Physicists, help me
October 22, 2015 2:01 PM Subscribe
Did Hanson et. al. just prove Bell's Theorem?
I deeply mistrust MSM reports about this kind of thing; they're generally given to hyperbole just to get a more spectacular headline.
The Wikipedia article about "Bell Test Experiments" says they closed two loopholes but one remains. However, I don't trust same-day Wikipedia updates, either.
So what's the real word? Has Bell's Theorem been proved?
I deeply mistrust MSM reports about this kind of thing; they're generally given to hyperbole just to get a more spectacular headline.
The Wikipedia article about "Bell Test Experiments" says they closed two loopholes but one remains. However, I don't trust same-day Wikipedia updates, either.
So what's the real word? Has Bell's Theorem been proved?
Best answer: This is how they address the third loophole in the Nature paper:
"Strictly speaking, no Bell experiment can exclude all conceivable
local-realist theories, because it is fundamentally impossible to prove
when and where free random input bits and output values came into
existence. Even so, our loophole-free Bell test opens the possibility to
progressively bound such less-conventional theories: by increasing the
distance between A and B (for example, to test theories with increased
speed of physical influence); by using different random input bit generators
(to test theories with specific free-will agents, for example,
humans); or by repositioning the random input bit generators (to
test theories where the inputs are already determined earlier, sometimes
referred to as ‘freedom-of-choice ). In fact, our experiment
already enables tests of all models that predict that the random inputs
are determined a maximum of 690 ns before we record them".
That Bell's inequality is violated has been shown beyond reasonable doubt, and I think that was the case before this experiment too. Now your objections would have to be very unreasonable. It's not quite my field, but I'm sure it's at the point where fraud or severe mistakes are more probable causes of error than any remaining theoretical "what-if".
posted by Herr Zebrurka at 3:45 PM on October 22, 2015
"Strictly speaking, no Bell experiment can exclude all conceivable
local-realist theories, because it is fundamentally impossible to prove
when and where free random input bits and output values came into
existence. Even so, our loophole-free Bell test opens the possibility to
progressively bound such less-conventional theories: by increasing the
distance between A and B (for example, to test theories with increased
speed of physical influence); by using different random input bit generators
(to test theories with specific free-will agents, for example,
humans); or by repositioning the random input bit generators (to
test theories where the inputs are already determined earlier, sometimes
referred to as ‘freedom-of-choice ). In fact, our experiment
already enables tests of all models that predict that the random inputs
are determined a maximum of 690 ns before we record them".
That Bell's inequality is violated has been shown beyond reasonable doubt, and I think that was the case before this experiment too. Now your objections would have to be very unreasonable. It's not quite my field, but I'm sure it's at the point where fraud or severe mistakes are more probable causes of error than any remaining theoretical "what-if".
posted by Herr Zebrurka at 3:45 PM on October 22, 2015
Best answer: Technically speaking, Bell proved Bell's Theorem, which is a general mathematical statement about a class of mathematical models of the world. The question is then whether our measurements of the real world are in agreement with this statement. Over the past 50 years (since the theorem was first stated), physicists have done a series of increasingly refined experiments that have shown that no, measurements we make in the real world do not obey Bell's Theorem.
To elaborate on this: Bell's Theorem deals with the correlations of measurements between two distinct locations; it says that if particles do indeed have real properties before you measure them, and that they can't communicate with each other when they're measured (or become correlated with each other via their interactions with the measuring apparatus), then the correlations will obey a certain inequality. Thus, if we can show, beyond the shadow of a doubt, that these correlations do not obey this inequality, then we can conclude that the particles don't actually have real properties before you measure them.
The simplest experiments you can do appear, on their surface, to be inconsistent with the inequality in Bell's theorem, and thus to show that particles' properties are not pre-existing. The trick is eliminating any & all possibilities that these violations of the inequalities are due to some kinds of conspiracy between the pre-existing variables (communicating with each other after measurement, for example.)
posted by Johnny Assay at 5:55 PM on October 22, 2015 [1 favorite]
To elaborate on this: Bell's Theorem deals with the correlations of measurements between two distinct locations; it says that if particles do indeed have real properties before you measure them, and that they can't communicate with each other when they're measured (or become correlated with each other via their interactions with the measuring apparatus), then the correlations will obey a certain inequality. Thus, if we can show, beyond the shadow of a doubt, that these correlations do not obey this inequality, then we can conclude that the particles don't actually have real properties before you measure them.
The simplest experiments you can do appear, on their surface, to be inconsistent with the inequality in Bell's theorem, and thus to show that particles' properties are not pre-existing. The trick is eliminating any & all possibilities that these violations of the inequalities are due to some kinds of conspiracy between the pre-existing variables (communicating with each other after measurement, for example.)
posted by Johnny Assay at 5:55 PM on October 22, 2015 [1 favorite]
Response by poster: I'm getting a bit confused by all the negatives, double-negatives, triple-negatives and so on. So let me state my understanding of the situation and see if it's correct:
Bell's Theorem is that Quantum Mechanics cannot be explained as being the result of hidden local variables. To explain QM, the universe has to be non-local in at least some way. (One possibility is non-local hidden variables. But there would still need to be a way for information, hidden or not, to get from one place to another faster than C, and possibly at infinite speed.)
Bell's Inequality is a description of how things would behave if Bell's Theorem was wrong. Therefore, an experimental result which violates Bell's Inequality is supporting evidence for Bell's Theorem.
Is that correct?
posted by Chocolate Pickle at 10:56 PM on October 22, 2015
Bell's Theorem is that Quantum Mechanics cannot be explained as being the result of hidden local variables. To explain QM, the universe has to be non-local in at least some way. (One possibility is non-local hidden variables. But there would still need to be a way for information, hidden or not, to get from one place to another faster than C, and possibly at infinite speed.)
