Can someone tell me how to get Maxwell equations in free space in tensorial form from $d*F=0$? Most places discuss how to go from differential forms notation directly to vectors $\vec{E},\vec{B}, etc.$ but not to the $\del_mu F^{\mu \nu}=0$ thing
I plugged in the definitions of $*$ and $d$ to get a $\varepsilon_{\mu \nu \rho \sigma}\delta_\eta F^\rho \sigma dx^\eta dx^\mu dx^\nu=0$ from $d*F=0$
@NairitSahoo To get to the standard form you have to dualise again, ie compute $\ast \mathrm{d} \ast F = 0$ and use the identities for products of 2 $\epsilons$
Just wanted to verify if chatgpt is being correct here in all these 7 convos...
I'm really sorry if this violates any community guidelines, I did not had that intention
@TobiasFünke Since I refuse to read what chatGPT says about physics, will you tell me what's unbelievable? The AI reply or that a user asked if the AI is correct?
@TobiasFünke and you have to consider that this is already one step above the worst case, which is just believing what it generates without trying to check
It's a turbocharged version of the crackpot problem - it has always been easier to produce nonsense than to debunk it, but now it's additional orders of magnitude easier
It has been quite a while since vzn ( @vzn ) posted, we're talking during covid times, unfortunately I think the worst can be presumed... I'll just say despite the raucous debate (something we all agree to in these scientific discussions) and the kinds of typical half-cocked layman mistakes, it was always fun chatting with vzn and I appreciated their desire for open-mindedness/truth
@SignorFeynman I don't think that 274d thing is right, the 'recent' tab gives 2021 as the most recent activity but that 274 days thing says that was when the last message was... Activity everywhere (blog etc) all just disappeared/stopped in the middle of a global pandemic
Judging by the blog about page and the chats here, he was an older software engineer who had the fire of vishnu lit underneath him to understand theory but didn't study it properly, activity stopped early in 2021 and the vaccines didn't come out until the end of the year en masse
Obviously anything could have happened, but yeah...
What To Do When The Trisector Comes claims that most cranks (for lack of a better word) are old men (trisector refers to a specific type of crank):
One obvious characteristic of trisectors is that they are old. The typical trisector heard of the trisection in his geometry class, but did not s...
If you read between the lines, I was trying to tell vzn not to waste his time doing physics without studying it properly (pretty sure I directly said to read the basics multiple times in here), this stuff is no joke, it's hard enough when you know the basics let alone ignoring them and plowing into it
> "Twelve-thousand working hours! Full-time is forty hours a week for fifty weeks, so the poor deluded man had devoted the equivalent of six years of his life to something as useless as trying to find two even integers whose sum is odd."
1.) How would you with an equation describe a canonical transformation? Is it $\delta f = \epsilon \{f,G\}$ where $f$ is some function $\epsilon$ is some incremental change and $G$ is the generator?
2.) Is the time flow a canonical transformation with the Hamltonian as the generating function?
@User198 there are several slightly inequivalent definitions of "canonical transformation", if you pick one where they are the symplectomorphisms, then yes, all such transformations are the flows of Hamiltonian vector fields
Uh, perhaps there needs to be a "locally" there - this is false on non-simply-connected phase spaces
If we consider curvature coupling terms like $R\phi$ for a Klein-Gordon field in curved (but non-dynamical) spacetime then there are certain values of the coefficient for which the theory is conformal. So $T:=T_{\mu}^\mu=0$. Now I was thinking that if I now make the gravity dynamical, $T=0$ implies that $R=0$ (via contraction of Einstein field equations) that is the curvature coupling vanishes. Is this correct line of thought or am I messing up the different notions of energy-momentum tensors?
This would be a strange conclusion, right? Gravity when made dynamical decouples "conformal scalar" with itself or something like that. (Although there's still minimal coupling...)
Wait am I even right or am I thinking of the Cotton tensor
let me check some things
The thing I have in mind is that in GR, you have roughly two components to the curvature, you have the dilations (volumes change), which are indicated by the Ricci scalar, and you have the shears (squeezing) which are indicated by the rest of the Riemann tensor
@ACuriousMind So the excitations of gauge fields are vector bosons? And all gauge fields are interaction fields among excitations of other fields which are not gauge ones i.e two spin1/2 field?
@imbAF I don't really like calling particles "excitations of fields", but yes, that terminology is common enough. I'm not sure what you mean by them being "interaction fields" - there is nothing else to interact with in free EM, for instance.
In QED the electrons and photons interact. It's common to call the photons the "mediators" of the EM force because the Coulomb force comes from a diagram where "two electrons exchange a photon". But you can have plenty of interactions between particles that don't involve gauge bosons (just write down a theory with two scalars $\phi_1,\phi_2$ and a term like $\phi_1^2\phi_2 ^2$)
I thought that interactions are made possible only, exclusively via gauge fields, the massless spin 1 vector field for interaction among charged particles, the gluons among quarks etc
@imbAF It's true that in the Standard Model, all the interactions are either via gauge bosons or things that come from gauge bosons (the W-/Z-bosons of the weak interaction are massive and hence not directly gauge bosons, you will learn about that when you learn the Higgs mechanism). But it is not a general rule in QFT, as I said you can easily write down interaction terms that do not involve gauge bosons.
One additional question. I might butcher what I am trying to say but hopefully you get the idea
A theory, the way I understand it, is represented via the lagrangian density. A free such lagrangian only "contains" in its description one type of particle (excitation). For a lagrangian which also contains an interaction part, this lagrangian involves 2 or more theories/ qfts in its description. In other words 2 or more different excitations
Just wanted to verify if chatgpt is being correct here in all these 7 convos...
I'm really sorry if this violates any community guidelines, I did not had that intention
What To Do When The Trisector Comes claims that most cranks (for lack of a better word) are old men (trisector refers to a specific type of crank):
One obvious characteristic of trisectors is that they are old. The typical trisector heard of the trisection in his geometry class, but did not s...
