Ken G said:Then I don't see how you are disagreeing with me at all, because that's pretty much the crux of what I'm saying. The state |R>|R>+|L>|L> causes its individual particles to behave differently from how |R>+|L> behaves, and that is trying to tell us something about the cat paradox.
Maxwell's equations aren't quantum mechanics. Didn't the Wiki I just cited make it perfeclty clear that entangled particles don't make double-slit patterns if the entanglement allows which-way information?Rap said:I am having trouble believing that down-converted electromagnetic radiation disobeys Maxwell's equations.
Ken G said:Let's dispense with the polarization, since we just want a state like |R>|R>+|L>|L>, we may as well use the setup in the Wiki article at http://en.wikipedia.org/wiki/Delayed...quantum_eraser . Then we don't have to worry what down-conversion does to polarization, we can use "R" and "L" to mean down-conversion at the "right" and "left" slits instead. Since the Wiki article asserts that we do not get a two-slit pattern in that case, it suffices to hold the point I'm making-- |R>|R>+|L>|L> does not yield the two-slit pattern that |R>+|L> does.
The question is whether or not entangled polarizations can be said to be vertically polarized, or if one must say they are entangled-polarized. This is such a subtle point that I really don't even know the answer-- we know that lasers don't do this, they can prepare many photons in the same single-photon state without entangling their polarizations, so I don't know of BBO crystals work in effect just like lasers. or if there is additional entanglement there which insures that both members of the pair must show with the same circular polarization on the grounds that they are in some sense constrained to act the same, or if they should give opposite polarization to conserve angular momentum, or if they should give statistically uncorrelated angular momenta like a laser does. So I'm realizing this is a technical detail that is probably worth its own thread, but is not really the thrust of what I'm saying about the cat paradox.Rap said:Just to be clear, is it true that you are saying that in the original case of a 2-slit/CP/VP device, Maxwell's equations will not hold for down-converted radiation - i.e. an interference pattern will not be observed for a vertically polarized plane wave?
That is probably not the best Wiki article I ever read, but the important point is that it has down-converters in front of each slit, which splits into "signal" and "idler" photons, and which-way information of the signal photon can be extracted by looking at the trajectory of the idler photon. As a result, if you don't do anything with the idler photons, the signal photons do not yield a two-slit pattern. Hence, if there was a black box where the BBO crystals are, you could tell that entanglement is occurring in that black box because of the absence of the two-slit pattern in the signal data, and the ability to recover the two-slit pattern by erasing and correlating with idler photons. There's nothing FTL there, you can get information about a black box by looking at what comes out of it. But if it's a cat and a kill-mechanism, you could never erase-and-correlate with anything going on in the kill mechanism, such that you could end up with superposition behavior in the cat-- even if the cat started out in a pure state.Regarding the wiki article, the introduction section, which I read, is not at all clear to me. I am not sure where the two slit device is located, I am not sure what "target" and "target phase" mean. Is the target the two slits or the detector? This section continually talks about which path the photon takes, or maybe both at once, and with my Copenhagen mentality, I have to continually interpret these classical-mentality statements in terms of measured results and the interpretation is difficult if not impossible at various points in the introduction.
As I've said, the only thing that matters about any of these gedankenexperiments is the basic quantum mechanical truth that |R>|R>+|L>|L> is not going to behave the same way as |R>+|L>, as the former will act like a mixed state and the latter a superposition state in regard to experiments on the single-particle component of the system. I should have just said that from the outset, and not brought in any gedankens-- the point was simply to boil down the cat-and-box as much as possible.Can we concentrate on one particular problem to its conclusion rather that bouncing from SC, to 2-slit/CP/VP, to quantum erasure, to your next gedanken experiment, etc. every time I have a question? Does this particular experiment illustrate your point? If so, let's stick with it to the conclusion.
It demands that they be isolated in the sense that any outside influences are of no significance to the experimental outcomes, the usual meaning of "isolated" in physics.Dadface said:1.Does Schroedingers experiment demand that all of the contents of the box be isolated from the surroundings when the box is closed?
