Now let the automata evolve for a billion generations according to its rules without collapsing the superposition. Now you have a superposition of all possible universes that are a billion generations old. But what you also have is a vast network of entanglements. The states of the cells are still in superposition but those states are no longer independent of each other. Asolutely brilliant Scott – cystal clear, simple and entertaining- ALL profound insights should look exactly like this when correctly stated – if they don’t, the theorist is doing it wrong. In particular, notice the words: “if,”“would,”“certain,”“similarities” etc. (Is skipping such words the reason you have difficulty understanding what I write? Were you very rapidly browsing what I wrote?) But quantum mechanics does treat and has to treat observers differently than the observed objects. So whether someone or something is a human or a machine, it’s a physical system that evolves to complex superpositions of states up to the very moment when it’s observed by an external agent, an observer.

The definition of the entropy was the reason why John von Neumann introduced the density matrix. The description of subsystems was the reason why Lev Landau independently invented the density matrix. And the absence of global phase is a good reason for physics students to not worry too much about the global phase. Zach #33: I’ve already decided that I’m not going to get upset when Lubos calls me “the most corrupt moral trash,” urges my students to spit in my face, etc. So by symmetry, I shouldn’t be gratified either if he happens to like something that I was involved with. Two particularly commendable aspect of the Kuprov et al. article are, first, the thousand-spin quantum mechanical predictions are compared in-depth with thousand-spin experimental observations, and second, the computational methods used are well-suited to scalably simulate the dozens-of-qubit experiments that the recent Martinis/Google preprint “Characterizing quantum supremacy in near-term devices” (2016, see #75) envisions.to each state of a QM system, there exists a different state of the environment that it is immersed in”,

But it just doesn’t matter. However they talk about it and whatever they use to represent it their complex numbers must in a deep sense be the same as ours. Doesn’t Occam’s razor direct that the dual observations (1) and (2) be reconciled, as reflections (for example) of the natural Occam-compatible postulate that the universe permits only those Hamiltonians that accomodate the causal spukhafte Fernwirkungen (that are beloved of quantum physicists and complexity theorists) on low-dimension tensor networks (that are cherished by algebraic geometers and simulationists)? Aaargh! I didn’t read through the comments before posting, and you already answered that one, sorry.

Looking for something different

In any case, essentially every known theory in physics can be “compiled down” to where its predictions can be calculated to arbitrary accuracy by a computer toggling 0’s and 1’s—the only exceptions (not coincidentally) being the theories that aren’t yet fully defined or understood. So should we say, on that basis, that you don’t need any nontrivial math to do physics: no complex numbers, no linear algebra, no calculus, not even arithmetic? Alas, not if you actually want to understand what the theories say, which David Deutsch reminds us is more important than calculating with them… 🙂