Talk:Copenhagen interpretation/Archive 1
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|Archive 1||Archive 2|
- 1 Old text
- 2 Criticisms
- 3 Query
- 4 "Mainstream"
- 5 Interpretation of classical mechanics
- 6 Introduction
- 7 Shut up and calculate
- 8 Outsider View
- 9 New material on Quantum reality
- 10 Contradicting Articles
- 11 Short,Sweet&CONCRETE
- 12 Internal Questions
- 13 Philosophical Ramfications?
- 14 Is Wikipedia intended to Confuse?
- 15 that damn cat again...
- 16 Run-On
- 17 Expert Attention Needed?
- 18 Is CI deterministic?
- 19 Video
- 20 Ensemble interpretation
- 21 A Caution Regarding Irrelevant Bias
- 22 How about this Idea
- 23 The lead...
- 24 "Pondicherry" link in the info box
- 25 Stuck on square one
- 26 Info about derivation of Born's rule in relative-state framework removed from article
- 27 MEANING OF THE WAVE FUNCTION.
- 28 Thoughts on the EPR (Einstein–Podolsky–Rosen) paradox
- 29 I'd suggest a brief discussion of methodology and the difference between realism and instrumentalism at the beginning of the article.
- 30 Wigner's Friend
- 31 EPR and special relativity
- 32 Complementarity
- 33 new lead
- 34 Making instrumentalism relevant
- 35 further edits
- 36 Misunderstanding of EPR true meaning?
When rolling a die, we use probabilites to describe the outcomes because we don't have enough information even though we believe that the whole process is deterministic.
isn't true if we accept the Copenhagen interpretation. A die roll is a chaotic process, and so is sensitive to initial conditions and tiny disturbances during the roll. Even thermal motion of atoms within it can affect the outcome. A die roll is just as deterministic or nondeterministic as the underlying quantum mechanics.
A better example of deterministic probabilities would be yesterday's lottery results, if I don't yet know the results. The winner has already been chosen, so awarding the prize will be deterministic. But I can still calculate the probability that I'll get the prize, because of my ignorance of the hidden state.
The point is well taken. However I don't like your example very much, because it adds the feature of past tense which confuses matters. How about this: "In classical physics, probabilities were used to describe the outcome of rolling a die, even though the proceess was thought to be completely deterministic. Probabilities served as a substitute for complete information." --AxelBoldt
Sure. That sounds good.
The text says that Aspect's experiment "confirmed the Copenhagen interpretation", which might be interpreted to mean that it disconfirmed the many-worlds interpretation or some others, when it did nothing of the sort. It merely confirmed that it is impossible to speak about the outcome of a measurement that isn't in fact made. Both interpretations of what that means are consistent with experiment, as are other interpretations (like "Decoherence"). --LDC
Good point, I'll fix it. Do you know anything about decoherence? --Axel
Decoherence isn't an interpretation in and of itself, it simply explains how the different parts of a wave function can disentangle themselves. You still need them to either disappear (Copenhagen) or persist (many-worlds).
The Aspect experiment is meaningless as far as interpretations of QM are concerned. It just means that QM is right (big f-ing surprise) not that some particular interpretation of it is right. In fact, if it did then Many-worlds would have to be wrong. Many-worlds is a deterministic, local, hidden-variables theory. It's a viable theory and a serious theory. Far more viable and serious than Copenhagen.
Also, I don't know about calling Copenhagen the mainstream interpretation. The mainstream interpretation is the null interpretation (ie, no interpretation). IOW, Feynman's "shut up and calculate".
With that out of the way, you have to ask yourself "in what community" is Copenhagen supposed to be the mainstream interpretation? Fundamental theoretical physicists? I don't hink so! FTP is dominated by strings theories and nobody working on strings would ever believe gibberish like Copenhagen. At least, nobody important.
The same applies to cosmologists, the people who care about the interpretation of QM. So in what community is Copenhagen the "mainstream"? Because outside of the groups I've already mentioned, interpretanios of QM are irrelevant.
So saying that Copenhagen is the "mainstream" among physicists (which is untrue) or laypeople (which is untrue again) is about as relevant as observing that mathematicians are very religious (compared to other academics), or that biologists have some weird ideas about physics. Like big f-ing deal.
Where is Copenhagen mainstream? Textbook writers, and science popularizers. BFG! -- ark
For what it's worth, I've found that whenever professional physicists have an opinion on the matter, they tend to find the (unfortunately-named) many-worlds interpretation more convincing. Consensus has been growing especially in the past two decades, which was when all this decoherence and entanglement stuff was worked out. Certainly, I haven't met a single serious proponent of the CI. Thus, I think simply calling the Copenhagen Interpretation "mainstream" is misleading. -- CYD
The arguments against Copenhagen aren't anywhere near as vicious as I'd like.
There should be a mention of the repeated historic blunders in support of the Copenhagen interpretation. And also the final nail in the coffin by Chaitin; his mathematical proof that the universe can never be proved unpredictable (let alone random) by any scientific process (making "non-determinism" an inherently unscientific assumption).
This sounds interesting. Can you write more about it? The Anome
He proved that there is a number K such that if you're given a sequence of numbers longer than K, it is impossible for you to prove the non-existence of an algorithm that compresses that sequence.
- See algorithmic information theory. The theorem talks about formal proofs in axiomatic systems and does not really constitute a "nail in the coffin" of any physical theory. AxelBoldt
- And what do you believe a physical theory is if not an axiomatic system? I concede that the axioms of physical theories are unknown and only vaguely guessed at until long after the physical theory has been worked out. But I have a hard time imagining a theoretician saying the axioms do not exist, or that they cannot be rigorously formulated after sufficient, tedious, effort by legions of mathematicians.
- For example, most people believe that Feynman's path integral formalism has a rigorous formulation. It's just that 50 years of effort looking for one weren't quite enough.
- If Chaitin's result is not the nail in the coffin of Copenhagen, that's only because most people aren't aware of the result. -- ark
So given a sequence of facts, observations or measurements about the world, when the sequence gets sufficiently long, it is impossible for you to ever prove that it is random; that patterns in the data do not exist.
http://www.mathpages.com/rr/s9-08/9-08.htm talks about this. It also talks about Bell's theorem in general, explaining in detail what it means, what motivated it, and its fatal limitations. -- ark
I left a note in the article at the "first thesis" of Copenhagen. What it's saying is wrong in a very subtle way but it's difficult to explain.
Basically, it says that in Copenhagen, the wavefunction contains all possible information about reality. Well, that's not true. Copenhagen assumes that the measurement process creates new information in reality. Collapse of the wavefunction destroys most of the information in the wavefunction. So when you run it backwards in time, Copenhagen creates new information. Even when you restrict yourself to going forwards in time, the information about which value the wavefunction collapses into is certainly new information that was never present before. <-- that might be a fair way to explain Copenhagen's claim of "indeterminacy".
- I don't understand the point. Wouldn't Copenhagenists argue that it is unknowable which option the measurement process picks out, that only the probabilities are knowable, and that therefore all knowable information about the state of the system before the measurement is indeed encoded in the wave function? It's true that the measurement process creates information though. AxelBoldt
- They would say that all information knowable at that point in time is encoded in the wavefunction. That's an important caveat absent in many-worlds. I guess that is my point. You've neatly clarified my thinking on the subject, thank you.
Also, saying that in Copenhagen, the wavefunction contains all possible knowledge (as opposed to all knowledge accessible to humans), even if this were true which it is not per the above, this would be irrelevant. It is not a feature unique to Copenhagen. In fact, Many-worlds has that feature by the simple virtue of making the wavefunction real.
- It doesn't say that the feature is unique to Copenhagen; it is nevertheless important to the Copenhagen school because they wanted to reject Einstein's hidden-variable attempts. AxelBoldt
- My only initial concern was that the point conflated "knowable information (ever)" with "indeterminacy". My rant grew from there and wasn't as coherent as it could have been. One of the concerns I try to express below is that if we treat Copenhagen as a viable theory then its historical conflict with Einstein is peripheral at best and more likely simply irrelevant to most people. And if we treat it as a dead theory (oh how I wish it were) then we still have to be very clear about disambiguating historical details from Copenhagen's essence. -- ark
That Copenhagen has to reiterate that "there exists nothing more fundamental than wavefunctions" despite considering the wavefunction to be unreal, is 1) contradictory, 2) gibberish, 3) a complication absent in other interpretations. But what you should get out of this is that Copenhagen's claim that the wavefunction contains all possible information is not equal to the claim that the universe is indeterminate. Not by a long shot.
(One way to explain it is that Copenhagenists, those people unfortunately sucked in to the religious cult that is Copenhagen belief, claim that under Copenhagen the wavefunction contains all possible knowledge. Of course, this is because they're not thinking clearly about what Copenhagen actually entails. Which is easy to do because Copenhagen's many claims are self-contradictory.)
It would be preferable to compare Copenhagen to other interpretations and modern ideas than to compare it with what 19th century physicists erroneously believed to be true (that point particles exist). Every time a popularizer of science refers back to what 19th century physicists believed, they only reinforce 19th century physics in the minds of laypeople. Better to simply say "it's a wave" than all these stupid contortions which make any smart person think something fishy is going on. What I mean by that is that we shouldn't talk about what Copenhagen's "three theses" are in comparison to 19th century physics. Nobody's going to understand the big deal unless they're a historian of physics. -- ark
The major overhaul of 24.* introduced a much worse version and was reverted. Specifically:
- It claimed that the Copenhagen interpretation holds as second axiom "the wave function is not real". This is not an axiom of the theory, never expressed in that form by Bohr et al., but rather a criticism by proponents of other interpretations.
