The h Bar

Charlie

01:45

@BioPhysicist physics.stackexchange.com/questions/575584/… might be a question you're interested in specifically

BioPhysicist

03:19

@Charlie It's an interesting question, although I agree with the closure of it here. Definitely way too broad and opinion based. "Biophysics" is definitely a very broad area of study,. so I'm not sure the question even has an answer.

user434058

06:32

Is there any way I can derive the E-L potential for an electromagnetic field from the Lorentz force without any guessing/claiming? In other words, how do I derive the potential from Lorentz assuming I don't know the final answer to the potential?

Slereah

Errrr

I mean you can do it assuming from a U(1) gauge theory

user434058

@Slereah what is that supposed to mean?

Slereah

But I'm not sure that would be a very intuitive answer

user434058

@Slereah ah, ok.

user434058

Looking it up.

Slereah

06:34

The EM potential is also the basic Lagrangian for a vector potential?

Well, the Proca Lagrangian is, I suppose

user434058

@Slereah What does that mean?

Slereah

@FakeMod Under a few assumptions, the EM Lagrangian is the simplest Lagrangian for a vector field you can have

user434058

@Slereah Ah, so the EM Lagrangian is kind of the basic framework for other Lagrangians. This makes understanding it even more important.

Slereah

Well, for vector fields, anyway

user434058

Specifically, can I analytically solve the equation $$\frac{\mathrm d(\nabla_v \: U)}{\mathrm dt}-\nabla U= q\left(-\nabla \phi - \frac{\partial \mathbf A}{\partial t}+ \nabla(\mathbf A\cdot \mathbf v)-(\nabla \cdot \mathbf v)\mathbf A\right)$$

user434058

06:42

to find $U$?

Slereah

Seems like a big one to solve analytically in the general case

Is that the Lorentz force?

user434058

@Slereah Yeah. Again giessing does easily give the answer, but analytical solution seems out of scope to me.

user434058

@Slereah yup. RHS is the Lorentz force.

Slereah

What are you solving here, is the EM field set?

You can try to use Green's functions to solve it I suppose

user434058

@Slereah I am trying to find the electromagnetic potential, which is to be input in the Lagrangian ($L=T-U$).

user434058

06:45

@Slereah Maybe. Though I barely know them, so I might not be adept enough.

user434058

Does Rayleigh's dissipation function work even if the velocity (or any of its components) of the particle reverses it's direction at any point during motion (of course, I am only talking about resistive forces which are proportional to the negative of velocity vector)? (I suppose the answer is yes)

ACuriousMind

07:06

@FakeMod You're not trying to solve this equation - "solving" it would mean that you're given some boundary/initial conditions and you're trying to compute $U$

Slereah

@ACuriousMind Maybe he needs the solution for every possible boundary conditions!

ACuriousMind

No, he's just trying to "derive" the Lagrangian for the particle in an electromagnetic field and doesn't want to "guess", but Lagrangians are always guessed :P

user434058

@ACuriousMind Can't we use $U=0$ when $\phi=0;\mathbf v=0$ and $U=0$ when $\phi=0;\mathbf A=0$ as a Neumann boundary conditions?

ACuriousMind

@FakeMod I don't know what you mean

The unknown $U$ you are looking for is a function $U(q,v,t)$.

user434058

@ACuriousMind So yeah, reframing, $U(q_1,0,t)=0$ when $\phi(q_1)=0$.

user434058

07:12

Is this better?

ACuriousMind

But why are you imposing random boundary conditions?

user434058

@ACuriousMind Just because I need them to solve the PDE.

user434058

@ACuriousMind Are they? I though we can always derive them from first principles...

ACuriousMind

@FakeMod I don't understand what about just showing that $U = q\phi - qA\cdot v$ fulfills this equation is unsatisfactory to you

user434058

@ACuriousMind Also, I don't see why that boundary condition is random. I am just using the fact that the electromagnetic potential must be zero when the electric potential is zero and the magnetic force is zero.

ACuriousMind

07:14

Think about it - how are you "solving" PDEs, anyway? You massage them until they come into a form for which someone one "guessed" the analytic solution correctly?

user434058

@ACuriousMind It just feels a bit out of the air. I mean we are lucky to find/guess it this time. We cannot be sure to be that lucky everytime.

