Why does Jackson say that experimental tests of the inverse square law of electromagnetism is equivalent to measuring the mass of the photon?

@SillyGoose he explains in the introduction

section I.2

oh oops

why do we impose that the azimuthal part of the electrostatic potential (thinking in spherical coordinates) needs to be single valued?

it seems rather that we want the electric field to be single valued

so as a consequence we have the azimuthal bit is single valued

what's the context of what you're reading/solving right now?

the textbook use of separation of variables to solve for an arbitrary electrostatic potential

@SillyGoose I see, Section 3.1 of Jackson. I think so, if your "azimuthal part" weren't single valued, then your potential wouldn't be, and neither would your field.

@Relativisticcucumber Yeah, it can be really intense, and definitely not fun to do it under time pressure. But if you understand that Fermi surface is a thing that defines metals, not needing much more than just this factoid, you would already have had a quantum leap in understanding of all materials. Totally different from any classical guesses.

@Relativisticcucumber It is a downgrade from normal momentum conservation, that the (q+k) is conserved, k is conserved, but different q might appear in that conservation, where q is a reciprocal lattice vector

and when q changes, the whole crystal recoils, to conserve normal momentum.

@SillyGoose i think one can't re-state the measurement postulate in an unambiguous manner

one needs precise dynamics to model measurements. this would involve modifying the entire theory

but some approaches like Many Worlds and Relational interpretation try to keep most of QM intact

but I think these two are just as ambiguous as QM itself. Many worlds won't precisely define what a world is. And Relational interpretations are ambiguous too (but I'm not sure how)

I think rovelli's paper on relational interpretation is too vague arxiv.org/abs/2109.09170

can someone help me with how the reciprocal basis vectrors are drawn in k space, when you have them expressed in the position space

e.g the reciprocal basis vectors of fcc are $K_1=\frac{2\pi}{a}(-1,1,1)$

How do I draw this in k-space where the unit vectors are $k_x,k_y,k_z$ ?

Hello Everyone...

hello

hello

I wrote up this 'proof' on why an object with less mass, colliding elastically with an object with greater mass but 0 momentum, can't have 0 momentum after the collision but I don't feel convinced that this is the whole story (obviously since it's just classical mech)

Is there a deeper reason why, perhaps what is classical mechanics approximating

a student asked why in this part of the experiment the initial cart ($p_1$ in the document) the cart moves back instead of staying still and I vaguely remembered that it's because of the mathematical nature of the momentum conservation + energy conservation equations but that's not a good explanation imo

that's like saying "because the model I chose to describe the system says so", as though these equations are law

I guess I should have said "because kinetic energy AND momentum is assumed to be conserved in elastic collisions (which we defined to be X)" but they were supposed to determine which quantities are conserved during which types of collisions so idk maybe I should just not answer and let them figure it out

If you "let them figure it out" on their own, it would be called "inquiry based learning" but, spoon feeding them answers will leave no impression on their long term memories.

Striking the right balance is called the Art of Teaching.

@think_meaning_builds a quote from the "Art of Teaching" written by Sun Tzu

:D

These quotes are getting out of hand @SineoftheTime

:(

The chat wasn't very active today

Nobody has tortured ACM... Mh.

What are asymptotic states? :P

Sun Tzu and The Art of Teaching

@SineoftheTime I had to look up the Dini's thm proof in order to study singular points of plane curves. Less scary than I remembered it to be

Did you see the proof of the general statement?

@Mr.Feynman grrr

i.e. when $F:\Bbb R^{n+m}\to \Bbb R^m$

@SineoftheTime The case $F(\mathbf{x},y), \mathbf{x} \in \mathbb{R}^n, y \in \mathbb{R}$

I see

I'm looking at it and there's also Dini's thm for systems

looks terrifying hahahah

but if the constraint is a curve you can parametrize, can't you?

for a non singular point, yes I suppose

when I mean singular, It means $\nabla F(\mathbf{x}_0) = 0$

@SineoftheTime yeah, unless you want classical mechanics to probably crumble down :P

which book do you use for analysis 2?

Fusco, Marcellini, Sbordone

Outside of Italy everything is different

@Claudio even inside. I used Giusti (second edition)

Third edition was meh

Giusti died in March :(

nah, I meant this: Dini's thm does not exist outside of Italy and (Munkres for instance) they prove the Inverse Function thm and then the Implicit function thm, while we first study Dini's thm and then global inversion thm

the names are probably wrong but the point stands

@Mr.Feynman do you like it?

@Mr.Feynman dang that's sad

@SineoftheTime u gotta tell us what book you used now

can't write properly at 1 am

I usually take a look at different books and then choose one, so it depends on the topic

but yeah, Marcellini Sbordone, Giusti and Pagani Salsa are all good

@SineoftheTime you're really good so you probably mastered all of them in no time hahah.

I'm not good actually ahahah

I'm average

you guys seems a lot knowledgeable than me

I stand corrected if you take into consideration the following result: $\text{average math student} = \text{excellent physics student}$

if you're sample contains ACM, then yeah

Fun fact: I did my first year at the physics department

dang

@SineoftheTime To expand my narrow horizons, I've decided I'm going to study Tao's proof and Rudin's now, I'll be back in 4 years :P

Better Proofs Than Rudin's For The Inverse And Implicit Function Theorems 57 upvotes hahhaha

@SineoftheTime not my favorite book, but anyways those books are not translated to English

Literatura is a mess so you'd better follow a set of notes

@SineoftheTime wait, are you Italian?

yep

yeah hahhaha, I thought it was well known

How dare you

ah ok maybe you told me in the math chat

@Claudio Is it in Baby or Papa Rudin?

Italians took over this chat smh

italians taking over mathematics and h bar

Heidelberg legions will soon fall

@SineoftheTime I don't know from experience since I've never read Rudin, but it's in Baby Rudin 9.18

fun fact: I've noticed Italian math professors and phds use ME, physics ones much less

As a community, Physics is smaller

yeah, but I remember during my QM oral exam, I talked to him about the PSE community, and he didn't even know it existed, and he's pretty young as well

@Claudio I haven't met any of mine

But here on PSE there is Valter Moretti, so we got the cream of the crop

me neither, the only one I know is Moretti at this point

lol exactly, he teaches Classical mechanics. UniTrento students really are privileged :P

@Claudio Folland is a good book for real analysis, you may enjoy it

lemme look at it

Like that time he commented an old post of mine saying that he'd published a new book I might be interested in, and I was like "damn, I'm important"

MrF thinking: I, indeed, might be him

Folland, "Advanced Calculus", chapter 3 is about implicit function theorem and it's applications

another fun fact: my friends had a professor called Moretti, he teaches QM

UniTrento?

nono

It's not the same professor

I checked

yeah he only taught courses in UniTrento

pretty good university

@SineoftheTime ok Ill take a look at it, probably tomorrow tho, Im a bit tired

Yeah

As far as I know, physics students attend the same lessons with math students for math exams like Analysis 1

His book "Meccanica Analitica" (recently translated to English with an additional chapter about relativity) is an expanded version of his 2nd year course on analytical mechanics

@SineoftheTime where, in Trento? I think it happens in some other universities too. It really depends on the curricula, though. Here, the version of analysis for physicists has less CFU

Yes, I meant Trento

I see

@SineoftheTime I looked at folland

it's very similar to my book

I like his books because they built intuition

and because I like harmonic analysis :)

like the part described in this question is almost exactly the same as FMS

weird that an Americal book uses the same approach to the proof. Other books are completely different

it is way too late, i didnt even realize, time to go to bed. See ya guys :P

G'night