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Comment by openasocket | Hacker News Reader

Maybe a physicist could help me out: the idea here of treating space as a simple discrete network, and particles just being emergent behavior sounds very interesting. But doesn't this violate Bell's Theorem, that no local hidden variables could completely explain quantum mechanics?

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I am not a physicist, but Wolfram covers this.

"Because there’s a theorem (Bell’s Theorem) that says that unless there’s instantaneous non-local propagation of information, no such “hidden variables” model can reproduce the quantum mechanical results that are observed experimentally."

Wolfram's continues by saying he is allowing instantaneous non-local propogation because network nodes have no coordinates; coordinates (and dimensions themselves) arise as a result of how nodes are connected.

"And even though the network may mostly correspond on a large scale to 3D space, it’s perfectly possible for there to be 'threads' that join what would otherwise be quite separated regions."

He has changed the definition of locality.

Scott Aaronson argues that, based on what we know about quantum mechanics, Wolfram's "long-range thread" cannot reproduce special relativity and Bell inequality violations:

www.scottaaronson.com/papers/nks.ps

It seems to me that Aaronson's argument can be easily bypassed by adding non-local hidden variables in the form of a loosely connected network that essentially injects pseudo-randomness into the approximately flat Minkowski spacetime network. Note that Bell's inequality does not rule out non-local hidden variables as a viable explanation of quantum mechanics.

So quantum effects like entanglement are distortions in the structure of the network. So basically quantum effects are due to distortions in space-time, i.e. there is a 'worm hole' type structure connecting entangled particles?

This is getting out of my depth, but isn't that basically what Loop Quantum Gravity proposes?

Bell's theorem assumes that spacetime is locally Euclidean so it is not relevant when there are networks and rules that allow for causal connections that appear to be an observer at a distance.

Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT) are two theories of quantum gravity that describe spacetime as arising from a network of sorts. For LQG, spacetime emerges from a spin foam quite elegantly. And for CDT things are also quite elegant. I'm not aware of either violating Bell's Theorem, but quantum gravity isn't my specialty.

Also, physicists don't generally take Wolfram's claims about how cellular automata are related to quantum or classical gravity or anything else in fundamental physics very seriously. A New Kind of Science cites very few sources and makes it seem like everything in there is new, which isn't the case. There was loads of criticism about that when the book was released. Nonetheless, it's an interesting idea and if something useful came from the work it would be good.

I read another Wolfram blog post where he answered those criticisms. http://blog.stephenwolfram.com/2012/05/living-a-paradigm-shi...

I don't think Bell's theorem raises a problem in either LQG and CDT because they have the traditional quantum theory built into them. They are not deterministic theories like Wolfram's. Bell's theorem discounts the possibility of quantum (as it is observed) if there were no long range connections defying locality.

IANAP, but if the values of the cells are real-world values like charge, momentum, or higgs field strength, then I don't think they are hidden variables. They are the same variables described by the standard model, but calculated discretely instead of continuously.

IANAP either, but wasn't the hidden variable problem resolved by the pilot wave theory?

It wasn't resolved. Pilot Waves have nonlocality, which contradicts Relativity. (I don't know, it may be correct that quantum mechanics is non-local, but Relativity-minded folk are rightfully suspicious of such a model.)

There are other formulations of relativity which aren't nonlocal!! Like the Tangherlini transformations.

I like this quote:

"Alice wants to synchronize her clock with Bob's, so this is how it might go:

At 12:00:00 pm Alice time, Alice sends out a beam of light to Bob, as a signal for Bob to tell Alice what time he has.

Once Bob receives the beam of light, Bob immediately sends Alice a beam of light telling her the time he has.

At 12:00:02 pm Alice time, Alice receives Bob's time, say 11:41:23 am.

At this point, how should Alice synchronize clocks? Clearly, 12:00:01 pm Alice time is 11:41:23 Bob time. We're done.

But we've unknowingly introduced an assumption here, namely that the speed of light travelling from Alice to Bob is identical to the speed of light travelling from Bob to Alice."

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