The h Bar

Silly Goose

12:00 AM

and so then what makes it a useful method for optimizing

ACuriousMind

looking at critical points without Lagrange multipliers also doesn't yield extrema necessarily!

what's your point?

this is very basic "$f'(x) = 0$ does not necessarily mean an extremum of $f$" stuff unless I misunderstood the question

Obliv

it yields extrema in the context of the constraints

ACuriousMind

@Obliv no, it may well just deliver stationary points

Silly Goose

well i think the conceptual understanding i had before today was that points are either local minima or global minima (for example) and that stationary points were one of either, but the example of like $f(x) = x^3$ is a counterexample to such a conceptualization

er i guess saddle points...

Obliv

by stationary points do you mean saddle points/inflection points? @ACuriousMind Or do you mean like they're the same function in the interval or..

ACuriousMind

12:05 AM

yes, $f(x) = x^3$ is the usual counterexample to thinking critical points have to be local extrema

Silly Goose

@Relativisticcucumber this is what i mean when my calculus is bad lol

Obliv

yeah true, so you gotta check all the solutions

@SillyGoose ripped from my multivar calc book

ACuriousMind

I have to say that I thought such basic elements of calculus were assumed to be obvious when talking to someone looking into QM and differential geometry

Obliv

never not underestimate a physics students' math skills or lack thereof

to be fair, one can only devote so much time to the immense ocean that is math

ACuriousMind

where I went to school, this was mandatory part of the math education you received before even going to university :P

Obliv

12:15 AM

where'd you go to school? In heidelberg?

Silly Goose

i took calc in before uni as well and then multivar in uni but i don't think i learned it in a very good way pre-uni or during uni and the multivar course did not seem to cover half the normal material of a multivar course

ACuriousMind

I grew up in Wuppertal

Silly Goose

i have been immersed in linear algebra land for a while :P i feel i do not really use technical bits of calculus (even minorly technical) day to day

Obliv

I'm lost in griffith's derivation of lorentz transformations. I followed the time dilation argument (I think), but not sure how he gets $$t = \gamma(\bar{t}+\frac{v}{c^2}\bar{x})$$ for change in time b/t two coordinate systems $S$ and $S'$

ACuriousMind

but an understanding of derivatives and how extrema/saddle points/derivatives relate was generally part of the curriculum, nothing special about the school I went to

Obliv

12:19 AM

@SillyGoose did you take real analysis? Maybe it would have been helpful

iirc u went straight to topology or something

ACuriousMind

did you never do all those exercises where you have to find an extremum of e.g. an energy function and you first look for candidates by looking for zeros of the first derivative and then checking whether the second derivative was zero to see if it's really an extremum???

Obliv

Is that in math? We don't really work with energy functions in math (from my experience)

Silly Goose

@Obliv my real analysis course stopped right before getting to differentiation xD

Obliv

We do the work-energy theorem in first year calculus and then rarely touch physics again

@SillyGoose bruh. isn't that the point lol, oh well you can learn anything you want now that you are mathematically mature or whatever that means

ACuriousMind

...I see I have to re-evaluate my assumptions on what people can be expected to be familiar with

this is a pedagogical tragedy, what even does an "analysis course" do if it stops before getting to differentiation

Silly Goose

12:23 AM

@ACuriousMind hm we did do this in high school, but i guess i was not really thinking...

ACuriousMind

@SillyGoose aha!

generally you may assume there's a point to the things you're learning :P

Silly Goose

@ACuriousMind indeed... we started with metric spaces and talking about point set topology and then continuity and then the end

oh and series and sequences

Obliv

I mean, I don't know how they do it in germany, but in 'murica we learn the hospital's rule and I can't remember the last time I ever had to use that.

but the chain rule goes hard

Silly Goose

@ACuriousMind i see that more these days :P

Obliv

I'm curious what German textbooks cover. I don't understand why we even cover Burnhard Riemann sums

