Talk:Afshar experiment/Archive 5
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Afshar's Error
Afshar's error is to assume, on the basis of a particle being found in a given lensed detector, that the particle must, therefore, have "passed through" the corresponding pinhole. But this is not the case. The only thing that passes through the pinhole is the probability of finding a particle there. This is not the same thing as actually finding a particle there. If you want to find a particle in the pinhole you have to measure it there. But in Afshar's experiment the particle is found (measured) at the detector - not at the pinhole.
Afshar's website says that the failure of aeroplanes without wings to fly should not be used to prove an aeroplane, with wings, can't fly. The analogy is in relation to an alternative experiment meant to discount Afhsar's.
But an interpretation of quantum theory is the same thing. You can't just ignore one of the principles (remove the wings) and then complain that one of the other principles fails (doesn't fly).
Particles are not things that pass through pinholes. They are more like events taking place in the measurement plane.
The Copenhagen interpretation of quantum theory is a reasonable deconstruction of the interference pattern for the purposes of a classical audience insisting on upstream causal models. The interference pattern can be reconstructed from such deconstructions. It certainly can't be constructed from classical models.
But there is nothing stopping neoclassical reinterpretions of quantum theory from working. The transactional theory is a good example. The "flight path" of a classical particle is theorised (but not observed!) as the result of a superpostion of classical waves, both of which propogate classically, but one of which is inverted with respect to the other in terms of it's temporal direction (it travels backwards through time!). The resulting classical image of a particle being somewhere (without being measured) correspondingly satisfys the classical mind.
And time travelling waves would appeal as well.
But the Copenhagen interpretation, while aimed at a classical audience, was not intended to entertain such an audience. It constitutes a criticism. It is an early example of critical deconstruction in which criticism (of the classical model) is done in terms of the very model being criticised.
For example, when Heisenberg introduces the uncertainty principle, he does not do so in terms of quantum particles (ie. those that are measured in the measuring plane). He does so by analogy, ie. in terms of colliding classical particles, in which the desired classical information is compromised. What he is introducing, to a classical audience, is that classical reality, on the quantum scale, can't actually be experienced (or "realised").
In and of itself this does not necessaily invalidate classical assumptions. It just prepares the classical audience for the principles they should need when dealing with what really will deconstruct their assumptions - namely the results of quantum experiments.
That said, there is always room for other ways of doing this.
Carl Looper 15 January 2006
- Dear Carl, the error of Afshar is not interpretation, but mathematics. This pseudo-professor is not aware that to claim that the photon carries the "which way" info is indeed to say that the photon arrives in a "mixed" state at the detectors. Actually the "mixed state" does not mean that the photon is in a classical state, but it maybe well entangled with its environment or agents that measure through which pinhole it passes. In contrast Afshar's result shows that the photon's state is pure state i.e. it is quantum coherent superposition. I do not want to teach Afshar about basics that he missed in the University, but I warn the readers that Afshar is incompetent fraud, than a real scientist. Danko Georgiev MD 09:49, 15 January 2006 (UTC)
Whether Afshar is a pseudo-professor or a fraud shouldn't really concern anyone. Experiment's are just experiments. Anyone can design one and say what they like about such. Including pseudo-professors.
Also mathematics and interpretation go hand in hand. The mathematics involved in the animation of King Kong is not invalidated by the fact that King Kong is wholly in the imagination of the animators and audience.
Afshar's Error(bis repetita)= I can not see a photon twice (without disturbing him at least)
There are many things on this page which are good or not concerning Afshar's claim . It seems that no body agree on the definition of the other and that math or philosophy are concerned. Now beeing physicist I want just (the last time I hope ) summarize why this experiment proves nothing concerning Bohr's principle.
Forget here entanglement: Afshar experiment does not need this concept to be disqualified.
Bohr's principle tells us that we can not with the same photon build up the statistical patterns of two non commutative observables associated with a given quantum state (wave function or density matrix ). Here the two mutually excluded cases are i) spots A' B' in the image plane (images of respectivelly pinholes A and B), and ii) the Fourier image in the back focal plane of the lens (i. e. the interference pattern).