- It claimed that the first axiom, namely that the wave function contains everything there is to know about the system, is unremarkable. In fact, this was the most controversial statement of Copenhagen, because it explicitly rejected hidden variable theories. It is still to this day most surprising to laymen.
Several other similar distortions throughout the article, it was not worth my while to correct each individually. AxelBoldt, Friday, June 7, 2002
Just great. The article is misleading and completely useless now.
It doesn't matter who expressed "the wave function is not real", it is an essential FEATURE of the theory. That's why it was in there. What you want, what you have now, is a "description" of the theory that's completely one-sided. It's "defined" exactly how the proponents want it defined. It's not descriptive, it's propagandistic. So you have a highly POV article. Bravo. Useless.
Axel, you're not a layman so don't you fucking dare speak about what laymen find surprising. If you show a wave to a layman and then tell them that it has "no absolute position" they won't find that surprising at all.
- No they won't. And if it were the situation that things had no absolute positions, we could all describe things as waves and be done with it. The trouble isn't that things have "no absolute position". The problem is that things sometimes *do* have "absolute positions" and sometimes they don't.
- That's not true. If your instruments are crude enough, any localized wave will look like it has "absolute position" but that doesn't imply it does. That's why you still have experiments saying that the mass of the photon is less than some awefully small number instead of being absolute zero.
- Absolute position isn't justified by experiments. And it isn't justified by theory either because if you get an absolute position, the next instant the particle is spread across the entire universe.
- The real reason why you insist on talking about hidden variables to laypeople is because you think in terms of hidden variables. YOU think that such a concept as "absolute position" is meaningful, when it clearly isn't!
And like I said, repeatedly ad nauseum, the hidden variables are COMPLETELY IRRELEVANT nowadays except for people who think in terms of 19th century physics. Nobody who knows anything about quantum mechanics expects this. So the comparison is bullshit. If you want to put in hidden variables as a historical detail, then make a separate HISTORY section. But you don't because physicists are fucking useless at history.
- Hidden variables are important because most layman when they first contact QM, assume that everything can be explained by a hidden variable theory. The hidden variable model is the most simple, natural, and inituitive model of quantum mechanics, and its important to recognize why it doesn't work. You yourself have proposed a model of QM which is a hidden variable theory.
- Many-worlds? I thought it was agreed it wasn't a hidden-variable model?
- The detour into hidden variables is useless if you tell people, with conviction, that it's all based on waves. That's ALL you have to do. But noooo ... you know better the needs of laypeople than they do themselves. The only thing you might be forced to do is to tell them that the waves are REAL, because that too is the most simple, natural and intuitive model of what a "mathematical construct" means in physics.
I give up. Unless it's recognized that the entries are for laymen and that they should have ultimate control over what's in them, the whole physics section is completely fucking useless.
Btw, you reverted because you don't want to justify anything and you're too fucking lazy. Admit it that way, there's nothing nice or noble about what you're doing! -- Ark
- Personal attacks and insults are an inappropriate use of talk pages Ark and are a violation of policy. There is no way in hell you are going to convince anyone you are right when you use such language. Axel, nor anyone else for that matter, deserves to be called “fucking lazy” for trying to contribute in the best way they know how. Axel in particular, has been an immense asset to the project – especially with the mathematics and physics articles. I would not consider this to be, in any way, lazy -- let alone fucking lazy. Please stop these personal attacks. --maveric149, Friday, June 7, 2002
Well, I've stopped watching the physics pages and if nobody talks about me, I'm ignoring them completely. Physicists (actually physics students) are the most arrogant sons of bitches in the universe. Axel thinks his judgement of what laymen think about physics is better than what a layman tells him. What do you think that makes him?
Oh, and "the best way they know how" simply isn't good enough. Laypeople are better served left to themselves on physics if the only thing physicists can give are meaningless disconnected tidbits you can find in any popular article, let alone book on modern physics! Because they don't want to provide any more than that, they are fucking lazy. Willfully destroying the work of anyone who tries to provide more than that goes beyond being fucking lazy. -- Ark
I added something about Copenhagen vs. many-worlds. One of misconceptions that Ark seemed to have in particle physics talk was that the dispute (at this point) is something other than aesthetics. Most cosmologists like many worlds over Copenhagen. They might prefer classical music over rock music or like carrots over brocolli. As things stand right all, it's a matter of personal preference. (But that's likely to change in the next decade or so.)
The other misconception Ark seems to have is the "unremarkableness" of the first axiom. It's *that* axiom that is really weird. Getting back to Chatin's theorem that Ark asserts means you can't prove that universe is random. What Ark seems to be saying is that Chatin's showed that you can't prove that there aren't some hidden variables underneath that are controlling things. It's the first axiom that says that this isn't the case. And while you can't show that there aren't hidden variables, you can show and what has been shown as that if there are hidden variables, it means that every particle in the universe is communicating with ever other particle in the universe instaneousenously (which is Bohms interpretation). --RoadRunner
What particle physicists think and what cosmologists think are very different matters. I don't give a damn what particle physicists think. For THEM it might be a matter of aesthetics, not for cosmologists!
First, cosmologists don't hold to logical positivism. So "aesthetics" is about the most important thing there is!
Second, do you know to what length cosmologists will hold go to to preserve conservation of information?
They'll postulate baby universes spawning out of black holes, precisely as garbage dumps for that information. They'll even postulate alter dimensions if they have to.
- I believe that I know more cosmologists than you do, and neither of your assertions is correct. --RoadRunner
What Ark seems to be saying is that Chatin's showed that you can't prove that there aren't some hidden variables underneath that are controlling things.
If you have a question of me, ask me damnit. As a matter of fact, that's NOT what I think. I think it means that if you have a choice between a deterministic and a non-deterministic interpretation (such as between many-worlds and copenhagen) then you're forced to choose for many-worlds. And if you only have a non-deterministic theory, then you're forced to junk it as completely unsatisfactory and be left with nothing at all.
- Then what does Chatin have to do with any of this?
- His theorem proves that non-deterministic theories are unsatisfactory. It proves that you can never prove a nondeterministic theory is minimal. And if a theory isn't minimal, and especially if it's very FAR from minimal (as all non-deterministic theories are, by definition), then you are obligated as a scientist to search for a better theory.
It's a popular game among physicists called "the layman is stupid" which you're engaging in. Obviously, you have nothing constructive to say to laypeople, despite your protestations yesterday. Ark, Friday, June 7, 2002
The flamewar is going out of control, so let's just stop. See Wikipedia:Wikipetiquette, particularly the section "How to avoid abuse of /Talk pages".
In summary, it has been suggested that the current article does not serve the layman well. An overhaul of the article was thought to have removed too much information, and was reverted. The best thing to do now w.r.t. the article is probably to merge the overhaul into the current article, avoiding any unnecessary deletion. The consensus seems to be that deleting the entire article is unnecessary deletion. To avoid controversy, it would be good to be extra meticulous. Before making a claim in the article, quote reputable sources, and document the references in a "references" section. Thanks. -- CYD
I lay that accusation against all the physics articles. You people need to find a layman who'll tell you what's comprehensible, what isn't, what's of no interest, what's irrelevant and what gratuitously creates confusion. And when you find that person, you should declare them Tyrant over all of the physics section. And if you're really smart, you'll also find a historian, a historian of physics if you're extremely lucky, to do the same job. Then you need to distinguish ontology, mathematics and history strictly.
So sayonara suckers and may a place be reserved for you in Gehenna.
--Ark, Friday, June 7, 2002
I don't have any objection to rewriting the physics pages to be comprehensible to the layman. My objection is that in the process of doing so, one absolutely, positively must not sacrifice correctness, and that the changes that Ark suggested did so.
Nobody understands quantum mechanics and no one is not confused by quantum mechanics. Much of the confusion arises from experiments that don't make any sense at all. The goal as I see it is to "present the confusion clearly" and explain clearly why it doesn't make any sense. -- RoadRunner
I removed the sentence:
- The results of this experiment are particularly preplexing when one considers that this is not a thought experiment, but an actual real experiment that can be quite easily performed with photons, electrons, atoms, molecules, and even small viruses.
Firstly, regardless of whether or not this experiment in the form noted is "quite easily performed", it wasn't in fact performed until 1989 (using electrons; see double-slit experiment). Thus, for the greatest part of its life, it was indeed a thought experiment; just as Schrodinger's cat experiment was (although the latter has now finally been performed, I think in 2000 - no cats were injured in the process of the experiment :) ).
Secondly, to perform the experiment with "... atoms, molecules, and even small viruses" would require a coherent source of these objects - something none too easily acheived. Certainly we can imagine that the results would be the same; but that again is the domain of a thought experiment. -- Chas 18 Oct 2001 19:10 UTC
The difference between uncertainty due to ignorance and uncertainty due to the information not existing may be interesting. Perhaps it can be moved into the article somehow. Perhaps into another article. — Preceding unsigned comment added by 18.104.22.168 (talk) 19:29, 31 May 2002 (UTC)
The choice between interpretations "is not as a matter of personal taste" - it should be based on a judgement of the difficulties associated with each interpretation.
