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I don't think this is accurate. There is no classical computation happening here, and there is no reason you have to have "room" for the classical computation t

I don't think this is accurate. There is no classical computation happening here, and there is no reason you have to have "room" for the classical computation to happen. That seems to be assuming that the universe is a classical substrate and a classical algorithm has to be instantiated somewhere. Quantum computing isn't classical computing. It isn't a Turing machine. It is a fundamentally different kind of information processing device, making use of non-classical physical phenomena. I'm not a defender of Copenhagen, but the wave collapse interpretation has no difficulty explaining quantum computation. A quantum computer creates extremely large, complexly entangled wave functions that upon collapse result in states that can be interpreted as solutions to problems that were encoded in the sequence of operations that setup the entangled wave function. The Everett interpretation is easier to think about in my opinion, and I prefer thinking in terms of MWI when I try to make sense of these results. But it is not necessary. Computer science is the study of universal Turing machines and their application. But Turing machines are only “universal” in the sense that they can represent any statement of mathematical logic, and that can (we believe) be used to simulate anything we can dream up. But there are intrinsic performance limitations of Turing machines, studied by algorithmic theory, which are artifacts of the Turing machine itself, not physical limitations of the universe we live in. That searching an unordered list with a serial processor takes O(n) time, for example. Grover showed that there are non-Turing machine quantum processes that could be used to perform the same computation in O(sqrt(n)) time. That doesn't mean we need to go looking for "where did that computation actually happen". That doesn't even make sense.

