The h Bar

DIRAC1930

00:00

@imbAF This all becomes clear in L&L 3

And then the rel case is somewhat analogous

imbAF

@DIRAC1930 Ok I will read it. Thanks for the suggestions

DIRAC1930

However go through it quickly so you understand the basics

Since I imagine you don't have much time if you are studying for a course

imbAF

@DIRAC1930 Semester finished so I am going through my notes to have a deeper understanding + differential geometry notes + linear algebra + group theory + programing, so i don't have time at all

imbAF

00:16

@DIRAC1930 Is this the 3rd volume? Because I cannot find the 2nd quantization

DIRAC1930

I think its under identical particles or something

Pg 221

imbAF

2nd quantization case of bose/fermi statistics ?

I found it

Allie

i hate thermodynamics

Allie

02:13

So in the Debye model, is it correct to say that you're basically treating a solid like a continuum but putting a limit on what wavelengths you consider based on the atomic spacing, so that you don't double count equivalent waves?

Or alternatively, so that your D.O.F. is the correct amount you expect for N atoms?

Silly Goose

04:20

Is the partition function for a non-interacting Bose gas in a harmonic potential analytically computable? I think yes because i got a result but i dont see any analytic computations having to do with bose gasses anywhere online

Ryder Rude

06:20

there seems to be a grave problem with realising classical mech as a 0+1 field theory

the internal degrees of freedom here are not a vector space, but a manifold. so one would need to implement diffeomorphism invariance as an internal symmetry

and there is a bigger problem. the Lagrangian needs a derivative term. but it doesnt make sense to compute $\partial _t x$ becuz $x$ is a manifold point of the internal degree of freedom

so one would first need to choose co ordinates on the internal degree of freedom (cuz co ordinates can be differentiated)

this means the Lagrangian is inherently co ordinate dependent

these problems arise because the 0+1 field is "manifold valued" instead of "vector space valued"

Tobias Fünke

@SillyGoose I've posted a link with the computation some days ago...

Tobias Fünke

06:52

@imbAF you seem very confused. IIRC, multiple times people gave you some literature suggestions: have you checked these? We cannot explain a whole QFT lecture here. In QFT, $\phi$ is an operator valued function, and $|p_1,p_2,\ldots\rangle$ a vector in the Fock space (a state).

@SillyGoose and I have some answer on the main site with many sources about combinatorics and stat. mech; in these sources probably more things are derived/explained

Sir Cumference

09:01

This terminology is a nightmare

What's even the point of using a term if it has so many contradictory meanings

qwerty

yeap.

just gotta use base quantities

Sir Cumference

One of the downsides of astro is just how handwavy it is with its language

qwerty

if you're in that view it can be somewhat fun to have a whinge and rewrite it like a mathematical physicist :)

Ryder Rude

some fields just invent jargon to sound smart

Sir Cumference

@qwerty well, wikipedia apparently tried to in that table lol

can't say those terms are easy to remember tho

Ryder Rude

09:15

e.g. finance jargon

and stock jargon

Sir Cumference

"Radiance", "irradiance", "radiosity", "radiant exitance", etc

Ryder Rude

and category theory jargon

Sir Cumference

Also a lot more that I couldn't fit in a screenshot

Ryder Rude

@SirCumference horrible

r these terms useful in research

Sir Cumference

@RyderRude well they're coming up in my research a lot, with very inconsistent meanings

Ryder Rude

09:17

oh

Sir Cumference

i just spent 6 hours trying to figure out what was wrong with my results, only to realize the paper i was comparing with used a different meaning for the term than I knew

so I'm gonna try to get some sleep

Ryder Rude

so these terms r not useful. they r just used

Tobias Fünke

oh :/

Ryder Rude

@SirCumference have a nice sleep

qwerty

@SirCumference ah well i worked in an astro-ish field and I avoided those terms in favour of base quantities and dimensional analysis. always fun to come across some "law" or formula that had slightly different powers because they were considering different astro quantities

@SirCumference hah, yeah, I know the feeling. dimensional analysis :')

Ryder Rude

09:20

i thought theoretical physicists wouldnt have to deal with these terms...

like, they can use more rigorous math terms

but maybe when connecting theory to experiments, u would have to deal with these terms

qwerty

@RyderRude ^that :P

Ryder Rude

they should provide the definitions of these terms in footnotes

no one should be forced to remember these

or just write their dimensions when they use them

but Sir Cumference's problem is more about the inconsistent use of these terms, rather than the problem of remembering them

User198

09:40

@naturallyInconsistent Yeah, thats the whole formalism. It would be cool if it was like the Poisson-Hamilton equation or Hamilton-Poisson.

