This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 | Archive 5 | → | Archive 10 |
"Typically, its values are complex numbers and, for a single particle, it is a function of space and time."
Is this true of any but a scalar particle? I know I'll probably spark a debate because this is not my area, but surely this is oversimplification to the point of confusion? For example, I'd expect any fermion to have a wavefunction that is spinor-valued, in which case complex numbers might come into it, depending on the representation chosen, but also might not. Shouldn't this description be changed? — Quondum 21:48, 15 March 2014 (UTC)
Nevertheless, RQM is only an approximation to a fully self-consistent relativistic theory of known particle interactions because it does not describe cases where the number of particles changes; for example in matter creation and annihilation.
Quondum, you refer to WP policies. One of the most important is to write from what most sources say: of course not like a textbook but as a plain English summary. Well, does anyone know how many introductory QM sources which do not use write wavefunctions as complex numbers or complex-valued vectors? Complex numbers are exclusively used in almost every single introductory QM book I've ever seen (anyone is welcome to contradict with examples). The only exception I can think of is when QM is written in the language of geometric algebra, which uses the field of real numbers. The restricted scope "introductory QM" is not meant to be pedagogic - this is one important level of sources we should use for this article.
As for:
the article has an ontology section linking to the main ontology article - saying the meaning of the wavefunction is unclear, and always has been from day 1. The sections on wavefunctions for one particle in 1d, and more particles in higher dimensions, all mention the Copenhagen interpretation, the most introductory interpretation of the wavefunction.
It's a bit unfair to say the lead totally violates the guidelines. It can be improved, but it gets the main points across. I'm not denying the article still needs work. But this discussion confuses me. M∧Ŝ c2ħε Иτlk 16:40, 22 March 2014 (UTC)
I'll have a very quick go at tweaking the lead along these lines. M∧Ŝ c2ħε Иτlk 16:56, 23 March 2014 (UTC)
I tried to explain a little. There are probably bugs in the new equations, possibly a missing minus sign (the plane wave), and possible a missing factor of one over two pi (delta function normalization). These things depend on conventions, including for the Fourier transform. Can anyone check what Griffith (the ref in the section) says? YohanN7 ( talk) 22:47, 15 March 2014 (UTC)
May I destroy [1]? This flickering picture that does not, actually, “animate” anything useful, only distracts attention and wastes the processor time. Incnis Mrsi ( talk) 13:36, 29 March 2014 (UTC)
I'm not a quantum mechanic (can't handle those teeny, tiny wrenches) so forgive me if I'm not putting this question correctly, but I wonder if someone could say (and maybe put in the article) something about how causality and the speed of light relate to the time-dependent wavefunction. I assume the wavefunction is causal? If the boundary conditions or the potential are altered in one place, do the resulting changes in the wavefunction propagate to other places at the speed of light? And what about the delayed quantum eraser experiment? Thanks. -- Chetvorno TALK 06:38, 27 October 2013 (UTC)
I have put into the lead some brief remarks on the domain of the wave function. To save editors the trouble of checking my sources, I copy quotes from them here.
References
Chjoaygame ( talk) 14:51, 31 July 2014 (UTC)
I think there is a need for a basic interpretation of the wave function before introducing the Copenhagen interpretation, and even measurements. I am thinking about things that are often misinterpreted. For instance (in a toy model), if a wave function is a superposition of two delta-like functions located at A and B (in position space), it does not mean any of the following:
Both statements are provably not true (actually, some "plausible" statements of this nature are not true/false but plain nonsense), using Hilbert space theory alone (they lead to contradictions of mathematical and even logical nature), but both of these interpretations are easy to be picked up by a novice, especially when fed the Copenhagen interpretation. (Note, no measurements are involved in the statements above) An example of a correct statement would be
A great source for stuff like this is Robert Griffith's Consistent Quantum Theory. This book is about an alternative (other than Copenhagen) interpretation of quantum theory, but the stuff I mentioned above is basic and independent of any interpretation. Well, my question is, should we have a "basic" section here or in a separate article, or does one already exist that handles matters like these? YohanN7 ( talk) 20:12, 28 August 2014 (UTC)
This article too presents the misconception that spin is a consequence of the Dirac wave functions. (Other common and incorrect formulations include that spin is a consequence of the Dirac equation.) The truth is that spin is a consequence of the symmetry group of special relativity, the Poincaré group, more precisely its subgroup, the Lorentz group — even more specifically it originates in its subgroup SO(3), the rotation group, which is doubly connected.
