4 ms·

Do you mind if I clarify something about this that I have never understood? Taking your example of the socks, with their varying and inverse properties, why do

Do you mind if I clarify something about this that I have never understood? Taking your example of the socks, with their varying and inverse properties, why do we need "spooky action at a distance" to describe the fact that one can test the properties of their local sock and therefore know the properties of the distant, entangled sock? If we now that the total value of each property will equal 1 (as in your case) then measuring the local sock will tell us the values of the distant sock. I am not sure what I am missing, only that I am missing something here.

eigenket 5y ago
So you can describe the set of possible joint probability distributions for the socks, and you can describe the set of possible probability distributions you can get out of quantum mechanics in a "Bell-type experiment". It turns out the set of probability distributions from quantum mechanics is strictly larger. Fundamentally the answer is that you can't break a Bell inequality with the socks, but you can with some entangled particles. The socks analogy kinda fails to capture the interesting stuff here, and I'm not sure if any classical analogy really works, but I'm gonna try to summarise the setup. You have two boxes (imagine they're in different rooms, being operated by different people), call them A and B. Each Box allows you to input a single bit, we'll call A's bit x and B's bit y. Each box outputs a single bit in response to the bit you give it, call the bit output by A a, and the bit output by B b. You can then form a probability distribution P(a,b | x, y) The joint probability distribution of a and b conditioned on the inputs x and y. Quantum mechanics predicts a particular form for this distribution, and in particular it does not depend where the boxes are, and when (in which order) the bits are input. Based on special relativity therefore we would expect that the distribution of a conditioned on x should be independent of the distribution of b conditioned on y. In maths this means that P(a,b | x, y) = sum_i P(i) P(a|x, i) P(b|y,i) Basically we're allowing the output bits to depend on some shared randomness P(i), but we're not allowing a to depend on y and we're not allowing b to depend on x. This is reasonable because we have the freedom to put x in a after we receive b from y, or vice-versa, or have them separated by arbitrary amounts of space, or whatever we like. It turns out that the probability distribution P(a,b|x,y) that quantum mechanics predicts is not of this form. The probability distributions we observe in reality, when we actually do the experiment are also not of this form. This seems to mean that somehow, even if they're separated by arbitrary amounts of space, or done in whatever order you like, or whatever the output bit a does somehow depend on what input you give box B and vice-versa.
- monkeydreams 5y ago
  Thank you for your explanation. I think I shall have to read it a couple of times and then try to work out where my intuition is leading me astray.
  - jahnu 5y ago
    Brian Greene's analogy on the simple English page here is quite good https://simple.m.wikipedia.org/wiki/Bell%27s_theorem https://simple.m.wikipedia.org/wiki/Bell%27s_theorem The book it's taken from is excellent
  - tsimionescu 5y ago
    I can also suggest a video that seemed to me to explain Bell's theorem and what it means that the correlations are stronger than classically possible here: [0] https://www.youtube.com/watch?v=zcqZHYo7ONs https://www.youtube.com/watch?v=zcqZHYo7ONs

eigenket 5y ago

So you can describe the set of possible joint probability distributions for the socks, and you can describe the set of possible probability distributions you can get out of quantum mechanics in a "Bell-type experiment". It turns out the set of probability distributions from quantum mechanics is strictly larger. Fundamentally the answer is that you can't break a Bell inequality with the socks, but you can with some entangled particles. The socks analogy kinda fails to capture the interesting stuff here, and I'm not sure if any classical analogy really works, but I'm gonna try to summarise the setup. You have two boxes (imagine they're in different rooms, being operated by different people), call them A and B. Each Box allows you to input a single bit, we'll call A's bit x and B's bit y. Each box outputs a single bit in response to the bit you give it, call the bit output by A a, and the bit output by B b. You can then form a probability distribution P(a,b | x, y) The joint probability distribution of a and b conditioned on the inputs x and y. Quantum mechanics predicts a particular form for this distribution, and in particular it does not depend where the boxes are, and when (in which order) the bits are input. Based on special relativity therefore we would expect that the distribution of a conditioned on x should be independent of the distribution of b conditioned on y. In maths this means that P(a,b | x, y) = sum_i P(i) P(a|x, i) P(b|y,i) Basically we're allowing the output bits to depend on some shared randomness P(i), but we're not allowing a to depend on y and we're not allowing b to depend on x. This is reasonable because we have the freedom to put x in a after we receive b from y, or vice-versa, or have them separated by arbitrary amounts of space, or whatever we like. It turns out that the probability distribution P(a,b|x,y) that quantum mechanics predicts is not of this form. The probability distributions we observe in reality, when we actually do the experiment are also not of this form. This seems to mean that somehow, even if they're separated by arbitrary amounts of space, or done in whatever order you like, or whatever the output bit a does somehow depend on what input you give box B and vice-versa.

monkeydreams 5y ago
Thank you for your explanation. I think I shall have to read it a couple of times and then try to work out where my intuition is leading me astray.
- jahnu 5y ago
  Brian Greene's analogy on the simple English page here is quite good https://simple.m.wikipedia.org/wiki/Bell%27s_theorem https://simple.m.wikipedia.org/wiki/Bell%27s_theorem The book it's taken from is excellent
- tsimionescu 5y ago
  I can also suggest a video that seemed to me to explain Bell's theorem and what it means that the correlations are stronger than classically possible here: [0] https://www.youtube.com/watch?v=zcqZHYo7ONs https://www.youtube.com/watch?v=zcqZHYo7ONs