slowmovintarget 2y ago
According to this ( https://arxiv.org/pdf/2302.10778 https://arxiv.org/pdf/2302.10778 ), there are no branches, just decoherence (minus the "collapse").
- adastra22 2y ago
  A paper proposing a radically different formulation of quantum mechanics, with only a half dozen non-author-citations, so heavy with jargon that it's hard to figure out what the author is claiming. Sorry, my crank meter is dialed to 11 right now and I don't think this is worth spending further time on.
  - slowmovintarget 2y ago
    Jacob Barandes is a professor of physics at Harvard (not a crank). He recently did a great podcast with Kurt Jaimungal [1]. In the interview he explains that every year he searches for a good way to introduce his students to quantum mechanics, and every year he's ended up being unsatisfied with the approach and started again. One year he decided to attempt describing systems with traditional mechanics, using probabilities (stochastic mechanics). He worked at it and worked at it, assuming that he would eventually have to take some leap to cross the chasm into the world of gauge theory, Lie Groups, and Hilbert spaces. What he found is, to his surprise, the math just seemed to fit together at some point. That is, he found a mapping, just as the path integral is a mapping into the math of the wave function, and it just kind of worked. He had been under the assumption that it shouldn't. It turns out, that in doing his stochastic mechanics, he had used mathematical descriptions that were indivisible. That is once a given process began, it could not be sliced into smaller and smaller time slices. It had to complete and yield a result. This was what he called a non-Markov stochastic process. Apparently all previous attempts at this used Markov processes, which are divisible like Hilbert vector calculations or the path integral. It turns out that things like "collapse" of the wave function, and all the quantum weirdness arose from how the math worked with the wave function and Hilbert space, not from anything intrinsic to the mechanics of the universe (at least that's what his equivalent math was telling him). So in his stochastic non-Markov model, there is no collapse, just decoherence. There is always a result, and the intermediate states (where all the quantum oddities live) aren't real. He mentions being really disappointed at seeing all the magic of quantum mechanics just kind of vanish. From what he could tell, it was just a trick of the wrong kind of math. [1] https://www.youtube.com/live/7oWip00iXbo https://www.youtube.com/live/7oWip00iXbo
    - adastra22 2y ago
      Mathematicians, even from prestigious universities, have been wrong before. It's the danger of a discipline that doesn't yet have machine-checkable proofs.
      - slowmovintarget 2y ago
lisper 2y ago
> Turing machines are only “universal” in the sense that they can represent any statement of mathematical logic That's not quite right. TM's in general are not universal. The "universality" of TMs has to do with the existence of a universal TM which is capable of emulating any other TM by putting a specification of the TM to be emulated on the universal TM's tape. The reason this matters is that once you've built a universal TM, you never have to build any more hardware. Any TM can then be emulated in software. That result is due to Turing. The relationship between TMs and mathematical logic is of a fundamentally different character. It turns out that any system of formal logic can be emulated by a TM (and hence by a UTM), but that is a different result, mainly due to Godel, not Turing. There is also the empirical observation (famously noted by Eugene Wigner [1]) that all known physical phenomena (with the exception of quantum measurements) can be modeled mathematically, and hence can be emulated by a TM, and hence can be emulated by a UTM. But it is entirely possible that a new class of physical phenomena could be discovered tomorrow that cannot be modeled mathematically. But here's the thing: no one has been able to come up with any idea of what such a phenomenon could possibly look like, and there is a reason to believe that this is not just a failure of imagination but actually a fundamental truth about the universe because our brains are physical systems which themselves can be modeled by mathematics, and that is (empirical) evidence that our universe is in some sense "closed" under Turing-equivalence (with quantum randomness being the lone notable exception). That is the kind of universality embodied in the idea that TM's can emulated "anything we can dream up". It's called the Church-Turing thesis [2] and unlike the universality of universal TM's it cannot be proven because a counterexample might be discovered at any time. [1] https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness... [2] https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis
- adastra22 2y ago
  I appreciate the detail, but for the record I don’t think we disagree. There’s a lot that I had to oversimplify in my already long comment.
- Y_Y 2y ago
  > all known physical phenomena (with the exception of quantum measurements) can be modeled mathematically Of course you can model quantum measurements! And Wigner certainly knew so.
fluoridation 2y ago
Hmm... Turing machines are "universal" in the sense that they can be used to model the behavior of any finite process that can compute a computable function. So if a process exists that can compute something, it must be modelable as a Turing machine, and its operation must be analyzable as a finite series of elementary instructions that are analogous to those of a Turing machine. So I don't see how it doesn't make sense to ask the question "if this process has a better asymptotic behavior than is theoretically possible, where did the computation take place?" I would be more inclined to believe that someone is not counting properly, than it being some kind of hypercomputer. Or even more simply that the process is just physically impossible.
- JumpCrisscross 2y ago
  > if a process exists that can compute something, it must be modelable as a Turing machine Yes. > and its operation must be analyzable as a finite series of elementary instructions that are analogous to those of a Turing machine Analyzable, sure. MWI is fine as an analytic tool in the same way e.g. virtual particles and holes are. Nothing here requires that any of these analytic tools are physically corresponded to.
  - fluoridation 2y ago
    I didn't say I favored the MWI. My point is simply that the question of where computation took place shouldn't be dismissed. Like I said, I would be more inclined to think someone is not counting properly. As a simple example, a parallel program may run in half the time, but that doesn't mean it executed half as many operations.
    - JumpCrisscross 2y ago
      > the question of where computation took place shouldn't be dismissed Sure. But it also shouldn’t be glorified as adding anything to an old debate—every QCD calculation has this dynamic of lots of classical “computations” happening seemingly simultaneously.
    - 2y ago

slowmovintarget 2y ago

According to this ( https://arxiv.org/pdf/2302.10778 https://arxiv.org/pdf/2302.10778 ), there are no branches, just decoherence (minus the "collapse").

adastra22 2y ago
A paper proposing a radically different formulation of quantum mechanics, with only a half dozen non-author-citations, so heavy with jargon that it's hard to figure out what the author is claiming. Sorry, my crank meter is dialed to 11 right now and I don't think this is worth spending further time on.
- slowmovintarget 2y ago
  Jacob Barandes is a professor of physics at Harvard (not a crank). He recently did a great podcast with Kurt Jaimungal [1]. In the interview he explains that every year he searches for a good way to introduce his students to quantum mechanics, and every year he's ended up being unsatisfied with the approach and started again. One year he decided to attempt describing systems with traditional mechanics, using probabilities (stochastic mechanics). He worked at it and worked at it, assuming that he would eventually have to take some leap to cross the chasm into the world of gauge theory, Lie Groups, and Hilbert spaces. What he found is, to his surprise, the math just seemed to fit together at some point. That is, he found a mapping, just as the path integral is a mapping into the math of the wave function, and it just kind of worked. He had been under the assumption that it shouldn't. It turns out, that in doing his stochastic mechanics, he had used mathematical descriptions that were indivisible. That is once a given process began, it could not be sliced into smaller and smaller time slices. It had to complete and yield a result. This was what he called a non-Markov stochastic process. Apparently all previous attempts at this used Markov processes, which are divisible like Hilbert vector calculations or the path integral. It turns out that things like "collapse" of the wave function, and all the quantum weirdness arose from how the math worked with the wave function and Hilbert space, not from anything intrinsic to the mechanics of the universe (at least that's what his equivalent math was telling him). So in his stochastic non-Markov model, there is no collapse, just decoherence. There is always a result, and the intermediate states (where all the quantum oddities live) aren't real. He mentions being really disappointed at seeing all the magic of quantum mechanics just kind of vanish. From what he could tell, it was just a trick of the wrong kind of math. [1] https://www.youtube.com/live/7oWip00iXbo https://www.youtube.com/live/7oWip00iXbo
  - adastra22 2y ago
    Mathematicians, even from prestigious universities, have been wrong before. It's the danger of a discipline that doesn't yet have machine-checkable proofs.
    - slowmovintarget 2y ago

