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I’m barely even a layman at machine learning or quantum mechanics. But isn’t a large essence of quantum mechanics essentially a love fest between probability an

I’m barely even a layman at machine learning or quantum mechanics. But isn’t a large essence of quantum mechanics essentially a love fest between probability and physics? And people keep complaining that AI/ML is just lots and lots of statistics? Should I be surprised that heavy duty statistics computing has a resonance with statistics of physics? I admit I only skimmed the article past the opening paragraphs (see layman).

frutiger 5y ago
> But isn’t a large essence of quantum mechanics essentially a love fest between probability and physics? Not really. Quantum physics is about state being represented by a linear combination of vectors in a state space rather than a point in a state space. Additionally, it’s about how that state evolves over time. And finally about how observables are projections of the state onto some ortholinear basis (this is where the probability creeps in and no one really understands why).
- raziel2701 5y ago
  Expectation values and psi^2 is literally probability. Quantum mechanics tells us nature is inherently probabilistic at the quantum scales.
  - mvakde 5y ago
    QM is perfectly deterministic. Probability only comes into play during measurement. Now here's the thing, nobody knows how does measurement work. Currently, we just assume measurement is a probabilistic black box. There are theories about measurement that do away with probability, but they have to skirt around Bell's inequality in ingenious ways
    - arrow7000 5y ago
      So in other words it's not perfectly deterministic at all?
      - FeepingCreature 5y ago
        Layman, but: there are perfectly deterministic interpretations. The "default" view (Copenhagen) has randomness, because it's trying to recover a classical measurement, but there's views that discard that entirely, such as many-worlds, which is completely deterministic, including measurement, at the expense of discarding any notion of definiteness. Ie. in MW you can't say that "outcome X happened, and outcome Y did not", only "we the observer have become entangled with outcome X." This does difficult things to probability, though there's approaches to recover a notion of likelihood even in this model, such as the decision theoretic approach https://en.wikipedia.org/wiki/Many-worlds_interpretation#Decision_theory https://en.wikipedia.org/wiki/Many-worlds_interpretation#Dec... where they :layman handwave: show that the Born probabilities are the only consistent assignment that exists at all, or something. I also vaguely remember reading an approach that showed that looking back at the ultimate history of the universe, all but a vanishing fraction of branches had experienced histories consistent with the Born rule, but I don't have a link or name for that. Anyways, in a MW universe there's no probability, because every outcome occurs, but there's still "indexical uncertainty", which is to say you don't necessarily know which branch of the universe you are presently inhabiting. Addendum: All (surviving) QM interpretations are empirically equivalent, anyways, so this is purely a philosophical question.
        mirekrusin 5y ago
        In other words you always win lottery, you just happen to be entangled with universe where you don't, sorry.
        FeepingCreature 5y ago
        That's correct.
      - mannerheim 5y ago
