wm said:
Yes, dependent. Hrm, did I misread the problem? Oh well, I'll think about it later.wm said:
DrChinese said:
DrChinese said:
DrChinese said:Perhaps I was not clear. Alice and Bob are intended to be synonymous with the entangled photons and their measurement. So I am providing a description of quantum objects. Yes, I totally agree that these are only "pristine" (to use your term) once. So no disagreement there.
But you say that Bob is not affected when the "sledgehammer" is applied to Alice. Oh, but that is NOT true at all! Bob absolutely acts as if he was given the same sledgehammer as Alice! That is the non-local collapse of the wave function, and it is definitely and demonstrably instantaneous. If this did not happen, we wouldn't have anything interesting to discuss in this thread.
wm said:
wm said:
Hurkyl said:
DrChinese said:
DrChinese said:
wm said:
wm said:
If both Alice's detector and Bob's director are "orthogonal to the line-of-flight axis", how is it that they have a choice of which angle to measure? Do you just mean that their own polarization sheets are directly facing the source, but that they can still rotate them about the line-of-flight axis, like if I were holding a piece of paper so you were viewing it head-on, but at the same time I was free to rotate the paper so that the letters on it could be right-side-up, sideways, upside-down, etc.?wm said:
OK, from your previous answers I get the idea that the point of the dichotomic-polariser is to ensure that even though the source is yoked to Alice's detector, she will still get a random combination of +'s and -'s on her measurements, rather than 100% +'s. But are the dichotomic-polarisers on each side some sort of electronic devices that can be "yoked" to one another, so that each pair of photons always have the same linear polarization, or could the photon received by Alice be a different polarization from its twin received by Bob?wm said:
This, I think, is the step where you violate one of the assumptions behind Bell's theorem, and for some setups it will be impossible to make it work without FTL signals between Alice's detector and the box, so you won't be able to replicate all possible EPR-style experiments using only classical devices. But more on this later, first I want to make sure I'm understanding what you're proposing.wm said:
Since I'm not so good on optics, can you go into a little more detail on the classical analysis involved? if an ordinary classical EM wave with a linear polarization in a certain direction is sent through a polarization filter at an angle A relative to it, what fraction of the wave (in terms of energy, perhaps, since for a wave with a single frequency the energy will be proportional to the number of photons when we go into quantum physics) will get through as a function of the angle? And in the quantum version of the same situation, what is the probability a photon known to have polarization in that direction (because it passed through a previous polarization filter) will make it through a polarization filter at angle A? Is it just cos^2(A) in both cases?wm said:
Can you state explicitly what individual angles you're assuming for the three possible detector settings a, b, and c?wm said:
JesseM said:
JesseM said:
DrChinese said:
DrChinese said:
vanesch said:
Right. It is the mechanics of the box which transmits the setting of Alice to Bob. But this means that Alice cannot change her axis in a space-like way independent from Bob's. In other words, Alice's setting information has been transmitted to Bob's side.wm said:
vanesch said:
wm said:
wm said:
Now, you said you were using the angles a = 0, b = 67.5, c = 45. So, calculating P(BC = S|bc), P(AC = D|ac) and P(AB = S|ab) explicitly, we have:wm said:
See above, I think it works if you just assume that the probability Bob sees a photon get through is equal to cos^2(angle of source polarization - angle of Bob's polaroid), and likewise that the probability Alice sees a photon get through is equal to cos^2(angle of source polarization - angle of Alice's polaroid), with the condition that the source is "yoked" to Alice's polaroid so there's a 50% chance it's parallel to hers and a 50% chance it's at 90 degrees relative to hers. Of course, the problem is that this yoked condition actually violates one of the basic assumptions behind Bell's theorem, namely that any properties of what it emits, "hidden" or otherwise, should be statistically independent of Alice and Bob's choice of detector settings on each trial.vanesch said:
Jesse said:
The problem is that by making this assumption, you're sidestepping the whole reason that violations of Bell's inequalities rules out local realism! Obviously your setup wouldn't work at all if Alice was regularly switching her detector settings, and the time x in seconds between switches was smaller than the distance y in light-seconds from Alice to the source--in this case, under a local theory, your "yoking" scheme can't work because by the time the source learns of each new detector setting, Alice has already switched to a different (random) detector setting. Now, you'd have to ask someone more familiar with experimental tests of the Bell inequalities to learn if the condition above has in fact been met; but there's no denying that quantum theory still predicts the Bell inequalities would be violated in this situation, and it's precisely this prediction that poses the fundamental problem for anyone trying to come up with a local realistic theory to match QM's predictions.wm said:
When I wrote this I was thinking of a well-known loophole in Bell's theorem, which I think would be explicitly ruled out with a statistical independence condition in any fully rigorous proof of the theorem. The loophole is that if the source is somehow able to "anticipate" the detector settings Alice and Bob choose ahead of time, then it can adjust the hidden variables based on this in such a way that Bell inequalities can be violated. This should be pretty obvious in the case where the source has foreknowledge of both Alice and Bob's detector settings--if they both choose the same detector, like B B, then the source just has to send out photons whose "hidden" states are identical for that setting, like {A+,B+,C-} and {A-,B+,C-}. On the other hand, if they choose different settings, like A C, the source can send out photons whose hidden states on those settings are different (like {A+, B-, C-} and {A+, B+, C-}) 3/4 of the time, and photons whose hidden states on those settings are identical (like {A-, B-, C+} and {A+, B-, C-}) 1/4 of the time, thus violating the Bell inequality which says that when Alice and Bob choose different detector settings, the probability they get the same answer must be greater than or equal to 1/3.
