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> And the answer is: the classical world emerges by a process of decoherence, which is to say, by the creation of large (O(10^23)) networks of entanglements whi

> And the answer is: the classical world emerges by a process of decoherence, which is to say, by the creation of large (O(10^23)) networks of entanglements which (it can be shown mathematically) have behavior that is indistinguishable from classical systems. This is the motivation for decoherence and for the Everettian view where the psi function is "the only real thing" and everything else is derived. It is often talked about as if actually accomplished. But it was not; the behaviour of quantum systems, even with decoherence, was not yet shown to be indistinguishable from the classical systems. Neither the fact that measurements have one outcome, nor Born's rules for probability were derived from this decoherence idea yet. One thing that follows from decoherence hypothesis is decay of coherence elements in density matrices, but this is not enough to get explanation for single outcomes or for Born's rules.

lisper 8y ago
Ironically, I am just in the process of preparing a talk on the history of the atomic theory. Even as late as 1905 when Einstein published his work on brownian motion it was still highly controversial whether atoms were "really real" or just a mathematical contrivance. Some people are able to maintain skepticism even in the face of overwhelming evidence. > Neither the fact that measurements have one outcome, nor Born's rules for probability were derived from this decoherence idea yet. That is because it is not the case that measurements have one outcome. Measurements appear to have one outcome from the perspective of a given classical observer, and the outcome observed by any given observer will be classically consistent with all the other observations that observer makes [1]. The Born rule (which, it must be stressed, is not fundamental, but only apparent from the point of view of any given observer) follows from that, not mathematically but logically [2]. [1] https://arxiv.org/pdf/quant-ph/9605002.pdf https://arxiv.org/pdf/quant-ph/9605002.pdf [2] https://www.scottaaronson.com/papers/island.pdf https://www.scottaaronson.com/papers/island.pdf
- posix_me_less 8y ago
  Thanks for the links. > "That is because it is not the case that measurements have one outcome. Measurements appear to have one outcome from the perspective of a given classical observer [but actually have none]" is a big claim, but it lacks "overwhelming evidence". Quantum theory self-consistency is a problem worthy of investigation, but achieving self-consistency is only one of the many possible valid results. This result is not needed as much as many people seem to think; certainly not as much as to reify psi function above objective results of measurements and claim the quoted part. It is a methodological error; instead of shaping the theory around the measurement results, it is rejecting the fact that those measurement results exist. > The Born rule (which, it must be stressed, is not fundamental, but only apparent from the point of view of any given observer) follows from that, not mathematically but logically I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea? All these kinds of proofs from algebraic formalism seem to achieve is something like "if Born's rule would not be true, we would have problems with the theory" which is not very interesting; we have some big problems with the theory even without decoherence.
  - lisper 8y ago
    > it is rejecting the fact that those measurement results exist Well, sort of. I prefer to think of it as replacing one explanatory hypothesis with a superior one, one that is actually consistent with the evidence. To wit: The observation that requires explaining is that classical measurements are consistent across space and time. The usual explanation for this is that a classical objective reality exists, and that measurement faithfully reflects the state of this reality. This is a plausible explanation. Einstein believed it. But Bell's theorem and subsequent experiments show it to be false. The correct explanation is that classical correlation emerges from the Shroedinger equation alone. There is no objective classical reality. If there were, it would be possible to construct a local hidden variable theory consistent with all observations. But it's not so there isn't. It is only because our subjective experience is (necessarily) classical that we find all this hard to accept. > I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea? It's the part about Gleason's theorem: https://en.wikipedia.org/wiki/Gleason%27s_theorem https://en.wikipedia.org/wiki/Gleason%27s_theorem See also: https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html
    - posix_me_less 8y ago
      > But Bell's theorem and subsequent experiments show it to be false. I think this is an unfounded conclusion. Sure, Bell's theorem and the experiments it inspired did make lots of contribution to investigation of these foundational problems. But Bell's theorem is about a specific class of probabilistic descriptions. It does not rule out "classical objective reality" unless you restrict meaning of this term so much as to achieve that. Bell himself and many other people who studied the theorem insisted that the theorem is about local hidden variable models, as opposed to nonlocal models. Nothing general is implied about "objective reality". On the experimental side, I am not aware of any experiment that had ruled out objective reality. How would you even test such a nebulous concept experimentally? We can test only specific predictions.
      - lisper 8y ago
        > Nothing general is implied about "objective reality". I disagree. The fact that nature cannot be described by any local hidden variable theory tells you a lot about the nature of reality. There is a real difference between quantum randomness and classical ignorance, and so there is a real difference -- one which you can experimentally measure -- between a particle whose position you don't know because you haven't looked at the result of a measurement, and a particle whose position you don't know because it hasn't been measured at all. It is still, perhaps, debatable whether that difference lies in the particle or in you. But if you want to argue that the difference lies in the particle then the burden is on you to provide an account of when and how the transition happens. No one has succeeded in this, and it's not for want of trying.

