# Does Schrodinger's Cat Paradox Suck?

• yuiop
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.

I am having trouble believing that down-converted electromagnetic radiation disobeys Maxwell's equations.

If you analyse a vertically polarized plane wave impinging on the 2-slit/CP/VP setup using Maxwell's equations, you will get a diffraction pattern. To say that you will not get a diffraction pattern is to violate Maxwell's equations.

Last edited:
I am having trouble believing that down-converted electromagnetic radiation disobeys Maxwell's equations.
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?

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 [Broken]. 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> doea, so by analogy to the cat in the box, the cat is not in a superpositon state like |Alive>+|Dead>. That's all I'm saying, it's wrong quantum mechanics to claim that the cat continues to stay in a pure state even if we could imagine that it was in a pure state when put in the box. If we take that full system and start asking about the state of the cat within that system, then we have a complicated entity that is a subspace of an entangled system, and it will behave much more like a mixed state than a superposition state.

So even though the official meaning of a mixed state is a situation where we have incomplete information, there is another situation where we can have complete information about the whole system, yet the cat subspace acts like a mixed state. We can get an effective mixed state even in a situation where we have complete information of the box before we open it, and this sets aside the usual way the cat paradox is expressed. What remains, and what distinguishes CI from MWI, is whether we believe that we really do possesses complete information about that system (MWI), or if the structure of quantum mechanics actually does not access all the information there. If we take the latter stance, and say that our approach to physics (determinism) is what makes it impossible to address the full information there, and the part that doesn't fit has to be treated statistically, we are using CI. If we think the full information there follows the basic prescriptions of how we do physics (i.e., is deterministic) but is not accessible to us by some pernicious limitation (akin to a kind of blindness), we are using a Bohm model. I think these distinctions make it clear why until there is some way to either access the information that is kept from us, or demonstrate that it does not exist, we will not be able to distinguish these interpretatons.

Last edited by a moderator:
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 [Broken]. 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.

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?

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.

This means I have to study the actual experimental setup and results, looking at the article itself and the various links. This will take me a while. 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.

Last edited by a moderator:
If it was possible that opening the box (looking) could resurrect a dead cat (change the result) than it would have been a better example. No less bizarre, but a better example.

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?
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.

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.
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.
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.
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.

The discussions are still continuing.Great stuff.I wonder if anyone here can answer these questions:
1.Does Schroedingers experiment demand that all of the contents of the box be isolated from the surroundings when the box is closed?
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?
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?
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.

1.Does Schroedingers experiment demand that all of the contents of the box be isolated from the surroundings when the box is closed?
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.
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?
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.
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?
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?
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.
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.

If you don't like that way of thinking about it, then recognize the cat-and-box is just an allegory for the entire universe. If the entire universe is like a cat in a box, then we can say we do have a truly isolated system, because what is outside the universe that could interact with it? (Barring some ambiguous meaning of what a "universe" is, like a multiverse "landscape".)

However, maybe your comments could be summarized as pointing out that the next theory of gravity might have something to say about the cat paradox, and I think that is probably true.

The question is whether or not entangled polarizations can be said to be vertically polarized, or if one must say they are entangled-polarized.

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. 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. The only surprising results are when you analyze it photon-by-photon.

Three points:

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. In the 2-slit/CP/VP device, I assumed no stray photons. The way I analyzed the 2-slit/CP/VP device was : I assumed that both signal and idler downshifted photons were circularly polarized in the same direction - possibly left, possibly right. The signal photon went thru a left-CP filter to a detector. The idler photon went thru a double slit, with a right-CP filter after the right slit, a left-CP filter after the left slit, then everything thru a VP filter just before the screen, then the screen. 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.

2. I am appealing to the correspondence principle here - QM must give the same results as classical physics when dealing with a classical problem. Dealing with the above setup classically, i.e. Maxwell's equations, you must observe an interference pattern on the 2 slit/CP/VP device, that is the idler beam must form an interference pattern.

3. Using the complementarity principle, you cannot have an interference pattern while knowing which slit the photon came through.

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. Note that this problem is not encountered in the wiki article - only simultaneous hits are considered. If you consider only simultaneous hits in our second device, then you must extract from the set of idler photon hits the subset of idler photons which were simultaneous with signal hits, and this subset of photons will not display an interference pattern on the idler device.

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.
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.

