This guy is simply crazy

so many advanced concepts in physics expressed in pretty pictures with intuitive explanations

@schn changes to the electric field propagate at the speed of light, so it would seem obvious that the field points to where the charge was a time x/c ago, where x is the distance to the charge.

Griffiths' point is that since the field always points to the current position of the charge it seems as if the field is propagating at infinite speed.

@Secret I didn't quite understand how phase in-variance (at 4:18) led to conservation of electric charge. And what does electric charge have anything to do with the phase of the wavefunction? And why electric charge, why not color charge or anything else?

@Yashas the symmetry is called U(1), and if you Google u(1) symmetry charge conservation or something like that you'll find lots of articles on it.

The symmetry responsible for conservation of colour charge is a different symmetry called SU(3).

@Yashas The video is simply wrong if it says that. It's a common confusion that the "phase invariance" of quantum mechanics is the symmetry for charge conservation. It's just that the U(1) symmetry of EM only has irreducible representations as changing the phase, but it is a different symmetry than the irrelevance of global phase.

That the global phase is irrelevant means that for three states $\lvert 0\rangle$, $\lvert 1\rangle$, $\lvert 2\rangle$ with charges 0,1,2 we have that multiplying all of them by some $\mathrm{e}^{\mathrm{i}\alpha}$ does nothing. That we have EM symmetry means that $\lvert 0\rangle\to\lvert 0\rangle$, $\lvert 1\rangle \to \mathrm{e}^{\mathrm{i}\alpha}\lvert 1 \rangle$, $\lvert 2 \rangle \to \mathrm{e}^{2\mathrm{i}\alpha}\lvert 2 \rangle$ is a symmetry.

heh, there's one (reasonably high rep) user who always seems to be backed up by the same couple of users whenever someone points out a mistake in their answer

The user in question has also answered all of the questions of these two helpers, each within less than 20 minutes

¯\_(ツ)_/¯

@NiharKarve Uhhh... Can you mod flag one of these posts?

(I'm not a mod on this site, but that's still what I'd suggest)

@Mithrandir24601 I'd do that if I had more solid evidence

currently it's hovering around the hunch-suspicion border

@NiharKarve If this were QC (i.e. where I am mod), "also answered all of the questions of these two helpers, each within less than 20 minutes" would be more than enough evidence for me to look into it :P

Well, unless 'all' was just a couple of questions or something

In short, mods have much better tooling

@Mithrandir24601 er, 4 each, 8 total

might just be a coincidence, but I'll notify the mods if necessary

@NiharKarve I'll just ping @ACuriousMind at this point :P

@NiharKarve Don't hesitate to flag even if it's just a suspicion - we'll usually mark such flags as helpful even if we don't find enough evidence to do anything either

@ACuriousMind all right

Thanks for taking the time to answer @NiharKarve

I see now

@Charlie no problem!

@JohnRennie Thanks for the reply! On a slightly related note, do you know why the angles will be greater than pi/2 for z1 or z2 smaller than 0. Is the answerer assuming the field point is at 0, the origin?

@JohnRennie By the way, regarding your answer to my question about the field of the moving point charge, how is this resolved...that the field seems to be moving at infinite speed?

Why does the dipole potential become a better approximation when the distance between the charges goes to zero (and charge to infinity)?

In the multipole expansion, is this distance squared, cubed, and so on?

@schn Because when the charges are right on top of each other their monopole field cancels out exactly

(of course that's handwaving since if they "really" canceled out each other there wouldn't be any field)

@ACuriousMind makes sense, however, they already do kind of cancel each other out, for points next to them (where the distance is the same to each charge), right?

sure, but the closer they are, the better the cancellation is for points not equidistant to them

true

are the higher order contributions of the potential affected by the distance shrinking between the charges, @ACuriousMind?

tricky question maybe :)

sure, in so far as they are not zero to begin with (the quadrupole moment of a dipole is zero, I don't know which of the higher terms is the first non-vanishing one)

and I assume this is because they all have the distance cubed, quadrupled,..., and so on

the distance in the multipole expansion is the distance from the multipole to the point where you want to know the electric field, not the distance between the charges

Right, but...

the dipole potential can be written in terms of the distance between the charges

and so I assume this can be done for all the other contributions as well

ah, sure, but I don't think the dependence of the higher terms on the distance between the charges is that simple (as I said, for instance the quadrupole is just zero, it has no dependence)

yeah