Talk:Stochastic quantum mechanics

First paragraph says "A stochastic interpretation of quantum mechanics due to persistent vacuum fluctuation." which is not a complete sentence....not sure how to fix. Vinniefalco (talk) 03:02, 26 July 2018 (UTC)

Needs work.

Just some of the issues with this page:

• Intro does not summarize article. Most of the intro content is not even discussed.
• No physical model discussed.
• No comparison to other models.
• Topics seem to be in random order.
• Can't decide if its physics or math.

Johnjbarton (talk) 16:38, 13 December 2023 (UTC)

I wonder about the 'quantum foam' part of the introduction. Does it really belong to this article, or would it be enough to discuss it on quantum foam? Is there a connection to stochastic mechanics? Jähmefyysikko (talk) 17:19, 13 December 2023 (UTC)

It's unreferenced, and out of place IMO Johnjbarton (talk) 18:51, 13 December 2023 (UTC)

I removed it. If spacetime fluctuations really are thought to be the underlying process here, it should be restored with references. Jähmefyysikko (talk) 19:55, 13 December 2023 (UTC)

I suspect that the article referred to a paper by Calogero from 1997. I agree that the text seems a bit out of place, so I agree with the omission. FJKuipers (talk) 16:56, 14 December 2023 (UTC)

I completely agree that the article needs work. I have started to make some improvements over the last months, but this is far from complete. I warmly invite the contribution of other authors, as the article may benefit from different perspectives.

Here is an incomplete list of my suggestions for possible additions:

- Historical overview. Since its introduction, the topic has been subjected to a small but continued interest in the physics community. It could be instructive to describe its development from the early days into the current theory, and refer to related developments in the physics literature.

- Discussion of the issue regarding multi-time correlations (cf. e.g. Nelson (1986)) and its solution.

- Relativistic stochastic mechanics.

- Stochastic mechanics on curved space(times).

- Discussion of simple examples, such as the harmonic oscillator in 1 dimension.

- Stochastic interpretation of quantum mechanics developed within stochastic mechanics. E.g. causality, locality, status of the wave function, measurement problem, Bell inequalities.

- I suggest to change the title to Stochastic mechanics, which is the term commonly used in the literature.

- Replacement of Stratonovich/Ito Lagrangian with first and second order Lagrangian (following terminology from Huang, Zambrini (2023)). (N.B. A discussion of the Lagrangian constructed by Yasue and Guerra and Morato, could be a nice addition to the suggested history section).

- Add a link to the page on the Kronecker delta, where it is first used.

- Start the stochastic quantization section directly with the general case.

Some responses to the earlier suggestions:

- The intro certainly needs improvement. Indeed, it does not cover the remainder of the article.

- The statement `no physical model discussed’ is vague. The article describes stochastic mechanics, which is a framework for deriving the equations of motion for a stochastic particle subjected to various forces. Two main applications of this framework are mentioned: description of Brownian motion and of quantum mechanics.

- Again, please clarify to which models you would like to compare.

- In my opinion, the main sections are presented in a rather coherent way: first, the relevant physical principles are stated; then, the equations of motion resulting from these principles are discussed. The presentation heavily relies on stochastic calculus and Lagrangian mechanics. Not all readers may be familiar with this, but there are plenty of references to other pages, where more details are given. Of course, any specific suggestions for improvement are welcome.

- The topic lies on the interface between mathematics and physics, as it has been developed by several mathematical physicists. Additionally, the topic has received interest in the foundations of physics community, but this is currently not much discussed in the article. It would be good to provide more input from these works. FJKuipers (talk) 17:32, 14 December 2023 (UTC)

Wikipedia "introduction" (top section) are really intended to be be summaries of the article, an aid to readers (do I want to read this? What parts are interesting?). That means the intro does not "set the stage" and often articles need an "overview" or "history" section for that purpose.

