What is gauge theory.If you can't explain it simply, then you don't understand it.
>>16920373What do you mean by "simply"
>>16920373>dude, invariancenice hat, though
>>16920373Try asking an AI
>>16920373Check out wikipedia and ask AI to summarize it for you and then another AI to summarize the summary if you still struggle.
>>16920381He means using simple language that anyone can understand.
>>16920373Theory of how forces work.>inb4 gravitysee tetradic Palatini action
>>16920373>If you can't explain it simply, then you don't understand it.False and gay. Like most things in maths/physics, you can't understand it if you can't do the maths. If you can do the maths, you're already close to understanding it and won't need 4chan's help. If you just want to feel like you "understand" it then ask AI.
>>16920373symmetry
Ask AI
>>16920373You pinch the reservoir tip and roll the base down
>>16920373imaginary sombreros
>>16920373a theory about gauges
>>16920500>>16920535>>16920393>>16920408HOLY SHIT NIGGERS FUCKING KILL YOURSELVES
>>16920658The absolute fucking state of this board. You do realize that literally no one worth their salt cares about your retarded hallucination slop machines, right? Just because they give you endless compliments and validate your bullshit doesn't mean this board should be filled to the brim with AI slop by idiots like you and advertisements for said slop.It's called "AI slop" for a reason.
>>16920663Which is why OP is mocked and told to fuck off.
>>16920373Is this the physics of a mexican hat?
>>16920373pic related seems to be foundry drawings about the chinese bullion|tael.
>>16920373Ask grok, saar
>>16920664this, also sorry I have to spoonfeed the fucking idiot OP for one secondOP is fucking retarded and doesn't understand people are telling him to "ask AI" because it's a /sci/ culture way of saying "you're fucking retarded please kill yourself"TL;DR, sorry OP, maybe you should also ask the AI why everyone is telling you to just ask AI you fucking clown
>>16920393>>16920535The hat is a sombrero.
well, gauge theory starts with an observable, in this case the norm of the wave function, psi* psi (psi wavefunction, * Hermitian transpose).This expression, which is a function of space and time, is a probability density, more precisely the probability that a particle will be at a certain position at a certain time.Now this expression (psi* psi) has a natural symmetry, namely it is preserved when psi is replaced by U psi, where U*=U^(-1) is a unitary operator. This symmetry is called a global symmetry. U does not depend on space or time.Gauge theory is essentially the effort to extend this global symmetry to operators U which DO depend on space and time. This is then called a local symmetry. This requires replacing derivatives with modified versions of them, similar to how the acceleration (time derivative of the velocity) of a particle gains additional terms (fictitious forces) in a rotating frame.In these modified derivatives, there are fields involved, the so-called gauge fields. Although one may think they are somewhat an arbitrary construct, it turns out that these are actually quite interesting by themselves. Indeed, one of the simplest gauge theories, when psi is a complex scalar function, corresponds exactly to electrodynamics and reproduces Maxwell's equations. neat! Different from Maxwell's equations, which were found well before anyone thought of gauge theories in the modern sense, afaik all higher order gauge theories (when psi is a n-dimensional complex vector), were found basically by exploring the corresponding gauge symmetries (invariance under these modified derivatives). In short, gauge theory is a tool to derive physical theories from generalizations (global to local) of the natural symmetry of the quantum wave function.
>>16922548Hey retard, there's a built-in TeX editor. Use that instead of flooding the thread with unformatted garbage, dyke.>>16921813>muh aikys>>16921778>muh aikys
>>16920373you know when your dad puts up his thumb and closes 1 eye to gague distance? it's nothing like that but there's a word overlap.
>>16922548neat!
It's what you get when you use scale invariance as a basic principle, only more so
>>16920373this idea that if the math gets too complicated and you start being able to use different numbers to reach the same result that you should cower away and give up and artificially truncate your equations to make them simpler, not further constraint your experiment to discount arbitrary version of A
>>16920500If you can do the maths without being able to explain it in simple terms you're most likely engaging in pure mental masturbation because the original physical assumptions the original model was valid under were silently forgotten 10 authors ago in a pursuit of fancier and prettier math and you can't see being obscured behind all the mumbo-jumbo that you only know and blindly trust.
>>16925806That's not what I said. Doing the maths is a prerequisite for understanding. Once you can do the maths, deeper understanding is possible.
>>16925813>Doing the maths is a prerequisite for understanding.You got it backwards. Math is just a tool to gain deeper understanding and to quantify it, as you correctly say next. But if you can't tell what you're doing without falling back to math (which would be a circular reasoning) then you don't understand it.
>>16925826No, I didn't. If you think you can "understand" maths, physics, chemistry etc without the maths then you're a delusional retard.
>thread posted two weeks ago>not one real answer in any of these postsbig oof
>>16925828You're conflating learning something and using that knowledge in practice. The latter indeed usually requires math because you want a specific answer only math can provide. But when learning the idea behind something (or explaining to someone unfamiliar with it) math is only an unnecessary layer of abstraction that obscures the concept and confuses the person trying to learn it. It also doesn't help that mathfags insist on everything being rigorous which more often than not turns a very simple thing that a toddler can understand into a boatload of incomprehensible garbage while adding nothing of substance for a first time learner.Naturally you must be able to explain the thing without involving math because math is not the thing itself. If you can't do that then you only know math but do not understand the actual thing it describes.