Without wire(s) of course this is true since one can not observe or absorb a photon twice (I consider only destructing detection in agreement with Afshar set up). Now the introduction of the wire change nothing of really fundamental : the wires absorb (practically ) nothing so the waves and the images are the same. For this reason the claim of Afshar is necessarily wrong :)
I will stop here since after I will be technical and go again into details
Aurelien Drezet, Graz Austria
Dear Drezet, stop repeating like parrot that you cannot measure photon twice, this is not relevant to the Afshar's experiment. There is a principle of counterfactual defitiness, that requires that if the photon's state is say A, you may imagine many such photons and measure them in your imagination. And what is more - your imaginary measurements will have to produce exactly results compatible with the photon being in state A. The real problem is that YOU, are ignorant in physics and you don't know whether the photon is in pure state, or mixed state at the detectors. If you say that the photon is in pure state of superposition A+B, THEN NO WHICH WAY info in there. And IF you say that the photon is in mixed state being either at A or at B, then THERE IS WHICH WAY info. You will not have good career in physics, simply because you don't understand basic principles, and you cannot clearly present your ideas when discuss the issue with someone. And do not be afraid to be "too technical" - I challenged all of you to write down the math, but as it seems I am the only one that has provided clear math formulas, all else posted here is just bla,bla,bla .. Danko Georgiev MD 09:27, 17 January 2006 (UTC)
Dear danko I first wrote a reply to you here but i removed it because I dont want finally to play with you on the same level: I am physicist you are not this is my final comment concerning you. Could I suggest you however to decrease your dose of coffee ?
Aurelien Drezet: parrot.
PS : I was the author of the theory section before that curious modification transforms it in what we have now. I can not even see a logic in the present structure : there is no reason to keep that here. PS: the math that you need are here [1] but you should start by tht beginning : first mechanics 2) optics 3 ) electromagnetism 4) QM and I forget 0) logic.
- Can you guys find some other forum to have this conversation? I don't beleive WP is the correct place to have debates over topics such as this. linas 01:09, 18 January 2006 (UTC)
Dear Drezet, in your arXiv pre-print I do not see written the density matrices of the photon wavefunctions! So there is missing mathematics, and this is exactly where my argument is. Try to write down the density matrices of both experiments when you use just double slit, and double slit with polarization filters. In both cases there will be again two well formed wells in the image plane, but in the first case the photons forming the image will be in pure state, while in the second case the photons forming the image will be in mixed state. Unless you understand his basic difference and unless you write down the density matrix of Afshar's setup, you have not proved anything, and the math in your draft v3 is off-topic. Danko Georgiev MD 02:54, 18 January 2006 (UTC)
Dear linas, conversation ?which conversation ? and with whom ? I only presented on this forum a solid argumentation showing that Afshar is wrong (I can summarize it in few words if you want: you can not absorb a photon twice (i.e. in the image and in the Fourier plane)). Now a guy (DG) came and said that I am a parrot. Personnaly I have nothing against parrots they are probably very friendly... but nevertheless ... since I believe (and I am not alone) that my argumentation is the only one which has a sense I dont see why I should not express it here. Secondly, in my point of view we should simply remove the complete page about Afshar's proposal from WP : this is not useful and even dangerous for people who want to learn something about physics. You should only accept on WP something which has been discussed in scientific litterature in order to inform the large public. If you introduce heretic notions like the one which are discussed here we have not science and the role of WP is not valid anymore. The founder of WP says recently :Wikipedia is first and foremost an effort to create and distribute a free encyclopedia of the highest possible quality... this is a very nice idea but I conclude thus that the Afshar page speaking about a controversial experiment (never published in any academic journal with referee) doesnt contribute to the task of this encyclopedia which is to inform not to disinform.
with best regards Aurelien (friend of parrots and physicists)
Real or virtual particles?
To the extent that Afshar's experiment identifys "which way" a particle has apparently gone it can be said to have made a "which way" measurement. We should, however, specify a dividing line between that which is being measured (ie. which way a particle has gone) and the actual measurement which is supposed to establish whether such a thing has indeed occured.
For example, we can draw a dividing line between the pinhole plane, where the "which way" event supposedly occurs, and the remainder of the apparatus, which otherwise measures, observes, experiences or exclusively infers such an event.
The necessity for any inference to be exclusive, is obvious. If the measurement permits equally valid but alternative inferences then it can't be said to have made a "which way" measurement (or inference) since the alternative is also possible.
On face value it does not look like we have any choice but to infer, from Afshar's apparatus and results, that a "which way" event is indeed the only inference we can make, and therefore such becomes a logical (or virtual) measurement of such.
But let us ask the question.
Can we infer, from the downstream apparatus and the results obtained, which way the particle must have gone?
The interesting answer is yes and no.
To the extent that a pinhole plane occupys the upstream side of the dividing line there is no choice but to infer (from the downstream data) that the location identified by the corresponding pinhole, is the location of which way the particle went. There are just no other path(s) available.
But, if the pinholes are left unspecified, then we can infer, (ie. from the downstream apparatus and data), other paths by which the same results, through the same apparatus, can be obtained. The required exclusivity of the "which way" inference is lost. A "which way" measurement is not logically sustained.
The only problem with this is that we know a pinhole plane is there. This knowledge effectively impedes the construction of another inference.
In many ways we might see in this experiment a demonstration of the transactional interpretation. If the upstream data (pinholes) and the downstream data (apparatus, results) are mutually given they will mutually impede the range of possible inferences, that each on their own might have otherwise allowed, in relation to the other.
But does this violate the principle of complementarity?
Maybe. It depends on whether the principle is applicable to virtual (inferred) measurements. Afshar's "which way" measurements are virtual measurements. No particles are actually measured in the pinholes. They are inferred as there.
But any reading of the Copenhagen Interpretation should acknowledge it's radically empericist origins. Emperical measurements are real measurements rather than virtual ones. Without this understanding we are free to imagine the Copenhagen Interpretation as saying something else. And that something else may very well be incorrect.
The hybrid rationalist/empericist models of neoclassical reconstructivism remain very interesting.
On the other hand ...
If my cat (if I had one) is incapable of demonstrating the principle of complementarity in her experiments with her cotton balls, should my cat be awarded a nobel prize?
Or if not, why not?
Carl Looper 19 January 2006
Virtual Pin Holes
In case it is not obvious how Afshar's results can still be obtained if, everything else being equal, we were permitted to respecify the upstream constraints, the following is an example.
1. Remove the pinhole construction. 2. Leave everything else as is, including Afshar's results. 3. Place pin size obstacles at those locations formerly occupied by the pinholes. 4. Place adjacent to such (at least a few pinhole widths away) a hologram of the pinholes. 5. Project laser light through the apparatus.
If properly constructed the downstream data will be the same as Afshar's.
Yet a "which way" inference (from the downstream data) would be incorrect since there are, in fact, obstacles at the inferred upstream locations.
In situ particle measurements made in the shadow of the pinsize obstacles would substantiate the invalidity of the inference. No particles would be detected there. But of course, Afshar's particles are measured ex situ.
Well in this experiment, we can also measure such particles, ie. ex situ. And we'd find they'd be doing exactly the same thing here as they do in Afshar's experiment:
ie. indicating "which way" they went, despite actual obstacles to such!
Should we conclude our pin size obstacles are not really there?
I guess we could ...
Carl Looper 19 January 2006
Dear Carl, please upload a diagram of your proposed experiment, otherwise I think noone can understand your idea. Use the upload file option in Wikipedia, and then read the instructions how you insert the image in your post. best, Danko Georgiev MD 07:00, 19 January 2006 (UTC)
Hi Danko, here it is:
Enjoy.
Dear Carl, your experiment seems good, and I do not see why in principle it cannot work. Actually some of the ideas presented by you are advocated by me in this forum, but nobody cares about arguments. Indeed I have said that the image at the image plane of Afshar is "hologram" [you can read my previous postings in this forum, or the pdf paper of mine, whose link is quoted in some old versions of the Afshar article]. The idea is clear because I have used the right mathematical representation via density matrices. When you have pure states [quantum coherent states] they are superpositions and do not carry which way info! I have many times said that the image of the two pinholes is produced by coherent light, so the photon is holographically at both detectors at once, and only the measurement/interaction with one of the detectors collapses it irreversibly. Why it is relevant? Well, the quantum wave function is continuous in space, so the holographic image cannot just "jump at the image plane" but is produced by interference. So in some sense the image information is available only at the image plane where the inverse Fourier transform is achieved, and outside the image plane, you have the waves from which the image is assembled. Now think about image produced by polarized L and R photons. There you can also produce the same two pinhole image, but this image is NEVER a hologram!!! In this case each photon coming to the image plane is like pixel, and deleting it you will have BLACK SPOT on the image plane. In contrast in the holographic image blocking a single photon, will not produce a black spot, but the the overall image will not be so "sharp". The generalization is that when you project hologram, each photon reaching the image plane IS CARRYING THE INFO OF THE WHOLE PICTURE, and it is really in superposition at every point of the image. Only the interaction with some detection aparatus that captures the picture, causes the photon to collapse at particular place, but you are not sure whether the photon you detect as a pixel is not assembled de novo by many photon pieces of other photons that also build up the image. In contrast the mixed state image, is projected onto the image plane pixel by pixel, and blocking some of the arriving pixels will form black spots. Thus the meaning of complementarity, is tightly connected to the nature of the density matrices of the images - pure state or mixed state, and this is tighly connected with HOW THE WAVEFUNCTION COMES TO THE IMAGE PLANE. Now suppose you put polarization filters on the pinholes, then immediately you will have the 6% loss in Afshar's experiment. But why? Afshar claims that there is "which way" why the additional "which way" labelling does matter? Conclusion" there IS NO which way info, and the polarization filters convert the pure state into mixed state, so the hologram at the image plane is no more there. Danko Georgiev MD 13:28, 19 January 2006 (UTC)
Carl:
I agree. I think we understand each other. Your comment about deleting a pixel is a good one. It is for similar reasons that the above specification of a hologram must sit at least a few pinhole widths away from the virtual pinhole plane!
But Afshar's debate is not (necessarily) with the mathematics behind quantum theory. Afshar's debate can be interpreted as a debate with the wording of Bohr's principle, rather than it's meaning.
But the reasons for that wording have less to do with the physics/ mathematics than it does the historical context in which the theory was translated.
That said, Bohr's meaning doesn't seem that difficult to get. Does Afshar get it or not?
If he does get it then his experiment is just misleading. And if he doesn't get it, then his experiment wouldn't help him.
SUGGESTED DELETION
The main entry of Afshar's experiment is suggested for deletion because it is self-promotion, provides untrustful information, and the article once was prevented from deletion due to sockpuppeting by Afshar and friends. Afshar was shown to use multiple user logs - sockpuppets - to keep his promo entry, and this is clearly showing that this entry per se does not contain valuable information which to force occasional Wikipedians to vote against deletion. Danko Georgiev MD 13:55, 19 January 2006 (UTC)
Indeed the page is only self-promotion: we should remove it. Aurelien drezet
Carl: Does deleting it also delete the counter arguments?
- It seems fairly notable though "Afshar experiment" gets 14k google hits [2] -- Astrokey44|talk 02:25, 20 January 2006 (UTC)
- Dear Carl, I have suggested deletion, because as IT IS the article is advertisement, instead of scientific entry. What about the wording Afshar does not say that "Bohr's popular description/wording of complementarity is false" AFSHAR says that HE VIOLATES COMPLEMENTARITY in mathematical sense where he obtains V^2 + K^2 = 2, where V stands for interference effects, and K stands for determination of the which pinhole the photon has passed. If the image is hologram, then the PHOTON cannot pass through only one pinhole, you need simultaneous passage through BOTH pinholes. This directly affects the density matrix that you need to describe the photon's state, hence Afshar's error is not about Bohr's wording, it is MATHEMATICAL and concerns wrong calculation of the density matrix. I am glad that we understand each other, because noone takes seriously my arguments due to propaganda of Afshar. In the vote for deletion page he mentions one of my withdrawn ArXiv pre-prints, where the error is result because I have used wrong values calculated by other [prominent] physicists, but only after that I decided to check also these values, and I have found that the whole work of mine should be re-build again. This is the reason why I am checking suspiciously every claim by any physicist, and I do confess that my interest of Afshar's experiment, was initially due to the announcement that it is evidence for transactional interpretation of QM [as suggested by Cramer himself], and I am studying the possible quantum transactions in brain. Alas, Afshar, Cramer, and others are dead wrong on the subject. Danko Georgiev MD 04:42, 20 January 2006 (UTC)
Carl: Hi Danko. I'm sure Afshar wouldn't agree with me that his experiment is just about the wording of Bohr's principle. I was being kind. But that is how it can be interpreted irregardless of what Afshar, himself, might say. I myself can't see, in his experiment, how it contradicts Bohr's principle. But I can see how it contradicts a (mis)reading of Bohr's principle. And in this respect, the experiment is a useful index.
Regarding deletion. I'd vote no. While Afshar's experiment is not in the same league as other attempts to misunderstand quantum theory, it is nevertheless, a reasonable one.
- Well, said. Afshar's claim is attempt to misunderstand quantum theory, and I think he has really succeded in misunderstanding it. Danko Georgiev MD 08:50, 20 January 2006 (UTC)
- Have continued discussion on Afshar's question blog. Carl.
Problems with the theory section
There are problems with the theory section. I tried to clean it up, but promptly got tangled. I'll try to fix it in time, but any discussion here would help clarify what the intent of this section was. linas 02:06, 7 December 2005 (UTC)
- The theory section was apparently added by anonymous user User:143.50.61.66 around 28 June 2005, but no matter how I try to fix it, it just seems broken. I'm punting for now. linas 04:03, 7 December 2005 (UTC)
-
- So... anyone care to help fix, or at least discuss, the theory section of this article? linas 15:25, 16 January 2006 (UTC)
Hey, linas - I have provided as much theory that you may write down a full length chapter on complementarity. Open your eyes, and stop calling me vandal. I have clearly shown that interference existense is NOT synomym of which-way or no-which way info - see the 4 slit experiment. I have clearly shown that IF Afshar's is right, then there will be E,t violation of Heisenberg's principle. I have shown that Afshar does not understand what is momentum in QM, and that it is not classical vector with well defined both magnitude and direction. I have contributed enough theory against this self-promotional article, and I think this is essential battle against pseudo-science, not vandalism. Danko Georgiev MD 11:03, 27 January 2006 (UTC)
Interpretive Section
I suggest an additional section with an interpretive angle (ie. in addition to the math) - one that summarises Afshar's interpretive approach. The debate regarding the math depends on what interpretive angle is chosen. The math one might use for Afshar's experiment can require a slightly different approach.
One can construct wave functions from the detector data and project them back towards the pinholes, in order to determine what information can be interpreted as in the detector data. Of course, the reconstruction of the pinhole plane requires data from both detectors.
Two pinholes - not one - would be reconstructed.
In other words, one can not tell, from BOTH detector's data, any which way information.
But in Afshar's experiment only the data from one detector would be used, so only one pinhole would be reconstructed. This establishes "which way" information. It is, however, completely analogous to the complementarity of forward computation in which one chooses whether one pinhole will admit light or both.
One chooses whether to use one detector's data - or both.
In Afshar's experiment it is the decision between whether to use the data from one or both detectors - for the reconstruction - that determines whether "which way" information is demonstrated (or not).
The "which way" information is not in the data - but in the decision.
This is the principle of complimentarity.
Carl Looper 22 January 2006
Why one cares about math of complementarity?
Dear Carl, I will NOT agree that which way is not in the data - but in the decision. See again the right mathematical formulation of complementarity that nobody wants to see. All this available in basic QM course held by prof. Bob Eisenstein. All the math below not only captures naive complementarity, but has more than this. In this paper[[3]] is presented the original idea of prof. Eisenstein that clearly explains HOW the seemingly wave-particle duality appears. ALL IS COMPLEX ALGEBRA - usually a complex number can be written as eix or cos(x) + isin(x). Now depending on the way you compute probability which way, or not, you may obtain "clumping" distribution with P depending on ex or "wave-like" distribution depending on cos(x). Seeing these deep roots of complementarity in the nature of complex numbers per se is more than simple wording done by various pseudo-physicists.
No which way is charachterized by probability distribution of pure state - so P = | ψ1 + ψ2 | 2 where ψ are complex numbers and denote the quantum amplitude. THIS IS CONTINUOUS FUNCTION IN SPACE!!!
Which way is characterized by probability distribution of mixed state - so P = | ψ1 | 2 + | ψ2 | 2. THIS IS CONTINUOUS FUNCTION IN SPACE!!!
So the which way or not is OBJECTIVELY THERE in space, and Afshar uses exactly this - he puts grid in the space before the lens absorbing some photons.
Below I present two scenarios with polarization filters [which way] and without filters [no which way] and you will see clear difference of the probability distribution [i.e. light intensity in space]. NOTE: the two tiny lines accompanying the central Airy disc in the first "which way" image stand for the DIFFRACTION single slit pattern, sorry for the ugly hand drawn images, but they are very useful for direct seeing of complementarity!