The article gives the impression that Many Worlds in the alternative to Copenhagen - it is not. Oz 19:56, 13 Sep 2003 (UTC)
If you post a criticism can you please outline that criticism. Just saying XXX says it gibberish is not a criticism. (My mum thinks Copenhagen is just fine). Also, a paradox such as Schrodingers Cat deserves analysis rather than a comment that it is intended to show how "absurd" something is. Oz 20:26, 13 Sep 2003 (UTC)
My Messiah textbook is good but old. I have not found the time to get and read a newer text, but I found a very good and up to date source in Physics Today and have quoted it in this article. Weinberg said there has been recent work, which may help to explain why my material from my older source did not satisfy some. The summary given in the quote is close to what I learned in graduate school, but better worded and supported by more recent physics. David R. Ingham 02:46, 14 May 2006 (UTC)
Did Bohr use the term "collapse of the wave function"? Oz 23:02, 13 Sep 2003 (UTC)
- Answer: No, he did not. A second "collapse" evolution is foreign to Bohr's account. It has its roots in von Neumann's version of QM, and should probably not be considered part of the Copenhagen Interpretation. PeterBokulich 18:43, 17 January 2007 (UTC)
Luminek, the study you cite provides the following poll results for the preferred interpretation of QM:
- Copenhagen: 13
- Many Worlds: 8
- Bohm: 4
- Consistent Histories: 4
- Modified dynamics (GRW/DRM): 1
- None of the above/undecided: 18
I removed the words "the mainstream" because that implies clear dominance over all other interpretations. While the Copenhagen interpretation is more accepted than MWI or any other specific competitor, it doesn't have a greater-than-50% majority. When more people report "undecided" than "Copenhagen interpretation", that should be a clear sign that it's not the mainstream interpretation. It's a mainstream interpretation, along with MWI, Bohm, and consistent histories. A 1995 study of 72 leading physicists reports that 58% believe MWI is true, so it appears this varies from study to study as well. While Copenhagen may indeed by the most-accepted interpretation, I feel the words "the mainstream interpretation" gave the false impression that all other interpretations where somehow non-mainstream, which is why I'm removing the phrase now.
I understand that, in the past, the Copenhagen interpretation did in fact have the sort of crushing dominance this article presently describes, and will make note of that. -- Schaefer 02:59, 28 Nov 2004 (UTC)
Interpretation of classical mechanics
It seems to me that the question of interpreting quantum mechanics was settled in the 20th century and is now historical: It is reality. Any remaining discussions should be called the "interpretation of classical mechanics". --David R. Ingham 22:16, 16 August 2005 (UTC)
- I don't understand your comment David. Are you saying that there is still no controversy over the interpretation of quantum mechanics? If that's what you're saying then I totally disagree. Trious 13:10, 25 September 2005 (UTC)
- Exactly: its interpretation belongs to *metaphysics*. It's therefore also misleading to have the opinion of *physicists* presented as if it represents an expert opinion - physicists are generally poorly educated about metaphysics. The only expert opinion about interpretation that I have read is that of Popper, and he rejected it. Consequently, I'll change the opinion header to "opinion of physicists"; only if a similar poll on people such as him is included, can the specification be scrapped. Harald, Lausanne, 14/10/2005
It seems to me that the trouble with the philosophy of science is that not even most physicists, let alone philosophers know enough physics to attempt to interpret it. I think that when one studies the early chapters in physics texts, instead of just doing the home work, it all becomes clear. David R. Ingham 03:33, 15 October 2005 (UTC)
David, when you say that the interpretation of QM was settled in the 20th century, what exactly do you mean? The word 'settled' suggests that a concensus of sorts was reached. Can you explain what this concensus view is?
Judging by Mr Ingham's comments elsewhere, he thinks interpretation boils down to a binary "QM is real, or QM is not real". In fact, of course, there are at least 8 major interpretations of quantum mechanics.1Z 16:00, 21 January 2007 (UTC)
Coming back after a long time, I am very happy to see the Steven Weinberg quote. I put it or a link to it somewhere once but didn't expect to see it now. What I want to add now is that, as far as I can tell, by careful reading of his Cat article, Shroedinger's ideas in 1935 were exactly those that Weinberg put so neatly in the quote. (See my comments on the Schrödinger's cat article.) David R. Ingham (talk) 00:31, 4 December 2009 (UTC)
As Wikipedia becomes more detailed, I suggest that interpretation of quantum mechanics be changed to Philosophical interpretation of classical physics to make this article more up to date. I think that, when the philosophy is settled, we should change that to "interpretation of classical physics" or "scientific interpretation of ordinary language". Language, being imprecise and restricted to common experience, by nature, cannot, without loss, interpret physics, which has become precise and general. David R. Ingham 09:12, 27 February 2006 (UTC)
- With respect, David, wouldn't the first change you suggest be confusing to almost everyone? It seems to me to confound "quantum mechanics" with "classical physics"; yet nothing is more certainly post-classical in physics than the various quantum theories. Further, by attempting to generalise the scope of the Copenhagen Interpretation beyond its historical scope, we'd certainly be doing a disservice to historical accuracy. yoyo (talk) 16:40, 10 June 2009 (UTC)
Shut up and calculate
About the famous quote "Shut up and calculate", usually attributed to Feynmann and in the Copenhagen interpretation article attributed to Dirac: http://www.aip.org/pt/vol-57/iss-5/p10.html Can someone provide any source proving that this quote is actually Dirac's?
- Well, N. David Mermin is pretty sure that the remark is Feynman's, but is looking for evidence (or was, back in 2004, cf. http://www.aip.org/pt/vol-57/iss-5/p10.html), because he had found the remark attributed to himself (cf. https://faculty.washington.edu/seattle/physics324/preface.pdf, page v).
- Charles Francis wrote in the sci.physics.research newsgroup in 2000, "Dirac's statement that we cannot speak of what happens prior to measurement is perhaps the beginnings of the 'shut up and calculate interpretation', but I don't believe that that is what he really meant." (Retrieved from http://www.lepp.cornell.edu/spr/2000-09/msg0027974.html)
- I found a blog where someone quoted this remark and attributed it to Dirac, but he did so in the precise wording found in Wikipedia. I also found several people who wrote that it must have been said by Dirac because Wikipedia says so (I'm not bothering with citations here).
- In absence of better evidence, I think it would be safe to change this article so that the remark is attributed to Feynman, not Dirac. --Swwright 23:27, 24 January 2007 (UTC)
- Or perhaps it is not as simple as one would desire. I just came across an attribution of this remark to Hans Bethe (with a note that it is frequently mis-attributed to Feynman). I found this at the end of L.G. Sobotka's notes for a physical chemistry course he teaches at Washington University (St. Louis, Missouri); cf. Physical Science in 12 Problems --Swwright 20:09, 25 January 2007 (UTC)
I'm a mathematician and philosopher, not a physicist. I find Many worlds and Consistent histories both east to understand as they are presented on WP, but after reading this article I can't say I'm any closer to understanding what the Copenhagen interpretation is. OK that's maybe an exaggeration but it certainly took a few reads. What is needed I think is for the first sentence of "The meaning of the wave function", with the two bullet points to be clearly separated from the rest of that section (ideally it should be the first/second sentence of the whole article) and the ambiguity over whether that sentence represents merely the "starting point" for the Copenhagen interpretation or the contents of the interpretation itself, needs to be removed. ("The Copenhagan interpretation merely states that ...") As an outsider it's hard to see that sentence as staking any claim at all really. It is ambiguous over whether it allows the selection of the result of a measurement to be amongst a probability distribution of probability distributions, or whether it always assumes that an observation produces a classical certainty. In the latter case as a non-physicist I would assume it was just wrong (?) and in the former I fail to see why Many-Worlds say would be inconsistent with it (?). If someone like me with a degree in the two subjects closest to but not covering this issue thinks it is unclear, then I can't imagine there is much hope for those with no background even remotely related to the question. --cfp 01:19, 8 August 2006 (UTC)
- Thank you for your comment. The point you make is very good. The trouble with many writers is that they will be satisfied if they predict to themselves that they will be able to make a good defense of the validity of what they have said should anyone challenge them. The very top physicists are also frequently the best writers for the average well-informed reader. They manage to say something in English that will give any reader a clear (and perhaps only qualitative) description of some phenomenon or theory, and yet they will not say anything that their colleagues who are well acquainted with the subject will take amiss. P0M 07:24, 10 August 2006 (UTC)
- Let's look at the top of section one:
The Copenhagen interpretation assumes that there are two processes influencing the wavefunction:
While there is no ambiguity about the former...
- the unitary evolution according to the Schrödinger equation
- the process of the measurement
- This way of discussing matters assumes that the reader has clicked on a previous link to "wavefunction" and now has internalized it well enough to know what the first sentence in this quotation means. In addition to that rather dubious assumption, the sentence hypostatizes or reifies the wavefunction. It implies that we already have an account according to which a mathematical function is such a perfect mapping of some thing (a proton, electron, etc) that we can speak of the one as the other and not get in trouble. The problem is that the Copenhagen interpretation is an explanation (one of many) of what the mathematics really tells us about the outside world. The mathematics tells us that at any given time we are more likely to observe an interaction between the proton, electron, or whatever and some other entity (such as a detection screen) that is placed at the points indicated by the theory -- provided that there is something there for it to interact with. But generally there are several points of high probability for "manifestation" along a continuum of points of lesser probabilities. We cannot fill out gaps in the theory and predict which of the high probability points it will actually "choose." The theory describes something about the "potentiality for manifestation" or "probability of materialization" (like a ghost "materializes" somewhere), but the theory does not take account of a physical barrier. It describes how a photon's probability distribution looks as time progresses, but it doesn't say anything about the presence of a physical barrier to further progress.