        This is dependent on your point of view. The Copenhagen interpretation is probabilistic. However, there are reasons to believe that wavefunction collapse is an illusion brought on by something called decoherence. The gist of decoherence is that the interaction of a quantum system with its surroundings couples that system to its environment, bringing about the appearance of wavefunction collapse, when the system + environment is still a single quantum system evolving together. This is a purely philosophical matter, though, and beyond the scope of science, since such things are not testable. However, there is a mathematical reason to prefer decoherence over Copenhagen, which is that wavefunction collapse is inherently non-unitary, which is to say that it's irreversible. The measurement process in Copenhagen is akin to applying a non-invertible matrix to the wavefunction, resulting in its appearance in a single state. The problem with this is that all known processes in quantum mechanics evolve according to unitary transformations. Interactions with electromagnetism and the strong and weak forces all involve unitary transformations. So where does this non-unitary behaviour come from? Decoherence theories suggest that when you're performing a measurement, this is a single transformation on the system + environment, which is still unitary, but when you examine the state of the system, for a given state of the environment, it appears to be non-unitary. In practice, however, measurements are still probabilistic, so in that sense it doesn't really matter; this is mostly just a philosophical question. However, in that sense, if somebody has this point of view, they could perhaps say that quantum mechanics is just as deterministic and not any more probabilistic than, say, classical statistical mechanics, where there's the appearance of randomness not because of non-deterministic laws of physics, but because of various issues like - even if they were classical particles, you couldn't hope to measure their positions and momenta - even if you could do so, calculation would be impractical to the point of impossibility - even if you had a supercomputer that was up to the feat, minuscule amounts of initial error (or accumulated rounding error over time) would result in drastically different long-term behaviour These combined would mean that only summary statistics and expectation values could be offered for such a system, even if all of the dynamics were fully deterministic with classical particles.
- omnicognate 5y ago
  It's the other way round. The vectors-in-state-spaces representation is necessitated by the fact that it is a probabilistic theory, and has no physical content itself besides that. The first half of "The Structure and Intepretation of Quantum Mechanics" by R.I.G. Hughes [1] lays this out very clearly. He derives most of the framework simply from the premise that it's a probabilistic physical theory. Then he shows how you can add a single extra element to it (eg. unitarity [2]) to turn it into full blown quantum mechanics (i.e. derive Schrodinger's equation), and lists several alternative ways you can do that. It's a great book, and accessible to the layman. [1] https://www.hup.harvard.edu/catalog.php?isbn=9780674843929 https://www.hup.harvard.edu/catalog.php?isbn=9780674843929 [2] https://en.wikipedia.org/wiki/Unitarity_(physics) https://en.wikipedia.org/wiki/Unitarity_(physics)
  - _0ffh 5y ago
    >The first half of "The Structure and Intepretation of Quantum Mechanics"... Is this a coincidence, or might that name be inspired by Abelson & Sussman?
    - omnicognate 5y ago
      I think it's a coincidence - an old comment of mine about that: https://news.ycombinator.com/item?id=19769946 https://news.ycombinator.com/item?id=19769946
  - l33tman 5y ago
    Well after all that was how QM was invented back in the days as well (they had to find underlying explanations for the probabilistic experiment outcomes). But see the PBR theorem ( https://en.wikipedia.org/wiki/PBR_theorem https://en.wikipedia.org/wiki/PBR_theorem ) regarding the importance of the quantum state itself and its "physical content".

