User talk:Roffaduft

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November 2023

Hello, I'm PiGuy3. I noticed that in this edit to Quantum state, you removed content without adequately explaining why. In the future, it would be helpful to others if you described your changes to Wikipedia with an edit summary. If this was a mistake, don't worry, the removed content has been restored. If you think I made a mistake, or if you have any questions, you can leave me a message on my talk page. Thank you. PiGuy3 (talk) 08:12, 9 November 2023 (UTC)

"rays" belong to projective hilbert spaces. See: Projective Hilbert space and Mathematical formulation of quantum mechanics. I've removed the references as Weinberg referred Hilbert spaces as "a kind of complex vector space" while Griffiths in footnote 6 of page 95 explained that his wording is not mathematically correct.

Furthermore, I've changed the math notation in order to avoid confusion with "probability" mentionned earlier on the page Roffaduft (talk) 08:23, 9 November 2023 (UTC)

Thanks for the much more detailed edit summary, I agree with your changes now. PiGuy3 (talk) 08:33, 9 November 2023 (UTC)

Regarding your recent edits on wavefunction article

Hey, I noticed your recent edits on wavefunction article. It seems like you're deleting paragraphs without checking if the content in them are discussed elsewhere. You seem to have removed the mention of Born rule without checking if it is also used in the redundant section and also a note on Von Neumann's construction. I make this post to tell you to please considering moving content before you remove them. I get that historical aspects of physics and interpretations of physics are of no concern and maybe even distracting to a mathematician but they are still relevant for a physics article. Hope you can agree with that.

Thanks for understanding! EditingPencil (talk) 08:48, 18 November 2023 (UTC)

You seem to have removed the mention of Born rule without checking if..

As noted in the summary, Born rule is mentionned several times in the article so I really don't understand your critique (a simple 'ctrl+f' would've sufficed).

Regarding the historical context: There is a nice subsection for that in the article called "Historical background". If you like to add historical aspects, that's the place to put them. Roffaduft (talk) 09:00, 18 November 2023 (UTC)

Born rule is motioned in text, and at the bottom of the article. Basically everywhere except the place that it is actually used. No need to be pedantic about this, it's just silly to talk about interpretation of QM without referring Born rule. I would edit it myself but I don't know if it will fly by you. EditingPencil (talk) 09:32, 18 November 2023 (UTC)

That's because you felt inclined to accuse me of randomly making edits without checking, even though that's clearly not the case given the edit summary. You'd also know if you did a simple search for "born rule" in the article before you send your reply. That kinda rubs me the wrong way.

I don't "just make edits". I leave stuff in place when I'm not sure. Also, I try to engage in conversation when I'm not sure about an edit. For instance, about "proper vectors". I also make an effort to look up the sources you mention, to get an understanding of what it is you mean.

The core of the problem is that I'm a mathematician and you're a physicist. There's a nice section of a lecture by Feynman on youtube: "Mathematicians versus Physicist"; one complements the other. I think that should be our starting point going forward. My apologies for sounding pedantic. Roffaduft (talk) 09:44, 18 November 2023 (UTC)

Hey, sorry for appearing overtly confrontational. It's not my point that you are doing this out of malice. TBH I can't deny that I'm biased because of previous arguments and the Von-Neumann thingy and not merely the isolated case of the Born's rule thingy, but I felt like its a pattern we can talk about anyway. I don't think there is any harm being extremely conservative on what goes onto an article but that can often slow down the state of the article. Just that sometimes it makes people's life hard unnecessarily when it can be easily avoided if one thinks practically and lets someone else improve 'problematic' (which I may disagree on) language instead of removing them. Anyway, I think I will let you decide if you want to add either of these edits yourself. I don't think its a big deal but it seems likely that you may run into troubles with more people like this.

Hope we are cool. Sorry for the troubles! ^^ EditingPencil (talk) 10:06, 18 November 2023 (UTC)

We're cool ;)

In the spirit of cooperation:

1. Wouldn't you agree the section "finite-dimensional Hilbert spaces" is better placed as a subsection of "Wave functions and function space"?

2. Placing the subsection "Wave functions and function space" above, say, the section "Time dependence"?

I think it goes much better with the flow of the article. Also, in future, i think its unavoidable to having to introduce some concepts from spectral theory, especially that of the discrete and continuous spectrum. Moving up the "Wave functions and function space" section is a good premise for that. (though that is better discussed on the talk:wave function page) Roffaduft (talk) 10:31, 18 November 2023 (UTC)

Alright, sweet. ^^

1. Maybe not because (a). That section introduces convention as well as mathematics to be used in the next section. (b). Also, sometimes in physics spatial wavefunction is ignored entirely when talking about separable Hamiltonians (since it acts on each independently of one another). So, that's from a finite dimensional Hilbert space and it fits 'other cases' section. (c). I feel like spin is just as much as a part of wavefunction as spatial wavefunction. I'm not sure if position enjoys a special role in physics so I don't see why spin should be an afterthought of spatial properties of wavefunction. I think spin deserves a mention in "Wave functions and function space" section though where it discusses finite dimensional Hilbert space since that's the bit relevant to physics.
2. Hm, this one I'm not sure. I think it was left there since most people visiting the page don't care about the details. Even if I personally agree with you, I think it is more convenient for majority of people to let it be where it is. What do you think?