Since it is a gedankenexperiment, we are free to either assert no gravity, or that gravity will not have a significant influence. Since gravity is not included fully self-consistently in quantum mechanics, it is never clear what gravity might do to the situation.2.If the answer to question 1. is yes then does the isolation need to be total,in other words is it necessary that the contents of the closed box have no interactions at all,not even gravitational interactions,with the surroundings?
That's exactly what is not clear. But the same is true even for a truly isolated system of a cat in a box-- the only way physics can answer if a system is truly isolated is if the outcomes of the experiment don't change as we further reduce the level of interaction with the environment. But the outcomes of the experiment are already the same, whether we have a pure or a mixed-state treatment of the entire system, so we could never tell how possible interactions with the environment adjudicate between a pure and a mixed state. What I've pointed to above is that it doesn't matter if the system as a whole is in a pure or a mixed state, because all results when we open the box and look at the cat are the same either way. That means we can always treat the cat as if it were alive or dead and we just don't know which, so if we can always treat the cat that way, how does it benefit us to imagine that something else might actually be true? What is "truth" outside of a consistent way for us to interact with and understand our environmental condition?3.If the answer to question 1. is yes and the answer to question 2. is no then can the needed level of isolation be defined and if so what is the needed level?
I think that's because we already find a resolution to the situation even if we imagine that a truly isolated cat-and-box is possible, and introducing the impossibility of complete isolation does not appear to alter that resolution. If we want to know if one resolution works in every situation, we must confront that resolution with its most difficult challenge, which in this case is an idealized perfectly isolated system.Thanks if anyone can answer these questions.I made some reference to these issues earlier on in this thread but did not pursue the matter to get exact answers.
Ken G said:The question is whether or not entangled polarizations can be said to be vertically polarized, or if one must say they are entangled-polarized.
The point is that putting down-converters in front of the slits destroys the two-slit pattern. You can see that, it jumps right out. Now does that violate Maxwell's equations? It certainly does if you think Maxwell's equations are describing a superposition of classical in-phase wave amplitudes emanating from the two down-converters. This does not mean Maxwell's equations are actually violated, it means they are being applied incorrectly if one imagines that the down-converters are acting classically.Rap said:I read the wiki article ( http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser ) you provided. It does not appear to me that Maxwell's equations are violated in the wiki article.
That depends entirely on how they are analyzing it. Let's say they treat each down-converter as if it simply multiplied the wave amplitude by 1/root(2), sent it along, and shunted a second wave of that amplitude off somewhere else. How could you tell them that they were applying Maxwell's equations incorrectly to the down-conversion process? It would seem like a perfectly natural way to apply Maxwell's equations there, the problem is that Maxwell's equations are not quantum mechanics.To someone analyzing it from an electromagnetic wave viewpoint (i.e. without detecting individual photons) there are no surprising results. One-slit patterns show no interference, two-slit patterns do - no problem.
I don't see any fundamental issue here, no doubt things would work fine if photons were sent through one at a time and all possibilities tracked.1. In the wiki article, there were many noise photons, so that only a simultaneous hit on D0 and D1-4 could be counted as two entangled photons.
I'm not sure what you mean here, a straightforward change in the apparatus in the Wiki article could easily obtain which-way information from every idler photon, in analogy to the polarization version.You can have four cases:
signal idler conclusion
------------------------------
no hit no hit downshifted photons were right polarized, idler photon slit inconclusive
no hit hit downshifted photons were right polarized, idler photon went thru right slit
hit no hit downshifted photons were left polarized, idler photon slit inconclusive
hit hit downshifted photons were left polarized, idler went thru left slit
In other words, for every idler photon hit on the 2-slit/CP/VP device, it could be decided which slit it came through, depending on whether or not there was a hit on the signal detector. This is in contrast to the wiki article which only counts simultaneous signal hits due to photon noise.
