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That's a lot to unpack - let me make sure I have this right. Quantum theorists see that light is necessary but not sufficient for some sort of electron behavio

That's a lot to unpack - let me make sure I have this right. Quantum theorists see that light is necessary but not sufficient for some sort of electron behavior. And I'm guessing that it's very hard to find an additional contributory/necessary cause that, when combined with light, would reliably predict the behavior. So they use probability to communicate their findings. If that additional contributory/necessary cause exists (but is just really hard to discover, or perhaps light itself is just highly contributory but not necessary/sufficient) then the probability is an effective way to communicate degree-of-belief, and helps to combine information about what they know with what they don't know. In other words, they are using probability to communicate partial findings. If that additional contributory/necessary cause doesn't exist, then the probability is a fixed, physical part of the science. In other words, they're communicating full findings; that light actually creates probability of an effect. And that confusion about "probability" is making people believe that the second case is true when they haven't necessarily disproved the first case yet? Which then serves as a curiosity-stopper and makes the science "mysterious". And this messes with scientific intuitions. Forgive me if I'm way off, I've only read the first few articles of the first couple lesswrong sequences.

Jach 14y ago
I thought I'd pop in and mention this set of lectures (now a book, huh) from Scott Aaronson on quantum mechanics and quantum computing: http://www.scottaaronson.com/democritus/ http://www.scottaaronson.com/democritus/ Particularly Lecture 9 goes into the basic mathematics of quantum mechanics, and explains why it's more appropriate to consider it an extension to probability theory using complex numbers and call them amplitudes, rather than classic probabilities. Not being a physicist myself I don't know if this is really helpful in clearing up professional scientists' intuitions, but it's helpful for me at least in grasping the basics. You're on the right track by noting that quantum theorists can use probability to communicate their findings. A single classical probability like 0.7 is a summary, not the whole picture. For the whole picture, you need a log of observations with time stamps, which is a tremendous amount of data because taken to the extreme it's a balancing act between maximizing the data you know about you and your surroundings and minimizing the number of planck unit time steps to collect the data. Even with more realistic amounts of data it's still a lot to pack around, so you can summarize it by constructing a probability distribution which is more convenient mathematically, and you can summarize that probability distribution into a handful of numbers if you need to because those are even easier to pack around. (Like the single probability 0.7, or two numbers u and s that characterize a Normal distribution, etc.) So if you think of probability as just summarizing your past observations and constraining your expectations for future observations (because what else can?), I think it's easy to see how two people can have different probabilities that represent a belief in a proposition or an abstract system or something else. If both are being honest (I'm packing a lot of assumptions in that word since this is basically Aumann's agreement theorem) and the probabilities are different, there are a couple reasons why: either at least one of them has information (observations) the other one does not, or they started out with different prior probabilities. In the former case, they can reach agreement by sharing data. In the latter case, they can eventually reach agreement by obtaining more data or choosing a common prior. With enough successive Bayesian updates, you can arrive at the same conclusion regardless of where you started. (In practice, of course, things are more hairy and not this simplistic, which is what the submitted pdf is addressing in part.) I find it hard to grok what it means for something to have a physical frequency property. I can understand it as a statistic of an abstract system, i.e. a probability, but in light of Many Worlds, I don't think a frequency can fundamentally be a property of something in the same way energy can be. But since the energy of a photon is related to the photon's "frequency" via its "wavelength", is energy really fundamental or is the relation just a convenient means of making the wave mechanics useful? I've read Feynman tell how the whole idea of forces is just a somewhat circular simplification that's not really