More accurate would be to say that the Dirac equation is a consequence of (the existence of) charged spin 1⁄2 quantum particles coupled to the EM field via minimal coupling with parity inversion symmetry (without the latter the Weyl equations arise). Dirac spinors have spin 1⁄2, they don't predict it. Paraphrased, "The DE doesn't predict spin 1⁄2, but spin 1⁄2 predicts the (free) DE". YohanN7 ( talk) 19:09, 28 August 2014 (UTC)
I want to emphasize that Dirac himself surely would have objected to the current article's formulation. He was well aware of the order of events. He actually published the Bargmann-Wigner equations a decade (or more, 1933?) before Bargmann and Wigner. Moreover, the investigations into the infinite-dimensional representations of the Lorentz group was instigated by him. That is, it is hardly to dishonor Dirac to take away the "prediction-of-spin-status" from the equation or its solutions.
The great thing that the Dirac equation actually did predict was the existence of positrons, or, in general, antiparticles for every particle obeying the DE. (Dirac initially speculated that they may be protons, this at a time before the discovery of the neutron. Someone else (don't remember who) showed that the positron must have the same mass as the electron, hence couldn't be a proton.) YohanN7 ( talk) 11:43, 29 August 2014 (UTC)
The definition of the "inner product" suffers from an annoying and confusing error omission that is present in most basic QM texts(, and some math texts too). The "inner product" is not an inner product, it is a semi-inner product. The resulting "norm" is a pseudo-norm semi-norm, and its "metric" is a pseudo-metric (not semi-metric).
There are standard ways (all equivalent I believe) of dealing with this. One way is to declare points at a zero distance apart to be equivalent. Then by passing to the quotient w r t this equivalence relation, one obtains a true inner product space. It's elements are equivalence classes of functions from the original "inner product space".
Before I (possibly) do anything, I'd like your opinion on whether this conceptually important, but practically unimportant, issue is worth mention in the article. IMO, QM books being generally crappy mathematically should not be a reason for this article to make the same mistakes.
There are probably three categories of students (of QM books or this article). The first category never notices the problem. The third category does notice the problem and also its solution. The second category will be left puzzled. I belonged once to the second category. The instructor did some hand-waving when I asked him (he really didn't know I think). YohanN7 ( talk) 12:20, 3 April 2014 (UTC)
For the purposes of this article, the following should be enough:
Only the latter point has a problem. Such a statement needs to be sourced. YohanN7 ( talk) 21:51, 3 April 2014 (UTC)
I think the conclusion may be this: With this choice of inner product, the space of functions should be the space of square-integrable functions period. No continuity assumptions allowed. Only then will we get a Hilbert space (upon taking an appropriate quotient). There are other possible Hilbert spaces to make use of, e.g. the Sobolev spaces. These are mentioned in the article. But, for these, the inner product given here is not the right one. YohanN7 ( talk) 13:54, 4 April 2014 (UTC)
So I finally took care of this. The beefing out can be found in a popup. YohanN7 ( talk) 11:47, 7 November 2014 (UTC)
Editor Maschen has been making several edits which I do not wish myself to try to fiddle with. But I would point out some things that I think Maschen should fix.
It is not good to use footnotes in Wikipedia articles. Either something deserves to be in the main text, or it doesn't have a place at all. The scope for ever-expanding confusion with footnotes is obvious. So I have moved Maschen's footnote into the main text.
On the same topic, I have also moved the recent footnote by Editor YohanN7 into the main text.
A sentence that begins "Actually, ..." is very often a stylistic failure or error, for reasons that I will not here try to expound. In a nutshell, I think Maschen should remove the word 'actually' from the relevant text sentence, and make what other adjustment he thinks best. A problem is that Maschen's edit is in the lead, and it may be making the lead grow like Topsy. Perhaps the footnote stratagem was intended to by-pass this problem. I think it won't do. Somehow Maschen should deal with this. Chjoaygame ( talk) 04:20, 6 December 2014 (UTC)
Sorry for the delay. Here is the
edit in question for reference.
Basically, the objection is to the nb in the lead, on bosons described by spinors. That's fine, but I thought the flow would be fine to say "fermionic wavefunctions are spinorial while bosonic wavefunctions are tensorial", with a digression that spinors can describe particles of any spin (after all tensors can be replaced by spinors can't they?).
But maybe it is also excessive wording. I'm neutral on how we do this. Perhaps the best solution is to delete the nb and replace the statement by
(no reference to abstractions and unfamiliar terminology like "spinor rank" etc. keep it simple, this is elaborated later on in this article and other articles anyway). I'll make that change, any alternative wording is fine, people should feel free to edit.
For completeness, my only other edit to the lead was the deletion of the underlined part:
since in the next paragraph, the position space and momentum space wavefunctions are described anyway.
Hope that clarifies things, I'm fine if there's any other objections. Best, M∧Ŝ c2ħε Иτlk 23:04, 6 December 2014 (UTC)
Just to offer an alternative, if we wanted to reinstate mention of fermions and bosons:
M∧Ŝ c2ħε Иτlk 23:25, 6 December 2014 (UTC)
This website refers to the 'requirements' as "Born's Conditions". I'm not sure if that is a common term. RJFJR ( talk) 17:33, 17 December 2014 (UTC)
I think the present account of the 2012 Nature paper by Pusey Barrett Rudolph gives it undue weight. In a brief section such as the current one headed Ontology, it is inappropriately recherché. The paper is, charitably read on its merits, of marginal value. And not suitable for an account, even a one-sentence one, appearing here. Editor Sbyrnes very kindly gave an interpretation of it. While admirable, that interpretation seems more original research or editorial commentary than immediate reporting of the source. I think the felt call for such interpretive explication would be better responded to by simply removing the present account of the paper. Chjoaygame ( talk) 16:08, 6 December 2014 (UTC)
A reference appeared in the form of a pdf from the same user that put in the original disputed piece of text (very shortly after the referenced paper was published). On closer inspection, this was the only non-peer reviewed paper appearing in the article (until the pdf). I therefore removed the text. We should require a doi at the very least for this article. Otherwise it will give a rather silly impression when the next reference is Einstein. YohanN7 ( talk) 23:27, 1 January 2015 (UTC)
Thank you for this comment. It is indeed a problem for a newcomer to make sense of articles on such matters. In particular you say that my term quantum analyzer is inscrutable, even to an expert. My term is intended as an ordinary language version of the QM term of art "measurement". The latter term in ordinary language as I read it refers to a combination of a quantum analyzer and particle detector. The Qm term of art "measurement" is in my opinion very definitely a term of art, not part of the ordinary language, even of the ordinary language of science, indeed even of the ordinary language of physics. The particle detector part is needed to produce numbers that can be tested against the probabilistic predictions of the mathematical theory. I guess that is not a worry to you.
But indeed the term quantum analyzer may be criticized. An ordinary language word is needed that labels the class of physical arrangements or devices that split the beam into the respective sub-beams that are fed to the particle detectors. The classic example is Newton's prism by which he split a daylight beam into coloured beams. The next classic example is perhaps the Stern-Gerlach magnet that splits the beam into two sub-beams. Another example is a calcite crystal that splits a beam into two polarized sub-beams. Another example is a half-silvered mirror. In general, a quantum analyzer analyzes beams of quantal entities or particles into sub-beams of quantum eigenstates. It is of interest that you have read dozens of QM textbooks and still cannot figure out what I mean here.
It is not too easy to define a wave function in physical terms. Since this is an article on quantum physics, I think it appropriate to try to do it. According to Dirac (4th edition), there should be a one-to-one correspondence between a mathematical formalism and a collection of experimental items. Dirac starts his definition of a wave function by saying that it is superposable (Section 5, pp. 14-18). This is only the first of a list of defining criteria. The next item on his list of definitive criteria (Secction 10, pp. 36-38) is the mathematical operators and their corresponding "measurements". Dirac writes "Any result of a measurement of a real dynamical variable is one of its eigenvalues." Further, "The question now presents itself - Can every observable [mathematical operator] be measured? The answer is theoretically yes. In practice it may be very awkward, or perhaps even beyond the ingenuity of the experimenter, to devise an apparatus which could measure some particular observable, but theory always allows one to imagine that the measurement can be made." Further, "It is often very difficult to decide mathematically whether a particular real dynamical variable satisfies the condition for being an observable or not, ... However ... good reason on experimental grounds ... even though mathematical proof may be missing." Both superposition and existence of eigenstates are needed for the definition of the wave function, as in the next paragraph.
Perhaps an unusual aspect of my definition is that it tries to fully obey the injunction of Niels Bohr, which he used to defeat the EPR paper. The very definition of the physical objects necessarily includes the method of measurement. The physical eigenstates, that are discriminated by the quantum analyzer, correspond one-to-one with the mathematical basis. The mathematical version of this is that the wave function must be defined with respect to some basis of the relevant Hilbert space. I have preferred the physical approach in an article on physics, especially in the light of Dirac's warnings about the mathematical concepts. Most texts on this subject start with a mathematical chapter or two, mainly on Hilbert spaces, before embarking on a definition. I think a physical approach is more appropriate for Wikipedia, which cannot easily make the reader do his Hilbert space homework. I think the texts assume that the reader obviously knows that the vector space basis corresponds with the physical eigenstates. Apart from a physical basis, the QM state, according to Bohr, is undefined. Like "measurement", a QM 'state' is a term of art, not part of the ordinary language. A classical state belongs to the particle apart from all else. That is why the classical state concept is misleading for QM. It is a regrettable relic of habitual classical thinking to presume that a QM 'state' belongs to the particle apart from the permitted set of operators and their associated eigenstate basis defined by the quantum analyzer. I have tried to tell that to the reader in physical terms. Chjoaygame ( talk) 18:21, 3 January 2015 (UTC)
Perhaps I should add that my thinking was significantly guided by page 29 of Julian Schwinger's (2001) Quantum Mechanics: Symbolism of Atomic Measurements, edited by B.-G. Englert, Springer, ISBN 3-540-41408-8. He writes
Schwinger goes on to work directly with Stern-Gerlach magnets without mention of Hilbert space and so forth. I followed that lead because this is an article about physics. Chjoaygame ( talk) 19:36, 3 January 2015 (UTC)
Englert, in his own Lectures on Quantum Mechanics in three short volumes, volume 1, Basic Matters, ISBN 981-256-790-9, uses this approach of Schwinger to introduce the ideas. I think it is pretty close to how Feynman introduces the ideas too. Chjoaygame ( talk) 20:30, 3 January 2015 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 | Archive 5 | → | Archive 10 |
"Typically, its values are complex numbers and, for a single particle, it is a function of space and time."
Is this true of any but a scalar particle? I know I'll probably spark a debate because this is not my area, but surely this is oversimplification to the point of confusion? For example, I'd expect any fermion to have a wavefunction that is spinor-valued, in which case complex numbers might come into it, depending on the representation chosen, but also might not. Shouldn't this description be changed? — Quondum 21:48, 15 March 2014 (UTC)
Nevertheless, RQM is only an approximation to a fully self-consistent relativistic theory of known particle interactions because it does not describe cases where the number of particles changes; for example in matter creation and annihilation.
Quondum, you refer to WP policies. One of the most important is to write from what most sources say: of course not like a textbook but as a plain English summary. Well, does anyone know how many introductory QM sources which do not use write wavefunctions as complex numbers or complex-valued vectors? Complex numbers are exclusively used in almost every single introductory QM book I've ever seen (anyone is welcome to contradict with examples). The only exception I can think of is when QM is written in the language of geometric algebra, which uses the field of real numbers. The restricted scope "introductory QM" is not meant to be pedagogic - this is one important level of sources we should use for this article.
As for:
the article has an ontology section linking to the main ontology article - saying the meaning of the wavefunction is unclear, and always has been from day 1. The sections on wavefunctions for one particle in 1d, and more particles in higher dimensions, all mention the Copenhagen interpretation, the most introductory interpretation of the wavefunction.
It's a bit unfair to say the lead totally violates the guidelines. It can be improved, but it gets the main points across. I'm not denying the article still needs work. But this discussion confuses me. M∧Ŝ c2ħε Иτlk 16:40, 22 March 2014 (UTC)
I'll have a very quick go at tweaking the lead along these lines. M∧Ŝ c2ħε Иτlk 16:56, 23 March 2014 (UTC)
I tried to explain a little. There are probably bugs in the new equations, possibly a missing minus sign (the plane wave), and possible a missing factor of one over two pi (delta function normalization). These things depend on conventions, including for the Fourier transform. Can anyone check what Griffith (the ref in the section) says? YohanN7 ( talk) 22:47, 15 March 2014 (UTC)
May I destroy [1]? This flickering picture that does not, actually, “animate” anything useful, only distracts attention and wastes the processor time. Incnis Mrsi ( talk) 13:36, 29 March 2014 (UTC)
I'm not a quantum mechanic (can't handle those teeny, tiny wrenches) so forgive me if I'm not putting this question correctly, but I wonder if someone could say (and maybe put in the article) something about how causality and the speed of light relate to the time-dependent wavefunction. I assume the wavefunction is causal? If the boundary conditions or the potential are altered in one place, do the resulting changes in the wavefunction propagate to other places at the speed of light? And what about the delayed quantum eraser experiment? Thanks. -- Chetvorno TALK 06:38, 27 October 2013 (UTC)
I have put into the lead some brief remarks on the domain of the wave function. To save editors the trouble of checking my sources, I copy quotes from them here.
References
Chjoaygame ( talk) 14:51, 31 July 2014 (UTC)
I think there is a need for a basic interpretation of the wave function before introducing the Copenhagen interpretation, and even measurements. I am thinking about things that are often misinterpreted. For instance (in a toy model), if a wave function is a superposition of two delta-like functions located at A and B (in position space), it does not mean any of the following:
Both statements are provably not true (actually, some "plausible" statements of this nature are not true/false but plain nonsense), using Hilbert space theory alone (they lead to contradictions of mathematical and even logical nature), but both of these interpretations are easy to be picked up by a novice, especially when fed the Copenhagen interpretation. (Note, no measurements are involved in the statements above) An example of a correct statement would be
A great source for stuff like this is Robert Griffith's Consistent Quantum Theory. This book is about an alternative (other than Copenhagen) interpretation of quantum theory, but the stuff I mentioned above is basic and independent of any interpretation. Well, my question is, should we have a "basic" section here or in a separate article, or does one already exist that handles matters like these? YohanN7 ( talk) 20:12, 28 August 2014 (UTC)
This article too presents the misconception that spin is a consequence of the Dirac wave functions. (Other common and incorrect formulations include that spin is a consequence of the Dirac equation.) The truth is that spin is a consequence of the symmetry group of special relativity, the Poincaré group, more precisely its subgroup, the Lorentz group — even more specifically it originates in its subgroup SO(3), the rotation group, which is doubly connected.
More accurate would be to say that the Dirac equation is a consequence of (the existence of) charged spin 1⁄2 quantum particles coupled to the EM field via minimal coupling with parity inversion symmetry (without the latter the Weyl equations arise). Dirac spinors have spin 1⁄2, they don't predict it. Paraphrased, "The DE doesn't predict spin 1⁄2, but spin 1⁄2 predicts the (free) DE". YohanN7 ( talk) 19:09, 28 August 2014 (UTC)
I want to emphasize that Dirac himself surely would have objected to the current article's formulation. He was well aware of the order of events. He actually published the Bargmann-Wigner equations a decade (or more, 1933?) before Bargmann and Wigner. Moreover, the investigations into the infinite-dimensional representations of the Lorentz group was instigated by him. That is, it is hardly to dishonor Dirac to take away the "prediction-of-spin-status" from the equation or its solutions.
The great thing that the Dirac equation actually did predict was the existence of positrons, or, in general, antiparticles for every particle obeying the DE. (Dirac initially speculated that they may be protons, this at a time before the discovery of the neutron. Someone else (don't remember who) showed that the positron must have the same mass as the electron, hence couldn't be a proton.) YohanN7 ( talk) 11:43, 29 August 2014 (UTC)
The definition of the "inner product" suffers from an annoying and confusing error omission that is present in most basic QM texts(, and some math texts too). The "inner product" is not an inner product, it is a semi-inner product. The resulting "norm" is a pseudo-norm semi-norm, and its "metric" is a pseudo-metric (not semi-metric).
There are standard ways (all equivalent I believe) of dealing with this. One way is to declare points at a zero distance apart to be equivalent. Then by passing to the quotient w r t this equivalence relation, one obtains a true inner product space. It's elements are equivalence classes of functions from the original "inner product space".
Before I (possibly) do anything, I'd like your opinion on whether this conceptually important, but practically unimportant, issue is worth mention in the article. IMO, QM books being generally crappy mathematically should not be a reason for this article to make the same mistakes.
There are probably three categories of students (of QM books or this article). The first category never notices the problem. The third category does notice the problem and also its solution. The second category will be left puzzled. I belonged once to the second category. The instructor did some hand-waving when I asked him (he really didn't know I think). YohanN7 ( talk) 12:20, 3 April 2014 (UTC)
For the purposes of this article, the following should be enough:
Only the latter point has a problem. Such a statement needs to be sourced. YohanN7 ( talk) 21:51, 3 April 2014 (UTC)
I think the conclusion may be this: With this choice of inner product, the space of functions should be the space of square-integrable functions period. No continuity assumptions allowed. Only then will we get a Hilbert space (upon taking an appropriate quotient). There are other possible Hilbert spaces to make use of, e.g. the Sobolev spaces. These are mentioned in the article. But, for these, the inner product given here is not the right one. YohanN7 ( talk) 13:54, 4 April 2014 (UTC)
So I finally took care of this. The beefing out can be found in a popup. YohanN7 ( talk) 11:47, 7 November 2014 (UTC)
Editor Maschen has been making several edits which I do not wish myself to try to fiddle with. But I would point out some things that I think Maschen should fix.
It is not good to use footnotes in Wikipedia articles. Either something deserves to be in the main text, or it doesn't have a place at all. The scope for ever-expanding confusion with footnotes is obvious. So I have moved Maschen's footnote into the main text.
On the same topic, I have also moved the recent footnote by Editor YohanN7 into the main text.
A sentence that begins "Actually, ..." is very often a stylistic failure or error, for reasons that I will not here try to expound. In a nutshell, I think Maschen should remove the word 'actually' from the relevant text sentence, and make what other adjustment he thinks best. A problem is that Maschen's edit is in the lead, and it may be making the lead grow like Topsy. Perhaps the footnote stratagem was intended to by-pass this problem. I think it won't do. Somehow Maschen should deal with this. Chjoaygame ( talk) 04:20, 6 December 2014 (UTC)
Sorry for the delay. Here is the
edit in question for reference.
Basically, the objection is to the nb in the lead, on bosons described by spinors. That's fine, but I thought the flow would be fine to say "fermionic wavefunctions are spinorial while bosonic wavefunctions are tensorial", with a digression that spinors can describe particles of any spin (after all tensors can be replaced by spinors can't they?).
But maybe it is also excessive wording. I'm neutral on how we do this. Perhaps the best solution is to delete the nb and replace the statement by
(no reference to abstractions and unfamiliar terminology like "spinor rank" etc. keep it simple, this is elaborated later on in this article and other articles anyway). I'll make that change, any alternative wording is fine, people should feel free to edit.
For completeness, my only other edit to the lead was the deletion of the underlined part:
since in the next paragraph, the position space and momentum space wavefunctions are described anyway.
Hope that clarifies things, I'm fine if there's any other objections. Best, M∧Ŝ c2ħε Иτlk 23:04, 6 December 2014 (UTC)
Just to offer an alternative, if we wanted to reinstate mention of fermions and bosons:
M∧Ŝ c2ħε Иτlk 23:25, 6 December 2014 (UTC)
This website refers to the 'requirements' as "Born's Conditions". I'm not sure if that is a common term. RJFJR ( talk) 17:33, 17 December 2014 (UTC)
I think the present account of the 2012 Nature paper by Pusey Barrett Rudolph gives it undue weight. In a brief section such as the current one headed Ontology, it is inappropriately recherché. The paper is, charitably read on its merits, of marginal value. And not suitable for an account, even a one-sentence one, appearing here. Editor Sbyrnes very kindly gave an interpretation of it. While admirable, that interpretation seems more original research or editorial commentary than immediate reporting of the source. I think the felt call for such interpretive explication would be better responded to by simply removing the present account of the paper. Chjoaygame ( talk) 16:08, 6 December 2014 (UTC)
A reference appeared in the form of a pdf from the same user that put in the original disputed piece of text (very shortly after the referenced paper was published). On closer inspection, this was the only non-peer reviewed paper appearing in the article (until the pdf). I therefore removed the text. We should require a doi at the very least for this article. Otherwise it will give a rather silly impression when the next reference is Einstein. YohanN7 ( talk) 23:27, 1 January 2015 (UTC)
Thank you for this comment. It is indeed a problem for a newcomer to make sense of articles on such matters. In particular you say that my term quantum analyzer is inscrutable, even to an expert. My term is intended as an ordinary language version of the QM term of art "measurement". The latter term in ordinary language as I read it refers to a combination of a quantum analyzer and particle detector. The Qm term of art "measurement" is in my opinion very definitely a term of art, not part of the ordinary language, even of the ordinary language of science, indeed even of the ordinary language of physics. The particle detector part is needed to produce numbers that can be tested against the probabilistic predictions of the mathematical theory. I guess that is not a worry to you.
