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I reverted this edit by user:Chjoaygame for the following reasons.
M ∧Ŝ c2ħε Иτlk 11:27, 24 March 2016 (UTC)
It seems I need to clarify here. Editor Maschen has made several objections to my post that he undid. Some of them are sound. But I have concentrated on the most substantial here: Dirac's statement. The matter can be considered through several questions.
I think so. I think this is denied by the above comment:
This question seems unsettled here.
I think so. There is an important difference between a vector and its representation by coordinates. A complex vector is complex by virtue of its being mulipliable by elements of its scalar field, not by virtue of its being resolvable into real and imaginary parts. Some complex vectors can indeed be resolved into real and imaginary parts, for example, wave functions. That is the most obvious example for the present discussion. The example of the Riemann-Silberstein vector is a little distant, referring to pre-quantum, mechanical thinking, but still valid. But that it is so for some does not imply that it is so for all.
Evidently, Editor Maschen thinks not, when he writes above:
I do not see that as a persuasive or sound argument to deal with the question as to whether bras and kets can be resolved into real and imaginary parts. They are abstract vectors, not fully reducible to any particular representation. That is part of how they are distinct from wave functions.
This question seems unsettled here.
With these two questions unsettled here, I think the undo remains unsettled. Chjoaygame ( talk) 07:11, 27 March 2016 (UTC)
I recommend these lecture notes. "Complex conjugation of the expansion coefficients in a certain basis Q" is a perfectly valid (antilinear!) operator on kets, kinda useful in discussing time-reversal symmetry. Call it K_Q. Then you can have "real vectors w.r.t. Q" in the sense that K_Q sends them to themselves, and "imaginary vectors w.r.t. Q" in the sense that K_Q sends them to their negatives. But it's not a ket itself that is real or imaginary, but rather the relation between a ket and a basis. The same ket can be real, imaginary, or neither in different bases. I don't think this topic needs to be discussed in this particular article. Well, I guess I'm not totally opposed to saying something simple like "You can't add a bra to a ket, just as you can't add a row-vector to a column-vector", if this is really a common misconception. -- Steve ( talk) 12:51, 3 April 2016 (UTC)
Editor YohanN7 has here undone a fair post by me. His edit summary is the one word "Gibberish". He made no talk page comment.
My edit was not gibberish. Chjoaygame ( talk) 14:58, 29 March 2016 (UTC)
(I had something here but found the answer below. Suffice it to say, if you wanted to make your point, it needed to be much, much clearer than what you originally wrote.) -- 100.14.175.181 ( talk) 11:50, 6 May 2016 (UTC)
The new edit here includes the following: "It should be kept in mind that ..." There are many other examples of such by the same editor. I do not recall the exact chapter and verse of Wiki policy for this, but I do recall that such language is deprecated in Wiki policy as condescending and didactic, in effect uncivil, not encyclopedic. Chjoaygame ( talk) 19:31, 29 March 2016 (UTC)
Editors YohanN7 and Maschen have, more or less collusively, undone my edits here and here, without talk page discussion when it would have been appropriate, or mandatory. This was high-handed action by them.
The two undone edits were about (a) Dirac's view that bras and kets cannot be resolved into real and imaginary parts; and (b) about a few writers' view that one can view bras and kets as about initial and final states of a quantum phenomenon.
As to (a). Editor Maschen has tried on the talk page to blow away Dirac's view, that my edit quoted. I think his undo is based in part on his belief that his try was valid or successful. I think I have above presented enough argument to dispel his try. Editor Maschen's undo had the edit summary "Remove Ch's personal misinterpretations once again, that bras and kets are "physically distinct"." My edit just quoted Dirac's view, not my interpretation of it. The problem here is that Editor Maschen thinks that Dirac was mistaken. I think not, but the point here is that Editor Maschen is confusing his rejection of Dirac's view with his thought that it is my view that is what I posted. I am accurately reporting Dirac's view, not inventing a view of my own. As it happens, I think Dirac is right, but that does not mean that I invented it. So far as I can see, Editor YohanN7 did not involve himself in this matter.
As to (b). Editor YohanN7 involved himself in this by naming me in his edit summary "Addressing Chjoaygame's perpetual concern". Editor Maschen did the actual undo. My post reported in brief summary four writers' views. The writers are respectable secondary sources, giving their opinions, which happen to be nearly enough concordant. Editor YohanN7 has expressed his deprecation of Feynman's Lectures, but I think Feynman's view deserves bring reported, since it agrees closely with that of Landau and Lifshitz. Again, I did not invent these views. I learnt Feynman's long ago, and recently found the others' concordance. My post made it clear that their view is not widely expressed. Editor YohanN7 has replaced my post with his own view in the lead, about S-matrices, not bras and kets as used by my four sources. Editor YohanN7 is competent to express views about S-matrices, but they are not directly about bras and kets as was my post. The topic of the article is bra-and-ket notation, not S-matrices. Editor Maschen has not very much engaged on this topic, beyond just now undoing my edit here on it.