>>16926047No, I'm not. If you don't understand the maths you don't understand anything. Maths is a language and a much more powerful one than wordies.
>>16926068Understanding math doesn't mean you really understand anything either. It's just a model, often grossly simplified under certain assumptions that make it still physically valid within distinct boundaries. If you don't understand the actual thing being modeled before any math is involved you'll easily overlook those boundaries and veer off into a world of mental masturbation where your math may look pretty but doesn't make any practical sense.
>>16926073Yes, I didn't say that it does, AS WE ALREADY DISCUSSED. I said it's a prerequisite to any understanding.
>>16926084>it's a prerequisite to any understandingNo it is not, AS WE ALREADY DISCUSSED. You're putting the cart before the horse.
>>16920373Made a similar thread awhile back about spin, just got schizobabble in response, the cleanest answer was that it is just a mathematical abstraction that sort of correlates with angular momentum. That was the best. The whole thing feels like a house of cards
>>16926087Go ask grok about it, maybe it'll tell you something you like better.
>>16926089It really isn't but people like you and OP are hardly worth talking to so only the schizos reply. I mean, look at the conversation he had with the other Anon about math. The take that "if you understand something you can explain something in simple terms" (which is correct) does not imply "if you are explained something in simple terms by someone who understands, you too will understand". Statement 1 is true, statement 2 is not only blatantly false but also the prime reason those schizos and dunning krugertards shitting up the board exist in the first place.
>>16926047You are conflating two things, actually: parroting and deriving. Understanding comes not from reciting someone else's explanation of a subject but from deriving one yourself. If you hear someone else's simple explanation you have not come to understand the subject; you have merely gained an initial foothold.
>If you can't explain it simply, then you don't understand it.ok so it sounds like you don't understand it. what specifically don't you understand. be very specific. you won't.
>>16926103>you have merely gained an initial footholdWhich is the real prerequisite for understanding. Math is just extra hurdle at this point.
>>16926109>prerequisite for understandingthat you acquire.. how?
>>16926110You don't if you can't get a foothold first, which is what a simple explanation is for.
>>16926111You don't if you don't have the math to continue working from there. Yet, strangely, there WERE people who did not have a simple explanation handed to them yet succeeded in developing one through math.Disagreeing with "Math is a prerequisite for understanding" implies you think "you can achieve understanding without math".Disagreeing with "simple explanations are a prerequisite for understanding" implies you think "you can achieve understanding without having had a simple explanation given to you".As such, saying math is not a prereq is moronic (your take), while saying that simple physical pictures are not a prereq (the other anon's take) is technically true but of course pedagogically unhelpful.
>>16920408>check out wiki>look up gauge>gauge theory is racismokay
>>16926112First you have a physical system you want to study. Next you use your basic understanding of it to formalize it by writing a mathematical model. Then you use that model to gain deeper and more detailed understanding of that system, and possibly to make more advanced models to study it further. Understanding comes first. Math comes second. There's no way around it. Putting math forward means you literally don't know what you're doing. That's also why you have to be able to explain it in simple terms without math. If you can't then you don't understand it.
>>16926127It's funny to watch you constantly weasel yourself out of a concession with qualifiers. > Basic understandingcomes first, long before modeling, yes. But "basic understanding" is not "thorough understanding". Basic understanding is insufficient to give explanations that aren't regurgitating existing explanations. If you can't show that you can gain deep, thorough understanding (which is the kind needed to make simple explanations in the first place) without math, then you are simply wrong for reasons I already explained. I know you will keep going in circles now. The fact that all your arguments stop at an absolutely rudimentary level of understanding that isn't useful to actually DEEPEN your understanding of subjects brands you as an eternal undergrad.
>>16920373Gauges are a generalization of reference frames from classical mechanics. Because everything you wish to describe is curved, the Cartesian picture of only having to choose the 3D orientation and absolute position of your coordinate system to pick falls apart and are replaced by infinitely many (point-wise) assertions. Even in classical mechanics you can easily see something like that happening when you go from Cartesian to curvelinear coordinates. At each point your coordinates are basically Cartesian for small displacements, and the curved parametrization is essentially infinitely many Cartesian frames glued together.While the choice of gauge is physically meaningless, sometimes you can have observable effects that can be attributed to properties that existing in all gauges simultaneously. Stern Gerlach is a famous experiment where you are basically measuring the fact that the experimental setup has no gauge that isn't discontinuous (even if the position of the discontinuity is gauge dependent, the observable only depends on one being there).
Probably wrong place to be asking this but seeing that I'm doing a course with 4 vector notation (which makes gauge invariance easy) this is tangentially related, so somebody might help me:Going through Tong's AED lecture notes and he wants to solve the wave equation in the Lorentz gauge, and to do that he basically has to prove retarded potentials. But, to do that it's a mix of Green's function, Helmholtz equation, AND fourier transforms, and I genuinely feel each step is an asspull I genuinely struggle to see why it's done like this. After spending some time reading into it I kinda get the concept of each operation, but when dealing with greens function of fourier transforms, why do you put the G inside the integral at the end????