- So, if we are looking at an electron in a double-split experiment, we do something to cause an electron to be emitted, we wait for a while, and then we see a sign that the electron has impacted somewhere on a capture screen. Why did it hit at point A instead of the center point directly across from the emitter and perpendicular to the screen containing the double slits? What do we make of the fact that x% of the time an electron will manifest itself at point B, y% of the time it will manifest itself at point D, etc.? Where was the electron in the interval between emission and collision? Did some unknown factor force the selection of one point rather an another for the electron to interact with? Did the electron actually show up at all points, but in our universe it ended up at one specific point, and all other impacts created separate universes in which those probabilities were realized. That kind of question involves "interpretation," i.e., saying what all the math says about the world of real things.
Having thought about this some more, I think the easiest way to present the Copenhagen interpretation (if I've understood it) would be by direct contrast to the many worlds interpretation. E.g. something like:
- The equations of quantum mechanics describe the probability of a certain result being obtained from a measurement. The many worlds interpretation postulates that the notion of probability is a broadly frequentist one. However as any measurement may only be performed once (indeed it is arguable that it could only be performed once), instead of counting occurrences across time or space, those who believe in the many worlds interpretation count frequencies across the same measurement in different "parallel" universes, which means that the particular measurement we obtain is just a result of the universe we happen to be in. Thus in the classic single-photon light diffraction experiment, the many worlds theorist believes that photons are taking every possible path, according to the predicted probability distribution, but in different universes. Those who believe in the Copenhagen interpretation on the other hand view the process of measurement itself as a "physically significant" operation. They believe that prior to a measurement the system is in a superposition of states, i.e. in the single photon slip experiment, the photon (in some sense) occupies every position in a triangle between the slit and the card. Measurement (they believe) just collapses the superposition into a single result, randomly, according to the probability distribution that gave the superposition. The chief point of contention between the Copenhagen interpretation and the many worlds one then is whether measurement does play this "selection" role (as in the Copenhagen interpretation), or whether the "selection" is made prior to the measurement (as in the Many Worlds interpretation, our own universe is selected). There is by definition no physical experiment that could decide between these two interpretations, since any attempt to see "if the selection had occurred yet" would involve a measurement, which, in either case, would result in a selection being returned.
What do you think? --cfp 15:28, 10 August 2006 (UTC)
- It seems o.k., except for "frequentist," which doesn't mean anything to me (except that I can guess from the total context of this discussion). Then there is the problem of how to explain "collapse of the wave function." One of the things that is clear from the double-slit experiment is that when there is an interaction between a photon or an electron and something in its path, then that determines one "event," i.e., we know that something was emitted because (1) we have a fairly reliable emitter device and we know how to trigger it, and (2) we saw something happen at the other end. (Something flashed on a screen, an electrical potential was jogged up a notch, etc.) That's what happens, for instance, if we put a detector in a slit in the double-slit apparatus. If a photon or electron triggers the detector and if a photon or electron continues on from that point and is detected on the screen, the wave function appropriate to the first half of the trip is different from this new wave function, and that is why there will be no interference effect. So wherever we say we "make a measurement" what we are really saying is that we get the absorption of one photon or electron, some change in the detector, and the subsequent emission of another one.
- So what does "collapse of the wave function" mean? It really just means "termination of the wave function." Why does it terminate here rather than there? I believe that many people insist that there must be a reason for its "collapse" (or the manifestation of the particle) at one point rather than another. But if that were the case then it seems to me that we should be able to disturb the probabilities by some simple manipulation of the detector screen. If I am flying a spinnaker from my sailboat and arrange a set of explosive devices that enables me to cut all connections to the boat at the same time, then I could throw the sail forward and it could impact a screen ahead. What part of the spinnaker hit the screen first would be fairly random, and over time I suppose that a fairly consistent pattern of hits would develop. Probably the sail would tend to hit the screen first at the center. But we should be able to change the most likely point of impact by slanting the screen so that the right end was closer to our boat and the right edge of the sail wold be more likely to hit it than the center or the left edge. But as far as I know nobody has ever suggested that the detector screen has to be exactly parallel to the screen containing the two slits. Does a pebble surface of the detection screen make any difference? But every screen is pebble surfaced. P0M 19:14, 10 August 2006 (UTC)
For frequentist see Frequency probability. Should have linked it sorry. That sentence wasn't very clear in any case. And if I was going to mention frequentism for many worlds I should have mentioned the rival theory (Bayesianism) for the Copenhangen interpretation. As this is a specific philosophy of science article I was assuming some general philosophy of science. Maybe I shouldn't have. Anyway as for angling the screen, just think of what happens when you do it with a multi photon beam rather than a single one. You can think of the waves as spreading out from the slits (think of ripples). As you change the angle of the screen you will change the point at which you are cutting the "ripples", so the pattern will change in a predictable way. It's not really an issue I don't think. --cfp 21:36, 10 August 2006 (UTC)
- The pattern changes in a predictable way, and one pattern is a mapping of the other pattern, no? I think we are saying the same thing in different ways. People who are wedded to the idea of hidden causal factors claim that there are real causal reasons for why a particle "chooses" the path it uses in each case. But if that were true it seems to me that people could easily find some way to mess with these hidden factors and change the experimental results. But I'm just speculating. Have you studied http://plato.stanford.edu/entries/qm-copenhagen/? P0M 01:53, 11 August 2006 (UTC)
Nope I hadn't seen that page. Looks like there's plenty to base an article on in there. Like I said I'm not a physicist so I don't know what I'm talking about. All I was saying was that this page needs a lot of work. --cfp 19:20, 11 August 2006 (UTC)
- I started out as a physics major and got seduced to the dark side of philosophy and Chinese language, so I'm not the ideal person to write an article like this even though I've maintained an interest in physics. On the other hand I am less likely than some to assume that I can't understand something because I'm too stupid. If the article does not make sense to you at some point then it is probably either wrong or else the writer knew what s/he was trying to say but it is not coming through right. P0M 20:41, 11 August 2006 (UTC)
New material on Quantum reality
Here is some new source material:
From The Road to Reality by Roger Penrose, 2004, section 21.6, (top of p. 508 in my copy):
- If we are to believe that any one thing in the quantum formalism is 'actually' real, for a quantum system, then I think that it has to be the wavefunction (or state vector) that describes quantum reality. (I shall be addressing some other possibilities later, in Chapter 29; see also the end of 22.4.) My own viewpoint is that the question of 'reality' must be addressed in quantum mechanics—especially if one takes the view (as many physicists appear to) that the quantum formalism applies universally to the whole of physics—for then, if there is no quantum reality, there can be no reality at any level (all levels being quantum levels, on this view). To me, it makes no sense to deny reality altogether in this way. We need a notion of physical reality, even if only a provisional or approximate one, for without it our objective universe, and thence the whole of science, simply evaporates before our contemplative gaze!
This illustrates my contention that the word "interpretation" in this article is a poor choice. The interpretation is clear: It is reality. This article is about how to make use of this theory, using our classical minds and notebooks and tools that we can only describe classically. David R. Ingham 04:06, 16 August 2006 (UTC)
I put this into two articles' discussion pages some time back, but it is also relevant here.
Physics Today, April 2006, "Weinberg replies", p. 16,
- ... but the apparatus that we use to measure these variables—and we ourselves—are described by a wave function that evolves deterministically. So there is a missing element in quantum mechanics: a demonstration that the deterministic evolution of the wave function of the apparatus and observer leads to the usual probabilistic rules [Copenhagen interpretation].
So the "Copenhagen interpretation" is not philosophy nor is it basic physics. It is an empirical rule, that has not yet been fully justified theoretically, for using the classical approximation in quantum experiments. David R. Ingham 04:22, 16 August 2006 (UTC)
Something of a problem: Sundry articles which link to this page, for example the EPR paradox page, claim that the Copenhagen interpretation treats measurement as significant and wavefunction collapse as an actual physical event or process (this is in fact the description that I have been taught, both by earlier articles at this location and by a couple of high school teachers). However, the article in its current state claims that collapse does not actually happen, and represents instead an approximation of the truth, which is (the article implies) that the particles has a definite speed and position at all times, which we are simply not aware of. Not only does this contradict summaries of this article present elsewhere, it is in blatant contradiction (as far as I can see) of the EPRB paradox. --22.214.171.124 23:17, 21 February 2007 (UTC) Minor edit a couple seconds later: Whoops, mislinked the EPR Paradox article. My bad.--126.96.36.199 23:18, 21 February 2007 (UTC)
The article should not say "Particles has a definite speed and position at all times", that is not Copenhagen and is contrary to almost every interpretation , in fact.1Z 01:24, 6 March 2007 (UTC)
I afraid I was taught Physics (graudate level) nearly 30 years ago, when Copenhagen was the only game in town. The waveform was presented as a "unreal" calculation tool. It wouldn't surprise me if a great deal of articles relating to this subject contradict each other, because (1) it is complex area, (2) a lot of the arguments surround issues of who said what (sometimes a single word or phrase in another language) and (3) even Great Minds contradict themselves. It seems to me (*** WARNING - opinion here ***) that the reality of the waveform is the late 20th Century equivalent to luminiferous ether, which seems to be making a comeback as well (sigh). The idea that a probability description is an approximation to the truth is not accepted by Copenhagen. What is truth? Positivist would say it is what is measured (or words to that effect). It is the only truth. That's why this topic is so difficult.
If there are conflicting views, the article should cover all of them (or at least the notable ones). The material you have been deleting has been appropriately cited. The material you have been inserting wasn't.1Z 01:22, 6 March 2007 (UTC)
??? The article should not say "Particles has a definite speed and position at all times", that is not Copenhagen and is contrary to almost every interpretation , in fact.1Z 01:24, 6 March 2007 (UTC) ???