I can hardly overcome this kind of attack. I can, however, say that I think it unethical. Both Editor YohanN7 and Editor Maschen have recently said they will not further engage on a talk-page with me. This does not entitle either of them to undo my edits without normal talk-page engagement. I think Editor Maschen's withdrawal is due to his failure to support his mistaken case with argument. Editor YohanN7 withdrew from talk about the traditional term "measurement". I think a large part of his difficulty there is in his not having read much literature on this topic. The kind of measurement considered by Dirac and the other relevant sources is essentially about many times repeated phenomena, not just one-off ones such as L&L discuss. Editor YohanN7 is right that a one-off "measurement" of the kind discussed by his source Landau nd Lifshitz does not fit with the traditional language used by the sources that are directly relevant to the topic that was being considered. But that does not mean that those relevant sources can be dismissed, and my post with them. I think Editor YohanN7 was significantly in error there, and has withdrawn because of that. Both of my present edits here took careful and adequate account of the objections of those editors against my previous versions of my edits. In short, I think Editors YohanN7 and Maschen are not entitled to avoid talk-page discussion of their present collusive undoing of my present edits. Chjoaygame ( talk) 11:36, 31 March 2016 (UTC)
There is a standard procedure: It probably translates, for the current situation, to refrain from editing until the editors of the page identify themselves as interested parties in the article.
Please assume good faith, for starters. There is a whole set of editorial guidelines which we can use to guide the development of the article. -- Ancheta Wis (talk | contribs) 21:00, 1 April 2016 (UTC)
I agree with the deletion of both those sections: The conjugation section is unnecessary and off-topic (while it's true that complex vectors don't have real and imaginary parts in the same way that complex numbers do, that has nothing to do with bra-ket notation), and the "interpretations" section is all wrong (for example, there are references in which people are describing mnemonics for reading this or that particular equation, but this is misunderstood as a description of bras and kets in general). Bra-ket notation is just a notation for linear algebra, it doesn't have or need any "interpretation" beyond that. -- Steve ( talk) 19:43, 3 April 2016 (UTC)
To close up my comments to this page, and (attempt to) satisfy Chjoaygame as he unearths an old thread here, I admit blindly thinking a complex vector could be generally split into real and imaginary parts exactly as for complex numbers, for any basis. However, for the a + ib example above, I did state what the basis was (ex, ey, ez), so the vector could be written that way. If another basis was used then the components would be different. Me admitting this mistake still does not excuse him from a ban. M ∧Ŝ c2ħε Иτlk 14:33, 4 April 2016 (UTC)
Coming back to (b) above, the 'two-aspects of a state' question of physics. I am here to learn. Editor Sbyrnes has my respect, but seems to reject the idea that I find in Feynman and in Landau & Lifshitz, that it is naturally symbolized in the bra-ket distinction.
I think one of prime fundamentals of the physics of quantum mechanics is that experiments are conducted by the contiguous placement of a source and a destination device (or eleborations thereof), which are often recognized as preparative and observational respectively. Repeated replicas of the quantum system are envisaged as passing from source to destination. I won't bore you with literature support for this. May I ask the assembled company of experts: in the mathematical formalism of quantum mechanics, how, if at all, is this fundamental physical distinction recognized? Chjoaygame ( talk) 03:19, 5 April 2016 (UTC)
Interpretation
Most writers do not mention a physical distinction between bras and kets, but a few interpret them as distinguishing initial and final conditions of a phenomenon. [1] [2] [3] [4] The theory is symmetrical between bras and kets, [5] so that it is merely conventional as which of bras or kets is taken as initial or final.
Copy-and-paste from my previous post in a separate section:
Thank you, Editor GangofOne, for your kind reply.
There is some syntactics and semantics here. I see the transformation of a ket to a ket (or a bra to a bra) as an evolution, within the fully developed preparative device, of an unobserved prepared state, or as an evolution within the observational device before detection. The step from prepared state to observed state is the one that I see Feynman and Landau & Lifshitz as indicating by the bra-to-ket change. Thus I do not see a ket-to-ket (or bra-to-bra) transformation as indicating the prepared-to-observed step. If a pure beam ψ is passed through a prism that will split it into sub-beams, but the sub-beams are not subjected to intervention, then the beam is still regarded by Dirac as in the state ψ. It may be conceptually analyzed as for example ψ = φ1 + φ2, and is thereby said to be in a superposition. This unobserved process I see as a ket-to-ket (or bra-to-bra) step. Re-assembly of the original beam is still possible. If an intervention, for example a detector, is put into one of the sub-beams, the superposition is broken because the original beam can no longer be re-assembled. This is said, in Heisenberg's word, to 'reduce' the state to the one (φ1 or φ2) that is pure with respect to the prism. I see such a 'reduction' as indicated by the ket-to-bra (or bra-to-ket) step. That is my reading of Feynman and of Landau & Lifshitz (and of a few others). Cohen-Tannoudji et al. do not mention this reading, as I read them. I am strongly driven by Dirac's view that the state has two equally ranking formal symbols, bra and ket. I do not see him as privileging the ket as the state. They are mutually dual. The state space is self-dual. Chjoaygame ( talk) 22:18, 5 April 2016 (UTC)
User:GangofOne, you should be aware that physically flawed editor Chjoaygame thinks bras and kets are physically different, that bras are "observed states" and kets are "prepared states" (or vice versa), and his last post is his inability to understand how to form an inner product to reflect this "fact". Then its a puzzle that "many writers ignore this question" and LL and Feynman are the minority of authors who supposedly agree with this "fact" (they don't, but never mind).
