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Not sure if you got what I'm saying...in case I didn't explain it clearly enough: Bell's inequalities show that quantum randomness CANNOT be explained by an und

by jules 14y ago

Not sure if you got what I'm saying...in case I didn't explain it clearly enough: Bell's inequalities show that quantum randomness CANNOT be explained by an underlying deterministic law of physics that we're ignoring. With ordinary probability you can never find out whether it's truly random or whether there is some underlying deterministic process that you just don't have knowledge about. Turns out with quantum mechanics, which works with probability amplitudes instead of just probabilities, you can rule out such an underlying deterministic process (again modulo technicalities). This is one of the most striking results of physics, and Einstein himself didn't believe it at first.

loup-vaillant 14y ago
Disclaimer: I have read http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ cover to cover. Let's see with an example. A half sievered mirror, a photon going through (or bouncing), and 2 detectors. You say there is no hidden variable that would allow us to predict which detector we will see go off. I agree. It doesn't mean however that the laws of physics have true randomness in them. Under the Everett interpretation, two "worlds" (blobs of amplitude) are created: one in which detector 1 goes off, and one in which detector 2 goes off. from the outside, this is purely deterministic. The only randomness lies in our subjective experience. The only question remaining is why do we experience the Born statistics (based on square moduli), rather than something else (like, based on moduli)? We would have true randomness at the fundamental level if some form of the Copenhagen interpretation where true. But believing the blob of amplitude we don't see would mysteriously disappear, violating the equations in the process? That's just nuts. If this idea appeared after the Everett interpretation, it would have been ridiculed.
- jules 14y ago
  Many Worlds vs Copenhagen is a largely irrelevant debate. It doesn't make any observable difference whatsoever, so it's metaphysics. By analogy to classical probability, Copenhagen is like looking at the sampling of a random variable, and Many Worlds is like looking a weighted list of possible outcomes. It's just a different perspective on the same thing. I say largely irrelevant because there is a minority of people (including, if I'm not mistaken, Nobel prize winner 't Hooft) who say that neither Many Worlds nor Copenhagen is right, because there are hidden assumptions in EPR that are overlooked. Since you seem to be a fan of lesswrong.com, this should appeal to you ;-). I think for the rest we are in agreement, I misinterpreted "as long as we didn't find complete laws of physics, we're bound to ignore something" and "Probability is still in the mind. Not in the territory.". The latter statement becomes rather tautological and its meaning rather weak if you include QM randomness though. In the context of the frequentist vs Bayesian debate it means something far stronger.
  - loup-vaillant 14y ago
    Funnily enough, "we didn't find complete laws of physics" is a reason why I'm pretty sure Many Worlds as is is false to some extent. I'm pretty sure however that the Copenhagen interpretation is much farther from the truth. As for how this is metaphysics… Sure, but no more that wondering if a photon (or a colonization ship) you just send into deep space, outside the observable universe, still exists. I mean, I don't care if it's meta or not. I just trust Occam's razor (to the extent it gives prior probabilities, not prior certainties), and leave it at that.
    - jules 14y ago
      Occams razor implies that you should be agnostic to things that are not observable, not that you should pick your metaphysics. Whether the alternative universes actually exist or not is completely irrelevant. The rational thing to say is "I don't care, I don't want to spend brainpower worrying about this". In mathematical terms, the hypothesis "many worlds is true" has more information content than "the predictions of QM are true" since the former implies the latter, hence Occam's razor prefers the latter. And indeed, you should also be agnostic to whether or not there is a teapot floating outside the observable universe.
      - loup-vaillant 14y ago
        I'm not sure I agree. Things such acausal trade may mean we should know about what we can't affect (nor can affect us). But even then, I was merely talking about truth for truth's sake, where otherwise worthless knowledge does matter. Nitpick: You didn't even need Occam's Razor: Many World implies that the QM predictions are true. of course the truth of those predictions are more probable than Many Worlds. I, on the other hand, used Occam's Razor to compare Many Worlds and Copenhagen, which are mutually exclusive. I agree agnosticism is good. I'd rather be aware of my own ignorance. I like it better however when I'm also aware of its magnitude. Probability theory does just that. I don't know if Many Worlds is true, nor do I know if Copenhagen is false. But my current state of ignorance is more precise than that.

