Is There a Set of Hamiltonians?

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There's an infinite number of hamiltonians i can write down, but at least for simple ones, there's a finite set of little rules that we can write down for our hypographs. So maybe there's a map from the set of rules to hamiltonians, but it's a very, very one, few to few, rather than covering the whole space of possible hamiltonians. Mayi onot be im: It looks like we get ones that show local gagin variance. And then we have to ask, you know. What kind of things emerge from this lower level structure? Because in our models, all we're talking about are particles.

It’s not easy, figuring out the fundamental laws of physics. It’s even harder when your chosen methodology is to essentially start from scratch, positing a simple underlying system and a simple set of rules for it, and hope that everything we know about the world somehow pops out. That’s the project being undertaken by Stephen Wolfram and his collaborators, who are working with a kind of discrete system called “hypergraphs.” We talk about what the basic ideas are, why one would choose this particular angle of attack on fundamental physics, and how ideas like quantum mechanics and general relativity might emerge from this simple framework.

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Stephen Wolfram received his Ph.D. in physics from Caltech. He is the founder and CEO of Wolfram Research, and the creator of Mathematica, Wolfram|Alpha, and the Wolfram Language. Among his awards are a MacArthur Fellowship. Among his books is A New Kind of Science. He recently launched the Wolfram Physics Project.

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