M
∧Ŝ
c2ħε
Иτlk
07:53, 6 April 2016 (UTC)
I see above that Chjoaygame is trying to create a different view of what his edits were about, changing history, so to speak, a bit. No, the reason you were reverted was not because of the only sane sentence in your edits (quoted in blue above by Chj). The reason was primarily this. It is so full of nonsense that it is nearly impossible to pinpoint exactly the nature of the misconceptions. Does this change in tactics to try to speak sanely have something to do with the present ANI proposal of a topic ban? YohanN7 ( talk) 09:18, 7 April 2016 (UTC)
For you benefit, here it is verbatim:
For starters,
is nonsense. They are equal. None is measurable (complex quantities aren't physically observable). Next,
is so goofy that it is beyond analysis. Sorting devices? It is meaningless to discuss nonsense with Chjoaygame. Reversion without comment saves time in the long run. YohanN7 ( talk) 10:04, 7 April 2016 (UTC)
@Chjoaygame, please stop. I thought you got the message when you mentioned your "post fails" ( 21:17, 6 April 2016) in reply to S Byrne. But something is impelling you to keep writing. Are you seeking validation from a community? Why here? Why do you not frequent a history of physics site, instead. This is supposed to be an encyclopedia and not a forum. -- Ancheta Wis (talk | contribs) 03:04, 9 April 2016 (UTC)
For me, at least, the linear operators section of the article seems have something missing, such as that which is covered in the 'Operators revisited' part of this physics course. -- Ancheta Wis (talk | contribs) 08:55, 1 April 2016 (UTC)
For starters, the applications of the notation seem wider than the history might suggest. As an example, the delta functions are definitely in use in at least 3 widely diverse areas extending beyond mathematics.
Perhaps other editors might suggest more applications.-- Ancheta Wis (talk | contribs) 20:59, 1 April 2016 (UTC)
In the interest of peace in this community (i.e., the readers of this page), can I ask that we all step back and refrain from editing, until our reflex actions cease to feed the spectacle, which is turning into entertainment, I suppose.
I found a citation in arXiv which addresses "the Culture of physics"; we are witnessing a culture clash, I think. Let's all relax a bit.
See also the following techniques:
-- Ancheta Wis (talk | contribs) 12:19, 9 April 2016 (UTC)
The later parts of this section seem odd to me. Certainly using one symbol as a label, a variable, and as an operator are confusing to newbies. No argument there. It is much less clear to me that it's actually an abuse of notation. When you use a variable name in a label, what you're doing is labeling by a quantity, and getting that quantity from the variable. So if you put an algebraic expression as a label, you're labeling the state with a quantity, and getting that quantity from the algebraic expression.
What else are you supposed to do - declare an entire new set of labels with an algebraic relation to the old labels and then use those? Use the same old labels and Dirac delta a difference between the label's value (which to be consistent must have a different symbol than the label itself) and the value we want? Either of those would be far more confusing, and I am not at all sure that either would actually solve the problem.
And naming the operator after the variable it extracts seems only natural. It has a hat - it's not the same thing. -- 100.14.175.181 ( talk) 12:10, 6 May 2016 (UTC)
What is significance of <B|A|C> A(inner part) in bra-ket notation. Also what does |P,Q> means?
Sorry if this is inappropriate place to ask.. But I was unable to find this on wiki and there is no proper explanation for "inner part" also in there. VaibhaW ( talk) 01:48, 13 October 2016 (UTC)
I'm new to quantum mechanics and dirac notation and I come to this page to learn. However, dirac notation is varied and taught differently depending on the type of background one comes from. I will be less confused if the vector quantities could have arrows placed over the characters. Thanks to whoever accomplishes this! Also, this my first post on Wikipedia--let me know if I'm doing something wrong! — Preceding unsigned comment added by Murphaid ( talk • contribs) 23:24, 1 November 2016 (UTC)
The notation may need further explanation. Coming from mathematics, I wasn't familiar with it and had to search for a while (other Wikipedia articles say it can mean "approximately equal" or "goes toward the limit" which isn't very helpful). It's an important point that a bra/ket is not identical to the actual vector but a coordinate-free representation of it. I like how the German article explains it. Also, is necessary in ? This looks like an equality to me, and in the figure an equals sign is used.-- 92.208.44.56 ( talk) 12:40, 3 January 2017 (UTC)
The Dirac notation was the unification of Heisenberg's matrix and Schrödinger's differential theory into one cohesive whole.
He's idea was that there were (are) many representations of a state or a transformation. This article does not convey Dirac's abstraction.
The misconception of the article: There is belief that p is the operator -i hbar gradient. This is only true in the coordinate basis. It happens to be p in the momentum basis and is some matrix in a given discrete basis. Dirac saw this. He invented the ket as an abstract state that when projected onto a basis would act like a vector (discrete) or function (continuous). Operators were abstract transformations of the states that when projected onto a basis would act like a matrix (discrete) or a differential operator (continuous). He invented the Dirac delta in order to generalized linear algebra to a continuous basis. (Although the Dirac delta is still looked at as NOT making "sense as a mathematical object" by too many mathematicians. See Delta Function talk page!)