No it doesn't. You will have to explain that one. It is not possible for an interpretation to be agnostic about whether the waveform is real or not; it is at the heart of any QM interpretation. I think that saying it is hard to reconcile the reality of the waveform with some of the statements of Bohr and Positivism is being kind. I also don't think that quotes work very well in this area, since it is possible to find a quote from someone backing up just about anything - a sea of contradictory quotes simply obfuscates. Some of the deleted material is just plain wrong: A probability description does not implies a hidden variable approach. It fails to understand the whole point of Copenhagen. The idea of "collapse" really originates with Von Neumann (I have the book ;-)). The use of a single word ("collapse" or "reduction") by Bohr or Heisenberg does not mean that user subscribes to the collapse of a real waveform. Using a quote to suggest otherwise is questionable. The term "Waveform Collapse" has aquired a specific meaning that I would argue it did not originally have. If QM is just rules for calculating the probability of outomes for a specific experiment, then once the measurement is made, the experiment is over and the "waveform" has served its purpose. I would argue that the "Waveform Collapse" now implies a real waveform, and from a pedagogic position, it becomes difficult to use that term without invoking images of a real waveform - something that is not part of Copenhagen.
An interpretation can be agnostic about anything. Shut-up-and-calculate is often said to be a popular interpretation, and it is agnostic about everything.
As explained in the article, the development of wave mechanics by Schrod. made it easier for Heis. to take a realistic stance. There is more than 1 person involved, and their views changed over time.
You must be unique among wikipedia editors in being able to easily find quotes. Most articles are planted with "citation needed" tags.
The article explains that collapse started as a formal procedure and became more ontological.
Using a quote to suggest otherwise is the only way of establishing the facts. 1Z 00:20, 7 March 2007 (UTC)
Can I emphasise again that there is no justification for removing relevant, sourced material from an article. If you disagree with it, that is just your WP:POV. If you can find contrary sources, there is a controversy, both sides of which should be reflected in the article. Please read and understand Wikipedia:Five_pillars
1Z 00:27, 7 March 2007 (UTC)
I am not defacing this article. I am editing it. Your quotes are misleading. One of the aims of this encyclopedia should be clarity. Some of your material is just plain wrong. You seem to think a probabilty description implies hidden variable.
- You need to explain which passage you are referring to.
You use this as justification for "defacing" (your term) my entry.
- editors don't own entries.
I will make an attempt at explaining why this is not so.
Kant (greatly paraphrased): We perceive the world through our senses. We build mental models of the world and apply logic to them. But the "real" world is "unknowable". And the mental models are not "real". Kant was talking, not about QM, but the division between science and meta-physics (including religion). In Kant's time, philosophers readily made pronouncements about God, Heaven etc. The Kantist division between Science and Religion is now well entrenched. Science is knowable, because it relates to what we can "sense". God and the great beyond is unknowable because we cannot sense it. Positivism goes even further and rejects all religion as meaningless since it cannot be sensed. The Copenhagen Interpretation is regarded as a Positivist (Sir Karl Popper) interpretation, or possibly Kantist. (Do a search on the web).
- I have already studied both Kant and the CI.
The idea then is the the whole world we reason with is a mental model. A good mental model means that real world as experienced through our senses does what we expect. Newtonian Gravity was "real" after Newton, but not after Einstein, in that the model was so good that it is easy to forget it was a model. That's why people like Einstein define what they mean by "reality".
Copenhagen says that all we can know about the world is obtained by measurement. It is an operational view + elements of Positivism and/or Kantism. It may be that the best "operational" mental model possible is probabalistic, but that does not imply underlying hidden variables or other such nonsense.
- I don't know who you think does believe that.
The other side of the measuring devices (senses) is unknowable (Kant, Bohr). I hope you understand the quote from Aage Petersen better now.
Copenhagen is subjective in the sense that different observers have different knowledge (their mental models are in different states - e.g. Wigner's friend), but objective in the sense that the model is a good one (the best possible) and so different observers in the same situation would have the same expectations and experience of the world.
- That is your version of CI. Other people think differently. The various authorities I have cited are not wrong just because they disagree with you.
Summary: (1) Probability descriptions do not imply hidden variables. Your assertion that it does is nonsense. As a result your analysis of EPR is faulty.
- I do not know which assertion you are referring to. You can be uncurious or agnostic about the fact that the observations of different observers correlate, but if the correlation is caused by anything, it is caused by something real. You still have the option of non-interpretation, as the article states ("A subjective approach is left with the claim that the observers have subjective knowledge that isn't knowledge of anything. But the knowledge of the observers is still correlated. It is just that without either an ontologically real wave function, or local hidden variables, the correlation cannot be explained")
- CI: The other side of the measuring device is "Unknowable". It might not be hidden variables, it might be angels with pins, or elephants all the way down. I think you miss the whole point of Copenhagen.
(2) By normal definitions of "reality", the Copenhagen waveform is not real.
I reserve the right to edit material which is just plain wrong and misleading.
- Your rights are defined in the wikipedia guidelines. Editors are required to make verifiable
claims, not just express personal opinions. 1Z 01:24, 7 March 2007 (UTC)
The Coppenhagen interpretation of QM says that nothing EXISTS in the world such as position and mometum -- NOT UNTIL A SENTIENT BEING MAKES A MEASUREMENT. It is not that there is uncertainty, it is that such a thing does not exist. The sentient creature capable of measurement does a GOD-LIKE act of CREATION when s/he/it performs the measurement and COLLAPSES the wavefunction. Prior to the measurement, yes, the wavefunction was "in a superposition of states" but what EXISTED was indeed that wavefunction. The wavefunction (by multiplying itself by its complex conjugate) becomes a probability distribution, but the WAVEFUNCTION ITSELF IS WHAT EXISTS in the world. The wavefunction exists in the world whether or not a mind ever existed, whether or not a measurement is ever made, whether or not the wavefunction ever gets collapsed by a creature wishing to do his/her God-like act of creating a magnitude into the world. So, Einstein, you focused only on what did NOT exist in the world without a mind -- which is what so riled you up about those Copenhagen folks. But Einstein, you forgot that the Copenhagen folks were just as vehement about the wavefunction EXISTING independent of any mind (like you greatly prefer) as they were about the magnitudes NOT existing until a mind collapsed the wavefunction. In short, Einstein saw the glass as half empty and then totally forgot that he was focused on only half of the glass. Another summary: as idealist (non-existence without mind) as the Coppenhagen folks were about magnitudes (position, momentum etc), those same Coppenhagen folks were total realists about the wavefunction's ontological status.
A BONUS ON UNDERSTANDING BAYESIAN STATISTICS
To the Sampling Theory statistician, the truth is a pure number. The unknown parameter, if given an audience with God, could be stated as e.g. 3.452. The data, however, are random variables. To the Bayesian, just the opposite is true. The Bayesian says, "waddaya mean my data are random variables? I got 2.17. What's random about that?" To the Bayesian, the parameter, the truth, is a probability density function. There are many implications for statistics, terminology, and computation procedure, but here the philosophy part of the Sampling Theory - Bayesian dichotomy is aided by a one-to-one correspondence of the Bayesian with the Coppenhagen interpretation of QM. When the Bayesian says "I got 2.17! What's random about that?", that is isomorphic to the Coppenhagen QM'er saying "That was the measurement result. I collapsed the wavefunction." When a Bayesian talks about the parameter, the truth being a probability density function, that is isomorphic to the Coppenhagen QM'er saying that "what really exists in the world is the wavefunction". When the Coppenhagen QM'er talks of this wavefunction being in a superposition of states, that is isomorphic to the Bayesian talking about the prior distribution on the parameter. Bayesian statistics may seem weird (in some ways: truth is a probability density function) but in other ways not (which I can't go into). But clearly the Bayesian Statistician's isomorphic ontology with the Coppenhagen QM'er makes Bayesian Statistics in a sense, well, sensible. Sampling Theory statistics is Newtonian; Bayesian Statistics is specifically Coppenhagen QM.188.8.131.52 19:24, 21 March 2007 (UTC)
- That seems an inaccurate representation of Bayesian ideas. He thought that all possibilities exist simultaneously or that possibility is the fundamental nature of reality? I got the impression that it was more about updating your calculation of a probability to account for incoming knowledge, and recognition of the fact that there can always be stuff we don't know, so we have to identify our prob. calculations as representations of our beliefs rather than of objective reality. Bleedingcherub (talk) 08:25, 27 April 2008 (UTC)
"But the knowledge of the observers is still correlated. It is just that without either an ontologically real wave function, or local hidden variables, the correlation cannot be explained."
- This last paragraph is nonsensical. It contains internal questions which are not answered
- It does; it is amounts to a criticism., that subjectivism does raise quesitons it cannot anser. 1Z 12:55, 20 July 2007 (UTC)
I visited this article about a year ago and seem to recall there was a section entitled Philosphical Ramifications (or something to that extent). I would like rationale as to why it was removed. I have noticed an addition of a "consciousness collapses wavefunction" article which attempts to do the job of articulating what was written in this article before yet there is no direct link to this page. Futhermore, it seems that this concept has been seperated entirely from the Copenhagen interpretation article although it is a philosophical consideration that extends from the Copenhagen Interpretation.
Sadly, there is currently no article on "Quantum Philosophy" which explains these concepts as considerations to quantum mechanics; in lieu of "quantum philsophy" is a redirect to a very biased article on "quantum mysticism". —Lehel Kovach (talk) 23:23, 12 January 2008 (UTC)
Is Wikipedia intended to Confuse?
