Talk:Mathematical formulation of quantum mechanics/Archive 1

message: The first sentence in this article as just revised is very abrupt! How 'bout a bit of context-setting first?  Michael Hardy 00:16, 16 November 2003 (UTC)
thread_title: Untitled

message: Thr backward reference to 'postulate 4.2' has been lost, after some edit. 
Charles Matthews 15:10, 12 July 2004 (UTC)
thread_title: Other formulations

message: The intro also refers to Schrödinger's picture of an electron as an
extended object.  This I think is historically right, however more explanation is needed on what that means, for instance a phrase such as the electron as an object smeared out over an extended, possibly infinite, volume of space CSTAR 15:14, 19 November 2004 (UTC)
thread_title: Electron as extended object

message: I'm still not satisfied with the introduction of the article, before the table-of-contents.  Some additional explanation:
* Mature physical theories are formulated in mathematical or quantitative language.
* Quantum mechanics represents a departure from the languages used in previous physical theories. 
The nature of that departure should be better explained in the introduction.CSTAR 00:36, 23 November 2004 (UTC)
replies: text:  Oops  and I forgot to sign the comment above ... or something.  CSTAR 17:50, 23 November 2004 (UTC)

text: I certainly don't agree with discussion of the photoelectric effect here; it's not quantum mechanics, in the sense that the mechanics only came around 1925. So I think I agree with the comment above (?). By all means write something about the 'old' theory in another article. But the continuities there seem to me (not an expert) to be in the physics, while in the mathematical formulation there was more like a break. Charles Matthews 17:44, 23 November 2004 (UTC)

text: The introduction now is certainly a lot better.  Your changes address my concerns.  Thanks. CSTAR 19:05, 23 November 2004 (UTC)

text: the name old quantum theory is what you find in physics textbooks. There can be more 'professionally-named' articles about the subtopics, such as Bohr model and Bohr-Sommerfeld quantization. — Miguel 20:41, 23 November 2004 (UTC)
thread_title:  Article introduction 

message: The assertion about the relation between separability of H and sufficiency of countably many observations is interesting, but may require more elucidiation. However, how is it related to epistemology?  I assume one could argue that there are sequences of observations Ai which ultimately distinguish a pair of states.  The problem with such a claim is that it will be inevitably subject to much critical examination.CSTAR 20:38, 24 November 2004 (UTC)
thread_title:  Epistemology and separability 

message: I did want to make one point: I object to formalism in relation to mathematics. It obscures a distinction: it can mean a notation, or I suppose it can mean the result of a formal development of a topic. There is a big problem in relation to mathematics/physics (I think) in that 'formal meaning' means opposite things depending on who you are. 'Mathematical formulation' implies to me that bra-ket notation is not just a formalism, but something with a very definite semantic content. Dirac's delta function was a formally-introduced symbol; then we had what you could call 'mathematical formulation of generalised functions' and δ(x) is a Schwartz distribution with a definite semantics. I realise it depends which side of the fence you stand, whether this is an issue or not. Given the article's title I feel that 'formalism' could be banished. 
Charles Matthews 09:32, 26 November 2004 (UTC)
replies: text: The article formalism does not address this, but it would help me if I could read an article about it. —Miguel 16:00, 26 November 2004 (UTC)
replies: text:  I put in a bullet in formalism.  This probably should be expanded in an article such as scientific formalism.CSTAR 18:03, 26 November 2004 (UTC)

text: Point taken.  I think we should address this concern.  I tend to melange the two, but I am aware of the distinction and am also picky about it when I notice.CSTAR 14:20, 26 November 2004 (UTC)
thread_title:  "Formalism" 

message: It would be nice to find out how in the world Heisenberg stumbled upon matrix mechanics. I just don't see how that would be likely. I can understand how Schrödinger came up with wave mechanics. That's a pretty natural consequence of de Broglie's ideas, but how did Heisenberg come up with matrix mechanics? Phys 05:37, 29 November 2004 (UTC)
thread_title:  Old quantum mechanics 