And yeah, I agree with you on the last part too. I'm excited for any plans to improve the last section. Admittedly this task seems too daunting for me to take on or provide meaningful input given my limited understanding of functional analysis lol. EditingPencil (talk) 10:57, 18 November 2023 (UTC)

I'm kinda running out of ADHD "wave function"-hyperfocus for today, but I'll probably make a topic about this on the wave function talk page soon. The main issue I have is that (generalizations of) Hilbert spaces are being introduced over and over again in the article. The above suggestions were a first attempt to start fixing this issue; improving the coherency of the article. Roffaduft (talk) 11:09, 18 November 2023 (UTC)

Hm, that's fair. EditingPencil (talk) 11:11, 18 November 2023 (UTC)

Also, i do understand the importance of the physicists interpretation of mathematics. I only remove it when it is clearly incorrectly formulated or redundant.

e.g. Von Neumann doens't "define a Hilbert space". He may have considered a type of Hilbert space, but that is something different. It's like saying: Von Neumann "defines stars as a type of moon".

Regarding the rest of that note: It is all covered under the redirect "separable Hilbert spaces", which I purposefully left intact. Roffaduft (talk) 09:16, 18 November 2023 (UTC)

You could've made this sentence pedantic-free and added it to the Hilbert space section of the article but you chose to remove it. These are what I consider aggressive edits. I think its better to be more passive and co-operative. Just my opinion though, so that we won't have to argue about less than a dozen words every time, unnecessarily. EditingPencil (talk) 09:29, 18 November 2023 (UTC)

I won't touch it though. It's fine if this material is off-page. But this is just a pattern that I have concern about since the last time we argued. Also apologies, if this has been unhelpful. EditingPencil (talk) 09:38, 18 November 2023 (UTC)

Just wanted to let you know I was wrong about this one.

_{e.g. Von Neumann doens't "define a Hilbert space". He may have considered a type of Hilbert space, but that is something different. It's like saying: Von Neumann "defines stars as a type of moon".}

I've just read (part of) Von Neumann's original paper "Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren" (General eigenvalue theory [for] Hermitian operators). You can indeed say that he was the first to use the term "Hilbert space". That is: the mathematical concept was studied before, but he was the one who referred to it "den abstrakten (komplexen) Hilbertschen Raum" (the abstract (complex) Hilbert space).

Ergo, my remark was premature. My apologies. Roffaduft (talk) 12:21, 18 November 2023 (UTC)

It's still infinite dimensional right? IIRC its isomorphic to l^2 sequence space so it can't be finite dimensional. So technically, it's a specific construction of a more general Hilbert space that includes finite dimensions, right? Anyway, it's very cool that you went back to his original work.

PS It's mentioned in the sequence space too. EditingPencil (talk) 12:35, 18 November 2023 (UTC)

Von Neumann defined 5 criteria, 4 of them basically correspond to being separable (which is a consequence of the choice of metric) and a complete inner product space. The other:

• "H besitzt beliebig (endlich!) viele lin. unabh. Elemente; Hierdurch wird die Möglichkeit, dass H ein endlichvieldimensionaler Euklidischer Raum sei, ausgeschlossen"

Which is German for: H is infinite-dimensional. You can say that:

• $\infty$-dimensional + separable $\Leftrightarrow$ isomorphic to $\ell ^{2}$ $\Leftrightarrow$ has a Schauder basis $\{b_{k}\}$ for $v=\sum _{k=0}^{\infty }\alpha _{k}b_{k}$ in $H$
• $N$-dimensional + separable $\Leftrightarrow$ isomorphic to $\mathbb {C} ^{N}$ $\Leftrightarrow$ has a Hamel basis $\{\mathbf {b} _{n}\}$ for $v=\lambda _{1}\mathbf {b} _{1}+\cdots +\lambda _{N}\mathbf {b} _{N}$ in $H$

It's fairly easy to see that on a finite field (i.e. $\{\alpha _{i}\}_{i=N+1}^{\infty }=0$), the former reduces to the latter. However, the converse is not possible. This is why the infinite dimensionality is so important in order to classify the Hilbert space as a generalization of the finite-dimensional case.

Once you've done so, however, you can always say that the finite-dimensional case is a specific example of a Hilbert space. For an infinite-dimensional Hilbert space, a specific example would be e.g. the $L^{2}$ space, or the H²-space Roffaduft (talk) 13:29, 18 November 2023 (UTC)