Is Wikipedia intended to Confuse?
[The following discussion was posted to the POSITIVISM talk page as a complaint against ambiguity. It serves as my example of what happens when a difficult to understand (imho) article refers to an ambiguously explained (imho) article. Also, how unfair it is to the reader. All this before I read the historical controversy about the Wikipeida "Copenhagen Interpretation" on this talk page. I now chastise myself. With all the contradictions, controversies, paradoxes, and unfullfilled desires expressed, does it occur to anyone that frantic attempts to get closer to truth are like attempts to hasten one's own death; they are against human nature, and inherently self-limiting? Or that calls for ever more precise language rendering of these ideas approach their own uncertainty limit? Perhaps the idea that every internally-consistent logical system of sufficient size contains theorems which, in principle, cannot be proven either true or false?
If the only things certain to be true are death and taxes, then I'm not sure I want to know the truth of my own death yet, and, by the way, my taxes are not done yet, either. By extension, frantic desires to learn the truth of how to release the vast amounts of energy contained within the most indivisible components of matter, without adequate consideration of the human consequences to self and others, might be more sensibly referred to a refresher course in "All I really need to know I learned in kindergarten", or the gentle human ways humans act to humans.
Once again, I now chastise myself. But rather more gently, I give myself credit for apologizing, and ask for your understanding and forgiveness. In the heat of the moment, human rants happen to humans...]
I got here from the "Copenhagen Interpretation of the Quantum Theory", section "The meaning of the wave function", wherein I quote,
"The Copenhagen Interpretation denies that any wave function is anything more than an abstraction, or is at least non-committal about its being a discrete entity or a discernible component of some discrete entity.
There are some who say that there are objective variants of the Copenhagen Interpretation that allow for a "real" wave function, but it is questionable whether that view is really consistent with POSITIVISM (link emphasized) and/or with some of Bohr's statements. Niels Bohr emphasized that science is concerned with predictions of the outcomes of experiments, and that any additional propositions offered are not scientific but rather meta-physical. Bohr was heavily influenced by positivism. On the other hand, Bohr and Heisenberg were not in complete agreement, and held different views at different times. Heisenberg in particular was prompted to move towards realism."
I came to understand and evaluate the validity of a train of scientific thought regarding "Zero-Point Energy" before I or my correspondent died. I understand there exists no general guarantee I will understand any particular topic by reading about it.
If I accept a wave function as a wave function, then I can use the wave function as like. Does the wave function hinder or enhance my functioning by its existence? I do not know. Does it predict things others feel do not exist, or only that which is generally accepted? Why should I care, until it matters to me? But, views put existence to work, so now I am left with the question of trying to imagine a situation where "Zero-Point Energy" could work as described. And, Wikipedia refers me to an article that describes (quoted below) how humanity (thus man) must go thru a three-stage process to reach the Positivism view that allows me to deny that the wave function of Zero-Point Energy, in reality, exists. The three-stage process is: accept received "facts", then respect humanity's rights (also a received "fact"), then accept the idea that one can achieve anything based on one's individual free will and authority (while respecting humanity's rights) (another received "fact"). Thus, by my Positivistic development of acceptance (Is this contrary to the skeptical nature of scientific inquiry?) , I can disprove a scientific theory. Or, scientific proof only works for those who respect human life?
But, at the Risk of Screaming, I state the main premise of my contribution here, "I AM NOW MORE CONFUSED THAN WHEN I STARTED." Is this the intent of Wikipedia? Is Wikipedia intended to confuse?
At the least, the following passage calls for some restriction or qualifications to the sentence "There is no higher power governing the masses and the intrigue of any one person than the idea that one can achieve anything based on one's individual free will and authority." Why can this sentence be confusing? Let me count the ways.
This is one possible parsing (forgive me if you think there exists a msitake here - I admit, the longer the sentence, the greater the possibility I make an error of understanding):
(There) is (no (higher (power))) (governing ((the masses) and (the (intrigue (of (any (one (person))))) than (the (idea (that (one) (can achieve) anything (based on (one's individual ((free will) and authority)))))))
a) too many clauses -> Can these be restated in separate sentences? b) "anything" is undefined -> Supposing one has the authority to violate human rights (stage 2), can one's free will achieve this violation and still be Positivist? c) Sentence construction is negative ("no higher power") -> can this be made more positive (Positivist?) d) The ambiguous nature of the common English usage of the word "and" ("both X and Y" versus "either X or Y, possibly without completely evaluating one or the other"), calls for breaking this long rambling sentence into separate sentences, with more specifics and examples. e) "any", "anything"-> Is it possible to think clearly in such expansive generalities? f) "one", "person", "achieve" -> Do these need to be defined? g) In order to even think concretely about this sentence, the following undefined variables need to be evaluated (matched) to the reader's known interpretation:
1) powers, higher than, negated, that could possibly govern 2) masses (which permution of six billion, currently) 3) persons, (which, of six billion), capable of which intrigues, 4 and 5) one (twice) times (which, of six billion) 6) anything, which is achievable 7) the idea 8) based on 9) one's individual (Is this redundant? Does anyone have group free will?) 10) authority 11) and (and its ambiguous interpretations)
Since most people can only think about a maximum of two to seven different things at a time, this sentence cannot even be read without significant thought, if at all, for the preceding listed reasons, namely it is too ambiguous, redundant, or hard.
CAN IT BE CLARIFIED ENOUGH SO I CAN DETERMINE THE DIFFERENCE BETWEEN BOHR AND HEISENBERG? [IN CAPITALS TO RESTATE MY GOAL, NOT TO SHOUT. (PARDON ME)]
Specifically, can the proposed content of this article be made relevant to our current shared existence? Can the historical develoment background be made understandable in a current events context? Can the opinions of the participants of the recent 2007-2008 presidential debates be characterized from a Positivist viewpoint? Is Positivism, as defined, too ambiguous to do so? Are the opinions, as stated, too ambiguous to do so? Does the Wikipedia Positivism explanation fail when brought to the specifics of defending the human rights of terrorists, at the expense of the safety and freedom of thought of the masses or any one person and their individual free will and authority?
In short, does this Wikipedia entry make sense to anybody outside of college philosophy majors?
Referenced Quote from this "Positivism" article: "The theological phase of man is based on whole-hearted belief in all things with reference to God. God, he says, had reigned supreme over human existence pre-Enlightenment. Humanity's place in society was governed by his association with the divine presences and with the church. The theological phase deals with humankind accepting the doctrines of the church (or place of worship) and not questioning the world. It dealt with the restrictions put in place by the religious organization at the time and the total acceptance of any “fact” placed forth for society to believe.
Comte describes the metaphysical phase of humanity as the time since the Enlightenment, a time steeped in logical rationalism, to the time right after the French Revolution. This second phase states that the universal rights of humanity are most important. The central idea is that humanity is born with certain rights, that should not and cannot be taken away, which must be respected. With this in mind democracies and dictators rose and fell in attempt to maintain the innate rights of humanity.
The final stage of the trilogy of Comte’s universal law is the scientific, or positive stage. The central idea of this phase is the idea that individual rights are more important than the rule of any one person. Comte stated the idea that humanity is able to govern itself is what makes this stage innately different from the rest. There is no higher power governing the masses and the intrigue of any one person than the idea that one can achieve anything based on one's individual free will and authority. The third principle is most important in the positive stage.
These three phases are what Comte calls the universal rule – in relation to society and its development. Neither the second nor the third phase can be reached without the completion and understanding of the preceding stage. All stages must be completed in progress." —Preceding unsigned comment added by SalineBrain (talk • contribs) 20:14, 11 February 2008 (UTC) SalineBrain (talk) 20:16, 11 February 2008 (UTC)
- Sometimes Wikipedia is very confusing without anyone editor really having an intention in that direction. For the reader this usually means that there's nothing wrong with their brains, nor language proficiency. Instead it is the articles that are badly written. This article has C-quality, meaning that it contains something more than just a short explaining intro, but many improvements can be made to it. Rursus dixit. (mbork3!) 12:59, 2 March 2010 (UTC)
that damn cat again...
"The wave function reflects our knowledge of the system. The wave function simply means that there is a 50-50 chance that the cat is alive or dead."
be right? Isn't it self-contradictory? You don't know the state the cat's in, so he ought to be in a superposition, both dead and alive (not either or), according to "The wave function reflects our knowledge of the system". But if one would consider the cat an object incapable of being both alive and dead, surely, the first part would be false, for the wave function reflects the cat's point of view, and thus, we'd run into all sort of trouble.
Schrödinger's_Cat#Copenhagen_interpretation seems to agree with my point of view that it should be discussed that it's hard to tell whether the cat is a classical observer or in superposition, so I suggest we do the same thing here. Besides, that was the whole point of this experiment! Boreras (talk) 00:01, 3 March 2008 (UTC)
This is a run-on in the 3rd paragraph. It is very hard to understand.
Bohr and Heisenberg had stepped beyond the world of empirical experiments, pragmatic predictions of such phenomena as the frequencies of light emitted under various conditions and the observation that a discrete quantities of energy must be postulated in order to avoid the paradoxes to which classical physics inevitably led when it was pushed to extremes, and found a new world of quanta of energy, entities that fit neither the classical ideas of particles nor the classical ideas of waves, elementary particles that behaved in ways highly regular when many similar interactions were analyzed yet highly unpredictable when one tried to predict things like individual trajectories through a simple physical apparatus.
I would just fix it, but I don't know enough about the subject to reword this correctly
The English(?) prose in much of this article is quite shockingly bad.