To a reader, the first section is "Stochastic Quantization" which starts "The postulates of... ". I'm sure the math is dear to your heart, but I immediately stopped reading at that line. I know a lot of math but in my experience with Wikipedia, the math is pointless. It requires quite a lot of background to read the math and appreciate how it relates to the physics. The math has very little "leverage": it's like reading the code for a computer game rather than having someone explain what the game is about and why it is fun. I want to read: What is stochastic mechanics about and why is it fun? If I get an interesting answer I will learn the math.

Scroll through the article: after several pages of math you come upon "Mathematical aspects". Most readers will be "really? finally some math? hah!".

"Not all readers will be familiar with this" is way off the mark. This is an encyclopedia. The first part of physics articles should be accessible to undergrads with an interest in physics because that includes the vast majority of readers. The article should not explain stochastic calculus and Lagrangian mechanics but it should have a sentence or two describing what they are, where to read more, and how they are related to the topic.

Hope this helps. Johnjbarton (talk) 18:30, 14 December 2023 (UTC)

There's constructive criticism and then there's this..

I'm sure the math is dear to your heart, but I immediately stopped reading at that line.

That's your prerogative. I personally almost never read the intro or history and go straight to the (mathematical) definition. That's how I instantly know if the page is of any use to me, especially when I have to go through lots of pages.

I consider this page to be a work in progress which, IMHO, could already benefit from a better section/subsection/subsubsection layout. Like you said, wikipedia is an encyclopedia. This has the benefit for FJKuipers that he can make improvements, big or small, whenever he feels like it. There's no deadline. He also has to realize that he's probably one of the few people with extensive knowledge on the subject. I really enjoy his enthusiasm and diligence, but he does have to realize that he will have to do most of the work himself.

Which leads me to WP:BEBOLD, to which I might add:

I want to read: What is stochastic mechanics about and why is it fun? If I get an interesting answer I will learn the math.

If that's what you want to read, then feel free to improve the page to your liking. Roffaduft (talk) 05:33, 15 December 2023 (UTC)

Dear @Johnjbarton and @Roffaduft, thanks a lot for your feedback.

I agree with @Johnjbarton that Wikipedia articles should strive to cater to a wide audience, even for topics that require some knowledge prerequisites. Of course, as @Roffaduft points out, this includes both people interested in technical aspects and people interested in the `bigger picture’. It is absolutely true that in the current article the bigger picture is largely absent and should be added. @Johnjbarton suggestion to add some more explanatory lines in the technical sections is very useful.

The current intro is more or less the text that was there, before I started adding more text in August. So far, I have tried to leave this earlier text intact as much as possible (I have only removed a section on stochastic electrodynamics, as there is another article on that topic). Now might be a good moment to adjust this text such that it covers the content of the page.

P.s. I think that the title of the section `mathematical aspects’ is poorly chosen (atm I just don’t have a better suggestion). Also this section might be expanded with a discussion of uncertainty relations and a `derivation’ of the commutation relation (similar to the stochastic derivation on the page Path integral).

The page is indeed work in pogress, and I apologize for the slow progress, but unfortunately time is limited. FJKuipers (talk) 09:49, 15 December 2023 (UTC)

Thanks. BTW I did not mean to imply personal criticism, I was just trying to give an different perspective on this article. Johnjbarton (talk) 16:45, 15 December 2023 (UTC)

The new intro and section are a huge improvement thanks! The very first sentence however left me with a puzzle:

• "dynamics of stochastic particles".

What are these and why do I care? I'm imagining something like

• "dynamics of stochastic particles, particles subject to an intrinsic random processes as well as various external forces".

Johnjbarton (talk) 16:57, 17 December 2023 (UTC)

Thanks! I think your sentence is spot on, so I have changed this part accordingly. Also, the requested citation has been added. Thanks for all the feedback. This really helps in improving the article more efficiently. FJKuipers (talk) 08:15, 18 December 2023 (UTC)