These ideas are all in Dirac's book on Quantum mechanics but I think Feynman may have covered it even better.
"The Feynman Lectures on Physics" Feynman, Leighton, Sands. See Chapters 16 and 20. In particular 16-5.
Sure, he was not rigorous (Was Newton? or Leibniz?). But Dirac was a genius. I believe Dirac deserves more credit than the mathematics community on Wikipedia is willing to give. In many aspects he was ahead of the mathematics community and it took decades for mathematicians to catch up. In some ways mathematics still hasn't... — Preceding unsigned comment added by 131.252.127.172 ( talk) 03:31, 6 August 2017 (UTC)
Two things I find misleading:
1) The pedagogy: Since so many students use Wikipedia to help learn concepts that are new to them, I think it is important that Wikipedia editors do their best to convey the ideas in a way that imparts the intended usage of the concept. Sure, this is all just linear algebra but Dirac generalized the idea into a more general algebra to unify Quantum Mechanics. And its not just any mathematical algebra, this algebra describes the world we live in very accurately.
2) The Machinery: In the section "Spinless position–space wave function", it has the p Psi(r) =def "bra r" p "ket Psi". That is not what Dirac defined. It is better to say -i hbar gradient psi(r) = integral "bra r" p "ket r' " "bra r' " "ket psi" d^3x' where "bra r" p "ket r' " = -i hbar psi(r') delta(r- r'). And the delta function and integral "cancel" each other out. Understanding the need for the delta function and integral is important once students begin applying QM (to ideas such as scattering) where we cannot just define the correct relationships but rather we need to calculate them.
This is done very clearly in Feynmans QM lectures 16-5. I hope the editors understand the difference between what the article states and what is explained by Feynman.
Also, it is traditional (standard?) to use lowercase psi for the position wavefunctions and capital Psi for the position and time wavefunctions. — Preceding unsigned comment added by 131.252.127.172 ( talk) 17:42, 6 August 2017 (UTC)
Did you even read Feynman? Your response seems like a knee jerk reaction! — Preceding unsigned comment added by 131.252.127.172 ( talk) 18:28, 6 August 2017 (UTC)
I have had mathematics students make statements like, "Isn't this all just linear algebra." Or "Quantum Mechanics is just Group Theory." True statements but these students are being mislead by the mathematicians. For example, High school physics uses basic algebra. Just because a student knows basics algebra does not mean he/she understands all of High School physics. The are concepts to be learned!
Read Dirac, Read Feynman. There is a difference. The difference is physics. In math you can define. In physics we need to agree with the experiments. Understanding the concepts are important.
Try to understand. — Preceding unsigned comment added by 131.252.127.172 ( talk) 18:43, 6 August 2017 (UTC)
The last psi(r') should have been a gradient! — Preceding unsigned comment added by 131.252.127.172 ( talk) 18:47, 6 August 2017 (UTC)
Yes and no. Isn't one of Wikipedia purposes to help young people become better educated? We need to remember that students use Wikipedia to look up these concepts. Yes, we should make the concepts as simple/straightforward as possible. “Everything should be made as simple as possible, but no simpler.” I think we disagree about where that line is.
Dirac notation is primarily a physics notation, invented to ease physics calculations. Students coming to the page are going to be primarily physics students. Sure, it could be used in linear algebra but that was not its intended purpose and I haven't seen it mentioned in any linear algebra textbook.
"We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations." - Richard P. Feynman 131.252.127.172 ( talk) 21:13, 6 August 2017 (UTC)
I just remembered a book that I think is a good compromise in the treatment of Dirac notation.
"Explorations in Mathematical Physics" Don Koks p. 41-71
He starts with the notion of the inner product of linear algebra and only mentions how it is applied to QM in last few pages at the end of the chapter. Most everything is there. Quite a bit would have to be cut out in order to be more concise. I think is shows the machinery without getting too much into its QM interpretations. Although, I still believe the best way to learn Dirac notation is to use it in the context of QM, I am willing to try to do so without it. If anyone knows of any other books that do something similar, then I am willing to read them. — Preceding unsigned comment added by 131.252.127.172 ( talk) 00:32, 7 August 2017 (UTC)
131.252.127.172 ( talk) 02:26, 7 August 2017 (UTC)
I wrote: "In mathematics, the term "vector" is used to refer generally to any element of any vector space. In physics, however, the term "vector" is much more specific: "Vector" then refers almost exclusively to quantities like displacement or velocity, which have three components that relate directly to the three dimensions of the real world." YohanN7 edited to say "In introductory physics", with the comment "usage far from universal". Well, I had thought it was universal or at least near-universal. What are the counterexamples?
Even if there are counterexamples that I haven't thought of (which is entirely possible), I more confidently object to the term "introductory". For example this usage is rampant in quantum field theory (vector particles, vector fields, as opposed to pseudovector or tensor etc.) and other advanced QM courses (spherical tensor operators, Wigner-Eckart theorem etc.), GR, etc. etc. Indeed, I didn't really fully appreciate this point until taking graduate physics courses. (OK sure, if I had read Feynman more carefully, I would have appreciated it sooner!) So if it's not universal, I vote for saying "often in physics" or "generally in physics" but I don't think we should say "in introductory physics". :-D -- Steve ( talk) 12:46, 14 September 2017 (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 |
I reverted this edit by user:Chjoaygame for the following reasons.
