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Can someone help me with the argument here? I understand the part about showing that solving Schrodinger's equation is NP-hard and thus extremely difficult for

Can someone help me with the argument here? I understand the part about showing that solving Schrodinger's equation is NP-hard and thus extremely difficult for large inputs (ie large physical systems). But when we make a statement such as "Problem X is NP-complete," we're making a formal claim about solving that problem with a particular symbolic model of computation. Is it obvious that such a model of computation applies to the universe? My layman's understanding is that there's still debate about whether the physical universe is fundamentally discrete or continuous. If the latter, then all the time the universe is effectively performing infinite-precision calculations, which we know to be impossible under the standard symbolic model of computing.

zmanian 12y ago
The perspective that the Church-Turing hypothesis applies to the physical universe is mainstream but unproven. It is implicit in the work in the original post. https://en.wikipedia.org/wiki/Digital_physics https://en.wikipedia.org/wiki/Digital_physics https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis
- seanp2k2 12y ago
  I had the same question as grandparent. Thanks for the links, and maybe I'm not getting this because it's just way over my head, but this article seems to assume that because the non-quantum computers of today can't simulate complex (particles numbering above ~Avogadro's number) quantum systems, they can't exist. This sounds like the article is claiming that the universe is a computer simulation, or that stuff can't exist if we can't compute it. Can someone please help me understand why something being able to exist in our universe depends on if we can calculate the physics for it, or where I've gone wrong in getting to this question?
- rwissmann 12y ago
  The paper furthermore appears to rely on specific interpretations of quantum mechanics. In the Many-Worlds Interpretation, the computing apparatus itself 'grows' exponentially over time.

zmanian 12y ago

The perspective that the Church-Turing hypothesis applies to the physical universe is mainstream but unproven. It is implicit in the work in the original post. https://en.wikipedia.org/wiki/Digital_physics https://en.wikipedia.org/wiki/Digital_physics https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis

seanp2k2 12y ago
I had the same question as grandparent. Thanks for the links, and maybe I'm not getting this because it's just way over my head, but this article seems to assume that because the non-quantum computers of today can't simulate complex (particles numbering above ~Avogadro's number) quantum systems, they can't exist. This sounds like the article is claiming that the universe is a computer simulation, or that stuff can't exist if we can't compute it. Can someone please help me understand why something being able to exist in our universe depends on if we can calculate the physics for it, or where I've gone wrong in getting to this question?
rwissmann 12y ago
The paper furthermore appears to rely on specific interpretations of quantum mechanics. In the Many-Worlds Interpretation, the computing apparatus itself 'grows' exponentially over time.