Bell's Inequality is a description of how things would behave if Bell's Theorem was wrong. Therefore, an experimental result which violates Bell's Inequality is supporting evidence for Bell's Theorem.
Is that correct?
posted by Chocolate Pickle at 10:56 PM on October 22, 2015
Best answer: I recommend this Shtetl-Optimized blog post.
posted by katrielalex at 4:09 AM on October 23, 2015
posted by katrielalex at 4:09 AM on October 23, 2015
Best answer: "Locality" is the assumed law that an event at on point cannot affect an event at another point until some matter or field has traversed the distance between the points, and that can happen no faster than the sped of light. There is also the assumption of "Realism", that things exist also when we don't look at them, but that's a much safer bet.
Bell's theorem says: "If locality is indeed a law (along with realism), certain correlations between measurements should obey my inequality". That's mathematically proven, which it needs to be to have the status of a theorem. This gives us a way to test for locality: We measure the correlations Bell said we should, and if they violate the inequality, we can infer from the theorem that locality isn't the case.
In practice, you do this by entangling two quantum systems (such as photons) in Lab A. You keep one of them where you are and send the other one away to Lab B, which is located entirely elsewhere. When the systems are separated, you apply some operation to the one in Lab A, another one in Lab B, and then you measure their two states. The two labs don't know what operation the other lab applies to any given photon. After you've done this with many photon pairs, you get together and compare notes. In this experiment, the operation and measurement could be applied very quickly, and the distance between the labs was vast. Even if information about the operation applied in Lab A somehow got on the loose and travelled by the speed of light toward Lab B, it wouldn't arrive before Lab B was already done with their measurement. If those are the conditions and you still find correlations between the measurements in the two labs that violate Bell's inequality, then you can be sure that locality doesn't hold true. Th measurement fidelity also needs to b very high, which it was in this case.
The remaining loophole is about how the operations applied in the two labs are chosen. Let's say a guy in Lab A writes a list of operations ahead of time and doesn't show it to anyone, and he applies those operations to the photons on his side. Well, the list has still existed long enough that the information on it could in principle have moved to the other lab. There is no sensible mechanism for this, but for his list to somehow affect the events in Lab B, nothing needs to travel faster than light. Let's instead say that they flip a coin once the two states are already far apart, and do it so quickly that the outcome can't be communicated to the other lab until it's too late. Well, the outcome of that flip could still be determined ahead of time, by how the coin was resting in your wallet and how sticky your flipping hand was. Information about your hand and your wallet could in principle have moved to the other lab at the speed of light and affected their outcome. In the experiment, thy used quantum-base random number generators, but you still can't be exactly sure when the number was actually decided, and hence if it would have had time to move between the labs.
Nobody would make the serious claim that this loophole actually matters, but there is always someone says "Ok you have solid evidence, but has it been proven? Like not 99.999% but 100%"? Then the scientists will say "Well, I'd probably add another couple of nines to your estimate, but we can never claim to be completely certain about experimental results", and the first person will say "A-HA! So it hasn't been proven after all!". Just, if you want to reject locality, a stronger claim is that the scientists just made everything up.
posted by Herr Zebrurka at 10:16 AM on October 23, 2015
Bell's theorem says: "If locality is indeed a law (along with realism), certain correlations between measurements should obey my inequality". That's mathematically proven, which it needs to be to have the status of a theorem. This gives us a way to test for locality: We measure the correlations Bell said we should, and if they violate the inequality, we can infer from the theorem that locality isn't the case.
In practice, you do this by entangling two quantum systems (such as photons) in Lab A. You keep one of them where you are and send the other one away to Lab B, which is located entirely elsewhere. When the systems are separated, you apply some operation to the one in Lab A, another one in Lab B, and then you measure their two states. The two labs don't know what operation the other lab applies to any given photon. After you've done this with many photon pairs, you get together and compare notes. In this experiment, the operation and measurement could be applied very quickly, and the distance between the labs was vast. Even if information about the operation applied in Lab A somehow got on the loose and travelled by the speed of light toward Lab B, it wouldn't arrive before Lab B was already done with their measurement. If those are the conditions and you still find correlations between the measurements in the two labs that violate Bell's inequality, then you can be sure that locality doesn't hold true. Th measurement fidelity also needs to b very high, which it was in this case.
The remaining loophole is about how the operations applied in the two labs are chosen. Let's say a guy in Lab A writes a list of operations ahead of time and doesn't show it to anyone, and he applies those operations to the photons on his side. Well, the list has still existed long enough that the information on it could in principle have moved to the other lab. There is no sensible mechanism for this, but for his list to somehow affect the events in Lab B, nothing needs to travel faster than light. Let's instead say that they flip a coin once the two states are already far apart, and do it so quickly that the outcome can't be communicated to the other lab until it's too late. Well, the outcome of that flip could still be determined ahead of time, by how the coin was resting in your wallet and how sticky your flipping hand was. Information about your hand and your wallet could in principle have moved to the other lab at the speed of light and affected their outcome. In the experiment, thy used quantum-base random number generators, but you still can't be exactly sure when the number was actually decided, and hence if it would have had time to move between the labs.
Nobody would make the serious claim that this loophole actually matters, but there is always someone says "Ok you have solid evidence, but has it been proven? Like not 99.999% but 100%"? Then the scientists will say "Well, I'd probably add another couple of nines to your estimate, but we can never claim to be completely certain about experimental results", and the first person will say "A-HA! So it hasn't been proven after all!". Just, if you want to reject locality, a stronger claim is that the scientists just made everything up.
posted by Herr Zebrurka at 10:16 AM on October 23, 2015
This thread is closed to new comments.
posted by sammyo at 3:32 PM on October 22, 2015