M ∧Ŝ c2ħε Иτlk 11:27, 24 March 2016 (UTC)
It seems I need to clarify here. Editor Maschen has made several objections to my post that he undid. Some of them are sound. But I have concentrated on the most substantial here: Dirac's statement. The matter can be considered through several questions.
I think so. I think this is denied by the above comment:
This question seems unsettled here.
I think so. There is an important difference between a vector and its representation by coordinates. A complex vector is complex by virtue of its being mulipliable by elements of its scalar field, not by virtue of its being resolvable into real and imaginary parts. Some complex vectors can indeed be resolved into real and imaginary parts, for example, wave functions. That is the most obvious example for the present discussion. The example of the Riemann-Silberstein vector is a little distant, referring to pre-quantum, mechanical thinking, but still valid. But that it is so for some does not imply that it is so for all.
Evidently, Editor Maschen thinks not, when he writes above:
I do not see that as a persuasive or sound argument to deal with the question as to whether bras and kets can be resolved into real and imaginary parts. They are abstract vectors, not fully reducible to any particular representation. That is part of how they are distinct from wave functions.
This question seems unsettled here.
With these two questions unsettled here, I think the undo remains unsettled. Chjoaygame ( talk) 07:11, 27 March 2016 (UTC)
I recommend these lecture notes. "Complex conjugation of the expansion coefficients in a certain basis Q" is a perfectly valid (antilinear!) operator on kets, kinda useful in discussing time-reversal symmetry. Call it K_Q. Then you can have "real vectors w.r.t. Q" in the sense that K_Q sends them to themselves, and "imaginary vectors w.r.t. Q" in the sense that K_Q sends them to their negatives. But it's not a ket itself that is real or imaginary, but rather the relation between a ket and a basis. The same ket can be real, imaginary, or neither in different bases. I don't think this topic needs to be discussed in this particular article. Well, I guess I'm not totally opposed to saying something simple like "You can't add a bra to a ket, just as you can't add a row-vector to a column-vector", if this is really a common misconception. -- Steve ( talk) 12:51, 3 April 2016 (UTC)
Editor YohanN7 has here undone a fair post by me. His edit summary is the one word "Gibberish". He made no talk page comment.
My edit was not gibberish. Chjoaygame ( talk) 14:58, 29 March 2016 (UTC)
(I had something here but found the answer below. Suffice it to say, if you wanted to make your point, it needed to be much, much clearer than what you originally wrote.) -- 100.14.175.181 ( talk) 11:50, 6 May 2016 (UTC)
The new edit here includes the following: "It should be kept in mind that ..." There are many other examples of such by the same editor. I do not recall the exact chapter and verse of Wiki policy for this, but I do recall that such language is deprecated in Wiki policy as condescending and didactic, in effect uncivil, not encyclopedic. Chjoaygame ( talk) 19:31, 29 March 2016 (UTC)
Editors YohanN7 and Maschen have, more or less collusively, undone my edits here and here, without talk page discussion when it would have been appropriate, or mandatory. This was high-handed action by them.
The two undone edits were about (a) Dirac's view that bras and kets cannot be resolved into real and imaginary parts; and (b) about a few writers' view that one can view bras and kets as about initial and final states of a quantum phenomenon.
As to (a). Editor Maschen has tried on the talk page to blow away Dirac's view, that my edit quoted. I think his undo is based in part on his belief that his try was valid or successful. I think I have above presented enough argument to dispel his try. Editor Maschen's undo had the edit summary "Remove Ch's personal misinterpretations once again, that bras and kets are "physically distinct"." My edit just quoted Dirac's view, not my interpretation of it. The problem here is that Editor Maschen thinks that Dirac was mistaken. I think not, but the point here is that Editor Maschen is confusing his rejection of Dirac's view with his thought that it is my view that is what I posted. I am accurately reporting Dirac's view, not inventing a view of my own. As it happens, I think Dirac is right, but that does not mean that I invented it. So far as I can see, Editor YohanN7 did not involve himself in this matter.
As to (b). Editor YohanN7 involved himself in this by naming me in his edit summary "Addressing Chjoaygame's perpetual concern". Editor Maschen did the actual undo. My post reported in brief summary four writers' views. The writers are respectable secondary sources, giving their opinions, which happen to be nearly enough concordant. Editor YohanN7 has expressed his deprecation of Feynman's Lectures, but I think Feynman's view deserves bring reported, since it agrees closely with that of Landau and Lifshitz. Again, I did not invent these views. I learnt Feynman's long ago, and recently found the others' concordance. My post made it clear that their view is not widely expressed. Editor YohanN7 has replaced my post with his own view in the lead, about S-matrices, not bras and kets as used by my four sources. Editor YohanN7 is competent to express views about S-matrices, but they are not directly about bras and kets as was my post. The topic of the article is bra-and-ket notation, not S-matrices. Editor Maschen has not very much engaged on this topic, beyond just now undoing my edit here on it.
