What's going on between Alice and Bob?

[TimH]

Hello to the forum (new user). I have a background in philosophy and have been reading Hughes' Structure and Interpretation of Quantum Mechanics. I have a question about entanglement.

When I first read the description of entanglement, in the above book, it did indeed seem like "spooky action at a distance." Now I'm a few chapters beyond that, and I've "lost the spookiness." Hughes has been arguing that quantum particles do not really have properties at all, that we can only talk about events.

My question is: Is there something undeniably spooky going on in entanglement, or is it simply spooky action-at-a-distance if you adopt a particular perspective (which I seem to have lost)? Or have I just forgotten how to see the spookiness?

Let me explain the Alice and Bob situation as I understand it. Then I'd appreciate someone commenting on my understanding. I'll use Bohm's example with electrons. So two electrons in the spin-singlet state rush off in opposite directions. Alice measures the z-axis spin on one electron and gets, say +z. She knows that Bob, at whatever distance he is, will get -z if he measures spin on the z-axis of his electron.

Now the entanglement comes when Bob measures a different, incompatible observable from the one Alice measures. Say Alice measures z again and finds z+. Bob instead measures x-axis spin and gets a random value. This is what we expect: the singlet state has "collapsed" into z+ and so x is equally likely to be x+ or x-. But if Alice measures x-spin instead of z, and Bob measures x, Bob will always get the opposite x-spin from Alice.

So when we compare the results we find that when Alice chose to measure z, the Bob x is random, and when Alice measures x, the Bob x is still random, but is also the opposite of Alice's.

Is this what happens? What is spooky about this? What am I missing? Thanks.

 

[Avodyne]

Nothing is spooky about the situation you describe, because it is easy to find a classical model that would do the same thing.

The best explanation I have ever read of the spookiness was given by David Mermin in a Physics Today article 20 years ago. Luckily, there is a pirated copy online:

www.physics.iitm.ac.in/~arvind/ph350/mermin.pdf[/URL]

 

[TimH]

Thanks so much for the quick response and the link. I've copied the article and will look at it tomorrow. So are you saying that there IS something spooky, that I haven't noticed, or that the facts of entanglement only seem spooky if you think about quantum particles as having properties in a particular way?

 

[cesiumfrog]

Nothing is spooky about the situation you describe, because it is easy to find a classical model that would do the same thing

Surely you mean that only as a criticism of the OP's description, since it is generally not possible to explain entanglement with any non-spooky classical model.

 

[JesseM]

What's spooky is that the statistics of Alice and Bob's measurements violate Bell's inequality. Here's an analogy I posted on another thread:

Suppose we have a machine that generates pairs of scratch lotto cards, each of which has three boxes that, when scratched, can reveal either a cherry or a lemon. We give one card to Alice and one to Bob, and each scratches only one of the three boxes. When we repeat this many times, we find that whenever they both pick the same box to scratch, they always get opposite results--if Bob scratches box A and finds a cherry, and Alice scratches box A on her card, she's guaranteed to find a lemon.

Classically, we might explain this by supposing that there is definitely either a cherry or a lemon in each box, even though we don't reveal it until we scratch it, and that the machine prints pairs of cards in such a way that the "hidden" fruit in a given box of one card is always the opposite of the hidden fruit in the same box of the other card. If we represent cherries as + and lemons as -, so that a B+ card would represent one where box B's hidden fruit is a cherry, then the classical assumption is that each card's +'s and -'s are the opposite of the other--if the first card was created with hidden fruits A+,B+,C-, then the other card must have been created with the hidden fruits A-,B-,C+.

The problem is that if this were true, it would force you to the conclusion that on those trials where Alice and Bob picked different boxes to scratch, they should find opposite fruits on at least 1/3 of the trials. For example, if we imagine Bob's card has the hidden fruits A+,B-,C+ and Alice's card has the hidden fruits A-,B+,C-, then we can look at each possible way that Alice and Bob can randomly choose different boxes to scratch, and what the results would be:

Bob picks A, Alice picks B: same result (Bob gets a cherry, Alice gets a cherry)

Bob picks A, Alice picks C: opposite results (Bob gets a cherry, Alice gets a lemon)

Bob picks B, Alice picks A: same result (Bob gets a lemon, Alice gets a lemon)

Bob picks B, Alice picks C: same result (Bob gets a lemon, Alice gets a lemon)