I guess for programming numerical integration

ACuriousMind

12:41 AM

@SillyGoose I mean, that's the normal beginning but in my experience "Analysis I" was that and differentiation and integration, "Analysis II" was differential equations and multi-variable calculus, "Analysis III" was whatever didn't fit into the previous two courses and some glimpses of differential geometry (like differential forms)

@Obliv what on earth is "Burnhard Riemann sums"?

do you just mean Riemann sums?

and is "Burnhard" a butchering of Riemann's actual name Bernhard? :P

Silly Goose

yes i was expecting to get into differentiation at least :P the final two weeks of class i think was relegated to group presentations on topics we didn't get to cover...but i think perhaps that was not really a good use of time

i could have done without a lecture on the cantor set and perfect sets lol

Relativisticcucumber

1:02 AM

@ACuriousMind this is indeed covered. i tutor the course that @SillyGoose took and im confident that they knew how to do this at one point since they got a perfect score on the ap calc exam which requires this knowledge. i guess they forgot

@SillyGoose in this course u learned that you find the critical points and check them to determine what they are. in checking this point, you ud find that it is "neither"

but its not that its not a requirement of the education system XD

Silly Goose

@Relativisticcucumber i think i did forget but i think that just means i never really learned the material

Relativisticcucumber

1:48 AM

@SillyGoose i dont see the logic here

naturallyInconsistent

@Obliv Maybe you should consult a 2nd book. Preferably from a totally different direction. I really like Minkowski diagram introductions to SR. Griffiths is a very good book, but it is not universally good everywhere.

lucabtz

2:26 AM

@Relativisticcucumber you and goose go to the same uni?

naturallyInconsistent

2:39 AM

@lucabtz used to.

Relativisticcucumber

3:52 AM

@lucabtz no but i do virtual tutoring for students from @SillyGoose's high school

@naturallyInconsistent no we never did XD

@lucabtz i did NYU's global program, so i spent one year at NYU New York, one year at NYU Abu Dhabi, and 2 years at NYU Shanghai. but i graduated last spring and now I'm doing a gap year as a research assistant at NYU Shanghai. We know eachother irl tho which is how I ended up doing the virtual tutoring gig

BUT we are starting PhDs at the same uni in august YAY

naturallyInconsistent

4:40 AM

YAY

John Rennie

5:38 AM

@Relativisticcucumber The three years I spent doing my PhD were the best years of my life. I know not everyone's PhD works out well, but I really hope you and @SillyGoose enjoy your time as much as I did.

Relativisticcucumber

@JohnRennie :DDD i hope so too

Silly Goose

@JohnRennie thank you :D i hope so also!!!

@naturallyInconsistent YAY indeed

Slereah

6:56 AM

> Among the magisterial mistakes of logic, one will first mention quantum logic, whose ridiculousness can only be ascribed to a feeling of superiority of the language – and ideas, even bad, as soon as they take a written form – over the physical world. Quantum logic is indeed a sort of punishment inflicted on nature, guilty of not yielding to the prejudices of logicians… just like Xerxes had the Hellespont – which had destroyed a boat bridge – whipped.

Slereah

7:09 AM

> The blind spot is what one does not see and what one is not even conscious of not seeing. The most trivial blind spot is the cheap modal logic justified by an even cheaper Kripke semantics and vice versa; but one finds similar blindings in the most elaborated interpretations.
The good news of these lectures is that the procedural standpoint seems to be capable of dislodging the unsaid, the unseen. Simply, while the absence of Hauptsatz is enough to show that logic S5 is nonsense, one has to work much more to imagine what could be wrong in the principles justifying – say – the function $2^n$.

Strong opinions

lucabtz

@Relativisticcucumber wow you traveled the world

Silly Goose

the cucumber makes use of its relativistic speeds >:D

user 70432

8:04 AM

c = ∞

}:D

Mr. Feynman

@JohnRennie well, I'm glad to read that

@Obliv well, in a real analysis class you would do that with generic functions without giving them any physical meaning but that's also what you'd do in a classical mechanics class

@ACuriousMind Up to Analysis II it's the same in Italy; regarding Analysis III it depends on where you are e.g. in Padua it's exactly like that

Don't assume I'm in Padua though :P

naturallyInconsistent

8:27 AM

@SillyGoose smirks meaningfully

Manas Dogra

9:37 AM

@SillyGoose Yes. I see you and @Relativisticcucumber are also enrolling for a Ph.D. at US. Congrats to both of you, too!

