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> We argue that many popular "quantum paradoxes" stem from a confusion between mathematical formalism and physics [...] most "conceptual puzzles" of QM are not

> We argue that many popular "quantum paradoxes" stem from a confusion between mathematical formalism and physics [...] most "conceptual puzzles" of QM are not much different from the well-known paradoxes from probability theory This is really really true. Particularly for any experiment with "delayed choice" in the name, where pop-science explanations follow correlations backwards instead of forwards then confuse correlation for causation and start talking about time travel (sigh).

mlevental 9y ago
i would love to see a translation of quantum paradoxes to probability paradoxes - e.g. quantum tunneling is the same as basically measure 0 events.
- whatshisface 9y ago
  Tunneling isn't really a paradox, it's just a direct contradiction with classical mechanics.
  - kurthr 9y ago
    Agreed... although a probabilistic energy distribution (e.g. thermal) could cause electron/hole current exponential with voltage, it would be unlike tunneling across a potential barrier that is too high. Thermal current would not be exponentially dependent on the separation gap.
- k__ 9y ago
  Or what about wave particle dualities? How can one particle interfere with itself?
  - deleted 9y ago
    [deleted]
  - tbabb 9y ago
    Personally I think the concept of "particle" needs to go away completely. I think really what "particle" means is that "all measurements are quantized". But the probabilities of any given measurement happening flows around as a wave. For example, "there is a quantity of energy `e` at location `x`" is an observation you could make. The answer to that question has a discrete yes/no answer. The probability of the answer being "yes" flows around like a wave between all the different possible `x` as time progresses.
    - k__ 9y ago
      Really? You mean all particles are virtual? Whaz is the alternative?
      - tbabb 9y ago
        No, I mean that there are no particles. Only waves. Only that if you try to measure something about the wave, you will always get a discrete "yes/no" answer.
        tedsanders 9y ago
        Particles are a really useful fiction. I'm having a tough time thinking of how to teach and explain chemistry without the concept of valence electrons. Do you have any ideas? (Related tangent: a super important but occasionally missed nuance of quantum mechanics is that the waves are not waves over 3D real space. They are waves over configuration space, with way more than 3 dimensions.)
        k__ 9y ago
        Then what are they in 3D space?
        tedsanders 9y ago
        The electromagnetic field and other fields exist over 3D space. But the probability waves that represent them are in infinite dimensional space, because each point in 3D can have multiple states at once (and these states are correlated/entangled over space).
  - mlevental 9y ago
    this was never a paradox to me; https://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle https://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_...
- Strilanc 9y ago
  Well, for example, the no cloning theorem has a classical analogy. I prepare a coin so that it is heads with probability p. I give you the coin. Your job is to prepare two coins so that they are independently heads with probability p. You aren't told p, you only get the coin to work with. We are going to repeat this many times, and with various values of p, and someone will test whether the coins you are producing follow the right distribution. It's obviously not possible for you to do particularly well at this task. See [1] I'm not aware of a probability analogy for tunneling. 1: https://marozols.wordpress.com/2012/05/21/three-myths-about-quantum-computing-part-2/ https://marozols.wordpress.com/2012/05/21/three-myths-about-...
- justinpombrio 9y ago
  > e.g. quantum tunneling is the same as basically measure 0 events. It is not. Quantum tunneling is just an event with low probability, and when you notice that quantum tunneling doesn't happen (on a macro scale), you're just noticing that events with sufficiently low probability don't happen. The probabilistic analogy is flipping a billion coins and having them all come up heads. Flipping a billion coins and having them all come up heads does not have measure zero. It has a positive measure. Contrast this to measure zero events. Flipping infinitely many coins and having them all come up heads has measure zero. You need measure theory to talk usefully about measure zero events. You don't need measure theory to talk about quantum tunneling. Just ordinary probability.
  - mlevental 9y ago
    > The probabilistic analogy is flipping a billion coins and having them all come up heads. Flipping a billion coins and having them all come up heads does not have measure zero. It has a positive measure. wut? 1. in each instance it's 1MM conditionally independent trials so i don't see the difference 2. any realization of any continuous random variable has measure zero >Contrast this to measure zero events. Flipping infinitely many coins and having them all come up heads has measure zero. you're playing fast and loose with the difference between a counting measure (no measure zero events) and a continuous/discrete measure. anyway my point was exactly that quantum tunneling is counterintuitive exactly for the same reason that measure zero events are counterintuitive

mlevental 9y ago

i would love to see a translation of quantum paradoxes to probability paradoxes - e.g. quantum tunneling is the same as basically measure 0 events.