fundamental, even though sometimes it seems like it is. While I have a high degree of certainty about the physics accurately describing reality as she is, my meta-belief / confidence about that high certainty isn't nearly as high simply because I feel a lot of confusion about the ultimate nature of reality. But at least at a higher level than fundamental physics, it's clear to me that saying a "fair coin" has p=0.5 per unique side is really just summarizing we don't have enough knowledge of the flipper and the environment it is flipped in to predict the result with certainty in the way we can predict the result of the output of a logic OR gate with low- and high- voltage inputs with certainty. This is different than the uncertainty of which branch you are within a Many Worlds universe, where it's more of a physical resolution problem rather than one of needing more knowledge, similar to not being able to find out what happens between planck unit time steps (if anything happens and if the question means anything). Ben Goertzel's book Probabilistic Logic Networks is another resource I'd recommend. Sorry if my branching reply is a bit big, but I'm constantly trying to clarify things for myself as well. ;)
- loup-vaillant 14y ago
  I have not read the Aaronson's book, but I'm already confident his use of the word "probability" is more confusing than helpful. Okay, the universe is made up of a wacky "configuration space" of "complex amplitudes" (in lay terms, a many-dimensional sea of complex numbers). And, there is a direct relationship between complex amplitudes and the degree of subjective belief of the physicist doing such and such experiment: take the norm of the amplitude, square it, compare that to the other relevant squared norms, and voilà, you have a probabilistic prediction for the result of your next experiment. (I sweep a lot under the carpet, but it really works like this.) Something to know however: assuming you made no mistake, then the result of the first experiment tells you nothing about the result of any subsequent trials. Here's an example: Let us send light through a half-sieved mirror. Have detectors on either side of the mirror to detect the light. Now, you can see that each detector detects half as much light as you originally sent (of course). Things gets interesting when you send photons one by one. The set up of the experiment is such that when you make your amplitude calculations, you find that the squared norm of the amplitudes at each detector is the same. Here, this means that when you send a single photon to the mirror, your should expect to see a single detector go off, but you have no idea which one (subjective belief of 1/2 for either side). But there's more. Once you made the calculation, you know all you could possibly know about the initial conditions of the experiment (according to current physics). Imagine you sent a photon for the first time, and you see it going through the mirror. Will that change anything to your expectation on the second trial? Not one bit. You will still bet 1/2 chances on either side. So this experiment is the perfect coin toss. Or is it? Imagine you send twenty photons, and you see they all made it past the mirror. Initially that's one chance in a million. In that case, you should be strongly tempted to expect the 21th to go through as well. The question is why? If you are absolutely sure you set up the experiment right, then you shouldn't change your mind, and still bet 1/2 on either side. But are you so sure of your accuracy that you could set up several millions experiments, and get all of them right? Probably not. The more likely explanation is that your so-called "half sieved mirror" is just a piece of glass. Maybe you were tired, and piked up the wrong one. Or maybe some graduate student played a joke on you. Conversely, an actual coin toss could be perfectly fair: there's a lot going on in a coin toss, and depending on the chosen procedure, you can't expect to have sufficient knowledge of the initial conditions to predict anything but 1/2 for heads, 1/2 for tails, even after seeing the the coin landing tails three times in a row. There is, even then, some kind of "frequency property" in the experiment. It's not because the laws of coin tossing are somehow indeterministic, but because the way the coin is tossed systematically hides relevant information about the exact initial conditions. (The formal Aumann agreement theorem is a bit stronger than that: two perfects Bayesians cannot have common knowledge of any disagreement. In practice, this means you can't start from different priors, because a prior embody background information, which can be shared. I know that there is controversy about "fully uninformed" priors, but in practice, they don't change posterior probabilities very much.)