I can hardly overcome this kind of attack. I can, however, say that I think it unethical. Both Editor YohanN7 and Editor Maschen have recently said they will not further engage on a talk-page with me. This does not entitle either of them to undo my edits without normal talk-page engagement. I think Editor Maschen's withdrawal is due to his failure to support his mistaken case with argument. Editor YohanN7 withdrew from talk about the traditional term "measurement". I think a large part of his difficulty there is in his not having read much literature on this topic. The kind of measurement considered by Dirac and the other relevant sources is essentially about many times repeated phenomena, not just one-off ones such as L&L discuss. Editor YohanN7 is right that a one-off "measurement" of the kind discussed by his source Landau nd Lifshitz does not fit with the traditional language used by the sources that are directly relevant to the topic that was being considered. But that does not mean that those relevant sources can be dismissed, and my post with them. I think Editor YohanN7 was significantly in error there, and has withdrawn because of that. Both of my present edits here took careful and adequate account of the objections of those editors against my previous versions of my edits. In short, I think Editors YohanN7 and Maschen are not entitled to avoid talk-page discussion of their present collusive undoing of my present edits. Chjoaygame ( talk) 11:36, 31 March 2016 (UTC)
There is a standard procedure: It probably translates, for the current situation, to refrain from editing until the editors of the page identify themselves as interested parties in the article.
Please assume good faith, for starters. There is a whole set of editorial guidelines which we can use to guide the development of the article. -- Ancheta Wis (talk | contribs) 21:00, 1 April 2016 (UTC)
I agree with the deletion of both those sections: The conjugation section is unnecessary and off-topic (while it's true that complex vectors don't have real and imaginary parts in the same way that complex numbers do, that has nothing to do with bra-ket notation), and the "interpretations" section is all wrong (for example, there are references in which people are describing mnemonics for reading this or that particular equation, but this is misunderstood as a description of bras and kets in general). Bra-ket notation is just a notation for linear algebra, it doesn't have or need any "interpretation" beyond that. -- Steve ( talk) 19:43, 3 April 2016 (UTC)
To close up my comments to this page, and (attempt to) satisfy Chjoaygame as he unearths an old thread here, I admit blindly thinking a complex vector could be generally split into real and imaginary parts exactly as for complex numbers, for any basis. However, for the a + ib example above, I did state what the basis was (ex, ey, ez), so the vector could be written that way. If another basis was used then the components would be different. Me admitting this mistake still does not excuse him from a ban. M ∧Ŝ c2ħε Иτlk 14:33, 4 April 2016 (UTC)
Coming back to (b) above, the 'two-aspects of a state' question of physics. I am here to learn. Editor Sbyrnes has my respect, but seems to reject the idea that I find in Feynman and in Landau & Lifshitz, that it is naturally symbolized in the bra-ket distinction.
I think one of prime fundamentals of the physics of quantum mechanics is that experiments are conducted by the contiguous placement of a source and a destination device (or eleborations thereof), which are often recognized as preparative and observational respectively. Repeated replicas of the quantum system are envisaged as passing from source to destination. I won't bore you with literature support for this. May I ask the assembled company of experts: in the mathematical formalism of quantum mechanics, how, if at all, is this fundamental physical distinction recognized? Chjoaygame ( talk) 03:19, 5 April 2016 (UTC)
Interpretation
Most writers do not mention a physical distinction between bras and kets, but a few interpret them as distinguishing initial and final conditions of a phenomenon. [1] [2] [3] [4] The theory is symmetrical between bras and kets, [5] so that it is merely conventional as which of bras or kets is taken as initial or final.
Copy-and-paste from my previous post in a separate section:
Thank you, Editor GangofOne, for your kind reply.
There is some syntactics and semantics here. I see the transformation of a ket to a ket (or a bra to a bra) as an evolution, within the fully developed preparative device, of an unobserved prepared state, or as an evolution within the observational device before detection. The step from prepared state to observed state is the one that I see Feynman and Landau & Lifshitz as indicating by the bra-to-ket change. Thus I do not see a ket-to-ket (or bra-to-bra) transformation as indicating the prepared-to-observed step. If a pure beam ψ is passed through a prism that will split it into sub-beams, but the sub-beams are not subjected to intervention, then the beam is still regarded by Dirac as in the state ψ. It may be conceptually analyzed as for example ψ = φ1 + φ2, and is thereby said to be in a superposition. This unobserved process I see as a ket-to-ket (or bra-to-bra) step. Re-assembly of the original beam is still possible. If an intervention, for example a detector, is put into one of the sub-beams, the superposition is broken because the original beam can no longer be re-assembled. This is said, in Heisenberg's word, to 'reduce' the state to the one (φ1 or φ2) that is pure with respect to the prism. I see such a 'reduction' as indicated by the ket-to-bra (or bra-to-ket) step. That is my reading of Feynman and of Landau & Lifshitz (and of a few others). Cohen-Tannoudji et al. do not mention this reading, as I read them. I am strongly driven by Dirac's view that the state has two equally ranking formal symbols, bra and ket. I do not see him as privileging the ket as the state. They are mutually dual. The state space is self-dual. Chjoaygame ( talk) 22:18, 5 April 2016 (UTC)
User:GangofOne, you should be aware that physically flawed editor Chjoaygame thinks bras and kets are physically different, that bras are "observed states" and kets are "prepared states" (or vice versa), and his last post is his inability to understand how to form an inner product to reflect this "fact". Then its a puzzle that "many writers ignore this question" and LL and Feynman are the minority of authors who supposedly agree with this "fact" (they don't, but never mind).
