Okay, I give. I’ll call Jeff on Monday.
By the way, in poking around I found that the theory we’ve been calling Bohm’s is also sometimes noted as the Bohm-Bub theory.
Quoth RM Mentock:
I used to think this, too. But it turns out that hidden variables carried with the particle still count as “local”, for purposes of Bell’s proof. Personally, I have a very difficult time coming to grips with this.
On the other hand, I definitely think that given the Bell results, nonlocal hidden variable theories are the “lesser of two evils”, so to speak. The conventional interpretation is still nonlocal, it’s just nonlocal quantum states instead of nonlocal hidden variables, and it throws away the notion of reality, too. I have a hard time seeing how anything that throws out reality can be considered physics.
How does Copenhagen throw away reality? EPR thought it wasn’t “realistic” (an accurate model of “what’s really going on”), but once Locality’s out, QM can be interpreted as Realistic without violating EPR. All Copenhagen throws out is an intuitive sense of measurement, which (AFAIK) HV theories don’t regain.
Can I try to dumb down Bell’s inequality?
I am far from an expert. Ever since reading “the dancing Wu Li masters” it has bothered me to not know (and later, not understand) the Bell inequality. Now I came across this thread, read the Wiki entry, and am trying again. Please you experts correct me…
The issue deals with “entangled particles”, a natural phenomenon predicted by quantum mechanics. Assume you have a machine that creates entangled pairs of electrons and sends then out in opposite directions. One electron is sent to Alice, the other is sent to Bob. Alice and Bob can each measure the spin of their photon in some direction (axis), say, horizontally. “Entangled” means that Alice and Bob always get opposite results (if one is up, then the other is down, and vice versa) if they measure in the same direction. That is, they never get the same result.
The central mystery: what happens if Alice and Bob can choose to measure their photons in different directions? E.g. each can measure either horizontal spin, or spin at an angle to the horizontal of either 22.5 or 45 degrees (randomly chosen per measurement). This means there are nine possible measurements overall. (Alice measures horizontal and Bob measures horizontal; Alice measures horitontal and Bob measures 22.5 degrees; etc.) Both Alice and Bob make their decision (what direction to measure this electron?) after that electron has been sent on its way.
Quantum mechanics predicts the correlations over time for each particular combination of measurements. The answer depends on the angle (theta) between Alice’s measurement and Bob’s. If theta = 0, then there is perfect correlation (never the same spin). If theta = 90 degrees, then there is no correlation at all (same spin half the time). If theta = 22.5 degrees, then Alice and Bob will see the same spin 7% of the time. (Formula from Wiki) If theta = 45 degrees, same spin 25% of the time.
A “hidden variable” theory is one that says these percentages are already built in to the electron pairs when they are created. That is, each electron pair is stamped with three numbers - the outcomes (up or down) for every possible measurement (horizontal, 22.5 or 45 degrees) that Alice/Bob might make.
The Bell inequality says that you can never stamp entangled electrons in such a way that you would see the percentages mentioned above! The argument is simply a counting of probabilities. See the Wiki entry for a tabulation. (I admit, though apparently simple, I’m still trying to intuitively wrap my head around this.)
Anyway, since those percentages have actually been measured in real experiments, the conclusion must be that entangled electrons cannot be “stamped” with spins in such a way to get the observed result. Conclusion: they aren’t stamped beforehand; the spins aren’t decided at the time the electrons are created, but at the time the measurements are done.
Is this a valid understanding of this phenomenon? Is it helpful?
Oops, inconsistent particles in my previous post. Please read either “electron” or “photon”…
Yes I mean superluminal, but correct me if I’m wrong I’ve always thought of tachyonic referring to anything with a relativistic velocity greater than c.
Idon’t see why there’s any need for hiddeen variables, just because you don’t see people walking down the street in a superpostion of states, surely that doesn’t mean that on a icroscopic level particles can’t be a superpostion of states. Even if you do start adding hidden variables you end up with theories that are still radically different from everyday experince.
Actually, this sort of thing has been well dealt with. “Really”, people walking down the street are in a superposition of states, but as Planck’s constant goes to zero (alternately, the characteristic action of a system gets very large with respect to h) the states which differ significantly from a “classical” state become very unlikely to obtain, since the contributions from most states cancel each other out in the large limit.
I’m not sure what you mean. The Bohmian non-local hidden variable is completely deterministic, right? That’s the concept behind Einstein’s “God doesn’t play dice…”
By conventional interpretation, you mean the Copenhagen one, right?
Einstein’s EPR objection actually wasn’t that QM wasn’t deterministic, but that it wasn’t realistic. He didn’t believe that the wave function corresponded to an “elemnt of physical reality”. The Bohm-Bub theory is nondeterministic, but the probabilities of an EPR experiment (for example) are determined by the hidden variables: extra information not contained in the wave function.
As an addendum, I reiterate my (possibly inexplicit) objection that I believe the question of physical reality is more satisfactorially addressed in QFT than in QM. Explaining “electrons” as certain modes of excitation of the electron field, some of which may indeed be very spatially localized, is very sufficiently realistic to me. I can see the mathematical formalism of a gauged field theory such as QED and have some handle on how “classical” pictures emerge as I zoom out, including how “quantum weirdness” begins to cancel itself out as the characteristic scale of action increases.
In short, I think that the presence of QFT renders the question of HV extensions of QM moot. It was mostly a philosophical question anyhow, imho.
Thanks for the replies everyone. I hadn’t found the Wiki article with googling: it did help me understand Bell inequalities, but that seems to be only half the issue.
The other, which I also could not find any explantary text online, appears to be the equations for determining the spin of the electron, which you would then plug in to the Bell inequalities to then hypothesize about what nonlocalized phenomena should appear like, statistically.
So, I take it an electron, if you find a way to “test” it, will have a spin of always exactly 1/2 or -1/2. But if take a pair of electrons and measure them at non-similar angles, you have a percentage that the spins will agree based on the differences in the measuring angle? Am i right?
I only skimmed through the thread, but this might help.
Frankenstein Monster: I think you did a fine job of dumbing down Bell’s inequalities.
Ludovic: You are right, in that the electronic spins will have a degree of correlation based on the relative measurement angle and the initial (pre-measurement) state. It is not a simple “percentage” which can be determined with trigonometry, however; actually deriving the predicted correlations requires that you do, well, quantum mechanics. This is the essence of the EPR “problem”–calculating those correlations with simple trigonometry (a local hidden variable theory) and with quantum mechanics, in certain situations, lead to quite different predictions. The Aspect, et al. experiment in 1986(?) proved quite conclusively that the predictions of quantum mechanics are the correct ones.
I think the best explanation is Bell’s own, in a paper with the wonderful title “Bertlemann’s Socks and the Nature of Reality.” It’s reprinted in this book , which unfortunately still hasn’t been released in reprint edition. You may be able to find the earlier edition in your library, tho.
In Bohm’s theory the particles are accompanied by a “guiding wave” which tells the particle where to go. From this site:
To put it as succinctly as possible, Bell’s theorem says you can’t have reality AND locality AND QM. The standard “Copenhagen” interpretation of QM eliminates “reality”, while Bohm eliminates “locality”. The third possiblilty, that QM is incorrect in some fashion, has been suggested in the GRW theory , but even the authors of the theory don’t seem too happy about it: