Talk:Afshar experiment/Archive 22

message: Dear ScienceApologist, below is my reply to your comment that I am oversimplifying the things with bijections, however I will clarify once again the things because you are new to this discussion. However for all others there is no excuse for not reading the sources that I have pointed and there is no excuse that they convert the whole discussion into futile excercise. Well in my wiki-post archived here I describe a 4 slit experiment in two cases [i] different polarization filters on slits A, B, compared to slits C,D, and [ii] a four slit coherent setup. Now in your post you argue that bijections are generally impossible, and I prove this is wrong - everything depends on how you will define the bijection function, and the domain and codomain of the function. 
Image:Dddd1.GIF
Look the case [i] and the figure. Since the polarization of the photon tells you through which two slits it has passed, then you have the following bijection \mathcal{F}1
: slits A & B -> double slit interference pattern 1 (DSIP1)
: slits C & D -> double slit interference pattern 2 (DSIP2)
: Domain (two elements only): {{slits A & B},{slits C & D}}
: Codomain (two elements only): {DSIP1, DSIP2}
: The above bijection function is "which way" function since it established one-to-one correspondence between possible passage through given set of slits, and the probability to hitting the screen, that is the observed intensity of light as distributed on the screen.
Image:Dddd2.GIF
Now look at the coherent setup in case [ii] - the "which way" information from the above bijection is erased, you have only one global bijection \mathcal{F}2 in the form:
: slits A,B,C,D -> 4-slit interference pattern
: The domain and the codomain contain only 1 element. 
Please do seriously consider the possibility that you learn something, and please stop the futile spoiling of the discussion. I have clearly formulated that bijections in QM does not contradict the Feynmann path integral method. Indeed in every setup there is both "which way" and "no which way" information, and this depends on what you have rigorously defined by mathematics.
: Example:
: Look at the case [i], the bijection function \mathcal{F}1, if you now look at the single mapping:
::: slits A & B -> double slit interference pattern 1 (DSIP1),
:then you don't have which way information for the photon whether it passed through slit A or slit B, indeed you have "no which way" information for that question, since the photon must pass through both slits!
:but YES, you have "which way information" for the question "Which way the photon passed:A,B or C,D?"
Conclusions - escape the popular discussion, and let's do rigorous mathematics. Once one realizes that the term "which way" is itself vacuous without proper definition, he will be able to make some progress and realize where Afshar is wrong.
p.s. My example has some connection with the quantification of information. For example let you know that a physical system is in state "A or B". Now how much information you have depends on how you quantify it. If you ask the question "Is the system in state A,B,C,D,E,F,G,H?" you have exaclty 2 bits of information! Yes, you have selected 1 couple of 4 possible couples! But if you ask the question "Is the system in state A or B?" then you have zero bits of information! You really don't know is it in A or B! So please remember this lesson - when you quantify information, the answer depends on the question. The same is in complementarity, the which way information is relative on the question you ask. Regards to everybody in this discussion Danko Georgiev MD 07:01, 29 January 2007 (UTC)
replies: text: Dear Danko, You are embroiled in the mathematics, but is there not a danger that by doing so you are unable to see the bigger picture?  I am not a mathematician, but I can think logically.  A true answer must answer all points at all levels.  It is not enough to have a proof that works at one level of abstraction only.  I am not qualified to assess if your arguments are valid but they do nothing to answer the questions I raise.  You appear to be saying "There is which way if you care to think about which way or there isn't if you care to think that there isn't".  Sorry but even with my limited grasp of scientific mathematics I knew this already.  Please look at the argument I presented for how there is a paradox with the Afshar experiement that can only lead to one conclusion... the concept of which-way (of path) has no validity for a photon.  I believe there is a self referential problem with the detailed mathematics somewhere, or the reliance on assumptions.  My point which is yet to be countered, is that anything to do with what a photon does between the time of its apparent creation to the time of its apparent detection (and destruction) will always be an assumption.  This is in my opinion pointing towards other explanations of the nature of reality.  Dndn1011 08:53, 29 January 2007 (UTC)
replies: text: Dear Danko, I follow you completely up until the point where you declare that this formalism somehow shows that Afshar is "wrong". All of what you discuss is covered in undergraduate quantum mechanics, at the level of the Feynman lectures even. So what, praytell, is your point? You were arguing that scenarios were either 1 to 1 or they weren't. However, if I look at your individual diffraction patters, the probabilities associated with the fringes are decreasing as we head outward from the central fringe. Obviously there isn't a 1 to 1 correspondence within the fringes themselves. You see what happens when you aren't careful with your wording? You end up declaring generalities that do not apply, and wasting kilobytes of space demonstrating ideas that are plainly noncontroversial but also seemingly irrelevant. --ScienceApologist 09:27, 29 January 2007 (UTC)

text: This is not a proposed edit to the article, it is an attempt to describe how "controversial" Afshar's statements really are. Danko is of the opinion that he has demonstrated that Afshar's "results" are bunk. However, what he goes by is his own original research. Right now, said original research is quoted directly in the article. The only reason it hasn't been removed yet is because Danko is basically arguing that it is akin to textbook knowledge that can be confirmed as an elementary thought experiment. However, some of the editors are under the impression that this may not be the case. Hilarity ensues. --ScienceApologist 09:27, 29 January 2007 (UTC)
replies: text: Thanks. I get the picture. That's the trouble with an article on a topic that is just now reaching the status of a peer-reviewed publication. At best the verifiability of critical appraisal of the idea can be assured, the reliability is already a problem, and peer-review impossible. On the other hand, it seems a shame not to include such a controversy in Wikipedia. I haven't decided whether to enter the fray, but I would like to note that it is not clear in the article whether Afshar is calling into question the methods we use to calculate optics/quantum mechanics, or just the philosophical interpretation of those calculations. It would also be of interest to learn how the optical power is split among detector 1, detector 2, and diffuse scattering for the cases with and without a wire grid. --Art Carlson 10:17, 29 January 2007 (UTC)
replies: text: Afshar is only questioning the philosophical interpretation of the results of the experiment, the latter which agree with the usual formal calculations (the "formalism").  You are correct: this is not clear from the ghastly mess of the article. --Michael C. Price talk 12:08, 29 January 2007 (UTC)
replies: text:  Dear ScienceApologist, I am not futile, nor doing original research! This is basic QM, and basic mathematics, and as was pointed by Prof. Qureshi, noone gives Nobel Prizes for that. All this is on topic because me, Qureshi and Reitzner have mathematically proved, that in Afshar's setup, even without the grid there is NO bijection: slit1 -> detector1, slit2->detector2, so there is NO which way information. Is it clear now? Afshar starts from wrong claim and gives no proof, and then derives a paradox. When me, and Qureshi asked Afshar - where is your proof of the claimed by you bijection, Afshar said "look my new paper". But then see several paragraphs above here - Afshar does not provide the missing proof, but does self-citation in refs 19, 20. Does this clarify why I am not doing OR, and why Afshar is deferring discussion at a very very strating point? Simply for me, Qureshi and Reitzner it is not clear on which fundament the Afshar thesis is built. The which way claim is vacuous, and how you can built science on unproved fact, which you take without any logical necessity. Of course that if you take any wrong thesis without a proof you will end with paradox at the end. Best Regards, Danko Georgiev MD 12:28, 29 January 2007 (UTC)
replies: text: Actually Afhsar has provided what I will call "proof producing a paradox".  A proof that generates a paradox usually means that something is broken... when you are faced with conflicting proofs it must mean that some underlying assumption is incorrect.  Afshar has shown this in my opinion, in the statement concerning "conservation of linear momentum".  This is basically saying that there should be a 1-1 mapping between hole and detector, because photons take predictable paths through the lens.  Additionally I raised with you my example of crosses marked on the holes, so that these crosses are focused on the targets and how claiming that if which way information is not 1-1 mapped to the detector it must mean that no path information (no which way) can exist for any photons anywhere under any cirumstances.  You have not actually disproved the "conservation of linear momentum", (unless I missed it, sorry this discussion is getting very messy) and if you were able to you would be in fact agreeing with me, for to disprove it is to say that we can have no true knowledge of the path of a photon (which logically means which-way has no meaning, and thus complementarity is not a useful tool).  So I am sorry Danko, but I have to say that you are pushing your own point of view, and I believe you are quite wrong.  Not in your mathematics, but in your application of mathematics and the conclusions your draw, which do not appear to me to prove Afhsar wrong at all.  You only see as far as trying to preserve the application of complementarity, but you appear to be blind to the consequences of doing so, which ultimately render complementarity inapplicable.  I really think you have a logical blind spot here.  But more than that, since I stopped taking an active role in editing the article, it has become an absolute mess and, Danko, regardless of who is right about the science, you have not helped the creation of a clear, fair and informative article which despite all these detours into actual physics, is *still* the aim of my own personal contributions are ultimately, and the purpose of this page.  You have not clarified things at all, you have merely confused them. Dndn1011 13:50, 29 January 2007 (UTC)
thread_title:  Bijections in QM and complementarity