message: I don't think this particular graf on E, t belongs here in thiis article, maybe in a separate article about issues in canonical quantization.CSTAR 21:36, 29 November 2004 (UTC)
thread_title:  Whatever the merits 

message: I am pretty happy with the article at this point. I think I am going to move on to quantization or something like that. — Miguel 07:05, 30 November 2004 (UTC)
thread_title:  ready to move on 

message: It's really equivalent to the mathematical machinery of quantum operations (via the Stinespring-Choi-Kraus represntation theorm).CSTAR 15:47, 30 November 2004 (UTC)
thread_title:  Relative state interpretation 

message: This is still an introductory article. Given that, why does it include the following sentence in the symmetries section 
: Gauge symmetries are not exactly and are dealt with in a more complicated manner using BRST.
::This is actually about field theory - yank it from the article, or put it in the "later developments" section. — Miguel 21:07, 11 December 2004 (UTC)
thread_title:  Symmetries 

message: What's all this stuff about irreducibles? One is interestd in the 
primary decomposition = factor decomposition = central decomposition = decomposition into multiples of irreducible representations (in type I case)
not so much of the group of symmetries as of the group of symmetries + algebra of local observables which it normalizes.
CSTAR 03:19, 27 December 2004 (UTC)
thread_title:  Decomposition of reps of symmetries

message: Please try not to mix history with theory , when someone is reading theory, he doesn't
need to read names of scientists and dates interspersed in between, it would
be much better to have a seperate section for all historical events, who did what and when etc...
Thanks  —Preceding unsigned comment added by 41.235.85.72 (talk) 23:38, 17 May 2008 (UTC)
thread_title:  Mixing history with theory 

message: bra-ket notation (a convention for brackets, denoted "<bra | ket>", later to be re-used in http's html) 
:I refer specifically to the HTML element#Links and anchors "A" form
:<A URL> Text displayed for the HTTP link</A>
:which clearly shows the provenance respected by Tim Berners-Lee, who was at CERN where the bra-ket notation is well-known and very complicated QM expressions involving multiple items follow this form.  --Ancheta Wis 16:51, 29 December 2005 (UTC)
replies: text: I am sorry, but I find this justification extremely weak. Anyway, the proper place to mention this connection in my opinion is bra-ket notation, but if you do not have more direct proof, I'd rather that it isn't mentioned at all. -- Jitse Niesen (talk) 15:04, 3 January 2006 (UTC)
thread_title:  [[bra-ket notation]]  

message: How does one go back and signed unsigned comments? Thanks. Mct mht 08:23, 3 April 2006 (UTC)
replies: text: Use the substituted Template:unsigned.  That is, where you want to put a signature, insert . -lethe talk [ +] 13:25, 3 April 2006 (UTC)
thread_title:  Sign unsigned 

message: Can anyone translate this for me?  I think it is a little over the head of the most of the world.
71.71.124.75 01:12, 18 September 2006 (UTC)
replies: text: Why are you trying to read "Mathematical formulation of quantum mechanics" rather than "Introduction to quantum mechanics"? —Keenan Pepper 19:08, 20 September 2006 (UTC)
thread_title:  English? 

message: This article, at least as far as I got into it, had been written with a tone wholly inappropriate for wikipedia.  A lead is supposed to summarize the information of the article, not expound on how remarkable the stuff it's about to talk about is.  It badly needs a rewrite to bring it into a style free of overwrought prose that hides the facts. Night Gyr (talk/Oy) 08:38, 17 October 2006 (UTC)
replies: text: seems pretty good to me. the intro gives a overview of the history and does give a summary. how exactly does it "expound on how remarkable the stuff it's about to talk about is" and "hides the facts"? Mct mht 09:28, 17 October 2006 (UTC)