ACuriousMind

Why do equations need big names? I find it a bit cringe that the quantum evolution equations all have different names when in the end they're all just "the Hamiltonian generates time translation" with a different hat on :P

2

bolbteppa

@imbAF Have a read of Section 75 of Landau's QED, there when they run up against the problem of avoiding poles of the momentum space propagator, they say the way to answer it is to go back to the time-ordered definition and insert the mode expansions, and then comparing this to the momentum space green function it tells you explicitly how one should circumvent the poles

ACuriousMind

@SirCumference the radiation terminology is very annoying, yes, but I kinda get why: All these quantities are measures for "how much energy" is delivered/absorbed/whatever. The obvious colloquial term is "intensity". But then you have all those technically different quantities for it and you need to name them something so you get stuff like "radiosity" :P but since those terms are so horrible, people just think about them as "something like intensity" anyway and sometimes that slips through

bolbteppa

@RyderRude loads of stuff, even hard SUGRA stuff

User198

@ACuriousMind True

@SirCumference Sir Cumference really cool name xD

Feynmate

09:58

@SirCumference All those cursed $\pi$ and $2$ factors :P

@ACuriousMind I think it's acceptable for equations to have names, it's more of a historical homage, if I may say so. Well, so long as people don't get upset over names and prioritize concepts. The real curse is that in Chemistry they have a name for every phenomelogical little relation :P

And even those that are established within the realm of physics as trivial consequences of thermodynamics, are labelled with some guy's name

qwerty

"don't get upset over names" I remind you of stigler's law :P en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

PM 2Ring

10:46

Donald Knuth first came to fame at the age of 19, with his article on Potrzebie units in Mad magazine. en.wikipedia.org/wiki/Potrzebie#System_of_measurement

Ryder Rude

@bolbteppa oh

bolbteppa

11:08

@imbAF My comment above will just answer how to figure out this pole thing and where it comes from, more generally it looks like you are trying to understand what second quantization really is which is very confusing sometimes, @DIRAC1930 suggested L&L for this which is great but QFT adds a slight spin on that perspective because of the antiparticles

@RyderRude I am even asking it about this 2nd quantization stuff and it's actually very good

Ryder Rude

@bolbteppa what is an example question u asked and what bot did u use

i have tried to use Oakbot for Ads/CFT questions. it seemed like it was right. but it sometimes retracted its answers

i also asked it about Benkenstein bound stuff

Feynmate

Do you know any place writing down explicitly the relation between the $n-$point GF and the connected $n-$point GF?

It should be easy to derive via induction but I'm lazy about combinatorics factors in there, if any

bolbteppa

@Feynmate ask gpt

Feynmate

GPT may even mess up the urn problem...

Ryder Rude

this is one of my conversations with oakbot chat.stackexchange.com/transcript/155368?m=66613935#66613935

it is about Ads/CFT dimensions

chat.stackexchange.com/transcript/155368?m=66621841#66621841 this is about Benkenstein bound

i couldnt verify the information it gave....

bolbteppa

11:30

There are different gpt models, the o1 and o3 will pass these standardized tests with like 83% rate vs 14% for gpt4, if you press the reason button on the free version you will get a better answer because it is tapping into o1 or o3 I forget, the difference was stark enough for me to give the full version a shot

That oak thing looks terrible in comparison

Ryder Rude

@bolbteppa oh. what is an example question u asked

@bolbteppa oakbot is maybe not designed for this

i think bots r getting good at standardised tests

bolbteppa

Based on the conversation above, I started a conversation asking it something along the lines of
'A non-relativistic state for a system of identical bosons is a fock state |n_1,n_2,...> = (a_1^{dagger})^{n_1} (a_2^{dagger})^{n_2} ... |0>. What is the analog for a relativistic complex Klein-Gordon particle?'