That is the prevailing point here-- although I'm not sure how down-converters will act in every situation (particularly in regard to polarization), in that uncontroversial Wiki setup we have an example where down-converters are simply not behaving as if they were operating on classical wave amplitudes and doing nothing more than reducing the field strength by 1/root(2) as the waves come through. If one imagines that is what Maxwell's equations tell us is happening there, then we can say that Maxwell's equations are wrong, expressly because Maxwell's equations have no clue what entanglement is. If, however, we incorporate the effects of entanglement manually, we can get Maxwell's equations to work on the modified outputs (which basically amounts to getting them to incorporate those subtle shifts that divide the entangled populations).

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.
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.
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 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.
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.
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.
2. I am appealing to the correspondence principle here - QM must give the same results as classical physics when dealing with a classical problem.
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.
3. Using the complementarity principle, you cannot have an interference pattern while knowing which slit the photon came through.
We definitely agree 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.
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.

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.

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. When the light from a single slit is detected at D3 and D4, there is no interference pattern, downconverted or not - just what you would expect classically. When light from both slits is combined at D1 and D2, there is an interference pattern, downconverted or not, again, just what you would expect classically. To quote the article: "However, what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler need not be made until after the position of the signal photon has already been measured by D0." But this is a photon counting and correlation result, not in the realm of the classical analysis.

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.
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?

So the question then becomes, can you understand that difference with classical fields acting under Maxwell's equations? No, you cannot-- you must add the entanglement by hand, Maxwell had no idea of anything like entanglement. That doesn't make his equations wrong, it makes them incomplete by themselves-- there's something very subtle happening in the BBO crystal, that causes a shift in the two-slit pattern with destroys it in the raw data. It is only recoverable in a way that is completely outside Maxwell's equations. So we're back to the fact that if the BBO crystal was in a black box, you could still tell that entanglement happened in there by the simple loss of the two-slit pattern in the raw data at D0. You would know, for example, that there was something more than a beam splitter in there, even before you noticed that the frequency was halved.

Last edited:
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.

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.

So we can get rid of all the clutter of the D1-D4 detectors, etc, and just say that if we pass a plane wave thru a double slit, then downconvert, the downconverted beams will not form an interference pattern, when beam splitters yielding the same direction and phase relationship between the two beams will.

Last edited:
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.
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.

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.

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.

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.
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.

So in that setup, where the entanglement is unambiguous, we can ask if Maxwell's equations are right or not, and again the answer depends on how we treat the classical action of the down-converters, just as it does in the polarization case. I'm confident that the correspondence principle is not broken, so Maxwell's equations have to be right, but that also means that Maxwell's equations have to predict the loss of the two-slit pattern in a large aggregate signal. So this means we would get the wrong answer, using Maxwell, if we thought that the wave amplitudes (now just classical fields) do nothing but get multiplied by 1/root(2) when passing through the down-converters (because that would still give us the two-slit pattern on the screen at D0). A classical analysis of those fields must take into account the generation of two different sets of fields, shifted laterally by a half a fringe width, which when added together, yields the observed classical fields.

So then the question is, what is the classical behavior that causes that shift between these two classical fields? I don't know, but it has to be something very subtle happening in those down-converters, to make the classical-field behavior consistent with what we know is happening due to the quantum entanglement. I've never seen a classical analysis of that answer, so I don't know what it is, but it doesn't make Maxwell right or wrong-- it means we have to work harder to find out why Maxwell is right, and we might have to be guided by the quantum result to even know what to do with the classical field sources in the first place. In short, Maxwell's equations can be made to work even in situations where those equations by themselves have no clue why they are behaving that way, it would have to do with very subtle behavior in the source terms of those equations (which the equations themselves tell you nothing about). But the same would also be true in the polarization case, which I confess I really don't know if it produces the |R>|R>+|L>|L> "Bell state" or not (and frankly I'm beginning to doubt that it does), and as far as the cat paradox goes, it isn't relevant if it doesn't so the Wiki setup is much better to think about.

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. 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. 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.

I've been looking for references. A good one is "Observation of induced coherence in parametric down conversion experiments" by Rene Stock. I also looked at my notes on spontaneous Raman scattering. Stock analyzes things three different ways, one of which is classical using vacuum fluctuations as a "given" which stands in for the "spontaneous". This is also true with my notes on spontaneous Raman. 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 think maybe. I know in Raman scattering, the off-pump frequencies are explained classically by saying the polarization of the medium is non-linear in the electric field, producing harmonics in the polarization, which then re-radiates. 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.

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.
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.

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.
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.

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.
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'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.
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 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.
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.