But indeed the term quantum analyzer may be criticized. An ordinary language word is needed that labels the class of physical arrangements or devices that split the beam into the respective sub-beams that are fed to the particle detectors. The classic example is Newton's prism by which he split a daylight beam into coloured beams. The next classic example is perhaps the Stern-Gerlach magnet that splits the beam into two sub-beams. Another example is a calcite crystal that splits a beam into two polarized sub-beams. Another example is a half-silvered mirror. In general, a quantum analyzer analyzes beams of quantal entities or particles into sub-beams of quantum eigenstates. It is of interest that you have read dozens of QM textbooks and still cannot figure out what I mean here.
It is not too easy to define a wave function in physical terms. Since this is an article on quantum physics, I think it appropriate to try to do it. According to Dirac (4th edition), there should be a one-to-one correspondence between a mathematical formalism and a collection of experimental items. Dirac starts his definition of a wave function by saying that it is superposable (Section 5, pp. 14-18). This is only the first of a list of defining criteria. The next item on his list of definitive criteria (Secction 10, pp. 36-38) is the mathematical operators and their corresponding "measurements". Dirac writes "Any result of a measurement of a real dynamical variable is one of its eigenvalues." Further, "The question now presents itself - Can every observable [mathematical operator] be measured? The answer is theoretically yes. In practice it may be very awkward, or perhaps even beyond the ingenuity of the experimenter, to devise an apparatus which could measure some particular observable, but theory always allows one to imagine that the measurement can be made." Further, "It is often very difficult to decide mathematically whether a particular real dynamical variable satisfies the condition for being an observable or not, ... However ... good reason on experimental grounds ... even though mathematical proof may be missing." Both superposition and existence of eigenstates are needed for the definition of the wave function, as in the next paragraph.
Perhaps an unusual aspect of my definition is that it tries to fully obey the injunction of Niels Bohr, which he used to defeat the EPR paper. The very definition of the physical objects necessarily includes the method of measurement. The physical eigenstates, that are discriminated by the quantum analyzer, correspond one-to-one with the mathematical basis. The mathematical version of this is that the wave function must be defined with respect to some basis of the relevant Hilbert space. I have preferred the physical approach in an article on physics, especially in the light of Dirac's warnings about the mathematical concepts. Most texts on this subject start with a mathematical chapter or two, mainly on Hilbert spaces, before embarking on a definition. I think a physical approach is more appropriate for Wikipedia, which cannot easily make the reader do his Hilbert space homework. I think the texts assume that the reader obviously knows that the vector space basis corresponds with the physical eigenstates. Apart from a physical basis, the QM state, according to Bohr, is undefined. Like "measurement", a QM 'state' is a term of art, not part of the ordinary language. A classical state belongs to the particle apart from all else. That is why the classical state concept is misleading for QM. It is a regrettable relic of habitual classical thinking to presume that a QM 'state' belongs to the particle apart from the permitted set of operators and their associated eigenstate basis defined by the quantum analyzer. I have tried to tell that to the reader in physical terms. Chjoaygame ( talk) 18:21, 3 January 2015 (UTC)
Perhaps I should add that my thinking was significantly guided by page 29 of Julian Schwinger's (2001) Quantum Mechanics: Symbolism of Atomic Measurements, edited by B.-G. Englert, Springer, ISBN 3-540-41408-8. He writes
Schwinger goes on to work directly with Stern-Gerlach magnets without mention of Hilbert space and so forth. I followed that lead because this is an article about physics. Chjoaygame ( talk) 19:36, 3 January 2015 (UTC)
Englert, in his own Lectures on Quantum Mechanics in three short volumes, volume 1, Basic Matters, ISBN 981-256-790-9, uses this approach of Schwinger to introduce the ideas. I think it is pretty close to how Feynman introduces the ideas too. Chjoaygame ( talk) 20:30, 3 January 2015 (UTC)