8 ms·

What did she mean by the quantum correlations being stronger than the non-quantum ones? She lost me there

lopuhin 5y ago
I think the second paragraph in the wiki page about Bell's theorem explains that: https://en.wikipedia.org/wiki/Bell%27s_theorem https://en.wikipedia.org/wiki/Bell%27s_theorem
tsimionescu 5y ago
Bell's theorem has proven that quantum entangled particles do not behave exactly like the socks. To understand it, let's imagine the sock experiment, but with 2 differences: one of the socks is red and fluffy, the other is blue and coarse; and you can't see exactly how red and how fluffy the sock you got is, you can only measure a combination of the two. So, you open your envelope and set your device to measure if the sock is 0.2 red and 0.8 soft (so, either blue or soft), and you get True. If the person who got the other sock set their device to 0.8 red and 0.2 soft, the classical probability that they get True would be 0.5 I believe. But if you perform this experiment with quantum entangled properties, you would see a greater value. Further, Bell has shown that one of 3 things must hold for quantum socks: - either they are neither blue/red nor coarse/fluffy until the measurement; after the measurement, your sock gets some value, and the other sock implicitly gets the opposite value, but there is no real "state change" since they didn't have any state to begin with (we reject realism) - they "tell" each other instantly in what state they were found (we reject locality) - the fact that you were always going to receive the red sock also caused you to choose 0.2 red and 0.8 soft, so what may look like a coincidence is in fact pre-determined (superdeterminism)
- goldenkey 5y ago
  Or.... consciousness collapses the wave function and solipsism is the nature of reality. Observables are just very large unevaluated expressions that collapse via lambda reduction ala becoming a tautology. As you gain more information, more alpha and beta reductions become possible, and expressions simplify into static values instead of multivariate/dependent expression trees. The universe is a first person JIT experience. Search for Wigner's friend. Relational quantum mechanics is the only logical and consistent epistemology for what all this means. Effectively, nothing ever changes, just extra information allows for simplification of observables backed by large expressions. The universe is inherently lazy, and it's like LISP. PG come at me!
  - tsimionescu 5y ago
    Well, if you go for pure solipsism, that is, your own consciousness is the only thing which exists in the universe, that can explain any phenomenon you want. But objective collapse due to anyone's consciousness does not solve anything - my observation of this particle still causes infinite speed effects on your particle, so the universe is anyway non-local.
    - goldenkey 5y ago
      It's only solipsism in the sense that my wavefunctions do not have to agree with yours. There is a correlation between us, still. So it isn't like our wavefunctions are going to be radically different. We both are entangled since the Big Bang and even after that many times over as shared information exchanges between us. https://en.wikipedia.org/wiki/Wigner%27s_friend https://en.wikipedia.org/wiki/Wigner%27s_friend
      - tsimionescu 5y ago
        The article you cite provides various alternatives to this world view. It even contains the fun observation that the experiment has actually been performed, but with photons instead of observers - showing just how important consciousness really is in physical theories. In general, I believe the most obvious interpretation of consciousness is simply as a computational process, so looking at consciousness as a key to QM is incompatible with my beliefs. Furthermore, given the classical-ness of the world we see everyday, I have huge problems believing theories like MWI or these consciousness-based ones that claim the world is entirely quantum everywhere and it's just some kind of accident that it seems so classical to us (contrast to relativity which has a very satisfying answer for why we don't notice the difference from classical mechanics).
        goldenkey 5y ago
        > I have huge problems believing The universe is indifferent to your persuasions. The double slit experiment has been successfully performed on large molecules of 810 atoms. Quantum mechanics is fundamentally about knowledge and information after interactions. You seem to be a physics guy but something tells me you aren't aware that every single interaction causes entanglement. Entanglement is simply a constraint on interaction products, given the input particles. It is just easier to see its effects on small objects since they are less likely to be perturbed. https://arxiv.org/abs/1310.8343 https://arxiv.org/abs/1310.8343
- monkeydreams 5y ago
  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.
- throwaway316943 5y ago
  Are the misses caused by the measurement equipment or do you really sometimes get true on both ends? If so, why?
  - tsimionescu 5y ago
    The sock metaphor is already stretched a little thin, and this problem doesn't happen with classical quantities/objects as far as we know. Basically what is happening is in some ways similar to what gives quantum computing its extra power compared to classical computers: as far as we can tell, quantities at the microscopic level are in fact complex numbers, and so combine in ways that give different values from the real-valued quantities we are used to from the classical world.