ACuriousMind

@FakeMod You can always add a total derivative to the Lagrangian without changing the physics, and in addition you have a gauge freedom. There are no facts about specific values of the electromagnetic potential, it is gauge-variant and not a physically measurable quantity.

user434058

@ACuriousMind O_O true. I concede and comcur. Thank you! :)

ACuriousMind

I mean, you don't have a "way of solving" $f' = f$ either. You just observe that $f= \mathrm{e}^x$ fits the bill and then use uniqueness theorems to argue it's a general solution up to a constant.

user434058

@ACuriousMind while you're here, please tell me whether it's a yes/no:

user434058

07:17

24 mins ago, by FakeMod

Does Rayleigh's dissipation function work even if the velocity (or any of its components) of the particle reverses it's direction at any point during motion (of course, I am only talking about resistive forces which are proportional to the negative of velocity vector)? (I suppose the answer is yes)

ACuriousMind

I have no idea what Rayleigh's dissipation function is without looking it up :P

Slereah

@ACuriousMind $$\frac{df}{dx} = f \to dx = \frac{df}{f}$$

Easy as pie!

user434058

@ACuriousMind Yes. In fact, I have often tried to solve it without guessing in an effort to rediscover the value of $e$, but I have always failed to rediscover the value of $e$.

user434058

@ACuriousMind no worries.

Slereah

Although then again, integrating $df/f$ also requires to just kind of know the solution

user434058

07:19

@ACuriousMind Right, but I was setting a reference point just to make things simpler. I know that an additive constant is harmless

ACuriousMind

@Slereah differentiation is mechanics, integration is art

user434058

@ACuriousMind *Integration is black magic.

user434058

Jk Integration is definitely an art

ACuriousMind

the underlying problem is that differentiation closes on the elementary functions (i.e. the derivative of a polynomial is a polynomial, etc.), but integration does not as soon as your "elementary functions" are reasonably many, like including fractions and square roots.

So you never have a guarantee that any solution to a differential equation is expressible "analytically" as anything other than "the function that is the solution to this integral"

Slereah

Just pick the set of all functions as your elementary set

bolbteppa

07:34

The Lorentz force law can be written as $\frac{d p^{\mu}}{d \tau} = e F^{\mu \nu} U_{\nu}$, where $F^{\mu \nu} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$, you can then view this as the extremum of a Lagrangian and integrate it against $\delta x^{\mu} d \tau$ and use integration by parts to end up with the potential

Lorentz force

In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of F = q E + q v × B {\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} } (in SI units)...

For one way to remember the potential, just remember $S = \int [\frac{1}{2} m v^2 - V(x)] d t$, this is the non-relativistic Lagrangian of a particle moving in a scalar potential $V(x)$. What should the potential term look like if it is not a scalar potential $V(x)$ but is instead a four-vector potential $A_{\mu}(t,x,y,z) = (V,\vec{A})$, added in a relativistically-invariant way, such that when $\vec{A} = 0$ we obtain the usual scalar potential.

Clearly $S = \int [\frac{1}{2} m v^2 - \frac{e}{c} A_{\mu} \frac{dx^{\mu}}{d t}] dt = \int [\frac{1}{2} m v^2 - e [V(x) \frac{ dt}{d t} + \frac{1}{c} A_i \frac{dx^i}{dt} ] d t$ will reduce to the right form

user434058

10:43

Thanks @bolbteppa but I don't understand any of that because I am incapable of doing so (as of now).

bolbteppa

Well, if you want to figure out the potential to go into $L = T - U$, a good way to try to see what it should be is to ask whether it relates to what you already know. The only difference is that the electromagnetic potential is a four-vector rather than a scalar, so $U$ is going to have to be a scalar built out of a four-vector. You're already some of the way there if that makes sense

ICCQBE

13:19

Hello everyone

Charlie

Hello

ICCQBE

I'm practicing mechanics but I got stuck on a problem

photos.app.goo.gl/9gV6iksvfm1tACnU9

This is the model of the question. It asks me to find the maximum displacement of $m_1$ and what is the velocity of $m_1$ after it falls 1 meter.

I think I should use both forces and conservation of energy

I tried to use conservation of energy but I don't have any information about gravitational potential energy, I mean if I choose floor as U=0, I don't know how far they are from the floor

I can select U=0 as the bottom of both objects, but I still don't have any information if they are at the same height.

So, I think I left with forces.

photos.app.goo.gl/XepiP8eaa9rmXEKK9

This image shows the forces. I found them like that

I don't know what to do, can you give me some tips? I don't need the whole solution, just please give me tips. Thanks

ZeroTheHero

13:37

@ACuriousMind Epigraph at the start of an French text on calculus: “Derive qui veut, integre qui peut” aka roughly “Take a derivative he who only so wishes, integrate only he who can”.

2

JingleBells

14:29

Did anyone show they need online video sharing platform before Youtube was built?

Emilio Pisanty

hmmmmmmmmmm. @Qmechanic has been busy on the site these past few months -- the gap between his/her rep and my total all-time earned rep has shrunk considerably.

Charlie

@JingleBells What do you mean?

Emilio Pisanty

@ZeroTheHero do you have the precise reference?

JingleBells

@Charlie nvm

Emilio Pisanty

@JingleBells depends what you mean by video sharing platform. If you mean places where you could go and watch videos, then there are forerunners like stupidvideos.com

JingleBells

14:33

nvm sorry

Emilio Pisanty

if you mean places where you could upload your own, early social media (think MySpace) had probably shown enough demand

but ultimately the founders just built it because they wanted it, and the demand came.

