4 ms·

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.
- l33tman 5y ago
  Decoherence is easiest to see in a MW setting. The basic observed fact is that at some point you need an observer that makes a clear, consistent observation. Decoherence is a concept about an isolated state (that can be multi-valued, like dead cat / alive cat) that leaks out into the environment by entanglement with more and more environment states, and proceeds to "pull in" versions of you (as the observer) one by one as the versions of you are also entangled with the environment. You can recurse this analysis and eventually you reach a point where the "leaf" quantum state only involves one outcome and is entangled with a single version of you, and at that point you don't need any collapse anymore. Also this process is completely deterministic. The Copenhagen interpretation is a shortcut that basically says let's ignore all those intermediate interactions between the original "weird" state and the observers, in a very real sense you "collapse" the chain of entanglements. You also ignore that you have multiple observer versions of yourself and instead explain it as a probabilistic distribution from the point of view of the "pre-split" observer. This has turned out to be a good enough strategy in practical physics since the 1920s! Note that none of this explains the quantitative aspect of it, the Born rule, or what it actually means that something's more probable than not. It just discusses how you can start with superpositions and end up with observers who don't see the superpositions.
mvakde 5y ago
Well, depends on your interpretation of QM, and whether you consider measurement to come under the purview of QM. I like to keep measurement separate from QM, since we don't have an acceptable theory to explain it. We don't even agree on how to define measurement. Parent comment saying "nature is inherently probabilistic" is false. At best, you can say "nature may be probabilistic". Saying "QM is perfectly deterministic" is fine because nature ≠ QM (although this is my opinion, maybe others disagree).
deleted 5y ago
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simiones 5y ago
It's deterministic in the sense that QM gives you an exact answer about what happens at the quantum scale for any interaction, without any probability involved. However, the exact values that QM predicts are not real numbers for speed etc, they are a complex numbers describing a wave, with different values for different positions in space-time. These numbers precisely describe how the wave-packet will interact with other wave-packets. But, if you want to do a classical measurement, then the only known relationship between the wave description and the outcome of your experiment is the Born rule - the amplitude of the wave at a point X in space-time is proportional to the probability that the particle will be detected at that point.

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.

l33tman 5y ago
Decoherence is easiest to see in a MW setting. The basic observed fact is that at some point you need an observer that makes a clear, consistent observation. Decoherence is a concept about an isolated state (that can be multi-valued, like dead cat / alive cat) that leaks out into the environment by entanglement with more and more environment states, and proceeds to "pull in" versions of you (as the observer) one by one as the versions of you are also entangled with the environment. You can recurse this analysis and eventually you reach a point where the "leaf" quantum state only involves one outcome and is entangled with a single version of you, and at that point you don't need any collapse anymore. Also this process is completely deterministic. The Copenhagen interpretation is a shortcut that basically says let's ignore all those intermediate interactions between the original "weird" state and the observers, in a very real sense you "collapse" the chain of entanglements. You also ignore that you have multiple observer versions of yourself and instead explain it as a probabilistic distribution from the point of view of the "pre-split" observer. This has turned out to be a good enough strategy in practical physics since the 1920s! Note that none of this explains the quantitative aspect of it, the Born rule, or what it actually means that something's more probable than not. It just discusses how you can start with superpositions and end up with observers who don't see the superpositions.

mvakde 5y ago

Well, depends on your interpretation of QM, and whether you consider measurement to come under the purview of QM. I like to keep measurement separate from QM, since we don't have an acceptable theory to explain it. We don't even agree on how to define measurement. Parent comment saying "nature is inherently probabilistic" is false. At best, you can say "nature may be probabilistic". Saying "QM is perfectly deterministic" is fine because nature ≠ QM (although this is my opinion, maybe others disagree).

deleted 5y ago

[deleted]

simiones 5y ago

It's deterministic in the sense that QM gives you an exact answer about what happens at the quantum scale for any interaction, without any probability involved. However, the exact values that QM predicts are not real numbers for speed etc, they are a complex numbers describing a wave, with different values for different positions in space-time. These numbers precisely describe how the wave-packet will interact with other wave-packets. But, if you want to do a classical measurement, then the only known relationship between the wave description and the outcome of your experiment is the Born rule - the amplitude of the wave at a point X in space-time is proportional to the probability that the particle will be detected at that point.