Does the uni happen to be anywhere near NEU by any chance :p

Ryder Rude

10:08 AM

@Slereah what r they saying

Slereah

11:37 AM

@RyderRude No idea

Nairit Sahoo

What are quantum corrections to the Lagrangian i.e. corrections proportional to the couplings?

I thought that the classical and quantum Lagrangian remains the same

Where can I read about quantum corrections to Lagrangians?

naturallyInconsistent

11:52 AM

@NairitSahoo You are assuming something wrong right there. Quantum corrections are not coming from the couplings. You have the same couplings as in classical physics, or at least the low energy limits are the same. The quantum corrections come in the quantisation of the fields that go into the Lagrangian, and the path integral corrections to the transition amplitudes.

Slereah

You can model some effects of the quantum model by modifying the Lagrangian to add some terms proportionals to powers of $\hbar$

Nairit Sahoo

@naturallyInconsistent I didn't mean that the quantum corrections are due to the coupling, but rather the quantum corrections contain higher powers of couplings

@Slereah Where can I find more about this?

Slereah

An example of this IIRC is nonlinear terms for EM due to photon-photon interactions

Can't remember a specific reference

look up for like effective lagrangian, nonlinear electrodynamics

naturallyInconsistent

@NairitSahoo Even that is wrong; why would you think that a semi-classical consideration of the field equations would fail to have higher powers of the couplings? It is simply not the natural way to state what the quantum corrections to things would be. But of course, if you want to work that out, you can express quantum corrections in powers of the couplings. It is the standard thing to do in renormalisation.

I mean, what precisely are you asking for?

Nairit Sahoo

@naturallyInconsistent No I didn't mean to say that a semi-classical consideration won't have higher powers of couplings...I wanted to know what precisely the form the action takes when quantization is done

@Slereah Is this the thing?

Slereah

12:00 PM

@NairitSahoo I mean you're the one asking :p

I'm not entirely sure what you want!

Like what have you seen that made you ask this

Nairit Sahoo

I don't know what "quantum perturbative corrections to the action" means in a QFT book.

Slereah

Can you send the page

naturallyInconsistent

@NairitSahoo And then this is where my original statement comes into play: The Lagrangian going into QED is the same Maxwell's action and Dirac action that the "classical" version thereof will be. The quantum corrections are just not there in the Lagrangian. It appears in the quantisation of the field operators that goes in the Lagrangian.

Nairit Sahoo

@Slereah Is it possible to share pictures here?

Ok wait

@naturallyInconsistent Yes that's where I was confused! I always thought that the Lagrangian remains the same after quantization but now I came to know that it gets modified somehow...

must be due to this renormalization thing everyone is talking about

naturallyInconsistent

@NairitSahoo Yes, when you get to the sadness, we have to introduce counterterms, and then the Lagrangian will be mutilated in extremely ugly ways.

Nairit Sahoo

12:13 PM

@naturallyInconsistent I am confused...I thought tree level is classical, loop level is quantum etc because of the $\hbar$ dependence but now it seems that in QED the higher loops have higher couplings also. E.g. Loop diagrams of QED have higher powers of $e$ where $e$ is the electric charge: the coupling constant of the theory

So is the Born-Dyson expansion, an expansion in coupling constant or $\hbar$

naturallyInconsistent

@NairitSahoo Your observation here is correct. Life is very confusing. But then again, it should not be too confusing: hbar is a dimension-ful constant, and so an expansion in terms of it is nonsense. For strict mathematical and physical meaningfulness, you have to expand upon a quantity that is dimensionless, and so it is the fine structure constant that you are actually expanding upon.

It is actually pretty difficult to express the classical approximation. If you dont care about any of the renormalisation headaches, yes, you can pretend that the tree level to be classical, with all the standard low energy limit values you just throw into it. However, if you really want to be consistent with your renormalisation, your semi-classical approximation is actually full of ladder-style approximations, with renormalised quantities everywhere.

