After using a ‘Physics for Dummies’ explanation of Bell’s Theorem, I see how it explains the measured behavior of entangled particles, but I’m missing the underlying ‘mechanism’ that wouldn’t work with a hidden variable.
It sounds like particles will measure an up or down spin along a particular axis, but there is an actual, unknown spin that may not be exactly aligned with that axis prior to measurement. If that is the case, then it would seem that some spins, prior to measurement would have an equal probability of being measured as either up or down, lets call that halfway spin. So if there was a hidden variable, entangled particles with that halfway spin could measure as both up, or both down, or opposite spins. Since measurement shows them as always opposite or always same spins (depending on the type of particle) then there could not be a hidden variable.
If I’m way off here, please give me a few hints. If not, please tell me how we know that entangled particles would have that halfway state, as opposed to all entangled particles having a spin that can only be measured as up or down.
Also, thanks to Chronos, Exapno Mapcase, Indistinquishable, and The Hamster King, et al, for their help so far.
You have the right start. But now consider rotating the axis and keep making measurements. Bell’s Thm essentially states that the only deterministic (and linear) theories that can predict the statistical results, which QM asserts are result from an inherent randomness, are nonlocal (i.e., require communication faster than the speed of light).
I should have added this url: http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html
Okay, I understand what Bell’s is stating. That is an explanation for the measured behavior. I’m still missing how a hidden variable in each entangled particle could not produce the same result unless the particles can be shown to have independent randomness. Perhaps the example above and Indistinquishable’s explanation here:http://boards.straightdope.com/sdmb/showpost.php?p=12330258&postcount=41 have the answer in that the hypothetical detector that measures first still has a random chance of showing one of three states, but the other one only shows an ‘opposite’ state.
Also, any good references for what ‘entanglement’ is? Besides the ‘spooky’ action, what else, if anything, distinquishes entangled from non-entangled particles?
I’m afraid it has been a long time since I was in grad school. I would try wikipedia, it is surprisingly good for this kind of thing.
An entangled quantum system is one for which you must specify the full quantum state of the system to describe a part of the system. For example, if I shoot two photons from two different atoms that are not correlated in any way, I can describe each photon individually, without worrying about the other one. The complete system is the simple composition of the two parts. Suppose, however, I have a spinless particle that emits two photons. To preserve angular momentum, they must have opposite momenta. The two photons now form an entangled system: you can not describe one without the other. The spookiness, is not that you know the angular momentum of one when you measure the other; that would be true classically. The spookiness is that neither has a specific angular momentum until you measure one, and then the other has the necessary angular momentum to conserve angular momentum.
And yes, indistinguishable’s post has the answer in there, although I don’t have time to read though it.
Thanks, you’re confirming what I’m having trouble putting into words. Wikipedia is light on details, except for the math, which is my achilles heel. I’m trying to get a more specific description of how we know that the measured spin of the entangled particles isn’t predetermined, but looking more at the general behavior or particles is revealing that. Bell’s describes the measured results, but I’m more comfortable looking for the underlying mechanism. I’ve never looked at quantum physics deeper than the ‘factoid’ level before, which has left a lot questions. Nothing but curiousity though, not much application for this stuff in my line of work.