M
∧Ŝ
c2ħε
Иτlk
07:53, 6 April 2016 (UTC)
I see above that Chjoaygame is trying to create a different view of what his edits were about, changing history, so to speak, a bit. No, the reason you were reverted was not because of the only sane sentence in your edits (quoted in blue above by Chj). The reason was primarily this. It is so full of nonsense that it is nearly impossible to pinpoint exactly the nature of the misconceptions. Does this change in tactics to try to speak sanely have something to do with the present ANI proposal of a topic ban? YohanN7 ( talk) 09:18, 7 April 2016 (UTC)
For you benefit, here it is verbatim:
For starters,
is nonsense. They are equal. None is measurable (complex quantities aren't physically observable). Next,
is so goofy that it is beyond analysis. Sorting devices? It is meaningless to discuss nonsense with Chjoaygame. Reversion without comment saves time in the long run. YohanN7 ( talk) 10:04, 7 April 2016 (UTC)
@Chjoaygame, please stop. I thought you got the message when you mentioned your "post fails" ( 21:17, 6 April 2016) in reply to S Byrne. But something is impelling you to keep writing. Are you seeking validation from a community? Why here? Why do you not frequent a history of physics site, instead. This is supposed to be an encyclopedia and not a forum. -- Ancheta Wis (talk | contribs) 03:04, 9 April 2016 (UTC)
For me, at least, the linear operators section of the article seems have something missing, such as that which is covered in the 'Operators revisited' part of this physics course. -- Ancheta Wis (talk | contribs) 08:55, 1 April 2016 (UTC)
For starters, the applications of the notation seem wider than the history might suggest. As an example, the delta functions are definitely in use in at least 3 widely diverse areas extending beyond mathematics.
Perhaps other editors might suggest more applications.-- Ancheta Wis (talk | contribs) 20:59, 1 April 2016 (UTC)
In the interest of peace in this community (i.e., the readers of this page), can I ask that we all step back and refrain from editing, until our reflex actions cease to feed the spectacle, which is turning into entertainment, I suppose.
I found a citation in arXiv which addresses "the Culture of physics"; we are witnessing a culture clash, I think. Let's all relax a bit.
See also the following techniques:
-- Ancheta Wis (talk | contribs) 12:19, 9 April 2016 (UTC)
The later parts of this section seem odd to me. Certainly using one symbol as a label, a variable, and as an operator are confusing to newbies. No argument there. It is much less clear to me that it's actually an abuse of notation. When you use a variable name in a label, what you're doing is labeling by a quantity, and getting that quantity from the variable. So if you put an algebraic expression as a label, you're labeling the state with a quantity, and getting that quantity from the algebraic expression.
What else are you supposed to do - declare an entire new set of labels with an algebraic relation to the old labels and then use those? Use the same old labels and Dirac delta a difference between the label's value (which to be consistent must have a different symbol than the label itself) and the value we want? Either of those would be far more confusing, and I am not at all sure that either would actually solve the problem.
And naming the operator after the variable it extracts seems only natural. It has a hat - it's not the same thing. -- 100.14.175.181 ( talk) 12:10, 6 May 2016 (UTC)
What is significance of <B|A|C> A(inner part) in bra-ket notation. Also what does |P,Q> means?
Sorry if this is inappropriate place to ask.. But I was unable to find this on wiki and there is no proper explanation for "inner part" also in there. VaibhaW ( talk) 01:48, 13 October 2016 (UTC)
I'm new to quantum mechanics and dirac notation and I come to this page to learn. However, dirac notation is varied and taught differently depending on the type of background one comes from. I will be less confused if the vector quantities could have arrows placed over the characters. Thanks to whoever accomplishes this! Also, this my first post on Wikipedia--let me know if I'm doing something wrong! — Preceding unsigned comment added by Murphaid ( talk • contribs) 23:24, 1 November 2016 (UTC)
The notation may need further explanation. Coming from mathematics, I wasn't familiar with it and had to search for a while (other Wikipedia articles say it can mean "approximately equal" or "goes toward the limit" which isn't very helpful). It's an important point that a bra/ket is not identical to the actual vector but a coordinate-free representation of it. I like how the German article explains it. Also, is necessary in ? This looks like an equality to me, and in the figure an equals sign is used.-- 92.208.44.56 ( talk) 12:40, 3 January 2017 (UTC)
The Dirac notation was the unification of Heisenberg's matrix and Schrödinger's differential theory into one cohesive whole.
He's idea was that there were (are) many representations of a state or a transformation. This article does not convey Dirac's abstraction.
The misconception of the article: There is belief that p is the operator -i hbar gradient. This is only true in the coordinate basis. It happens to be p in the momentum basis and is some matrix in a given discrete basis. Dirac saw this. He invented the ket as an abstract state that when projected onto a basis would act like a vector (discrete) or function (continuous). Operators were abstract transformations of the states that when projected onto a basis would act like a matrix (discrete) or a differential operator (continuous). He invented the Dirac delta in order to generalized linear algebra to a continuous basis. (Although the Dirac delta is still looked at as NOT making "sense as a mathematical object" by too many mathematicians. See Delta Function talk page!)