And I have to also point out that, if you naïvely consider the expansion in terms of the fine structure constant, the hbar is in the denominator, and so in a sense you are expanding in reciprocal hbars. There is a LOT of nonsense if you look at things too naïvely. Luckily, in QED there is only the fine structure constant to expand upon, and it is also clear that fine structure constant is < 1, and so there is no problem with interpretation.

Ryder Rude

Something Strange Happens When You Follow Einstein's Math

►

it's about black holes and parallel universes

fqq

12:29 PM

@ACuriousMind did they use the schwebebahn as an example of the importance of constraints when optimising?

You might want to maximise the speed, but it's pretty important not to fly off the inverted rail thing

Nairit Sahoo

@fqq So when we go to higher loops in QFT does the exponent of $\hbar$ or the coupling increase...or do both increase?

Is this a double expansion in that case?

naturallyInconsistent

@NairitSahoo I think you tagged the wrong guy. Higher loop corrections in QFT have higher powers of the fine structure constant. hbar does not appear independently of the fine structure constant.

Nairit Sahoo

@naturallyInconsistent Oh yes...sorry I @ the wrong person. I understand what you are saying

But I am not able to make it consistent with the following answer

1

Q: Power-series expansion in coupling/Planck constant

By using Feynman rules of the interacting theory, one obtains the scattering amplitude $$\mathcal{M} = \mathcal{M}_0 + \mathcal{M}_1 + \cdots = \sum^{\infty}_{i = 0}\mathcal{M}_i\tag{1}$$ Where $\mathcal{M}_i$ denotes $i$-level loop scattering amplitude. If $i = 0$, then obtains tree-level contr...

In the question...which out of (2) and (3) is my Dyson series?

I know the form in wiki

Dyson series

In scattering theory, a part of mathematical physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by a sum of Feynman diagrams. This series diverges asymptotically, but in quantum electrodynamics (QED) at the second order the difference from experimental data is in the order of 10−10. This close agreement holds because the coupling constant (also known as the fine-structure constant) of QED is much less than 1. == Dyson operator == Suppose that we have a Hamiltonian H, which...

The last expression in the derivation section

naturallyInconsistent

12:45 PM

again, I have been stressing to you that an expansion in hbar is nonsense. $H_{\text{int}}$ is explicitly dependent upon the fine structure constant, your only coupling constant, and thus the only possible thing to expand upon. There is no expansion in terms of hbar. That answer is just wrong.

Nairit Sahoo

@naturallyInconsistent That's what I am starting to think: $\hbar$ has dimensions...we can speak of a number getting smaller when squared, or cubed...not a dimensionful thing---Is this what you are saying?

naturallyInconsistent

Correct. There are many mathematical trickery that we like to do, that is only doable if the quantity is dimensionless. This is one of them.

Also, in natural units, we set $\hslash=1$, and then that kind of expansion makes absolutely no sense.

Not to mention, that as I mentioned earlier, we are only expanding in powers of $\alpha$ i.e. reciprocal powers of $\hslash$

brb

Ryder Rude

1:24 PM

i think it is okay to expand in dimensional quantities. WKB expansion does this

just choose units where the dimensional quantity has a <1 magnitude

Claudio Menchinelli

2:04 PM

I watched the new Veritasium video on Einstein's general relativity. Although, The thing I'm most surprised about is that they were able to convince Maldacena to participate (this won't spoil anything, since it's written in the description)

I must admit I would've preferred seeing Thorne in this one: I'll take a GOAT for a GOAT :P

More Anonymous

2:20 PM

I'm curious if measurements can be made in antiverse

It's not obvious to me

Ryder Rude

Derek said gravity is anti in the antiverse

More Anonymous

Yea ... So everything would just explode

*almost

Ryder Rude

idk

More Anonymous

Hmmm 🤔

What happens to the second law

I wonder

Ryder Rude

of thermodynamics or Newton?