frutiger 5y ago

> But isn’t a large essence of quantum mechanics essentially a love fest between probability and physics? Not really. Quantum physics is about state being represented by a linear combination of vectors in a state space rather than a point in a state space. Additionally, it’s about how that state evolves over time. And finally about how observables are projections of the state onto some ortholinear basis (this is where the probability creeps in and no one really understands why).

raziel2701 5y ago
Expectation values and psi^2 is literally probability. Quantum mechanics tells us nature is inherently probabilistic at the quantum scales.
- mvakde 5y ago
  QM is perfectly deterministic. Probability only comes into play during measurement. Now here's the thing, nobody knows how does measurement work. Currently, we just assume measurement is a probabilistic black box. There are theories about measurement that do away with probability, but they have to skirt around Bell's inequality in ingenious ways
  - arrow7000 5y ago
    So in other words it's not perfectly deterministic at all?
    - FeepingCreature 5y ago
      Layman, but: there are perfectly deterministic interpretations. The "default" view (Copenhagen) has randomness, because it's trying to recover a classical measurement, but there's views that discard that entirely, such as many-worlds, which is completely deterministic, including measurement, at the expense of discarding any notion of definiteness. Ie. in MW you can't say that "outcome X happened, and outcome Y did not", only "we the observer have become entangled with outcome X." This does difficult things to probability, though there's approaches to recover a notion of likelihood even in this model, such as the decision theoretic approach https://en.wikipedia.org/wiki/Many-worlds_interpretation#Decision_theory https://en.wikipedia.org/wiki/Many-worlds_interpretation#Dec... where they :layman handwave: show that the Born probabilities are the only consistent assignment that exists at all, or something. I also vaguely remember reading an approach that showed that looking back at the ultimate history of the universe, all but a vanishing fraction of branches had experienced histories consistent with the Born rule, but I don't have a link or name for that. Anyways, in a MW universe there's no probability, because every outcome occurs, but there's still "indexical uncertainty", which is to say you don't necessarily know which branch of the universe you are presently inhabiting. Addendum: All (surviving) QM interpretations are empirically equivalent, anyways, so this is purely a philosophical question.
      - mirekrusin 5y ago
        In other words you always win lottery, you just happen to be entangled with universe where you don't, sorry.
        FeepingCreature 5y ago
        That's correct.
    - mannerheim 5y ago
      This is dependent on your point of view. The Copenhagen interpretation is probabilistic. However, there are reasons to believe that wavefunction collapse is an illusion brought on by something called decoherence. The gist of decoherence is that the interaction of a quantum system with its surroundings couples that system to its environment, bringing about the appearance of wavefunction collapse, when the system + environment is still a single quantum system evolving together. This is a purely philosophical matter, though, and beyond the scope of science, since such things are not testable. However, there is a mathematical reason to prefer decoherence over Copenhagen, which is that wavefunction collapse is inherently non-unitary, which is to say that it's irreversible. The measurement process in Copenhagen is akin to applying a non-invertible matrix to the wavefunction, resulting in its appearance in a single state. The problem with this is that all known processes in quantum mechanics evolve according to unitary transformations. Interactions with electromagnetism and the strong and weak forces all involve unitary transformations. So where does this non-unitary behaviour come from? Decoherence theories suggest that when you're performing a measurement, this is a single transformation on the system + environment, which is still unitary, but when you examine the state of the system, for a given state of the environment, it appears to be non-unitary. In practice, however, measurements are still probabilistic, so in that sense it doesn't really matter; this is mostly just a philosophical question. However, in that sense, if somebody has this point of view, they could perhaps say that quantum mechanics is just as deterministic and not any more probabilistic than, say, classical statistical mechanics, where there's the appearance of randomness not because of non-deterministic laws of physics, but because of various issues like - even if they were classical particles, you couldn't hope to measure their positions and momenta - even if you could do so, calculation would be impractical to the point of impossibility - even if you had a supercomputer that was up to the feat, minuscule amounts of initial error (or accumulated rounding error over time) would result in drastically different long-term behaviour These combined would mean that only summary statistics and expectation values could be offered for such a system, even if all of the dynamics were fully deterministic with classical particles.
omnicognate 5y ago
It's the other way round. The vectors-in-state-spaces representation is necessitated by the fact that it is a probabilistic theory, and has no physical content itself besides that. The first half of "The Structure and Intepretation of Quantum Mechanics" by R.I.G. Hughes [1] lays this out very clearly. He derives most of the framework simply from the premise that it's a probabilistic physical theory. Then he shows how you can add a single extra element to it (eg. unitarity [2]) to turn it into full blown quantum mechanics (i.e. derive Schrodinger's equation), and lists several alternative ways you can do that. It's a great book, and accessible to the layman. [1] https://www.hup.harvard.edu/catalog.php?isbn=9780674843929 https://www.hup.harvard.edu/catalog.php?isbn=9780674843929 [2] https://en.wikipedia.org/wiki/Unitarity_(physics) https://en.wikipedia.org/wiki/Unitarity_(physics)
- _0ffh 5y ago
  >The first half of "The Structure and Intepretation of Quantum Mechanics"... Is this a coincidence, or might that name be inspired by Abelson & Sussman?
  - omnicognate 5y ago
    I think it's a coincidence - an old comment of mine about that: https://news.ycombinator.com/item?id=19769946 https://news.ycombinator.com/item?id=19769946
- l33tman 5y ago
  Well after all that was how QM was invented back in the days as well (they had to find underlying explanations for the probabilistic experiment outcomes). But see the PBR theorem ( https://en.wikipedia.org/wiki/PBR_theorem https://en.wikipedia.org/wiki/PBR_theorem ) regarding the importance of the quantum state itself and its "physical content".