Now as I have said in my previous post, polarization filters produce mixed state, but you can do it by first closing on slit, record some light, then close the second slit, record some light, and then take the average of the two single slit experiments. In this time you have mixed state because the distinguisable photons have different time arrival/detection.
UNLESS there is clear link with density matrix formalism, distinguishability of q-particles, and probability distribution you do not speak of complementarity but some WRONG popular wording. Exactly the OBJECTIVE math criteria are forcing you in your holographic experiment to project from special position behind the "virtual pinhole". I do not want to repeat myself, there is pdf of mine in the web also [[4]].Danko Georgiev MD 07:19, 22 January 2006 (UTC)
- Dear Carl, you may insert the link to my pdf in the main article - it was deleted by Afshar, because it is the only REAL math objection to his wrong math. There are numerous quotations by Afshar - where you may notice that he does not understand the difference between mixed state, and pure state - he gives award of 1000$ but he says "if you prove that the photon's density matrix in a mixed state" - but this is exactly what ONE SHOULD NOT DO in order to SHOW that Afshar is WRONG - he must show that the photon is in superposition - hence no which way info! I consider this as equivalent to previous offers that he gives 1000$ to one that disproves him. But corectly interpreted the quoted text in my pdf shoul mean "I give 1000$ to one who proves I am right". So the conclusion is that he has not correct idea of what density matrices mean - so whatever you write down, Afshar cannot understand whether the equation proves him or not. Funny, isn't it? Danko Georgiev MD 07:37, 22 January 2006 (UTC)
Density matrix
By the way - untill there is ONLY ONE density matrix - the experiment will be either WHICH WAY or NOT WHICH WAY. If Afshar wants to disprove complementarity he MUST prove that the photon HAS 2 DIFFERENT DENSITY MATRICES AT THE SAME TIME i.e. being in mixed state and pure state AT ONCE. What is this - new math, or new physics? Danko Georgiev MD 07:43, 22 January 2006 (UTC)
Retrospective Wave functions
Forward wave functions.
The wave functions used to predict downstream data are constructed from information regarding the upstream constraints one has imposed on the lightwaves/photons/electromagentic radiation/electron waves/carbon molecules ...
To the extent that one might introduce polarisers, pinholes, mirrors, lenses, holograms (etc.) one will accordingly adjust the way the wave function is computed.
At the end of the day there is a real life pattern on the screen with which to compare both one's mathematical model and/or the accuracy of one's measurements ...
Retrospective wave functions.
These waves are used to "predict" the upstream constraints that were in place, eg. whether one pinhole was open or two. Of course, if you know that then there's no point predicting it. You have to sort of, turn off any information, that you know about the pinholes and determine it just from the detector data. Therefore you are not permitted to use any forward wave functions in determining what is represented in the detector data. Otherwise you will be cheating!
Now obviously, if we only choose one detector's data, we could only determine if one pinhole was open, (or not). Think about it. You are not permitted to know what lies in the pinhole plane, or further upstream. So you are not allowed to use the wave functions that you might have otherwise industrially computed, eg. the interference patterns (in front of the apertures).
Remember, waves pass through one another, and other than the region where they interfere, don't affect each other.
If you project the data back, from BOTH detectors, they WILL interfere with each other. They will also give you the status of both pinholes - telling you whether they were both open, one closed, or the other, or both closed.
Now I don't know what it really means to superimpose the forward wave function from two pinholes, with the backward wave function from just one detector.
It's not that it's "incorrect" - it's just that it's not clear what it would demonstrate.