But I want to write this down in terms of stationary states not creation and annihilation operators

So you should ask, how do you even define |n_1,n_2,...> in the first place, where does it come from?

You can literally get gpt to bring you back to first principles and write out how to get it from a general wave function Psi(x_1,...,x_n) and its doing it correctly

But you can easily get lost or go on a tangent or confuse it etc

Ryder Rude

@bolbteppa wow

bolbteppa

But you have to be careful, at this stage it will give a bluff answer if you aren't careful

Ryder Rude

this means it is still confused

@bolbteppa how many reason button clicks do they give u

bolbteppa

11:44

I play completely dumb, I want to start from absolutely nothing, so I just want to start from the general wave function for a system of n identical bosons, Psi(x_1,..,x_n), and I want to end up defining |n_1,n_2,...> from this starting point. In fact, if I fourier expand Psi as Psi(x_1,..,x_n) = sum_{m_1,..,m_n} c_{m_1,..,m_n} psi_{m_1}(x_1) .. psi_{m_n}(x_n), I should be able to beat this into the form of something involving the |n_1,n_2,..> gpt does it correctly,

I think you only get a few I can't remember

Ryder Rude

can u ask it how do u boost a time dependent wavefunction in relativistic QFT? and ask it how to boost moments of wavefunction collapse?

bolbteppa

It keeps doing stupid things and trying to veer off or it does things I know can easily be done in stupid ways and I have to waste time getting it to do a certain step better, so if I didn't know that I think it would be harder and it may not always work out, but if you keep at it I think it gets one somewhere good

Ryder Rude

i think it would be useful in trying to improvise research papers

bolbteppa

Okay if you ask it to boost wavefunction collapse you are veering off the deep edge and it will give this nonsense positive reinforcement and encourage bad habits :p

Ryder Rude

it would check for errors and make the paper's calculations better

@bolbteppa oh

bolbteppa

11:49

I think gpt4 was a bit of a yes man, while the reason stuff was less so, but I think it will always try and give a positive spin which is not always great,though in such cases it will give a substanceless answer just confirming the biases of the questioner

Ryder Rude

yes

but now it can check for reasoning errors

bolbteppa

In fact, gpt4 was giving me tons of wrong answers, I should actually recheck some stuff!

Ryder Rude

what quantum interpretation does it believe

nvm it will just give a cookie cutter answer

it doesnt have opinions

ooh i had some ideas that i wanted checked

@bolbteppa this post physics.stackexchange.com/q/837045/156987

it is not speculative. it is just a mathematical idea. gpt can check it for errors

also tell it that it is not supposed to be rigorous yet. it is a possible research direction

i need some feedback

bolbteppa

12:07

That looks like a question it could help you with if you broke it down carefully

Ryder Rude

oh

how to access this bot

i think bots would be useful as tools for research

like, u think some approach is promising. u ask the bot to try it out

like, once u have something that is specific enough, u can ask the bot to do some of the labor

like, Dirac comes up with the Dirac eqn and asks a bot to run the predictions

bolbteppa

12:25

Its just chatgpt

Ryder Rude

oh. have they upgraded it

ACuriousMind

@bolbteppa The problem here is that you know the right answer and the right way to do it, so you ask leading questions that push the model in the right direction, and if it generates something wrong, you can tell and change the approach. But this is very different from someone who doesn't know the answer and tries to learn from the model. They will not ask the questions in the leading pattern you use, and they will happily accept any nonsense answer as truth.

The paradox is that you essentially need to be able to do the thing you're asking it to do yourself in order to reliably prevent nonsense output. Which can still be useful, but is a far shot from how people are trying to use it in most cases.

Slereah

Physics communities have been getting a lot of people getting bad ideas because they asked the robot to solve their problems

bolbteppa

Yeah definitely, it's very frustrating even when you know the right answer or at least know the start and end point and know vaguely how things should go, even then it does stupid things, however if you are able for that you can really use it to flesh things out or to ask it questions about little details or to do something a different way etc

'Can you give a simpler/alternative proof/derivation of ...'