whatshisface 9y ago
Tunneling isn't really a paradox, it's just a direct contradiction with classical mechanics.
- kurthr 9y ago
  Agreed... although a probabilistic energy distribution (e.g. thermal) could cause electron/hole current exponential with voltage, it would be unlike tunneling across a potential barrier that is too high. Thermal current would not be exponentially dependent on the separation gap.
k__ 9y ago
Or what about wave particle dualities? How can one particle interfere with itself?
- deleted 9y ago
  [deleted]
- tbabb 9y ago
  Personally I think the concept of "particle" needs to go away completely. I think really what "particle" means is that "all measurements are quantized". But the probabilities of any given measurement happening flows around as a wave. For example, "there is a quantity of energy `e` at location `x`" is an observation you could make. The answer to that question has a discrete yes/no answer. The probability of the answer being "yes" flows around like a wave between all the different possible `x` as time progresses.
  - k__ 9y ago
    Really? You mean all particles are virtual? Whaz is the alternative?
    - tbabb 9y ago
      No, I mean that there are no particles. Only waves. Only that if you try to measure something about the wave, you will always get a discrete "yes/no" answer.
      - tedsanders 9y ago
        Particles are a really useful fiction. I'm having a tough time thinking of how to teach and explain chemistry without the concept of valence electrons. Do you have any ideas? (Related tangent: a super important but occasionally missed nuance of quantum mechanics is that the waves are not waves over 3D real space. They are waves over configuration space, with way more than 3 dimensions.)
        k__ 9y ago
        Then what are they in 3D space?
        tedsanders 9y ago
        The electromagnetic field and other fields exist over 3D space. But the probability waves that represent them are in infinite dimensional space, because each point in 3D can have multiple states at once (and these states are correlated/entangled over space).
- mlevental 9y ago
  this was never a paradox to me; https://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle https://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_...
Strilanc 9y ago
Well, for example, the no cloning theorem has a classical analogy. I prepare a coin so that it is heads with probability p. I give you the coin. Your job is to prepare two coins so that they are independently heads with probability p. You aren't told p, you only get the coin to work with. We are going to repeat this many times, and with various values of p, and someone will test whether the coins you are producing follow the right distribution. It's obviously not possible for you to do particularly well at this task. See [1] I'm not aware of a probability analogy for tunneling. 1: https://marozols.wordpress.com/2012/05/21/three-myths-about-quantum-computing-part-2/ https://marozols.wordpress.com/2012/05/21/three-myths-about-...
justinpombrio 9y ago
> e.g. quantum tunneling is the same as basically measure 0 events. It is not. Quantum tunneling is just an event with low probability, and when you notice that quantum tunneling doesn't happen (on a macro scale), you're just noticing that events with sufficiently low probability don't happen. The probabilistic analogy is flipping a billion coins and having them all come up heads. Flipping a billion coins and having them all come up heads does not have measure zero. It has a positive measure. Contrast this to measure zero events. Flipping infinitely many coins and having them all come up heads has measure zero. You need measure theory to talk usefully about measure zero events. You don't need measure theory to talk about quantum tunneling. Just ordinary probability.
- mlevental 9y ago
  > The probabilistic analogy is flipping a billion coins and having them all come up heads. Flipping a billion coins and having them all come up heads does not have measure zero. It has a positive measure. wut? 1. in each instance it's 1MM conditionally independent trials so i don't see the difference 2. any realization of any continuous random variable has measure zero >Contrast this to measure zero events. Flipping infinitely many coins and having them all come up heads has measure zero. you're playing fast and loose with the difference between a counting measure (no measure zero events) and a continuous/discrete measure. anyway my point was exactly that quantum tunneling is counterintuitive exactly for the same reason that measure zero events are counterintuitive