Immediately following the above gem we have:
Not only did laboratory experiments disclose the fact, but the new theories predicted the consequences that the fundamental composition of matter is neither wave nor particle, that knowing the position of a particle prevents us from knowing its direction and velocity (and vice-versa), that the very fact of detecting whether a small object such as a photon or electron passes through an apparatus by one path or another can change the end result of the experiment when that small entity reaches a detection screen.
And then the tin-eared:
The results of their own burgeoning understanding disoriented Bohr and Heisenberg. And their results seemed to some people to indicate, for instance, that the fact that a human being had observed some event changed the reality of the event.
This hurts to (attempt to) read.
One needn't understand the physics (or philosophy, or flaming) at all to have a stab at righting these syntactic disasters. Please, have at it! —Preceding unsigned comment added by 184.108.40.206 (talk) 05:23, 4 August 2008 (UTC)
Expert Attention Needed?
Is CI deterministic?
I wish something more could be said in the article about probability. Back when I went to school 30 years ago we were told that one difference between classical mechanics and (CI) quantum mechanics was that classical physics is deterministic, while CI isn't. Probability in continuum physics just expresses lack of knowlege, here knowlege of initial conditions. If I flip a classical coin, by knowing the mechanics of the flip closely enough I can predict the outcome to any desired tolerance. In a QM version of a coin flip, an atom emits a photon, which is measured to determine its spin. What actually chooses the spin observed when the superposition collapses? Does CI allow there to be initial conditions somewhere which, if they were known, could predict the result? If not, isn't there more information (less entropy) in the universe after the collapse than before? If I understand it, the MWI avoids this in a sense, because with no collapse, all the possibilities continue to be present in different branches of the wavefunction. --ChetvornoTALK 13:52, 18 June 2008 (UTC)
- According to Bell's Theorem, no version of Quantum Mechanics (including the Copenhagen Interpretation) "allows there to be initial conditions somewhere which, if they were known, could predict the result", since this is a "hidden variables" interpretation. So no modern version of CI (and there are many) could be deterministic, unless, as some e.g. Joy Christian claim, they can falsify Bell's Theorem. yoyo (talk) 17:19, 10 June 2009 (UTC)
The link to the Video demonstration in the article is broken. -- fatka
The section The meaning of the wave function, with which most editors struggle, ends with this singularly uninformative statement:
- "The subjective view, that the wave function is merely a mathematical tool for calculating probabilities of specific experiment, is a similar approach to the Ensemble interpretation."
What? Are we to hare off to read yet another linked article, before we can begin to make sense of even this one, short section?
I implore any sufficiently informed editor to take just this one little section in hand, and rewrite it to clearly and succinctly state:
- what the Copenhagen school's founders interpretation(s) of the wave function were; and
- what other interpretations have since been made of it by their intellectual heirs;
naming the holders of each such interpretation, and preferably providing citations to actual text written by the physicist/philosophers so identified.
A Caution Regarding Irrelevant Bias
Observations such as, "... (In other words, Copenhagenists have never rejected collapse, even in the early days of quantum physics, in the way that adherents of the Many-worlds interpretation do.)..." read like a petulant child wrote them. At least pretend to be an impartial, educated source for the sake of Wikipedia's reputation. The only acceptable context in which to mention other interpretations of QM in this article is to compare and contrast with the subject of this article, and not to make feeble attacks on the thinking of the author's intellectual betters in a forum where such behaviour is less likely to cause you embarrassment. Grow up. 220.127.116.11 (talk) 04:01, 10 July 2009 (UTC)
How about this Idea
the duality of matter might be explained by two states. It is either matter or light and tranforms readily between the two states. When light hits matter, it transforms to matter. When matter is excited enough, it transforms to light. What does this fail to explain.
I think that the lead should focus less on generalizations that apply to quantum mechanics in general and attempt to identify what is unique about CI.--18.104.22.168 (talk) 07:08, 19 October 2010 (UTC)
In the info box under "interpretations" there is a link called "Pondicherry". Clicking this link takes you to Ulrich Mohrhoff who looks to be a teacher at a Pondicherry (university?) There is no information on any "Pondicherry interpretation" at Ulrich Mohrhoff. I'm guessing this should be edited out, or maybe the redirect should be fixed if there is an actual interpretation associated with Pondicherry. LazyMapleSunday (talk) 18:26, 8 March 2011 (UTC)
Stuck on square one
The article starts out with "Classical physics draws a distinction between particles and energy, holding that only the latter exhibit waveform characteristics." I'm not sure what this is intended to convey. Any classical object of mass m moving with velocity v has energy ½mv², regardless of whether the object is a proton or the Moon. What "waveform characteristic" does an object with this energy exhibit, classically? Likewise Einstein equated the total energy of mass m with mc². Did he have any waves in mind there?
If you mean that EM radiation has waveform characteristics then you should say so. Energy can take various forms, not all of which are waves classically. --Vaughan Pratt (talk) 06:13, 19 April 2011 (UTC)
Two paragraphs later I'm stuck again. The article says "The Copenhagen interpretation is an attempt to explain the results of the experiments and their mathematical formulations, in terms of quantum mechanics. It was devised by Bohr, Werner Heisenberg and others in the years 1924–27."
This seems like a gross misrepresentation of how quantum mechanics evolved. Heisenberg in collaboration with Born and Jordan invented matrix mechanics in 1925 based on commutators. This was the "first complete and correct definition of quantum mechanics." In early 1926 Schrödinger invented the wave function formulation of quantum mechanics, which made the exactly the same predictions as Heisenberg's matrix mechanics. In at least part to satisfy Heisenberg's doubts that wave functions accurately captured the discreteness of matrix mechanics, in December 1926 Schrödinger proved in formal detail a precise correspondence between matrix mechanics and his wave function account of the same phenomena.
These two formally equivalent accounts of quantum behavior together constituted the new quantum mechanics, replacing the old quantum theory that had gradually evolved with the work of Planck, Einstein, Debye, Bohr, Sommerfeld, De Broglie, and Kramers. These accounts do not depend on any particular interpretation, they stand alone as "complete and correct" accounts of QM.
The Copenhagen interpretation is predicated on the notion of collapse of the wavefunction. Since the wavefunction concept did not even enter QM until 1926, and then only by Schrödinger, it is a gross misrepresentation to say that the Copenhagen interpretation "was devised by Bohr, Werner Heisenberg and others in the years 1924–27." The Copenhagen interpretation emerged slowly after 1927 in an attempt to make sense of those elements of the Heisenberg-Schrödinger theory that could not be easily reconciled with classical mechanics. Since the latter naturally involves multiple particles, any such reconciliation naturally draws the Copenhagen interpretation into the deeper issues surrounding canonical quantization. --Vaughan Pratt (talk) 07:11, 19 April 2011 (UTC)
Info about derivation of Born's rule in relative-state framework removed from article
I removed the following recent addition to the article because it regards the relative-state (i.e., many-worlds) interpretation, not the Copenhagen interpretation. Born's rule and Many-worlds interpretation are instead the appropriate articles for this information.J-Wiki (talk) 23:43, 14 September 2011 (UTC)
- "The Born rule and the collapse of the wave function have been obtained in the framework of the relative-state formulation of quantum mechanics by the brazilian physicist Armando V.D.B. Assis. He has proved that the Born rule and the collapse of the wave function follow from a game-theoretical strategy, namely the Nash equilibrium within a von Neumann zero-sum game between nature and observer."
MEANING OF THE WAVE FUNCTION.
'It seems to me that in the first line of this chapter could be a contradiction. Are you sure that the word "denies" is not inappropriate considering the subsequent text?paolo de magistris 13:04, 12 May 2012 (UTC) — Preceding unsigned comment added by Demaag (talk • contribs)
Thoughts on the EPR (Einstein–Podolsky–Rosen) paradox
Here is a proposed explanation of why the EPR does not violate the impossibility of information transmission. Assume that two observers A and B meet up and agree to nuke one of their planets a or b, depending on the outcome of a measurement. Then subsequently travel back to their plants, light-years apart and afterwards are in possession of the entangled objects. If, now, A makes a measurement he known the outcome (as does B). If it is b, he therefore knows that B has just nuked his planet. The reason why this does not violate special relativity is that the same experiment can also be carried out in a classical setting: A and B meet up and both get two identical oracles (a mechanism in a box) that can't be opened without being destroyed. They travel back to their planets at light speed. Afterwards, the outcome of the oracle determines the actions of A and B. — Preceding unsigned comment added by 22.214.171.124 (talk) 23:14, 18 January 2013 (UTC)
I'd suggest a brief discussion of methodology and the difference between realism and instrumentalism at the beginning of the article.
This article suffers from too many contributions from those who simply do not understand Bohr & Heisenberg's views. The problems which ensue if we consider the wavefunction to be real are not problems for Bohr or Heisenberg. This is well dealt with in the 'consequences' section, but the rest of the article contains considerable (common) misunderstandings. I'd suggest that some work needs to be done on an introductory section explaining the methodological reasons for adopting 'the Copenhagen interpretation', as these are the key to understanding _why_ the 'subjective' or 'epistemological' approach was adopted. [an analogy could be drawn with the revision of 'classical' concepts such as simultaneity in light of relativity]. This would obviously need to be done by someone who has actually read Bohr & Heisenberg. I've only been studying them (mostly Heisenberg, a little Bohr) closely for the past couple of months, so would rather defer this to someone more exposed to their work. I'll see if I can work on something though in case there are no takers. — Preceding unsigned comment added by 126.96.36.199 (talk) 15:41, 18 July 2012 (UTC)
It seems that the response to the Wigner's Friend experiment as has been stated here does not reflect the point of view of Copenhagen interpretation. In Copenhagen interpretation there could not be different wave functions and different observers. The stated point of view belongs to the Relational interpretation. I have changed the response.--Anixx1 (talk) 01:58, 17 March 2013 (UTC)
EPR and special relativity
I have added the following text:
"On the other hand, it should be noted that the special theory of relativity contains no notion of information at all. The fact that no classical body can exceed the speed of light (no matter how much acceleration applied) is a consequence of classical relativistic mechanics. As the correlation between the two particles in an EPR experiment is most probably not established by classical bodies or light signals, the displayed non-locality is not at odds with special relativity."