lisper 8y ago

Ironically, I am just in the process of preparing a talk on the history of the atomic theory. Even as late as 1905 when Einstein published his work on brownian motion it was still highly controversial whether atoms were "really real" or just a mathematical contrivance. Some people are able to maintain skepticism even in the face of overwhelming evidence. > Neither the fact that measurements have one outcome, nor Born's rules for probability were derived from this decoherence idea yet. That is because it is not the case that measurements have one outcome. Measurements appear to have one outcome from the perspective of a given classical observer, and the outcome observed by any given observer will be classically consistent with all the other observations that observer makes [1]. The Born rule (which, it must be stressed, is not fundamental, but only apparent from the point of view of any given observer) follows from that, not mathematically but logically [2]. [1] https://arxiv.org/pdf/quant-ph/9605002.pdf https://arxiv.org/pdf/quant-ph/9605002.pdf [2] https://www.scottaaronson.com/papers/island.pdf https://www.scottaaronson.com/papers/island.pdf

posix_me_less 8y ago
Thanks for the links. > "That is because it is not the case that measurements have one outcome. Measurements appear to have one outcome from the perspective of a given classical observer [but actually have none]" is a big claim, but it lacks "overwhelming evidence". Quantum theory self-consistency is a problem worthy of investigation, but achieving self-consistency is only one of the many possible valid results. This result is not needed as much as many people seem to think; certainly not as much as to reify psi function above objective results of measurements and claim the quoted part. It is a methodological error; instead of shaping the theory around the measurement results, it is rejecting the fact that those measurement results exist. > The Born rule (which, it must be stressed, is not fundamental, but only apparent from the point of view of any given observer) follows from that, not mathematically but logically I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea? All these kinds of proofs from algebraic formalism seem to achieve is something like "if Born's rule would not be true, we would have problems with the theory" which is not very interesting; we have some big problems with the theory even without decoherence.
- lisper 8y ago
  > it is rejecting the fact that those measurement results exist Well, sort of. I prefer to think of it as replacing one explanatory hypothesis with a superior one, one that is actually consistent with the evidence. To wit: The observation that requires explaining is that classical measurements are consistent across space and time. The usual explanation for this is that a classical objective reality exists, and that measurement faithfully reflects the state of this reality. This is a plausible explanation. Einstein believed it. But Bell's theorem and subsequent experiments show it to be false. The correct explanation is that classical correlation emerges from the Shroedinger equation alone. There is no objective classical reality. If there were, it would be possible to construct a local hidden variable theory consistent with all observations. But it's not so there isn't. It is only because our subjective experience is (necessarily) classical that we find all this hard to accept. > I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea? It's the part about Gleason's theorem: https://en.wikipedia.org/wiki/Gleason%27s_theorem https://en.wikipedia.org/wiki/Gleason%27s_theorem See also: https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html
  - posix_me_less 8y ago
    > But Bell's theorem and subsequent experiments show it to be false. I think this is an unfounded conclusion. Sure, Bell's theorem and the experiments it inspired did make lots of contribution to investigation of these foundational problems. But Bell's theorem is about a specific class of probabilistic descriptions. It does not rule out "classical objective reality" unless you restrict meaning of this term so much as to achieve that. Bell himself and many other people who studied the theorem insisted that the theorem is about local hidden variable models, as opposed to nonlocal models. Nothing general is implied about "objective reality". On the experimental side, I am not aware of any experiment that had ruled out objective reality. How would you even test such a nebulous concept experimentally? We can test only specific predictions.
    - lisper 8y ago
      > Nothing general is implied about "objective reality". I disagree. The fact that nature cannot be described by any local hidden variable theory tells you a lot about the nature of reality. There is a real difference between quantum randomness and classical ignorance, and so there is a real difference -- one which you can experimentally measure -- between a particle whose position you don't know because you haven't looked at the result of a measurement, and a particle whose position you don't know because it hasn't been measured at all. It is still, perhaps, debatable whether that difference lies in the particle or in you. But if you want to argue that the difference lies in the particle then the burden is on you to provide an account of when and how the transition happens. No one has succeeded in this, and it's not for want of trying.