@ZeroTheHero (or, alternatively, a screenshot)

@ACuriousMind yeah, I think it's at the center of a loose cloud of similar questions

JingleBells

I was just wondering how they got the idea, but I googled. It came from their own frustration

ZeroTheHero

15:03

@EmilioPisanty Unfortunately I don’t. I saw this while in a bookstore in Paris 20years ago.

ZeroTheHero

15:17

Google doesn’t turn up anything useful in terms of sourcing... just a link to some comment on the teaching of math in Quebec.

Emilio Pisanty

@ZeroTheHero that's a shame ¯\ _(ツ)_/¯

Charlie

17:13

I know recommendations questions are a bit annoying, but my master's (theoretical) starts in ~1 month and we cover qft at some point. I basically have a month from today to get as much of a head start as I can, so are there any topics/books you guys who have done an MSc particularly wish you had covered before the course had started?

specifically relating to quantum field theory

skullpatrol

17:30

\o @FadedGiant et al

Faded Giant

@skullpatrol hi

skullpatrol

how goes it; my friend?

Faded Giant

It's okay. A lot of work to do.

skullpatrol

yup, same here

ZeroTheHero

@EmilioPisanty well... of course you can always try to find it by yourself: this would entail a trip to Paris and an afternoon of browsing at Gibert-Joseph on Boul. St. Michel. (gibert.com/stores/paris-vi-gibert-joseph-librairie). There are much worse things in life to do in pursuit academic trivia.

There is an entire floor of science books... maybe an afternoon is not enough.

Philip

17:46

@ZeroTheHero More importantly, an entire floor of english books. I lived right opposite it, spent most of my weekends there

ZeroTheHero

Yeah that place is a required pilgrimage for any serious academic. I do remember a fair number of books in French, which suits me fine as my students will never find them online...

but you’re right... I’d say 70% of the texts are in English.

Philip

I agree. I used problems from my french texts with my students. Especially for introductory QM. Most of the other problems have solutions online. :/

Philip

18:01

@EmilioPisanty Incidentally, I remember a friend telling me the same phrase when I was studying in Paris, my friend called it a "Math proverb" as a joke. Oddly enough I can't find a reference anywhere online.

skullpatrol

A mathematician turns coffee into proverbs.

user434058

@skullpatrol So long, man. Went on a break?

skullpatrol

yup, dropped all internet activity in the the name of #BLM

user434058

Oh, noble initiative. Though I wonder that would make any difference 🤔

user434058

But it's not bad if you are willing to drop your internet activity for a month.

skullpatrol

18:10

using my time to try and make a difference for BLM

user434058

Nice

Emilio Pisanty

18:26

@Philip hmmmm, that's a thought, for sure

Philip

@EmilioPisanty And the French texts actually have a very nice way of doing stuff, especially for QM. (I'm counting Messiah as a french text too ;) )

ZeroTheHero

@Philip well the French have a very French way of doing things. We should ask the British if they think it's nice.

Philip

@ZeroTheHero

I hated it for the most part ;P

skullpatrol

@ZeroTheHero and vice versa

ZeroTheHero

oh yes.

Philip

18:32

I have a question: if you cite a paper and there's a freely available version online (non arxiv), is there anything strictly wrong with placing that in your question? I understand that one should include the DOI, but I don't see why it has to be placed behind a paywall if a free version is available.

ZeroTheHero

@skullpatrol and of course as an example recall that the English expression "to take a French leave" translates in French to "filer a l'Anglaise" (aka to take an English leave)!

2

skullpatrol

Well said.

ACuriousMind

@Philip if it's on arXiv or another relatively stable (and unquestionably legal) source, I see nothing wrong with including the link, but I think in all other cases you should let people find the paper on their own, rather than having a broken link in your question a few months or years from now or linking to a questionable source

especially pdfs hosted on the personal pages of people have a tendency to disappear or move around

Emilio Pisanty

@Philip if it's unquestionably legal and looks reasonably stable, the paper is otherwise behind a paywall, and a stable DOI link, then I think it's OK to include.

I'd give a thumbs up to eprints posted on the author's personal page, even given the danger of link rot (as long as a stable DOI link is also provided)

personal pages of other people probably fail the 'unquestionably legal' test.

Philip

@ACuriousMind @ZeroTheHero So if the paper was uploaded to a university website, for example. Or a professor's (not the author) personal site, would that count as "legal" or "illegal"?

(whoops, tagged the wrong person @EmilioPisanty :P)

ACuriousMind

18:45

probably hard to tell whether it's legal or illegal in a specific instance, but I wouldn't count it as "unquestionably legal"

Philip

I see. Thanks!

skullpatrol

19:34

It's been a pleasure chatting with you all. Take care my friends.

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