In special relativity there is no talk about information but about light signals and classical bodies. According to SR these objects cannot exceed the speed of light. It is highly unlikely that the correlation between the two particles in an EPR experiment is established by one of these objects in the sense that when the spin of one of the particles is measured a light signal relays the information about which spin has been measured to the other particle such that there the opposite spin is measured. Therefore, the EPR experiments are not at odds with special relativity. The correlation is rather of a completely different kind characteristic of quantum mechanics which may well be superluminal.
Of course, the emergence of classical special relativistic mechanics from quantum mechanics has to be explained ultimately, but this is yet a completely different story (and necessarily involves relativistic quantum physics at that. — Preceding unsigned comment added by 188.8.131.52 (talk) 05:31, 2 April 2013 (UTC)
The Wave particle mentions: "in some experiments both of these complementary viewpoints must be invoked to explain the results" but the double slit: "but not both at the same time". That seems to conflict. I suppose that the output of a double (or single) slit can indeed only be explained when both (some) particle and wave properties are taken into account. I think it needs a clear citation from Bohr about this fundamental principle. DParlevliet (talk) 10:46, 18 April 2014 (UTC)
I have re-constructed and shortened the lead, intending to make it less prejudging of the actual content of the Copenhagen interpretation, in accord with the now-first reference in the lead. If that reference is wrong, it needs to be replaced by something better. Probably it needs further reference support anyway.Chjoaygame (talk) 14:27, 17 September 2014 (UTC)
- Why not add a cn tag to the old one? Why do you say prejudice?—Machine Elf 1735 14:41, 17 September 2014 (UTC)
- Thank you for this prompt response. I think it not enough just to add a tag. The subject is very vexed, and Wikipedia should not imagine that it can jump the difficulties. Reliability is very important for Wikipedia. Do you think the first reference is wrong? I say prejudice because in the absence of a well-defined statement of the supposed "interpretation", Wikipedia is not in a position to say much about its content. The lead I have shortened did pretend to be able to jump over the difficulties; I call that prejudice, when it appears in the lead. Thank you again for your prompt response. I look forward to more comment from you.Chjoaygame (talk) 15:02, 17 September 2014 (UTC)
- I think that the word "orthodox" is too strong. As far as I can tell (but I'm certainly no expert), it is merely one of the leading/dominant working interpretations.
- The lead should at least characterize the topic of the article; at the moment one gets no sense of what it actually is. A key point appears to be wave function collapse (Copenhagen_interpretation#Nature_of_collapse), and such characteristics should be mentioned in the lead. —Quondum 15:32, 17 September 2014 (UTC)
- Thank you for this valuable comment. Reliability is very important for Wikipedia. If one cannot know exactly "what it actually is", then Wikipedia should say so, and not pretend to jump that difficulty. You say that a key point seems to be wave function collapse, and I think you are right. But what seems right to you and me is not a good enough criterion to put it into the lead, because I am not a reliable source, though I am of course not sure about you in that respect. I am not opposed to putting it into the lead, but I think it needs to be done carefully and with some context.
- Replacing "orthodox" with "often-used" might work. You are right that WP should not hide that it does not have a complete characterization, but it can try to present that part which is generally accepted. The bit that you added seems to be headed in the right direction of giving an outline, but will still need work. Also, I am not an authority on this, so regard my input as merely opinion. —Quondum 16:18, 17 September 2014 (UTC)
- I think that "orthodox" is actually often said. We might or might not like it, but I think it is often said and we should probably recognize that. I would rather delete the whole sentence than weaken it to "often-used". Once we say just often-used, we are asking for other common usages to be mentioned.Chjoaygame (talk) 16:25, 17 September 2014 (UTC)
- In response to your view that something needs to be said, I have posted an edit. The problem here that I see is that much of what Heisenberg and Bohr have to say presupposes unstated ideas. In particular for the present edit, their general statements have little to say about preparation of the beam, but I think they presuppose that physicists know what that is. So it is hard to point to a reliable source about preparation as viewed in the Copenhagen interpretation. Perhaps you can supply one?Chjoaygame (talk) 16:21, 17 September 2014 (UTC)
- It seems to me that Heisenberg defines the Copenhagen interpretation as settled by 1927, pretty much defined by the views of Bohr and Heisenberg. This more or less excludes von Neumann, as far as can see? But I think it includes Max Born? Chjoaygame, about 17:45, 17 Sep 2014.
I have restored the previous introduction because the present version is not readable and much to large. An introduction should be short and clear. And it is prejudging to the actual content of the Copenhagen interpretation because it is the goal of Wikipedia to give the most recent state of science. The article mentiones several times that there are different interpretations. If there are topics not mentioned in the article then add a charter and write it, including scientific references. Also write the chapter first in a sandbox to prevent so many edits within a short time. DParlevliet (talk) 18:56, 18 September 2014 (UTC)
- Yes, I agree. I slept on it and on waking was about to revert, when I found DParlevliet had done it already.
- Perhaps DParlevliet will clarify his sentence "And it is prejudging to the actual content of the Copenhagen interpretation because it is the goal of Wikipedia to give the most recent state of science." As it stands, that sentence is not clear to me.
- I feel that the lead needs revision, but how to do it is not so easy to see. The problem I see is that the present lead makes it seem that the Copenhagen interpretation is more clearly defined that it is in reality. And the definition that it presents is not a safe report of the reality.Chjoaygame (talk) 01:53, 19 September 2014 (UTC)Chjoaygame (talk) 02:24, 19 September 2014 (UTC)
- It is probably not far off the mark with respect to core features of the dominant interpretation(s); perhaps it would make more sense to first identify instances where this outline of the general interpretation does not fit something labelled the Copenhagen interpretation. —Quondum 03:07, 19 September 2014 (UTC)
- I think Heisenberg was right: 'Copenhagen interpretation' is a label that is not validly attachable to any definite thing. There is no "something" that can validly be labeled 'the Copenhagen interpretation'. Chjoaygame, about 03:40, 19 Sep 2014.
- An introduction is a short description about what, according the present science, is the Copenhagen interpretation. The rest of the article mentions that there are different views about parts of this interpretation, so it is not clearly defined. If you think that some views are missing, you can add them (if referenced). DParlevliet (talk) 07:12, 19 September 2014 (UTC)
On page 330, Max Jammer talks of " 'identity of states of preparation' as in a pure case" as a "tacit assumption". I think it is one the most profoundly quantal of all the ideas. It is a great pain that it is nevertheless more or less tacit. Chjoaygame, about 18:25, 17 Sep 2014.
Making instrumentalism relevant
Forwarding an invite to the editors here.—Machine Elf 1735 22:36, 20 September 2014 (UTC)
- I invite comments on a proposed revision of Instrumentalism, incorporating the conflicting roles of Popper and Dewey in defining the movement and its dependence on induction, and showing current practice of those roles. See talk: Instrumentalism, entries 20 and 21.TBR-qed (talk) 15:10, 20 September 2014 (UTC)
As you can see, I have now taken the bull by the horns !! Chjoaygame, about 20:25, 17 Sep 2014.
I didn't give citations for this, but I think I can justify every statement by reference to writings of the masters if necessary. Chjoaygame, about 22:55, 17 Sep 2014.
- Might be a bit too much for most readers but I enjoyed it. Have a look at Talk:Instrumentalism too, there might be some synergy...—Machine Elf 1735 22:36, 20 September 2014 (UTC)
Misunderstanding of EPR true meaning?
"A further argument is that relativistic difficulties about establishing which measurement occurred first also undermine the idea that one observer is causing what the other is measuring."
The author missed the sense in that both observers should, according to common sense, observe at the same instant of time in a common space-time foliation, so that nobody causes the other one. (Thus nobody speaks about any causation! only about strange nonlocal connectivity) The "requirement" of simultaneity would be there precisely because if you measure a particle in moment A then it can have spin X, but in moment A+Dt it could theoretically have spin Y assuming that everything measured is at bottom random. The only certain thing is that in both places of measurement one outcome will match the other made in exactly the same time; so that randomness does not interfere "in between."
As you well note the special relativity implies relativity of simultaneity, so the randomness at bottom is even more a question mark -- from a certain perspective even two measurements in "different" instants should give the same result (because they did in a frame where both were simultaneous), although there is no causation in one or other side. So it would seem the randomness must not touch the polarization of spin, then?... i.e. it is excluded from uncertainty of measurements, left as a "constant." Which violates the general rule that everything in measurement should be random, and not like "established once and forever" -- the lack of real variables -- the very rule at bottom of the Copenhagen interpretation ("a measurement gives a random result described with probabilities").
- Armando V.D.B. Assis (2011). "Assis, Armando V.D.B. On the nature of and the emergence of the Born rule. Annalen der Physik, 2011.". Annalen der Physik (Berlin). 2011: 1–15. doi:10.1002/andp.201100062.