It's good for stuff like that

Feynmate

For me the dealbreaker is that even when a correct answer is given, it takes one message to convince it that it's wrong

bolbteppa

12:32

That happened for the 'yes man' gpt 4, but I'm not so sure about o1 or o3

Ryder Rude

@ACuriousMind it is still good at standardised tests tho. so one can reliably ask it to do much of the boring labor

Feynmate

I'm not so acquainted with the different models. Are o1 and o3 newer models or old models that were restricted?

Ryder Rude

but maybe one cant ask it open ended questions

ACuriousMind

@Feynmate They're newer, in OpenAI's world the number after 4 is o1 :P

@RyderRude What relation do "standardized tests" have to "labor"?

Ryder Rude

@ACuriousMind like, u can ask it to do a computation

when the problem is well defined and within established knowledge, it is in the realm of standardised tests

Feynmate

12:35

I think that RR is saying (and I care to say I disagree) that we should leave to AI stuff that has already been explored by somebody (?)

That's a great path towards the mass extinction of the physicist kind :P

Ryder Rude

no... i mean this can be useful in actual research. say, u want to investigate some modification of the Scheodinger eqn. u can ask the ai to compute out the predictions

because that computation is standardised

u just give it any well defined problem which can be computed using established knowledge

ACuriousMind

You don't need an "AI" to compute equations. We already have tools for that, they're called "calculators" and "computer algebra systems" and "numerical methods"

Ryder Rude

this is much better than that stuff. because none of that stuff scores 85% on standardised tests

ACuriousMind

And no, just because the model "passes" some standardized test, it does not imply it has the "skills" you would imagine a human passing that test to have. Most models will happily talk to you about linguistics and the history of the alphabet but are unable to count the number of letters in longer words

Feynmate

Maybe with some more - uhm - ad hoc model that could make sense, but... As far as I know, everywhere in research where we need computers, it's just about giving computers the instructions and let them "crunch the numbers". We already have the computational power and the brain part is left to actual humans, which are currently superior to AI model in sheer logic

bolbteppa

12:38

Given how easy it is for this thing to go off on a tangent or say something stupid, it makes it even more clear that people need to learn the basic principles, this stuff can help with the menial work in getting that done, it's basically asking a text editor some questions about the text it contains

Feynmate

The only "advantage" would be that you don't have to write down a program to compute your stuff, but...

1. The human is the one who decides what is relevant to compute, that's probably the most important thing in research;
2. The only difference would be that you just tell the AI "hey, solve this equation" insetad of putting your equation into a program. No big difference;

ACuriousMind

@RyderRude ...have you looked at what tests those are? Have you tried to use it in any field where you have enough expertise to actually evaluate the correctness of its answers? You baselessly dream of using this for "research" when you clearly have no actual idea of how good the output is.

Ryder Rude

@Feynmate there is no computer in the world to which u can just instruct to compute predictions of modified Schrodinger eqn. u need to give much more careful instructions there

because gpt uses human language, u can give it far more complex instructions than a computer @Feynmate

qwerty

for me personally, i think that it would be extremely irresponsible (and wrong) to encourage any random person to learn from the robot. that being said, i think it is useful for some things if you have a good bullshit radar or have good background in the subject. the fact that it is sometimes completely incorrect is not all that different to talking to a random classmate or colleague. the problem then is that "you don't know what you don't know", i.e. we might overestimate our own BS radar

Feynmate

I think that AI can play a significant role in bibliography stuff for example. If you are able to ask the right questions and it has access to all knowledge on the internet, you could use it to ask "has anyone ever written a paper about quantum coherent spinning cats?"

ACuriousMind

12:40

@Feynmate Also, they are really really bad at computations. A computer algebra system does prime factorization of numbers deterministically 100% correctly. An LLM might give you the right answer, with the probability of the answer being right going down as the number gets bigger

qwerty

but using it "for research" sounds silly imo

ACuriousMind

The idea to replace actual computations with asking LLMs is just ridiculous

Ryder Rude

@ACuriousMind i have not used it for research, yes. but it is common among experts to believe that this will be a useful tool for research. it is like a computer which can take in far more complex instructions than any other computer

Feynmate

@ACuriousMind Finally there is another problem (although I'm not sure about this, so I may be wrong about how this works): if you have some given computational power - of course finite - you want to use it for the actual calculations, not sacrifice part of it to have an AI (?)

@RyderRude Which makes it more easy to fuck it up.

The great thing about giving detailed instructions to computers is that they're also unequivocal

ACuriousMind

@Feynmate yes, especially for easy computations running an LLM is orders of magnitudes more expensive in terms of computing power than just doing the traditional computation

Ryder Rude

12:44

@Feynmate yes but it is scoring 85%..... . it is at least as reliable as humans when it comes to standardises tests-type labor

so anyting that it could screw up, a human could too

ACuriousMind

@RyderRude No, that's not what it is. And most experts I know are deeply concerned about people having exactly your attitude which is based in hype and misunderstanding rather than actual evaluation.

you didn't even know it scored that good until bolbteppa told you! Why are you acting as if you understand what this means when you clearly have not looked into the topic yourself at all?

Ryder Rude

@ACuriousMind but i knew about a similar score. i linked that article a few weeks ago

@ACuriousMind if some experts believe that this will be useless for research, they are being just as unrealistic as the experts who believe that this would do all research on its own

ACuriousMind

@Feynmate The lure of writing software was always that, unlike humans, the machine can't misunderstand you :P

Ryder Rude

the reality is that it will be useful for research, about as much as computers or CAS are

becuz it is like a computer but it takes complex instructions and is known to perform 85% on certain tasks

Feynmate

@ACuriousMind As my programming professor used to say: your computer is like a very stupid child (he was not so politically correct) who does whatever you tell it*

ACuriousMind

12:49

yes, exactly

Ryder Rude

@ACuriousMind note that this criticism also applies to humans. humans cant do the standardises tests type labor with 100% probability. the reason CAS have high accuracy is because their tasks are a lower complexity than standardised tests

i think i saw Tao saying that this will be useful for research

Feynmate

Also, I wouldn't take that 85% thing as a big deal. First, being good at standardized tests doesn't imply proficiency in real research, where even in "standard" things something new may come up. But most importantly, whenever there is work that can be given to machine, we already do. It's not like PhD students are forced to do long calculations by hand (oh, wait... :P)

ACuriousMind

@RyderRude Of course a CAS can solve 100% of the tasks on a standardized algebra test ("diagonalize this matrix", "solve this equation for x", etc.). What kind of tests are you talking about?

Ryder Rude

@ACuriousMind i mean the kind of tests on which gpt scored 85%. it is called an IMO test

this test nature.com/articles/d41586-025-00406-7

i am saying that CAS and gpt have different applications in research, based on the kind of labor they can do

ACuriousMind

There are many proficient scientists and mathematicians who are not good at solving these olympiad-style problems. Even for humans, proficiency in that kind of problem and proficiency at what mathematicians do is not always correlated.

Ryder Rude

12:57

@Feynmate good points... but it i think it is too pessimistic to say that it will be useless. standardised tests have limitations. but some problems like those will show up in research.

Feynmate

I greatly fear those who are proficient at those things (olympiads&co.), by the way. I had some trauma back in the day :P

Ryder Rude

@ACuriousMind i am just saying that there is some correlation. if these problems show up in research, then one can dostribute that labor to gpt

i am not saying that gpt will do 100% of research

ACuriousMind

@RyderRude And how do you check the result? Who is responsible when the answer is wrong?

Feynmate

I always sucked at those problems. People say that it takes a lot of practice, but I could never be interested enough in such problems to actually do that practice

And as of today, I panic whenever I meet someone who is good at those D.

ACuriousMind

again, in order to use this responsibly you need to already be able to do the stuff you ask it to do yourself. for such tasks, it can be useful (mostly a timesaver) when proofreading the response and correcting mistakes is faster than writing it down yourself

Ryder Rude

12:59

@ACuriousMind how do u know if u didnt make a mistake while working on the problem urself? one only has probabilities. what matters here is that gpt scores a good probability

bolbteppa

Forget about research for now, I'm just saying this thing is very useful as an aid when learning stuff in standard books, it lets you ask questions, or you can ask it to do something in a different way, yes if you don't ask the right question you will go down a blind alley so it's definitely not going to replace learning from books, but as a complement it has a lot of potential

Ryder Rude

the ONE problem we face is :determine with good probability if a research sub-problem is similar to a standardised tests problem. it can be worked out as we go along, trying to figure out the sweet spot that gpt would occupy in research

@Feynmate lol

ACuriousMind

My position is not "this thing is useless", it's that its actual usefulness is much more constrained than its peddlers want you to believe, and that there is a great danger of people who have no way to evaluating the correctness of the answers relying on them even when they are wrong.