vanesch said:
Well, what do you mean by "a Bell-type test"? He's suggesting an experiment similar to Bell's in that each experimenter can choose between three possible detector settings which will each give yes/no answers, and looking at the correlation depending on whether the experimenters use the same setting or different settings. But the "yoking" of the source to one experimenter's setting on each trial violates one of the basic assumptions that must be used when proving Bell's theorem rigorously (and as I mentioned in an earlier post to wm, this sort of yoking would be impossible under a local theory if the time between the experimenter switching detector settings was sufficiently small and the distance between the experimenter and the source was sufficiently large).DrChinese said:
But the cos^2 rule would still work if you weren't talking about the probability of individual photons being detected, but instead talking about the reduction in intensity of classical EM waves of a single frequency as a polarized beam from the source passes through an experimenter's polarization filter, depending on the angle between their filter and the angle of the filter at the source (a setup like the one shown on http://scholar.hw.ac.uk/site/physics/topic6.asp?outline= ). And of course, a computer could use this ratio between (intensity of light getting through source's filter) and (intensity of light getting through experimenter's filter) as a probability to display a + on the experimenter's screen. The probabilities of getting a + vs. a - would be exactly the same, given the experiment wm described, as if + and - corresponded to individual entangled photons making it through/not making it through the experimenter's filter. So, the fact that he finds a violation of a Bell inequality does not really have anything to do with quantum physics, it's just a consequence of this "yoking".DrChinese said:
wm said:
JesseM said:
)wm is not directly applying Malus' law to the correlation between Alice's result and Bob's result. wm's example just uses Malus' law to find the probability that each one individually sees a photon when they orient their polarizers at a certain angle, given that the angle of the polarizer at the source is "yoked" to Alice's polarizer (using ordinary classical signals, so there must be a built-in delay) in such a way that it has a 50% chance of being at the same angle and a 50% chance of being at a 90-degree angle relative to hers (the random element is included just to ensure that she sees a random mix of + and - results, rather than all +'s). In other words, the two angles being fed into the cos^2(angle_1 - angle_2) are not the angles of Alice and Bob's polarizers, they are the angles of Bob's polarizer and the source's polarizer. So any entanglement is irrelevant, if you were just using classical EM waves it would still be true that the light reaching Bob is reduced in intensity by a factor of cos^2(angle_1 - angle_2). And of course in QM, intensity is proportional to the number of photons making it through, or the probability an individual photon makes it through.DrChinese said:
Yes, this is what is assumed in wm's example.DrChinese said:
That would be true if the source's polarization was statistically independent of Alice's choice of how to orient her polarizer, as would be assumed in a proof of Bell's theorem, but it's not true in wm's example because of the "yoking" he assumes. Of course if the yoking is done by classical means, there will be a delay which will cause wm's classical experiment to deviate somewhat from quantum predictions, and the classical setup will be wholly unable to replicate quantum predictions in the case where Alice is rapidly switching measurement angles in such a way that by the time a classical signal about each new angle has made it to the source, she has already switched to a different angle. In this case, all the Bell inequalities will be obeyed in wm's classical experiment, so this type of "yoking" will not allow a local hidden variables theory to replicate quantum predictions about entanglement in general.DrChinese said:
DrChinese said:
JesseM said:
But with the yoking, you're making the entanglement irrelevant so it can be viewed as a classical problem, and of course wm is trying to show that violations of the Bell inequality can occur in classical situations. Think of it this way--the experiment would work exactly the same way if you took Alice out of the picture entirely and just used single photons, and you had the source itself randomly pick three angles A, B, and C, and then used some other event like an atomic decay to decide whether to have its polarizer be at the 0 degrees relative to the angle it had chosen or at 90 degrees relative to it. If you mark every trial where it picks 0 degrees as + and every trial where it picks 90 degrees as -, then the polarizer's recorded series of +'s and -'s are 100% guaranteed to be exactly the same as the series Alice would have recorded if you were using pairs of entangled photons and the source was yoked to Alice's choice of measurement angle (assuming you ignore the possibility of delays in the yoking which might allow occasional photons to be emitted between the time Alice changes her angle and the time the source updates its own angle in response). So the violation of Bell's inequality that wm derives would also occur if you were looking at correlations between the +'s and -'s recorded by the source (which were based on something like the decay of a radioactive atom which was not entangled with the photon emitted by the source) and the +'s and -'s recorded by Bob. Also, as noted above, you could get the exact same violation if you were assuming classical EM waves rather than photons, with Bob's computer choosing the probability to display a + on each trial based on the reduction in intensity of the light passing through his polarizing filter. But these are not genuine violations of Bell's theorem, because Bell's theorem only says the inequalities must be obeyed under certain conditions, and one of the conditions is the statistical independence of the properties of signals/particles emitted by the source and experimenters' choice of what to measure (not true in the case where the source is yoked to Alice's measurements via an ordinary classical signal), while another condition is that there be a spacelike separation between each pair of measurements (not true in the case of the radioactive decay and Bob's measurement, since the decay actually has a causal effect on Bob's measurement in terms of the source's polarizer angle depending on it).DrChinese said: