Talk:Afshar experiment/Archive 16

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Removed reference to text within Unruh's "Quantum Rebel" page.

The quoted text creates the impression that the text is refering to Afshar's experiement. In fact it is not, it is refering to Unruh's example experiements which he claims are equivalent, although this is perhaps debateable. Additionally the only way we could be sure of what Bohr would think about any experiment would be to ask him, and Bohr is currently unavailable for comment. Dndn1011 10:00, 22 November 2006 (UTC)

The experiment is really equivalent, but Unruh's analysis is wrong. So whether you will keep the reference or not is of no importance. Danko Georgiev MD 10:19, 22 November 2006 (UTC)

You are both judging content which is OR -- the text reports Unruh's opinion, which is noteworthy and credible because of Unruh's reputation & trackrecord as a physicist. I think the correct response is to add a rider that Unruh's comments are about a setup he claims is equivalent to Afshar's. --Michael C. Price ^talk 10:21, 22 November 2006 (UTC)

No after reading Unruh's text it became clear that he was not refering to Afsha's experiment. But the statement itself is expressing Unruh's opinion of what Bohr's opinon might have been on Unruh's experiment. That's three levels of indirection, and it is this I objected to. As for the experiements being equivalent, I am not so sure. I mean I may be wildly wrong but I get the impression the argument goes "We can express both experiments the same way methematically therefore they are equivelent". This is logical only as long as the assumptions being made are valid and equivalent for both experiments. The biggest difference I see is simply that Afshar's experiment does not require multiple runs with modifications to the set up to show wave or particle behavior. Afshar's experiment shows both at the same time, in the same experiment, without the need to modify the apparatus. Each photon in its course unambiguously demonstrates how a single photon has both passed through both holes and only one hole in the course of its journey, and thus how it has behaved according to both models. This is not the case in Unruh's example. That such a conlusion should be impossible means that an assumption is being made, such as the assumption that photons actually travel. To quote Bohr "Nothing exists until it is measured". If we believe this then there is no conflict, and no explanation. Dndn1011 13:23, 22 November 2006 (UTC)

Since Unruh believes his setup equivalent to Afshar's his comments are addressed to both experiments. You say Afshar's experiment does not require multiple runs, but it does in the sense that many photons must pass through the apparatus. I don't think you are in a position to give a meaningful critique of Unruh's experiment in comparison to Afshar's when you don't have a deep understanding of the physics. (I don't mean that in a nasty way, but you are clearly in the process of learning about the basics of quantum mechanics: Unruh has spent his entire career on very advanced quantum physics.) --Michael C. Price ^talk 06:57, 23 November 2006 (UTC)

I make no claim to be knowledgeable in Quantum Mechanics, but I am good at perceiving holes in logical arguments. I may not have spent my entire career on very advanced quantum physics, but I have spent my entire career on very advanced computer programming. And so I am very well trained in logical reasoning. I am qualified to make observations about the comparison of the two experiments without needing to know about the details of quantum mechanics. I can not do this formally (I am lacking the training to do so). But I can present a logical argument. And here it is: if we find that fewer photons than expected are lost through hitting the wires and more than expected land on either detector, then we conclude that some photons must have avoided the wires due to interference and also been detected. To clarify by example: if 100 photons are fired and 99 hit the targets, where we would expect only 93 to do so (which can be verified by looking at the loss with one hole closed), then we conclude that 6 photons must have avoided the wires where they would be expected to hit them, while also being detected as having come through a particular hole. This is just logical. It is also very different from Unruh's experiement which although fascinating and worthy of an expert in very advanced quantum physics, does not deomnstrate the same thing at all for the reasons I already gave. Incidentally I agree with you that in a sense Afshar's experiement requires multiple runs, if we take each photon fired as a run through the experiement, but you have conveniently ignored the other crucial thing I said: that Unruh's experiment requires modification of the apparatus between runs whereas Afshar's does not (in the sense that once both holes are open and the wires are in place the behavior that is alledged to invalidate complementarity is demonstrated without needing to adjust the apparatus). And if I am wrong, I'm the first who'd like to know. But sorry to be satisified I need to see some counter argument better than "you are not qualified to comment". And I don't mean that in a nasty way either. Dndn1011 09:50, 23 November 2006 (UTC)

It is only Fig2 that Unruh presents as equivalent to Afshar's experiment, which is why he refers to "this experiment"; the other set-ups are to illustrate how the concept of complementarity changes with changes of the experimental apparatus, even parts of the apparatus that do not interact with the photons. And specifically how the insertion of the absorber at 4 (the equivalent of Afshar's wires) changes the interpretation of what complementarity means, from how it would be interpreted within the unwired version of the double slit experiment (or Wheeler's delayed choice experiment, which the unwired Afshar experiment is identical to) -- irrespective of whether the wires/absorber absorbs or scatters any photons. --Michael C. Price ^talk 12:10, 23 November 2006 (UTC)

Thanks for this it has helped me focus better on the problem. I do see the similarity now (I was getting the wrong end of the stick). However I still have problems with the asymmetry of Unruh's experiment versus the symmetry of Afhsar's, although it is not clear to me if that makes a difference. Also I am not sure that the final half silvered mirror is a correct analogy for the lens. In Unruh's experiment the concept of which way the photon went (so to speak) is hidden behind two half silvered mirrors, whereas in Afshar's the mechanism for detection is a lens which we think of as reliably showing us where light comes from. In figure 2 we can in truth not know which path (1 or 2) a photon detected at 5 or 6 took because we cannot measure this. It is an assumption based on the behaviors obvserved in figures 1 and 1a. However the lens should be quite clear about it. We should be observing the equivalent of path 1 or 2 directly... unless a lens connot be assumed to demonstrate where photons came from. This may be what Danko was hinting at with something significant about "lens function". Anyway, I will look into this more. Dndn1011 14:07, 23 November 2006 (UTC)

Glad it helped. Reading (and re-reading) Unruh's experiment helped me develop my understanding of complementarity as well: complementarity seems to be a protean shape-shifter that can adapt to conform to any experimental set-up. Re mirrors vs lenses, IRL we find they are both equally reliable, so I don't see substituting one for the other is a problem, although the experiment would need a bit of redesign to accommodate this. --Michael C. Price ^talk 14:24, 23 November 2006 (UTC)

Re: shapeshifter. Yes, this much I had gathered and rather like a claim that certain substances cure all ilnesses, I have to admit it does not sit well with me. If taken too far it becomes "We can explain why we do not need to try to answer that question", applied to every occasion we find a conflict. It may be true, or it may be it is masking the truth. As for the half silvered mirrors vs. lenses, lenses behave entirely predictably whereas half silvered mirrors are unpredictable (taken on a photon per photon basis). This might be a crucial difference. Dndn1011 14:52, 23 November 2006 (UTC)

Good point about the half silvered mirrors: I was thinking only about fully silvered ones. --Michael C. Price ^talk 17:17, 23 November 2006 (UTC)

Dear Mike, before I upload my paper at PhilSci I asked personally Unruh, what is according to him the density matrix of the whole setup, because it is not explicitly stated. Unruh was not cooperative at all, and said "I have said, what I have said". Further, Unruh irrelevantly pointed that his web page is written in "clear English", which of course is nonsense - English is not mathematics. So, from Unruh's web is not clear whether he makes experimentally wrong claim [which way + mixed density matrix] or makes mathematically inconsistent claim [which way + pure state]. I personally don't think that adding or removing of Unruh's paper as reference is important, because his experiment is well described and completely "mathematically clothed" in my paper. Danko Georgiev MD 11:07, 22 November 2006 (UTC)

Danko, English can describe QM as well as maths. You, like Afshar, are too quick to assume others are idiots, which reduces your credibility to near Afshar's I'm afraid. Please adhere to your earlier agreement not to edit the article. I shall look at your paper shortly; no matter what I think of it I strongly urge you to consider why it is that you use as many exclamations marks "!" as Afshar. And do you really think that impresses people about anything except your emotional balance and lack of objectivity? --Michael C. Price ^talk 06:57, 23 November 2006 (UTC)

Dear Mike, I am exhausted from derrogative attacks such as yours. Whether I use exclamation marks, or not is my own business. This does NOT change the importance of my work - if it is mathematically correct, nothing can change this fact. However you show your incompetence on very basic things, and even do not try to do GOOGLE search before posting your stupid questions. If you find error in my work please post it, but do not accuse me in something before you do efforts to check and verify that what I have written is really wrong. Thank you for your cooperation in advance. I have decided to reply only e-mail queries, and work on something else. Afshar's discussion is closed topic for me. What I wanted to say, is said in my PhilSci paper, ID 3048. Danko Georgiev MD 12:33, 24 November 2006 (UTC)

Reflection by mirror at 90 degrees

Danko, in your paper you say that the reflection amplitudes are multiplied by an additional "i", with respect to tranmission amplitudes. I think that should be "-1" (you are perhaps confusing right-angle rotations in the complex Argand plane with reflections in space?). Also I do not understand the relevance of your discussion of "mixed" vs "pure". Unruh's and Afshar's experiments would give the same results if they ran the photons through it one by one, i.e. as a succession of pure states, although Afshar's requires multiple runs, in this sense, I think Unruh's does not require multiple runs (it is indifferent to the issue). This is probably why Unruh did not adopt your suggestion about density matrices. --Michael C. Price ^talk 07:24, 23 November 2006 (UTC)

Direct quotation: "When light is reflected from a mirror at 90 degrees it picks up a phase of $e^{\imath {\frac {\pi }{2}}}=\imath$ , where the origin of this phase is purely classical and can be derived from Maxwell's equations. See this textbook chapter, page 10. Also you can verify that the complex algebraic equation $e^{\imath {\frac {\pi }{2}}}=\imath$ is trivial.

Dear Mike, please don't use such a harsh style. The exposition follows Penrose, so you overlook something. If you have two superposed states the + and - signs refer to opposite direction. For example if a photon is emitted in superposition in two opposite directions, its state will be superposion of + |x> and -|x>. However a superposition of photon traveling both in direction x, and perpendicular direction y is |x> + i|y>. Please note that taking the "real" direction is arbitrary. Nevertheless the reflection of q-amplitude at right angle in the complex plane is multiplication by i. So the text in my article is very concrete - I say that when photon falls onto a mirror at pi/4, it is reflected perpendicularly, hence multiplied by i. I hope you realize that your remark is flawed, and is irrelevant to what I prove in my paper. There is difference whether you reflect by mirror at 90 degrees [ $\times i$ ], or you reflect by mirror at 180 degrees [ $\times i^{2}=-1$ ]. Also I speak about quantum amplitudes which means that we work in Hilbert space, hence we have complex plane. You are confusing something, not me. I don't speak about reflection of classical photon [squared quantum amplitude $|\psi |^{2}$ , I speak about quantum amplitudes, so my terminology is very strict. Concerning your second question on "pure state" vs. "mixed state" obviously you have no idea what these two terms mean. Whether you will run many times, or not is not relevant. Mixed state can be obtained if you put different polarization filters R and L on each of the interferometer paths [or slits]. Thus the two amplitudes will not interfere and the reduced density matrix of the setup describing the two paths will be of mixed type. Instead you can run two different experiments, one closing one path, then closing the other path, and then taking statistical average 1/2 of each run. Now you get again "mixed setup". The main thing is that in the mixed state the density matrix or the reduced density matrix of the setup has zero off-diagonal elements, and as written in my paper when squared it does not turn into itself. In contrast pure state density matrix has non-zero off diagonal elements, and when squared returns again itself. Also note that I have said that in case of inserting polarization filters the relevant "reduced density matrix" is of mixed type. Here the "reduced" has a very concrete meaning and is of critical importance. What I say is connected with the subtle difference between theories relying on decoherence and theories relying on irreversible collapse. Basicly the measurement postulate with collapse is irreversible evolution of the density matrix, and you cannot undo the measurement, while the decoherence makes only the "reduced density matrix" of mixed type, but the whole system environment + studied quantum system is in a pure state, and quantum erasure done on the whole system can recover the interference [recover the previously zeroed off-diagonal elements of the reduced density matrix]. For example when you introduce polarization filters, their quantum states also get entangled with the photon and the system is not just a photon, with mirrors and detectors, now you have all this PLUS polarization filters. When you look only of the photon you speak then of "reduced density matrix" because you don't look at other entangled with the photon quantum systems. So, please try to understand and learn all this basic information before you start to accuse me. My terminology is very precise everywhere, and when you understand the difference between mixed state, and pure state, you will see that sometimes

[1] the photon is in a pure state alone,
[2] sometimes the photon is entangled with external q-systems but still its reduced density matrix is in a pure state,
[3] sometimes the photon is entangled with external systems so when you look at the photon only, its "reduced density matrix" is in mixed state.

All these 3 possibilities describe a real quantum state of the photon. However there is a 4th possibility for the photon. The density matrix can be alone in "mixed state" and the photon is not entangled with anything else. But this is a statistical mixture of two experiments. This does not refer to real photon state. This refers to a kind of "fiction" created by taking classical XOR average of two or more experiments. Such "fiction" mixtures does not necessarily be 50-50 mixtures. You can make any x%/y% mixture, where x + y = 100. All this describes the closing one pinhole, closing the other pinhole examples, plus deriving conclusions from the single pinhole/single path experiments. Danko Georgiev MD 04:19, 24 November 2006 (UTC)

Yes, the origin of the phase change upon reflection is purely classical. However upon reflection (at any angle) the phase change is 180, not 90, i.e. a sign of -1, not i. And I quote "The wave is said undergo a 180 o change of phase on reflection". This because the fields have to vanish at the surface of an idealised relector. Why your source says otherwise puzzles me. --Michael C. Price ^talk 23:34, 24 November 2006 (UTC)

Also check out Reflection (physics) where it says of mirrors:

When light reflects off a material denser (with higher refractive index) than the external medium, it undergoes a 180° phase reversal. In contrast, a less dense, lower refractive index material will reflect light in phase. This is an important principle in the field of thin-film optics.

--Michael C. Price ^talk 00:04, 25 November 2006 (UTC)

Dear Mike, """my""" source, is Roger Penrose, Vlatko Vedral etc. The chapter of the book is from prof. Vlatko Vedral's Modern Foundations of Quantum Optics, also see his lecture course where the book is in a form of lectures zipped book/lecture course. You are atacking a detail of my paper, that is not the main thesis at all. Stop thinking that I must be necessarily wrong, instead try to understand what I have proved. For further questions, please consult GOOGLE before you post. The Wiki-entries contain a lot of misinformation, so Wikipedia is not always the best source. By the way I am not specialist on reflection, and it is not needed at all in order to understand the mathematical formulation of complementarity. Danko Georgiev MD 08:08, 25 November 2006 (UTC)

More sources from google:

I have emailed Vedral asking for clarification of his sources or reasoning. --Michael C. Price ^talk 09:53, 25 November 2006 (UTC)

I see a possible resolution of the apparent conflict between the sources. My sources were talking about fully-silvered mirrors (where angle of reflection doesn't matter and the phase change is always 180 o), and Vedral's quote is from his "Geometic and Wave Optics" notes -- we need to see his more advanced "Quantum Optics" notes to see his factor of "i" is still valid for polarised light reflected from half-silvered mirrors. It make sense that the angle of reflection might induce a polarisation dependent phase change, since the reflection probability depends on angle and polarisation. --Michael C. Price ^talk 13:47, 26 November 2006 (UTC)

Granted it is a bit confusing, but this is all ancient history guys; no need for quantum mechanics. The "phase" difference depends on the polarization, difference in the indices of refraction of the two media, the critical angle etc. You should also realize that the electromagnetic wave is composed of E and B 3D vectors, so when you talk about the phase change you should be careful about what component and at what angle relative to the plane of incidence you are talking about... Please take a look at Optics by Hecht (1979) section 4.3 pp. 71-89. Regards.-- Prof. Afshar 16:22, 26 November 2006 (UTC)

I would appreciate if you continue discussing Danko's "paper" on your user pages. Thank you.-- Prof. Afshar 05:22, 24 November 2006 (UTC)

Reference section removed

I have inserted all the web links into the article, because the big reference section with long web links was too ugly. Now all the links are hidden in the text and clickable. I hope the article looks better now, I haven't touched the content of it. Danko Georgiev MD 11:30, 22 November 2006 (UTC)

I don't like it and wish to restore the reference section, which is the normal part of an article. Who, apart from Danko, objects? --Michael C. Price ^talk 06:39, 23 November 2006 (UTC)

I have restored the standard reference format. --Michael C. Price ^talk 07:42, 23 November 2006 (UTC)

Though an eye-sore, it is more factual and useful. BTW/ thanks for your kind words as usual.-- Prof. Afshar 08:10, 23 November 2006 (UTC)

I'm glad to see we can agree on somethings. --Michael C. Price ^talk 08:33, 23 November 2006 (UTC)