These ideas are all in Dirac's book on Quantum mechanics but I think Feynman may have covered it even better.
"The Feynman Lectures on Physics" Feynman, Leighton, Sands. See Chapters 16 and 20. In particular 16-5.
Sure, he was not rigorous (Was Newton? or Leibniz?). But Dirac was a genius. I believe Dirac deserves more credit than the mathematics community on Wikipedia is willing to give. In many aspects he was ahead of the mathematics community and it took decades for mathematicians to catch up. In some ways mathematics still hasn't... — Preceding unsigned comment added by 131.252.127.172 ( talk) 03:31, 6 August 2017 (UTC)
Two things I find misleading:
1) The pedagogy: Since so many students use Wikipedia to help learn concepts that are new to them, I think it is important that Wikipedia editors do their best to convey the ideas in a way that imparts the intended usage of the concept. Sure, this is all just linear algebra but Dirac generalized the idea into a more general algebra to unify Quantum Mechanics. And its not just any mathematical algebra, this algebra describes the world we live in very accurately.
2) The Machinery: In the section "Spinless position–space wave function", it has the p Psi(r) =def "bra r" p "ket Psi". That is not what Dirac defined. It is better to say -i hbar gradient psi(r) = integral "bra r" p "ket r' " "bra r' " "ket psi" d^3x' where "bra r" p "ket r' " = -i hbar psi(r') delta(r- r'). And the delta function and integral "cancel" each other out. Understanding the need for the delta function and integral is important once students begin applying QM (to ideas such as scattering) where we cannot just define the correct relationships but rather we need to calculate them.
This is done very clearly in Feynmans QM lectures 16-5. I hope the editors understand the difference between what the article states and what is explained by Feynman.
Also, it is traditional (standard?) to use lowercase psi for the position wavefunctions and capital Psi for the position and time wavefunctions. — Preceding unsigned comment added by 131.252.127.172 ( talk) 17:42, 6 August 2017 (UTC)
Did you even read Feynman? Your response seems like a knee jerk reaction! — Preceding unsigned comment added by 131.252.127.172 ( talk) 18:28, 6 August 2017 (UTC)
I have had mathematics students make statements like, "Isn't this all just linear algebra." Or "Quantum Mechanics is just Group Theory." True statements but these students are being mislead by the mathematicians. For example, High school physics uses basic algebra. Just because a student knows basics algebra does not mean he/she understands all of High School physics. The are concepts to be learned!
Read Dirac, Read Feynman. There is a difference. The difference is physics. In math you can define. In physics we need to agree with the experiments. Understanding the concepts are important.
Try to understand. — Preceding unsigned comment added by 131.252.127.172 ( talk) 18:43, 6 August 2017 (UTC)
The last psi(r') should have been a gradient! — Preceding unsigned comment added by 131.252.127.172 ( talk) 18:47, 6 August 2017 (UTC)
Yes and no. Isn't one of Wikipedia purposes to help young people become better educated? We need to remember that students use Wikipedia to look up these concepts. Yes, we should make the concepts as simple/straightforward as possible. “Everything should be made as simple as possible, but no simpler.” I think we disagree about where that line is.
Dirac notation is primarily a physics notation, invented to ease physics calculations. Students coming to the page are going to be primarily physics students. Sure, it could be used in linear algebra but that was not its intended purpose and I haven't seen it mentioned in any linear algebra textbook.
"We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations." - Richard P. Feynman 131.252.127.172 ( talk) 21:13, 6 August 2017 (UTC)
I just remembered a book that I think is a good compromise in the treatment of Dirac notation.
"Explorations in Mathematical Physics" Don Koks p. 41-71
He starts with the notion of the inner product of linear algebra and only mentions how it is applied to QM in last few pages at the end of the chapter. Most everything is there. Quite a bit would have to be cut out in order to be more concise. I think is shows the machinery without getting too much into its QM interpretations. Although, I still believe the best way to learn Dirac notation is to use it in the context of QM, I am willing to try to do so without it. If anyone knows of any other books that do something similar, then I am willing to read them. — Preceding unsigned comment added by 131.252.127.172 ( talk) 00:32, 7 August 2017 (UTC)
131.252.127.172 ( talk) 02:26, 7 August 2017 (UTC)
I wrote: "In mathematics, the term "vector" is used to refer generally to any element of any vector space. In physics, however, the term "vector" is much more specific: "Vector" then refers almost exclusively to quantities like displacement or velocity, which have three components that relate directly to the three dimensions of the real world." YohanN7 edited to say "In introductory physics", with the comment "usage far from universal". Well, I had thought it was universal or at least near-universal. What are the counterexamples?
Even if there are counterexamples that I haven't thought of (which is entirely possible), I more confidently object to the term "introductory". For example this usage is rampant in quantum field theory (vector particles, vector fields, as opposed to pseudovector or tensor etc.) and other advanced QM courses (spherical tensor operators, Wigner-Eckart theorem etc.), GR, etc. etc. Indeed, I didn't really fully appreciate this point until taking graduate physics courses. (OK sure, if I had read Feynman more carefully, I would have appreciated it sooner!) So if it's not universal, I vote for saying "often in physics" or "generally in physics" but I don't think we should say "in introductory physics". :-D -- Steve ( talk) 12:46, 14 September 2017 (UTC)