More Anonymous

2:23 PM

Thermo

Ryder Rude

it is still true probably

the video talked about a multiverse highway

More Anonymous

I had worked a lot of insights in this ... Only to forget them ... Sigh

Ryder Rude

did u not write them down

the multiverse highway probably exists in the human future

the humans who havent been born yet will be using it

and they will get to know different cultures from different universes

More Anonymous

I mean yes ... But I don't know where those pieces of parchments are anymore

Probably gone :///

I had like equations

One liner ones

In which those insights were expressed

I'll have to one day relearn all of physics

And I wouldn't mind that

I just wanna make sure I don't forget my insights this time

Anyway

In thermo we work out a directionality of the time variable

In QM u can define the present of that when the measurement took place

What happens if I make a measurement at the boundary

Musings ...

Ryder Rude

2:41 PM

@MoreAnonymous oh

tough :(

@MoreAnonymous the exact nature of measurements remains unknown

More Anonymous

@RyderRude I see :///

Obliv

4:40 PM

Can a photocurrent be produced even when the photocathode isn't near the anode i.e., so that the anode doesn't catch the ejected electrons?

why doesn't the cathode just catch the ejected electrons again? Does the angle of the light hitting the metal matter?

Ryder Rude

wow i read cathode and anode after a long time

had to pause to remember the meaning

Obliv

:)

Claudio Menchinelli

4:58 PM

does/did anybody use Fowler's text for the studying of Optics?

I've been using it as my Professor's choice but I'd like to start reading a less $introductory$ book.

Obliv

you can try pedrotti or hecht

Claudio Menchinelli

I've heard good things about Hecht

I'll look into it then. Thanks

Obliv

although less detailed, pedrotti covers a lot of topics as well

Silly Goose

5:49 PM

@ManasDogra in rochester new york, so somewhat close

Obliv

6:01 PM

can I imply from the equipartition theorem for a gas $U = Nk_BT\frac{f}{2}$ that $T = \frac{2U}{Nk_Bf}$

what would $S$ be in this situation

since $\partial S = \frac{\partial U}{T}$. I guess just $Nk_B\frac{f}{2}$

I wonder why it's half of the degrees of freedom though. I know it's from each gas particles kinetic energy w.r.t. the degree of freedom it's oscillating in but idk that looks weird

naturallyInconsistent

6:59 PM

when f > 3 equipartition theorem famously fails to account for quantum corrections.

Silly Goose

7:30 PM

Where does this split in talking about algebraic vs. geometric formalisms of physics come from

it seems like e.g. even in the “geometric” formalism of field theory (bundles and co.) it is very much algebraic

and vice versa

maybe it is just a nonsensical split anyways :P

DIRAC1930

8:09 PM

@RyderRude Another classic from Veritasium

It is interesting to see how Witten and Maldecena seem to get attacked relentlessly for the state of modern theoretical physics when in every interview I watch with them, they are the only ones taking a relatively conservative approach

They are very forthcoming about the fact that string theory may or may not be realised in the real world

Silly Goose

i watched a few interviews recently of witten as well and your observation is interesting as he does seem conservative and even states himself that stuff like AdS-CFT maybe sheds some light on what we're after but emphatically is not what we really care about

i also have the impression that witten is more interested in the connections between mathematics and physics as opposed to finding a unified theory of physics

DIRAC1930

9:43 PM

I hope he writes multiple textbooks now that he is retired

Silly Goose

9:56 PM

Witten is retired?

DIRAC1930

10:17 PM

Well hes under faculty emeritus here ias.edu/sns/physics-people

I doubt it changes the output of his work much

it might just be a rule in the IAS that once you reach 70 or something, you have to formally retire

I don't know though

Silly Goose

@Relativisticcucumber did u know the Princeton IAS has a center for systems biology?

oh man they have an ultra quantum matter summer school this summer :0

DIRAC1930

10:48 PM

Hopefully the lectures will be broadcast on YouTube

DIRAC1930

10:59 PM

Man, just judging from some of these older summer schools, cond-mat theory seems way healthier in America compared to where I live pccm.princeton.edu/education/psscmp

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