Carl
Dear Carl, there are some important issues, and actually if you see the work of Lev Vaidman [5] you will see that this superimposing of forward and backward wavefunctions is very essential to properly define/understand the pure state, that quantum coherent superposition. Actually if you have quantum interference [NOTE: THIS IS NOT CLASSICAL ONE!] then this is expressed by NON-ZERO off-diagonal elements in the density matrix. This means that 
and 
are not zeroes. The forward wave could have passed through one pinhole and then returned through the other, or could have passed by half through both pinholes, and returned by half through both pinholes - it does not matter. If you have mixed state density matrix however YOU HAVE ZERO off-diagonal elements in the density matrix. In this case and are ZEROs, so you cannot have the situation when the wave have passed through pinhole 1 forward, and then returned back through pinhole 2. Actually the transactional interpretation makes the picture more intuitive, and more imaginable, yet this is not something new and you have it in the matrix formalism of standard QM - ket is forward function | ψ > or just ψ, while bra is < ψ | or ψ * , where it is transposed and complex conjugated ket - J.G. Cramer is not the first one to notice that bra is time inverse of ket, Wigner has already shown this. So there the superimposition that you wonder about is the ESSENCE of quantum coherence/pure state/interference. Note - in quantum interference you add quantum amplitudes and then square the result to produce the observable probability distribution e.g. light intensity, in classical interference you add classical amplitudes that are observables, so you add the squared probabilities [i.e. mixed state density matrix, see the complementarity principle in which way case where P = | ψ1 | 2 + | ψ2 | 2. Danko Georgiev MD 03:31, 24 January 2006 (UTC)
Hi Danko. Thanks for the comments. The backward waves about which I was speaking were not the back moving waves (or wavelets) of the quantum waves (computed from the pinholes) - but the waves (classical or complex) one might compute from transforms of the observables (ie. from the detector data). It is the superimposition of the complex waves (from the pinholes), with the "classical" waves (from a single detector's data (or both!)) which I'm questioning. It is this sort of superimposition that is difficult to assign a meaning.
I guess what I'm trying to get at is not *how* Afshar is wrong but *why* is he wrong. It's not enough to say that he is using the wrong math. How do we know it's the wrong math? Because Bob Eisenstein said so? Or Heisenberg/Bohr? Well sure, but it's too easy an answer. We have to know why. And that's harder.
Why does Afshar mix the functions?
As far as I can tell it's by way of a circular argument. To prove complimentarity wrong one just uses the math that violates the principle. To justify the math we use the supposed "fact" that a particle captured by one detector means it "came from" the pinhole opposite that detector. But of course, it's just not demonstrateable. That same particle might not have appeared where it did. It could have just as easily appeared in the other detector - as we know. The particles/data in a given detector are just the result of that particular detector's point of view. That doesn't mean it came from the corresponding pinhole. It only means we can image the corresponding pinhole (ie. reconstruct a pinhole from the data).
The wave from which a particle is otherwise plucked (so to speak) is spread across *both* detectors. So the particle doesn't "come from" the pinhole. We know that. It's just standard QM, albeit, with it's so called "measurement problem".
But it's not about whether Afshar's math is right or wrong - but why. Why use such math? What is one trying to say with such. Or what causes someone to use such math? What is it about quantum theory that is so unsatisfying that it must be turned in on itself?
I mean it's not as if there is anything surprising in Afshar's experimental data that should cause us to run back to the drawing board. But it's a tradition going back to Einstein's debate with Bohr. It's to do with what can be thought as much as what can be seen. And it's okay. It's an okay tradition. It's an ongoing debate between Cartesian rationalism on the one hand and empericism on the other. Heisenberg puts it well but who cares?
it requires stepping back from the physics, back into a wider context. To speak outside of physics is not be a pseudo-physicist. But of course one can inadvertently bring back into physics something that doesn't quite work. But we can't know that in advance. Otherwise we'd still be living in caves and explaing to some young ape that the reason his wheel won't work is because the ape in the tree yonder said so. On the other hand the ape in the tree might be right! One way is to test the wheel.
But there is no observable/testable wheel in Afshar's experiment. Afshar's wheel is a mathematical entity. There is nothing necessarily wrong with this. It's just difficult to determine what the picture is that he's trying to paint.
There are clues in his simulations.
The fact is that a branch of physics is moving towards what can be *simulated* rather than what the ape in the tree yonder says. As such we need to apply a form of criticism that draws on domains of knowledge traditionally beyond physics. Information theory is a young "science" but it is also one of the oldest "arts". In computer animation, for example, one uses algorithms that trace rays from the eye out into the world. It's an ancient Greek idea. But why? Because that which is being simulated is a point of view image. What does the world look like from here? It's also because it's less intensive on computer resources. But one of the main reasons is that many people like point of view images. It underwrites the computer game industry and hollywood special effects.
Anyway, I'm raving on. We're supposed to be talking about the article ... but heh, lets just call this an extended discussion of context regarding what might, or might not end up in the article.
Carl