lisper 2y ago

> Turing machines are only “universal” in the sense that they can represent any statement of mathematical logic That's not quite right. TM's in general are not universal. The "universality" of TMs has to do with the existence of a universal TM which is capable of emulating any other TM by putting a specification of the TM to be emulated on the universal TM's tape. The reason this matters is that once you've built a universal TM, you never have to build any more hardware. Any TM can then be emulated in software. That result is due to Turing. The relationship between TMs and mathematical logic is of a fundamentally different character. It turns out that any system of formal logic can be emulated by a TM (and hence by a UTM), but that is a different result, mainly due to Godel, not Turing. There is also the empirical observation (famously noted by Eugene Wigner [1]) that all known physical phenomena (with the exception of quantum measurements) can be modeled mathematically, and hence can be emulated by a TM, and hence can be emulated by a UTM. But it is entirely possible that a new class of physical phenomena could be discovered tomorrow that cannot be modeled mathematically. But here's the thing: no one has been able to come up with any idea of what such a phenomenon could possibly look like, and there is a reason to believe that this is not just a failure of imagination but actually a fundamental truth about the universe because our brains are physical systems which themselves can be modeled by mathematics, and that is (empirical) evidence that our universe is in some sense "closed" under Turing-equivalence (with quantum randomness being the lone notable exception). That is the kind of universality embodied in the idea that TM's can emulated "anything we can dream up". It's called the Church-Turing thesis [2] and unlike the universality of universal TM's it cannot be proven because a counterexample might be discovered at any time. [1] https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness... [2] https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis

adastra22 2y ago
I appreciate the detail, but for the record I don’t think we disagree. There’s a lot that I had to oversimplify in my already long comment.
Y_Y 2y ago
> all known physical phenomena (with the exception of quantum measurements) can be modeled mathematically Of course you can model quantum measurements! And Wigner certainly knew so.

fluoridation 2y ago

Hmm... Turing machines are "universal" in the sense that they can be used to model the behavior of any finite process that can compute a computable function. So if a process exists that can compute something, it must be modelable as a Turing machine, and its operation must be analyzable as a finite series of elementary instructions that are analogous to those of a Turing machine. So I don't see how it doesn't make sense to ask the question "if this process has a better asymptotic behavior than is theoretically possible, where did the computation take place?" I would be more inclined to believe that someone is not counting properly, than it being some kind of hypercomputer. Or even more simply that the process is just physically impossible.

JumpCrisscross 2y ago
> if a process exists that can compute something, it must be modelable as a Turing machine Yes. > and its operation must be analyzable as a finite series of elementary instructions that are analogous to those of a Turing machine Analyzable, sure. MWI is fine as an analytic tool in the same way e.g. virtual particles and holes are. Nothing here requires that any of these analytic tools are physically corresponded to.
- fluoridation 2y ago
  I didn't say I favored the MWI. My point is simply that the question of where computation took place shouldn't be dismissed. Like I said, I would be more inclined to think someone is not counting properly. As a simple example, a parallel program may run in half the time, but that doesn't mean it executed half as many operations.
  - JumpCrisscross 2y ago
    > the question of where computation took place shouldn't be dismissed Sure. But it also shouldn’t be glorified as adding anything to an old debate—every QCD calculation has this dynamic of lots of classical “computations” happening seemingly simultaneously.
  - 2y ago