I don't understand your reasoning. In or to create a nice web page, all links should be hidden. When you give reference, you should provide description e.g. "Lubos Motl's blog" and the link to it be hidden. What is the purpose of web page adress as reference if the reader does not know where he will arive at all. What if this is link to advertisement, or something else. This is encyclopedia, and you's better try to read some of the instructions how to make Wiki-articles. The reference section with web page adresses is ugly, and does not provide any information before clicking on the link. Danko Georgiev MD 08:51, 24 November 2006 (UTC)

I'm not sure what you mean by hidden. Do you mean hidden within the reference, as some of them where originally? BTW the section is awful now and full of illogical clunky OR and not very informative. --Michael C. Price ^talk 10:07, 24 November 2006 (UTC)

I mean this:

case 1: http://en.wikipedia.org/wiki/Talk:Afshar_experiment
case 2: A nice talk on Afshar experiment
case 3: A nice talk on Afshar experiment [1]

I prefer case 2. The web link is clickable, and the web adress remains hidden. See the code, when you edit the section, also use the show preview option/button Danko Georgiev MD 11:45, 24 November 2006 (UTC)

Cases 2 or 3 looks OK to me. Case 1 is definitely not OK. --Michael C. Price ^talk 21:21, 24 November 2006 (UTC)

If so, you can repair the references and notes 6-13, where nude web addresses appear. Better provide some information where these adresses lead to, and hide the web address. The Wikicode for hiding the web adress is shown above in my previous post/example. Danko Georgiev MD 08:17, 25 November 2006 (UTC)

Ongoing debate

Dear Carl Looper, please kindly revert your last edit on the "Ongoing debate" section. Bohr never suggested a mathematical formulation for Complementarity; it was derived by a number of other investigators in the last 25 years based on Bohr's discussions and papers on the subject. The V^2 +K^2 <=1 is the best mathematical representation of PC and it is this relationship that is violated in my experiment.-- Prof. Afshar 05:19, 24 November 2006 (UTC)

Thanks for that. I was getting carried away. --Carl A Looper 05:48, 24 November 2006 (UTC)

It is still misleading. Please revert it back to the original version before the first edit. Thanks.- Prof.Afshar 06:30, 24 November 2006 (UTC)

Carl A Looper, thanks for tidying up my text, yes that is exactly what I was trying to say. My only query is that you state "It is such assumptions the Afshar experiment exposes.". Is the concencus now that this is true, or should it state "It is such assumptions the Afshar experiment apparently exposes." or some other qualifier? Dndn1011 11:39, 24 November 2006 (UTC)

The experiment definitely exposes assumptions. There is no doubt about it. As to whether this is a consensual view will emerge in due course. --Carl A Looper 12:22, 24 November 2006 (UTC)

I am glad to see someone who agrees with me. I think a lot of the critique misses the point, and in this is the biggest weakness of the article currently. Dndn1011 13:43, 24 November 2006 (UTC)

Ignoring the content for the moment (which I don't agree with), the style is terrible. Let's look at the first 3 sentences:

"The reader should understand..." is redundant and counter to the style guidelines: Just say what you mean, don't pad it out. And don't explain basics about axioms, just link in axiom and let that link do it for you. "Bohr's principle of complementarity is a philosophical system applied in experimental physics. " says nothing about what complementarity is, just link complementarity in and be done with it. "Mathematical axioms have been developed to embody this philosophical system." Again, wafflely and rather content-free. Too passive: who developed what axioms? Either give a source or a link. I always keep the following on my talk page for easy reference.

As for content I don't agree with the interpretation of Unruh's critique: far to simplistic (see the earlier discussion Dndn1011 and I had about it). Removing the actual quote of Bohr is a backward step (and the other quotes also, to a lesser extent, IMO). All the critiques I listed were saying the same thing: Afshar's experiment conforms to the formalism, therefore it can't violate complementarity. That sense has been lost.

