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.
This is the deep end. In Branchial Space we built a map of how the multiway system’s branches sit relative to one another. Now we ask the boldest question in the whole project: could that branching be quantum mechanics?
The intuition is disarmingly simple. A multiway system refuses to pick one history — when the rule can fire in several places, it keeps every outcome and follows them all. So at any moment the system isn’t in one state; it’s spread across many co-existing branches. That already smells like quantum superposition, where a particle isn’t “here or there” but described by all its possibilities at once. Wolfram’s proposal is that the resemblance is not a metaphor: the superposed branches of the multiway graph are meant to be the superposed histories of quantum mechanics. [conjecture] (2020 announcement)
Before going further, the honest headline: of everything in these notes, this is the least settled. The popular essays present it as promising but openly aspirational; a much more careful treatment lives in Gorard’s technical paper. Nobody has confirmed that the universe works this way, and you should read every claim below as a proposal, not a result.
Many branches as one superposition
Here is the same little string system we’ve used all along, BA → AB, branching from
BABA. Read it now with quantum eyes: each node is a possible state, and the system is
imagined to be all of them at once, weighted somehow, rather than sitting on any
single path.
BA → AB — wherever you see BA, you may replace it with AB. Green-outlined states are final (no move left).Try this: play it through and watch two branches split and later merge back into the same node. In the quantum reading, that re-merging is the interesting bit: two different histories arriving at the same state is exactly the setup for interference — paths that reinforce or cancel depending on how they meet. [conjecture]
The map of which branches are “close” — built from shared ancestry — is branchial space, and the project proposes that position in branchial space is what plays the role of a quantum state. [setup→claimed correspondence] (2021 update)
Interactive planned: a bespoke branchial graph view that lays branches out by branchial distance and lets you watch interference-like reinforcement build up as paths reconverge. For now the multiway view above carries the idea — the branches are the superposed histories.
Where do amplitudes and interference come from?
A superposition is more than a list of possibilities — each possibility carries an amplitude, a number whose phase lets contributions add or cancel. The proposal is that this structure is supposed to come out of the geometry of the multiway / branchial graph: how many ways a branch can be reached, and how branches are related, is meant to play the role of amplitudes, with reconverging paths producing interference. [conjecture] The popular essays gesture at this; they do not work it out in detail (2020 announcement). The serious version is in Gorard’s paper.
The precise version: path integral, categorical QM, Bell/CHSH
Two distinct things get conflated in casual summaries, so keep them apart.
Gorard’s technical paper (“Some Quantum Mechanical Properties of the Wolfram Model,” Complex Systems 29(2), 2020) is the rigorous counterpart. It develops quantum-mechanical behaviour from multiway systems and branchial space, and draws explicit connections to:
- the Feynman path integral — summing contributions over the many branches/paths, which is the natural formal home for “many histories with amplitudes”; and
- Bell / CHSH inequalities — the standard tests for genuinely quantum (non-classical) correlations.
All of this is [derived-in-model]: worked out inside the framework’s assumptions, in a peer-reviewed venue — not an independent experimental confirmation that nature is built this way. Prefer this paper over the blog essays for anything quantum. (Gorard — quantum)
Wolfram’s 2021 update frames the correspondence differently again: quantum mechanics is claimed to “correspond to” categorical quantum mechanics, described as a “proof by compilation” — the idea being that standard QM can be compiled into the multiway models, structure for structure. That is a claim about a formal correspondence, and it is the strongest-sounding phrasing in the sources, so handle it with care: it is [derived-in-model] (a claimed correspondence within the formalism), not a demonstration that the models predict new quantum phenomena. (2021 update)
Keep the math light here on purpose. The one piece of standard machinery worth naming is the path integral: Feynman’s recipe of obtaining quantum predictions by summing over all possible paths a system could take. The multiway graph is, almost by construction, a sum-over-histories object — which is exactly why it is the framework’s chosen bridge to quantum mechanics. [conjecture]
How a single classical world gets experienced
If everything is branching all the time, why do we only ever see one outcome? The proposed answer reuses the project’s favourite idea. The observer is internal to the universe and computationally bounded, and is conjectured to “knit together” nearby branches into a single experienced history — so the branching is real underneath, but a bounded observer perceives one classical reality on top of it. [conjecture] (2020 announcement) This is offered as a sketch of measurement, not a finished account of the measurement problem.
A note of caution
This is the page where the gap between elegant story and established physics is widest, so keep the balance firmly in mind. Quantum superposition, interference, and entanglement falling out of “follow every branch at once” is a beautiful idea — but a framework flexible enough to recover quantum mechanics after the fact is also flexible enough to worry skeptics. Reviewing the project in Scientific American, Scott Aaronson argued the framework is “infinitely flexible” — able to accommodate almost any result retroactively — which blunts its predictive force, and another physicist called the claimed successes “at best, qualitative.” The QM claims in particular are self-described in Wolfram’s essays as early-stage, and the work bypassed normal peer review. [setup] (Scientific American critique)
So: the project does not “explain” or “prove” quantum mechanics. It offers a proposal that quantum behaviour might emerge from multiway branching, a claimed formal correspondence to categorical quantum mechanics, and a rigorous-but-internal derivation (path integral, Bell/CHSH) in Gorard’s paper. None of it is experimentally confirmed as a description of our universe.
Where the branches sit relative to each other turns out to matter as much as the branching itself — and that relative geometry is where the project locates entanglement. That’s Entanglement & Branchial Distance, next.
Sources for this page: Gorard — quantum · 2021 update · 2020 announcement · Scientific American critique