Does Schrodinger's Cat Paradox Suck?

[Rap]

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.

 

[Ken G]

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.

 

[Rap]

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.

 

[Ken G]

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.

 

[Rap]

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.

 

[Ken G]

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.

 

[Rap]

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.

 

[Ken G]

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.