Jach 14y ago

I thought I'd pop in and mention this set of lectures (now a book, huh) from Scott Aaronson on quantum mechanics and quantum computing: http://www.scottaaronson.com/democritus/ http://www.scottaaronson.com/democritus/ Particularly Lecture 9 goes into the basic mathematics of quantum mechanics, and explains why it's more appropriate to consider it an extension to probability theory using complex numbers and call them amplitudes, rather than classic probabilities. Not being a physicist myself I don't know if this is really helpful in clearing up professional scientists' intuitions, but it's helpful for me at least in grasping the basics. You're on the right track by noting that quantum theorists can use probability to communicate their findings. A single classical probability like 0.7 is a summary, not the whole picture. For the whole picture, you need a log of observations with time stamps, which is a tremendous amount of data because taken to the extreme it's a balancing act between maximizing the data you know about you and your surroundings and minimizing the number of planck unit time steps to collect the data. Even with more realistic amounts of data it's still a lot to pack around, so you can summarize it by constructing a probability distribution which is more convenient mathematically, and you can summarize that probability distribution into a handful of numbers if you need to because those are even easier to pack around. (Like the single probability 0.7, or two numbers u and s that characterize a Normal distribution, etc.) So if you think of probability as just summarizing your past observations and constraining your expectations for future observations (because what else can?), I think it's easy to see how two people can have different probabilities that represent a belief in a proposition or an abstract system or something else. If both are being honest (I'm packing a lot of assumptions in that word since this is basically Aumann's agreement theorem) and the probabilities are different, there are a couple reasons why: either at least one of them has information (observations) the other one does not, or they started out with different prior probabilities. In the former case, they can reach agreement by sharing data. In the latter case, they can eventually reach agreement by obtaining more data or choosing a common prior. With enough successive Bayesian updates, you can arrive at the same conclusion regardless of where you started. (In practice, of course, things are more hairy and not this simplistic, which is what the submitted pdf is addressing in part.) I find it hard to grok what it means for something to have a physical frequency property. I can understand it as a statistic of an abstract system, i.e. a probability, but in light of Many Worlds, I don't think a frequency can fundamentally be a property of something in the same way energy can be. But since the energy of a photon is related to the photon's "frequency" via its "wavelength", is energy really fundamental or is the relation just a convenient means of making the wave mechanics useful? I've read Feynman tell how the whole idea of forces is just a somewhat circular simplification that's not really fundamental, even though sometimes it seems like it is. While I have a high degree of certainty about the physics accurately describing reality as she is, my meta-belief / confidence about that high certainty isn't nearly as high simply because I feel a lot of confusion about the ultimate nature of reality. But at least at a higher level than fundamental physics, it's clear to me that saying a "fair coin" has p=0.5 per unique side is really just summarizing we don't have enough knowledge of the flipper and the environment it is flipped in to predict the result with certainty in the way we can predict the result of the output of a logic OR gate with low- and high- voltage inputs with certainty. This is different than the uncertainty of which branch you are within a Many Worlds universe, where it's more of a physical resolution problem rather than one of needing more knowledge, similar to not being able to find out what happens between planck unit time steps (if anything happens and if the question means anything). Ben Goertzel's book Probabilistic Logic Networks is another resource I'd recommend. Sorry if my branching reply is a bit big, but I'm constantly trying to clarify things for myself as well. ;)

loup-vaillant 14y ago
I have not read the Aaronson's book, but I'm already confident his use of the word "probability" is more confusing than helpful. Okay, the universe is made up of a wacky "configuration space" of "complex amplitudes" (in lay terms, a many-dimensional sea of complex numbers). And, there is a direct relationship between complex amplitudes and the degree of subjective belief of the physicist doing such and such experiment: take the norm of the amplitude, square it, compare that to the other relevant squared norms, and voilà, you have a probabilistic prediction for the result of your next experiment. (I sweep a lot under the carpet, but it really works like this.) Something to know however: assuming you made no mistake, then the result of the first experiment tells you nothing about the result of any subsequent trials. Here's an example: Let us send light through a half-sieved mirror. Have detectors on either side of the mirror to detect the light. Now, you can see that each detector detects half as much light as you originally sent (of course). Things gets interesting when you send photons one by one. The set up of the experiment is such that when you make your amplitude calculations, you find that the squared norm of the amplitudes at each detector is the same. Here, this means that when you send a single photon to the mirror, your should expect to see a single detector go off, but you have no idea which one (subjective belief of 1/2 for either side). But there's more. Once you made the calculation, you know all you could possibly know about the initial conditions of the experiment (according to current physics). Imagine you sent a photon for the first time, and you see it going through the mirror. Will that change anything to your expectation on the second trial? Not one bit. You will still bet 1/2 chances on either side. So this experiment is the perfect coin toss. Or is it? Imagine you send twenty photons, and you see they all made it past the mirror. Initially that's one chance in a million. In that case, you should be strongly tempted to expect the 21th to go through as well. The question is why? If you are absolutely sure you set up the experiment right, then you shouldn't change your mind, and still bet 1/2 on either side. But are you so sure of your accuracy that you could set up several millions experiments, and get all of them right? Probably not. The more likely explanation is that your so-called "half sieved mirror" is just a piece of glass. Maybe you were tired, and piked up the wrong one. Or maybe some graduate student played a joke on you. Conversely, an actual coin toss could be perfectly fair: there's a lot going on in a coin toss, and depending on the chosen procedure, you can't expect to have sufficient knowledge of the initial conditions to predict anything but 1/2 for heads, 1/2 for tails, even after seeing the the coin landing tails three times in a row. There is, even then, some kind of "frequency property" in the experiment. It's not because the laws of coin tossing are somehow indeterministic, but because the way the coin is tossed systematically hides relevant information about the exact initial conditions. (The formal Aumann agreement theorem is a bit stronger than that: two perfects Bayesians cannot have common knowledge of any disagreement. In practice, this means you can't start from different priors, because a prior embody background information, which can be shared. I know that there is controversy about "fully uninformed" priors, but in practice, they don't change posterior probabilities very much.)