Talk:Introduction to gauge theory

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Further explanation necessary

@Himaldrmann I'm putting your edit summary here:

Aharonov–Bohm experiment: I think that this is unclear—and the preceding comment about which quantity is "fundamental" (field or potential), as well as the succeeding "Explanation with potentials", are also—to a general reader. To wit:

• In the introduction, it is stated that these fields are unobservable: only quantities associated with them are observable (for example, one might infer, electrical potentials in an electrical field). A paragraph later, it is explained that the fields are observable and potentials are not: 'In field theories, different configurations of the unobservable fields can result in identical observable quantities. [ . . . ] For example, in electromagnetism the electric field E and the magnetic field B are observable, while the potentials V ("voltage") and A (the vector potential) are not.' This is confusing, and compounds the later uncertainty (see below), IMO.
• If a field is composed of potentials: 'A static electric field can be described in terms of an electric potential (voltage, V) that is defined at every point in space . . .' ... then, when one asks: '. . . whether it [is] the fields E and B or the potentials V and A that [are] the fundamental quantities', what differentiates the two possibilities—what distinction is then being drawn?
• Similarly, in the description of the Aharonov–Bohm effect, what is meant by: 'It is the electric potential that occurs here, not the electric field'...? In the preceding set-up, it was said that the electron would be exposed to an electric field; the natural thought, then (to me, anyway), is "aren't both 'occurring'?" (note: not sure if "occurs" is the word that we want to use, either... but as said, I'm just a dilettante & my own understanding may be flawed.)
• In the next section, we have: '. . . we can see that the gauge transformations, which change V and A, have real physical significance, rather than being merely mathematical artifacts.' This is the only part that I'm completely sure of my own understanding... being incomplete, that is; heh. I.e., as is mentioned in the subsequent part of the article about clock-faces, I had understood "exposing only one side of the apparatus to an electrical field" to not be a "gauge transformation", and that it is the new difference in phase that causes the experimental results to differ rather than choosing a different gauge...
• ...and, as most of the article talks about gauge invariance with examples re: how the choice of ground is relative, and so on, this means the reader has likely understood the concept in such terms heretofore—only to have an implication along the lines of "so, as you can see, gauge transformations are a physical manipulation one can perform to change the result of an experiment" thrown at him/her!
• TL;DR, it hence seems to me that the following are unclear:
  • (a), what is meant by "fundamental" in this context—if I weren't somewhat familiar with the lingo from my dilettanting, so to speak, I think I'd have no idea!;
  • (b), what distinction is being made between a "field" [being fundamental] and "potentials" [being fundamental] (and maybe something could be thrown in to clarify why it is often said that the fields of QFT are about as fundamental as one can get, and what e.g. an electrical field is if the way I was taught to conceive of them—as a collection of electrical potentials, at each point over some volume—is wrong!);
  • (c), how the Aharonov–Bohm experiment demonstrates that fields are not fundamental; and
  • (d), how to distinguish between a gauge transformation and a different experimental manipulation.

(Please note that I'm not saying it's a bad article; and perhaps I'm just dumber than most, or my previous readings are confusing me whereas someone who started from scratch here would learn gooder than I have; I just figured that those who know more might find it fairly easy to rectify these possible confusions! Cheers.)

Comments like this are better in the Talk page where people can see them. Johnjbarton (talk) 17:18, 16 December 2024 (UTC)

Thanks, amigo. I think you're right—I would have been able to expand on exactly what I thought was unclear or confusing; I've edited the comment to reflect what I had wanted to put as my edit summary, had I the space! Hopefully, someone will come along and see what I mean (...or else say "what? himaldr bro no one would think of this dumb stuff that's all you", either/or–)

Himaldrmann (talk) 03:01, 17 December 2024 (UTC)

Thanks. In future please just reply. Do not edit other people's posts on Talk pages, its bad form: WP:TPO. Johnjbarton (talk) 17:21, 17 December 2024 (UTC)