I think the second paragraph in the wiki page about Bell's theorem explains that: https://en.wikipedia.org/wiki/Bell%27s_theorem https://en.wikipedia.org/wiki/Bell%27s_theorem

tsimionescu 5y ago

Bell's theorem has proven that quantum entangled particles do not behave exactly like the socks. To understand it, let's imagine the sock experiment, but with 2 differences: one of the socks is red and fluffy, the other is blue and coarse; and you can't see exactly how red and how fluffy the sock you got is, you can only measure a combination of the two. So, you open your envelope and set your device to measure if the sock is 0.2 red and 0.8 soft (so, either blue or soft), and you get True. If the person who got the other sock set their device to 0.8 red and 0.2 soft, the classical probability that they get True would be 0.5 I believe. But if you perform this experiment with quantum entangled properties, you would see a greater value. Further, Bell has shown that one of 3 things must hold for quantum socks: - either they are neither blue/red nor coarse/fluffy until the measurement; after the measurement, your sock gets some value, and the other sock implicitly gets the opposite value, but there is no real "state change" since they didn't have any state to begin with (we reject realism) - they "tell" each other instantly in what state they were found (we reject locality) - the fact that you were always going to receive the red sock also caused you to choose 0.2 red and 0.8 soft, so what may look like a coincidence is in fact pre-determined (superdeterminism)

goldenkey 5y ago
Or.... consciousness collapses the wave function and solipsism is the nature of reality. Observables are just very large unevaluated expressions that collapse via lambda reduction ala becoming a tautology. As you gain more information, more alpha and beta reductions become possible, and expressions simplify into static values instead of multivariate/dependent expression trees. The universe is a first person JIT experience. Search for Wigner's friend. Relational quantum mechanics is the only logical and consistent epistemology for what all this means. Effectively, nothing ever changes, just extra information allows for simplification of observables backed by large expressions. The universe is inherently lazy, and it's like LISP. PG come at me!
- tsimionescu 5y ago
  Well, if you go for pure solipsism, that is, your own consciousness is the only thing which exists in the universe, that can explain any phenomenon you want. But objective collapse due to anyone's consciousness does not solve anything - my observation of this particle still causes infinite speed effects on your particle, so the universe is anyway non-local.
  - goldenkey 5y ago
    It's only solipsism in the sense that my wavefunctions do not have to agree with yours. There is a correlation between us, still. So it isn't like our wavefunctions are going to be radically different. We both are entangled since the Big Bang and even after that many times over as shared information exchanges between us. https://en.wikipedia.org/wiki/Wigner%27s_friend https://en.wikipedia.org/wiki/Wigner%27s_friend
    - tsimionescu 5y ago
      The article you cite provides various alternatives to this world view. It even contains the fun observation that the experiment has actually been performed, but with photons instead of observers - showing just how important consciousness really is in physical theories. In general, I believe the most obvious interpretation of consciousness is simply as a computational process, so looking at consciousness as a key to QM is incompatible with my beliefs. Furthermore, given the classical-ness of the world we see everyday, I have huge problems believing theories like MWI or these consciousness-based ones that claim the world is entirely quantum everywhere and it's just some kind of accident that it seems so classical to us (contrast to relativity which has a very satisfying answer for why we don't notice the difference from classical mechanics).
      - goldenkey 5y ago
        > I have huge problems believing The universe is indifferent to your persuasions. The double slit experiment has been successfully performed on large molecules of 810 atoms. Quantum mechanics is fundamentally about knowledge and information after interactions. You seem to be a physics guy but something tells me you aren't aware that every single interaction causes entanglement. Entanglement is simply a constraint on interaction products, given the input particles. It is just easier to see its effects on small objects since they are less likely to be perturbed. https://arxiv.org/abs/1310.8343 https://arxiv.org/abs/1310.8343
monkeydreams 5y ago
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.
throwaway316943 5y ago
Are the misses caused by the measurement equipment or do you really sometimes get true on both ends? If so, why?
- tsimionescu 5y ago
  The sock metaphor is already stretched a little thin, and this problem doesn't happen with classical quantities/objects as far as we know. Basically what is happening is in some ways similar to what gives quantum computing its extra power compared to classical computers: as far as we can tell, quantities at the microscopic level are in fact complex numbers, and so combine in ways that give different values from the real-valued quantities we are used to from the classical world.