text: the first coupla sentence alludes to it. the subject matter requires laying out some background. how would you write it? Mct mht 09:56, 17 October 2006 (UTC)
replies: text: Any necessary background would be technical; I don't think the history is necessary to say what comes in the final sentence of the first paragraph.  Isn't there a second half to the sentence "The mathematical formulation of quantum mechanics is..." or if there's more than one a slight variation? Night Gyr (talk/Oy) 10:02, 17 October 2006 (UTC)
replies: text: one can fill a volume completing that sentence (see references). a short summary would be along the lines of "Mathematical structure of quantum mechanics" section in article. seems to me that starting the article saying "The mathematical formulation of quantum mechanics is that the state space of a quantum system is a subspace of a Hilbert space, and observables are..." is not advisable. Mct mht 17:54, 17 October 2006 (UTC)

text: I totally disagree with Oy's assesmnent.  History is important, even for an encyclopedia article. Frankly, this is one the oddest criticisms I have ever heard. --CSTAR 14:54, 17 October 2006 (UTC)

text: second above. history is important for this particular article. i am gonna remove that tone tag (article can always use knowledgable copyedit). Mct mht 17:54, 17 October 2006 (UTC)
thread_title:  tone 

message: The 2nd graf currently starts off with 
:This formulation of quantum mechanics, called canonical quantization, continues to be used today, and still forms the basis of ab-initio calculations in atomic, molecular and solid-state physics.
Canonical quantization I that referred to an attempt at "functorializing" the relation between classical and quantum mechanics.  It is one area of MFQM, but the sentence seems to suggest this is equivalent to it. Am I misunderstanding something here?--CSTAR 17:26, 19 October 2006 (UTC)
replies: text: maybe remove that phrase from the sentence. a brief note explaining how one goes from CM to QM via quantization, with link, can be added somewhere. Mct mht 05:02, 20 October 2006 (UTC)
thread_title:  Canonical quantization 

message: "the Copenhagen interpretation of quantum mechanics which held until the Many Worlds Interpretation which resolved its many paradoxes."
Is it true that the many worlds interpretaiton of Quantum Mechanics is the favored interpretation? As far as I know, the Copenhagen interpetation is still the most favored one and according to the page of the many worlds interpretation there are presently no way found to distinguish one from the other.
--Sikory 15:44, 15 July 2008 (UTC)
replies: text: I only discovered your question today. I think your reservations with respect to the many worlds interpretation are justified. I have attended many conferences on the Foundations of Quantum Mechanics, but I cannot remember to have met any physicist who took the many worlds interpretation seriously. Contrary to the many worlds interpretation most physicists take von Neumann projection seriously, either as something "really" happening to an individual microscopic object, or as a selection of a subensemble (within an ensemble interpretation). In my observation the general feeling is that the many worlds interpretation is not backed by any observational evidence, and is just explaining problems away.WMdeMuynck (talk) 13:39, 13 September 2008 (UTC)
thread_title:  many worlds resolved paradoxes? 

message: The article says: "Many of these structures were drawn from functional analysis, a research area within pure mathematics that developed in parallel with, and was influenced by the needs of, quantum mechanics."
Is this true? Functional analysis was founded by Stefan Banach, a pure mathematician who was not interested in physics. So considering that it was not founded with any intention of being used for quantum mechanics but rather it was applied to quantum mechanics by physicists after it had been developed, how can it be claimed that it was "developed in parallel with, and was influenced by the needs of, quantum mechanics." selfwormTalk) 06:37, 13 September 2008 (UTC)
replies: text: Yes by most accounts it is true. Stefan Banach developed one area of functional analysis, but Weyl's and von Neumann's contributions to functional analysis (for instance Rings of Operators) were most certainly influenced by applications to QM.--CSTAR (talk) 18:26, 23 October 2008 (UTC)
thread_title: Functional analysis

message: Isn't this an axiom implicitly assumed for the probability amplitude function? --82.112.218.84 (talk) 12:44, 22 October 2008 (UTC)
thread_title: [[Probability flux]]