But one has to know how to do the classical problem. If you tell me how you would treat the Wiki apparatus entirely in the language of Maxwell's equations applied to fields, I could understand.2. I am appealing to the correspondence principle here - QM must give the same results as classical physics when dealing with a classical problem.
We definitely agree there.3. Using the complementarity principle, you cannot have an interference pattern while knowing which slit the photon came through.
I don't know that the polarization apparatus achieves the desired |R>|R>+|L>|L> state, but I do know that the Wiki setup does, so I think we should just use the Wiki setup. Everything I'm saying applies just as well there.Points 1, 2, and 3 are incompatible, one must be wrong or incorrectly applied, I cannot figure out which at this point. My intuition is that 1 is the problem.
Ken G said:The point is that putting down-converters in front of the slits destroys the two-slit pattern. You can see that, it jumps right out. Now does that violate Maxwell's equations? It certainly does if you think Maxwell's equations are describing a superposition of classical in-phase wave amplitudes emanating from the two down-converters. This does not mean Maxwell's equations are actually violated, it means they are being applied incorrectly if one imagines that the down-converters are acting classically.
Not so, if you had a beam splitter, at D0 you would have a two-slit pattern, since no entanglement is induced by beam splitting. However, when you have down conversion in a BBO crystal, you do not get a two-slit pattern at D0. None of this has anything to do with any of the other detectors, they only come into play when the signal at D0 is correlated with other things. There is no need to do any correlating to see that with the entangled photons, you do not get a two-slit pattern in the raw data at D0, and with a beam splitter, you do. Yes?Rap said:I don't think the downconverter destroys the interference pattern. If you simply had a beam splitter instead of the downconverter, the classical results would be the same.
Ken G said:Not so, if you had a beam splitter, at D0 you would have a two-slit pattern, since no entanglement is induced by beam splitting. However, when you have down conversion in a BBO crystal, you do not get a two-slit pattern at D0. None of this has anything to do with and of the other detectors, they only come into play when the signal at D0 is correlated with other things. There is no need to do any correlating to see that with the entangled photons, you do not get a two-slit pattern, and with a beam splitter, you do.
Excellent, I think we are on the same page now. Frankly I have no idea what is happening in that BBO crystal, and I agree that the correspondence principle is not suspended-- Maxwell must get the right answer for the aggregate behavior, so if we can tell those equations what they need to do inside that crystal, we could understand the loss of the interference pattern in the classical fields. But something is percolating up from the entanglement level that gives the amazing correlations among the quantum events, and when treated at the aggregate classical level, yields Maxwell equations that describe the loss of the aggregate interference pattern. So it's not so much that Maxwell is wrong, it's that something well outside what they taught us how to use Maxwell to treat is happening inside that darn crystal.Rap said:Ah, ok, I see. I was concentrating on the D1-D4 detectors and did not appreciate the statement at the bottom that there was no interference pattern at D0. Let me ponder this for a while, try to understand in more detail what goes on in a BBO crystal. If this is the case, then Maxwell's equations are in fact wrong, and I finally understand your point about how the cat's "past history" is important, something I never understood before.
Ken G said:Excellent, I think we are on the same page now. Frankly I have no idea what is happening in that BBO crystal, and I agree that the correspondence principle is not suspended-- Maxwell must get the right answer for the aggregate behavior, so if we can tell those equations what they need to do inside that crystal, we could understand the loss of the interference pattern in the classical fields. But something is percolating up from the entanglement level that gives the amazing correlations among the quantum events, and when treated at the aggregate classical level, yields Maxwell equations that describe the loss of the aggregate interference pattern. So it's not so much that Maxwell is wrong, it's that something well outside what they taught us how to use Maxwell to treat is happening inside that darn crystal.