--Michael C. Price ^talk 21:41, 24 November 2006 (UTC)

I don't know it seems quite clear to me. The problem ultimately is that saying "Afshar's experiment conforms to the formalism" is a bit circular. Afhsar's experiment is in the universe and the universe obeys complementarity therefore it can't break it". OK I am exaggerating. But anyway, saying Afshar's experiment conforms to the formallism is just not true. It is clear that it does not. Either that or lenses do not work the way they we think they do. There is no escape. One or the other has to give. Having reviewed the critiques I find them wanting. Many people were quick to criticise Afshar before properly reasoning it through, and I feel that Afshar has had a pretty undeserved rough ride thus far. To be honest I can't blame him even for the use of excalamation marks! As for the article it is a complete mess. It should be re-written from scratch. Dndn1011 22:47, 24 November 2006 (UTC)

You must have a misunderstanding of what the formalism means: Afshar's experiment does conform to the formalism, although this is only an empirical fact, not a logical truth.
As you've found, it's not obvious that Afshar's experiment conforms to the formalism since it is an experiment; therefore this should be mentioned.
The point is that the critics made the point that Afshar's experiment conformed to the formalism and therefore couldn't violate complementarity. Perhaps their logic is debatable, but the fact is that that this was their argument and it should be reported as such.--Michael C. Price ^talk 23:08, 24 November 2006 (UTC)

Re: fromalism: Formalism has many meanings. In math it is a rigorous mathematical method. It can also be an argument outside of math. We need to be clear what formalism. My assumption has been that this was a claim that Afshar's experiment conforms to the formalism of complementarity. It is hard to see in this case how this can be true, when the experiment deomnstrates otherwise. I argue that it is obvious that it does not conform. Unless of course the argument is that Afhsar's experiment is the same as another experiment that does conform to the formalism and therefore can not violate complementarity. This is all down to Unruh who I think in his rush to show Afshar to be a fool, was not aware of his own assumptions. The argument as I understand is simple. AE (Afshar's Experiment) is argued to be logically equivalent to UE (Unruh's Experiemnt). Since UE obeys the formalism, it is argued that so must AE, which means AE cannot violate complementarity. The problem as I have indicated is that the assumption that AE is logically equivalent to UE is flawed because, very crucially, there is no actual measurement of the path of the photon possible in UE with both paths open whereas (unless there is something strange about lenses which means they can't be trusted, which is of course possible but equally groundbreaking) we do know precisely which path the photon has taken in AE. In UE, by the time the photon exits the experiement, the two 'paths' will have been brought together twice by two half silvered mirrors so that path information is lost. Of course UE obeys the formalism. It obeys it because it can't measure the path of the photon with both paths open. Only by blocking one or other paths can one perform a measuremeant on the path. UE is just another version of the original double slit experiment. This is what I meant by UE requiring multiple runs with modifications to the equipment (I was right all along on that point, sorry). AE on the other hand allows measurement of which path the photon has taken (directly, if retrospectively) with both paths open. Thus, you can measure something in AE (the actual path taken with both paths open) than you cannot meaure in UE (you can measure the exit path in UE but this tells you nothing about which path was taken at the first half silvered mirror). This makes the two experiments different. Unruh's experiment is a complete red herring and unfortunately is pollutes thinking on the subject and the article. Sorry, but that's what I believe. For now, heh.Dndn1011 00:07, 25 November 2006 (UTC)

You might like to revisit all the above in light of the fact that "formalism of QM" refers to the mathematical equations (e.g. Schrodinger's equation, Dirac's equation, Klein-Gordon etc etc), which are not in dispute here. "Formalism of complementarity" is a no-no, since within quantum theory formalism never refers to the interpretative aspects of the field (such as complementarity). I think this is something that Afshar and myself can agree on? --Michael C. Price ^talk 00:21, 25 November 2006 (UTC)

This is confusing. If C (complementarity) is an interpretation of QM then the exepriment can expose assumptions inherent within C and throw C into question without violating QM, which may not be fully specified because it QM currently does not deal with certain questions that, according to C, need not or cannot be dealt with. If C is untrue, it just means that QM needs to be expanded to cover the exposed assumption of C. So the statement "Afshar's experiment conformed to the formalism and therefore couldn't violate complementarity" is a nonsense. It can conform to the formalism *and* expose assumptions that reveal that the formalism is incomplete. At least to my sense of logic. Where is this argument of mine flawed then? Dndn1011 08:58, 25 November 2006 (UTC)

You making the assumption that the are certain questions that, according to complementarity, "need not or cannot be dealt with" within the formal structure of QM. Suppose there are none? IOW that complementarity is already expansive enough. --Michael C. Price ^talk 11:38, 25 November 2006 (UTC)

Have reinserted lost material to the "Ongoing Debate" section, and expanded explanations. --Michael C. Price ^talk 12:03, 28 November 2006 (UTC)