Bob picks C, Alice picks A: opposite results (Bob gets a cherry, Alice gets a lemon)

Bob picks C, Alice picks picks B: same result (Bob gets a cherry, Alice gets a cherry)

In this case, you can see that in 1/3 of trials where they pick different boxes, they should get opposite results. You'd get the same answer if you assumed any other preexisting state where there are two fruits of one type and one of the other, like A+,B+,C-/A-,B-,C+ or A+,B-,C-/A-,B+,C+. On the other hand, if you assume a state where each card has the same fruit behind all three boxes, like A+,B+,C+/A-,B-,C-, then of course even if Alice and Bob pick different boxes to scratch they're guaranteed to get opposite fruits with probability 1. So if you imagine that when multiple pairs of cards are generated by the machine, some fraction of pairs are created in inhomogoneous preexisting states like A+,B-,C-/A-,B+,C+ while other pairs are created in homogoneous preexisting states like A+,B+,C+/A-,B-,C-, then the probability of getting opposite fruits when you scratch different boxes should be somewhere between 1/3 and 1. 1/3 is the lower bound, though--even if 100% of all the pairs were created in inhomogoneous preexisting states, it wouldn't make sense for you to get opposite answers in less than 1/3 of trials where you scratch different boxes, provided you assume that each card has such a preexisting state with "hidden fruits" in each box.

But now suppose Alice and Bob look at all the trials where they picked different boxes, and found that they only got opposite fruits 1/4 of the time! That would be the violation of Bell's inequality, and something equivalent actually can happen when you measure the spin of entangled photons along one of three different possible axes. So in this example, it seems we can't resolve the mystery by just assuming the machine creates two cards with definite "hidden fruits" behind each box, such that the two cards always have opposite fruits in a given box.

 

[Avodyne]

Surely you mean that only as a criticism of the OP's description

I meant that perfect correlation when they measure the same property, and no correlation when they measure different properties (the case described by the OP) is not at all spooky.

The machine/card model that JesseM describes is spooky. This model was first discussed by Mermin in the paper that I cited.

 

[TimH]

Thanks for the great post Jesse, that really helps me understand Bell's inqualities. It convinces me that spin is definitely weird.

My question now is: Must the measures at A and B be affecting each other to explain the violation of Bell's inequalities (action at a distance), or if we give up the idea of classical properties, can spin be conceived of as non-classical in a different sort of way. What I mean is, Hughes in his book (see OP) suggests that incompatible observables are incompatible because they are deeply related to each other. So spin values in different directions are all knit together in a way that is impossible to imagine. And this way they are knit together is revealed in entanglement experiments, without having to say that the experiments are affecting each other over the space between them. Is other words, is resorting to action-at-a-distance an attempt to keep some sort of individual identity to different spin axis measures?

 

[alphachapmtl]

... So when we compare the results we find that when Alice chose to measure z, the Bob x is random, and when Alice measures x, the Bob x is still random, but is also the opposite of Alice's.
Is this what happens? What is spooky about this? What am I missing? Thanks.

It is spooky when you consider subsets of measurement.
-- 1st case: when Alice measure z, Bob x is random.
consider the subset Alice.z+, then Bob.x is random : no problem here.
-- 2nd case: when Alice measure x, Bob x is random and opposite to Alice's x.
consider the subset Alice.x+, then Bob.x is not random : spookiness here.

 

[JesseM]

It is spooky when you consider subsets of measurement.
-- 1st case: when Alice measure z, Bob x is random.
consider the subset Alice.z+, then Bob.x is random : no problem here.
-- 2nd case: when Alice measure x, Bob x is random and opposite to Alice's x.
consider the subset Alice.x+, then Bob.x is not random : spookiness here.

That in itself is not spooky; it is quite possible for a local hidden variables theory to replicate the prediction that when Bob measures a different axis than Alice, he has a 50% chance of getting the same result and a 50% chance of getting a different one, but when he measures the same axis he has a 100% chance of getting a different one (if on each trial you just flip a coin to determine the hidden spin on each of the three axes of Bob's electron, and set the hidden spins on Alice's electron to be the opposite, then these will be the statistics you'll get after many trials). As I said in my post above, it's only when Bob's chances of getting a different result go below 1/3 in the case where he chooses a different axis that you get something that cannot be explained by a local hidden variables theory.