recovers Einstein's equations only for empty space, with no way yet to add the energy and matter that bend it (the stress-energy tensor), leaving gravity without anything to act on.
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Multiway Systems and Quantum Mechanics

2020 · Fringe

Relativistic and Gravitational Properties

2020 · Fringe

Proposed

2020

Key figures

Jonathan Gorard

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.

Gorard's companion arXiv paper derived Lorentzian-signature geodesics, the Schwarzschild metric around a dense hyperedge cluster, and the vacuum Einstein equations from the geodesic ball volume formula of the causal graphs produced by causal-invariant hypergraph rules.

Predictions

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

A dense hyperedge cluster in the rewriting rule's graph produces a causal structure identical to the Schwarzschild spacetime in the continuum limit, with an event horizon at the correct radius for the effective mass
Gravitational waves correspond to propagating disturbances in the geodesic structure of the causal graph; their speed is the speed of light, the maximum hyperedge propagation rate
The coupling constant in the Einstein equations, Newton's constant, is determined by the combinatorics of the rewriting rule; different rules give different effective values of the gravitational coupling
The Penrose-Hawking singularity theorems, the results in general relativity showing that collapsing matter is forced to form singularities once gravity has positive energy and a well-defined cause-and-effect ordering, should have counterparts in the hypergraph framework that follow from how its causal graph links earlier events to later ones

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 mathematical machinery of quantum mechanics (Hilbert space, the abstract space of quantum states, along with the inner products, hermitian operators, and spectral theorem built on top of it) is described as an analogy rather than derived with the rigor needed to match experiment
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

The derivation fills in multiple steps heuristically; going from geodesic volume scaling to the full Einstein equations with the correct energy-momentum source term requires the identification of what plays the role of the stress-energy tensor, which has not been rigorously carried out
The Schwarzschild derivation holds in the pure-gravity case of an empty background with one dense patch; extending to matter coupling and non-vacuum spacetimes has not been demonstrated with the same precision
The derivation assumes a specific continuum limit procedure that is not derived from the discrete rules themselves; different choices of continuum limit could give different equations, and the correct procedure has not been uniquely specified
Renate Loll and others have noted that the Wolfram causal graph has not been formally connected to causal dynamical triangulations, a rival quantum gravity approach that also builds spacetime from tiny discrete pieces and then adds up all possible geometries, so it is not clear whether the two programs agree or contradict each other

Key unresolved problem

The probability problem: no one has shown how the familiar odds of quantum measurements (the Born rule) arise from the branching structure of the multiway system.

The no-matter problem: the derivation recovers Einstein's equations only for empty space, with no way yet to add the energy and matter that bend it (the stress-energy tensor), leaving gravity without anything to act on.

Reader vote

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