by jules 14y ago

loup-vaillant 14y ago

Disclaimer: I have read http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ cover to cover. Let's see with an example. A half sievered mirror, a photon going through (or bouncing), and 2 detectors. You say there is no hidden variable that would allow us to predict which detector we will see go off. I agree. It doesn't mean however that the laws of physics have true randomness in them. Under the Everett interpretation, two "worlds" (blobs of amplitude) are created: one in which detector 1 goes off, and one in which detector 2 goes off. from the outside, this is purely deterministic. The only randomness lies in our subjective experience. The only question remaining is why do we experience the Born statistics (based on square moduli), rather than something else (like, based on moduli)? We would have true randomness at the fundamental level if some form of the Copenhagen interpretation where true. But believing the blob of amplitude we don't see would mysteriously disappear, violating the equations in the process? That's just nuts. If this idea appeared after the Everett interpretation, it would have been ridiculed.

jules 14y ago
Many Worlds vs Copenhagen is a largely irrelevant debate. It doesn't make any observable difference whatsoever, so it's metaphysics. By analogy to classical probability, Copenhagen is like looking at the sampling of a random variable, and Many Worlds is like looking a weighted list of possible outcomes. It's just a different perspective on the same thing. I say largely irrelevant because there is a minority of people (including, if I'm not mistaken, Nobel prize winner 't Hooft) who say that neither Many Worlds nor Copenhagen is right, because there are hidden assumptions in EPR that are overlooked. Since you seem to be a fan of lesswrong.com, this should appeal to you ;-). I think for the rest we are in agreement, I misinterpreted "as long as we didn't find complete laws of physics, we're bound to ignore something" and "Probability is still in the mind. Not in the territory.". The latter statement becomes rather tautological and its meaning rather weak if you include QM randomness though. In the context of the frequentist vs Bayesian debate it means something far stronger.
- loup-vaillant 14y ago
  Funnily enough, "we didn't find complete laws of physics" is a reason why I'm pretty sure Many Worlds as is is false to some extent. I'm pretty sure however that the Copenhagen interpretation is much farther from the truth. As for how this is metaphysics… Sure, but no more that wondering if a photon (or a colonization ship) you just send into deep space, outside the observable universe, still exists. I mean, I don't care if it's meta or not. I just trust Occam's razor (to the extent it gives prior probabilities, not prior certainties), and leave it at that.
  - jules 14y ago
    Occams razor implies that you should be agnostic to things that are not observable, not that you should pick your metaphysics. Whether the alternative universes actually exist or not is completely irrelevant. The rational thing to say is "I don't care, I don't want to spend brainpower worrying about this". In mathematical terms, the hypothesis "many worlds is true" has more information content than "the predictions of QM are true" since the former implies the latter, hence Occam's razor prefers the latter. And indeed, you should also be agnostic to whether or not there is a teapot floating outside the observable universe.
    - loup-vaillant 14y ago
      I'm not sure I agree. Things such acausal trade may mean we should know about what we can't affect (nor can affect us). But even then, I was merely talking about truth for truth's sake, where otherwise worthless knowledge does matter. Nitpick: You didn't even need Occam's Razor: Many World implies that the QM predictions are true. of course the truth of those predictions are more probable than Many Worlds. I, on the other hand, used Occam's Razor to compare Many Worlds and Copenhagen, which are mutually exclusive. I agree agnosticism is good. I'd rather be aware of my own ignorance. I like it better however when I'm also aware of its magnitude. Probability theory does just that. I don't know if Many Worlds is true, nor do I know if Copenhagen is false. But my current state of ignorance is more precise than that.