We don't know if the 2-slit/CP/VP analysis is wrong or not because it all depends on whether down-conversion creates an entangled polarization state like |R>|R>+|L>|L> in regard to subsequent circular polarization measurements. But whether it does or not has nothing to do with whether or not Maxwell's equations are right. To see this, it's easier to use the Wiki setup, where we know the two down-converters are giving us a |R>|R>+|L>|L> entangled state, where now we interpret the "R" and "L" as meaning right and left slit, rather than right and left polarization.Rap said:Well, Maxwell's equations are simple when it comes to the 2-slit experiment. Two point sources of radiation separated by some distance, same frequency, identically polarized and in phase, will produce an interference pattern, high where the path lengths are different by n wavelengths, low where they differ by (n+1/2) wavelengths where n is an integer. If this is not the case when the photons of each source have an entangled partner somewhere , then Maxwell's equations are wrong. If, on the other hand, there is a classical description for the lack of interference pattern, then the paradoxical aspect of the experiment lies in the photon "bookkeeping" (taking subsets, etc.), a totally quantum phenomenon. In all of the photon paradoxes I have ever seen (Bell, EPR, etc.), the paradox is not that classical behavior (EM wave analysis) is violated, but that photon bookkeeping or statistics yields counter-intuitive results, so that is why I would be surprised if there were a violation of Maxwell's equations, and surprised by my possibly faulty analysis of the 2-slit/CP/VP setup.
But how do you know that statement holds inside BBO crystals? Apparently something more complicated is going on in there, generating entanglement at the quantum level, and there's no guarantee there's any easy way to treat that classically. There are many tricks used to get the right classical behavior, look at something as basic as radiative damping for example, it is completely heuristic as a classical argument but the argument does work. There should be something like that for down-conversion, I agree, but it might not look like susceptibilities and indices of refraction.Rap said:When doing EM wave analysis in media, there are a number of media properties which come into play (index of refraction, susceptibilities, etc.). These media properties are determined by classical (macroscopic) measurements and do not need to be theoretically determined by a microscopic (e.g. quantum) theory in order to be used.
Now you are talking about measurements, but Maxwell's equations are theory. If one needs QM to trick the classical equations into giving correct theoretical predictions of specific heat, I would not be at all surprised if the same game must go on in BBO crystals.Its like the specific heat in thermodynamics, its just a measurement that you make and then you are good to go with your thermodynamic calculations, but to predict the specific heat for a particular substance, you have to step outside of thermodynamics and develop a quantum theory of specific heat.
Maxwell's equations involve more than empirically determined media parameters, they involve source terms too. Apparently the source terms are doing something very tricky in a BBO crystal, which you can't get from Ohm's law or some such simple media parametrization. Maxwell's equations don't require that there's some simple way to back-relate the sources to the fields, as Maxwell separates the fields and the sources. Other laws, like Ohm, are needed to close the equations, and that's apparently where entanglement is sticking its neck out in BBO crystals at the classical level. But we certainly agree that the correspondence principle is at play here-- the information can flow seamlessly from the quantum mechanical to the classical level, there's just no guarantee the classical level can be made to work without guidance from the quantum domain.I think that Maxwell's equations along with all the macroscopically, empirically determined media parameters and relationships will yield a consistent, accurate description of how the EM waves will behave.
That's fine, and I do like classical explanations, I'm just saying that no way does anyone come up with that classical explanation without quantum guidance. It's not a priori classical reasoning, it's a way, schooled by QM, for us to still think classically and get a basic understanding. That's what I mean by Maxwell still working to provide a theoretical expectation, but only after-the-fact with the appropriate quantum-inspired tweaks.I'm winging it here, but it seems that the vacuum fluctuations are coherent over the distance of the slits, producing coherent radiation from the slits. If the two slits are walled off from each other, the vacuum fluctuations are no longer coherent, which yields no interference fringes. This gives a classical explanation.
I agree that it would be interesting to have a better classical feel for how down-conversion works, I'm a fan of classical analogs. One should be able to get the gross data patterns classically, it should only be the quantized correlations that classical arguments can't touch.I'm thinking the same flavor of explanation will explain the two downconversion frequencies. Again, these are empirical approaches which work in aggregate, and make no attempt to go outside classical EM to determine why the empirical parameters have the values that they have, which is where the QED analysis would be the best.