If some mathematician uses it to generate a proof and then corrects a few mistakes in the generated proof rather than writing out the proof themself and that's faster, sure, that can happen, it's great

but I see vast overestimation of how many such tasks there are in actual day-to-day work

Slereah

also there are better softwares for proof automation :p

ACuriousMind

@Slereah yes, but they don't produce output you can put in your textbook :P

Slereah

13:06

I mean you can, I'm not sure it will be very popular though

Ryder Rude

@ACuriousMind people will figure out its place as they go along, trying to use it in research. its extent of usefulness will become clear in the coming 7-8 years

Slereah

unimath.github.io/agda-unimath/…

Ryder Rude

it will find some place

Slereah

fun times

Ryder Rude

i think these bots dont have an internal experience, which is why they cant just do all research on their own

bolbteppa

13:07

Yeah I think this thing will lead people down bad roads if not carefully used

Slereah

What do you mean "lead"

It's already there

Ryder Rude

humans need to use their intuition and inspirations and stuff to come up with the right research directions. then some labor can be distributed to the bots if the problem is well defined

human consciousness is a complex thing. the bot is a language imitator. it doesnt have a unified experience

it is like the chinese room. the room doesnt have a unified experience

ACuriousMind

@bolbteppa The genie is already out of the bottle: my search results are full of generated garbage, we're seeing papers containing obvious generated text that has not even been proofread to remove the most telling sign, I'm getting emails that clearly no human bothered to write but expects me to read

Slereah

pivot-to-ai.com/2025/02/15/…

4

Ryder Rude

i think these olympiad problems r dumb anyway

ACuriousMind

13:10

Instead of getting actual documentation, I'm being told to just ask an AI

the list goes on

Ryder Rude

they treat math like a game

math is not a game. it is more about research

but some of these problems may show up in research

qwerty

@ACuriousMind wtf o.o

like actual developers are saying that?

ACuriousMind

it has happened, yes

qwerty

D:

skullpatrol

@Slereah whelp, people tend to be lead by example...no

thanx for the link

Slereah

13:14

also really fundamentally why do you not want to work through a problem yourself :p

naturallyInconsistent

my colleagues often just use ai

Slereah

If you're forced to for your job sure, but if you just like physics read it

naturallyInconsistent

some of them in coding

ACuriousMind

but it's not just technical documentation, also process documentation and other things. I get malls where "in case of questions" I'm asked to first ask their AI. Which is clearly just GPT that someone fed their documentation as the system prompt, i.e. it cannot possibly tell me anything I could not already have understood by reading the documentation.

one chatbot I encountered had clearly been instructed to finish every response with a quote from a list of quotes it had been given in the system prompt - which were all quotes from a high-level executive, and which the bot happily put at the end of every response, no matter how inappropriate

Slereah

fortunately I work in a bank so they are pretty wary about employing an outside AI :p

ACuriousMind

13:17

it's bizarre what people are trying to use this stuff for

Feynmate

@ACuriousMind do you have Weinberg II at hand for a question, if you're available?

It's nothing big, just the background field method

ACuriousMind

@Feynmate nope, if it's specific to something in Weinberg ask me again tomorrow

Feynmate

Okie dokie, I will ask again tomorrow. Thanks

ACuriousMind

@Slereah so you're growing your own, which then has all the same effects but it's worse than the outside models :P

Slereah

@ACuriousMind Well we had an AI even before chat GPT :p

Who do you think answers the client's questions on the hotline!

ACuriousMind

13:21

I did not know any questions got answered on hotlines anymore :P

Slereah

Except it's not an LLM, it just learns to recognize keywords and give a canned answer

ACuriousMind

sure, we've had those systems for a while

Slereah

they're also developping an LLM for... some purpose?

To keep up with the joneses

ACuriousMind

because it's the hot new thing

Slereah

I mean I'm not gonna complain about probably useless trends, I'm on the quantum computing division :p

ACuriousMind

13:23

there's probably some kind of financial forecasting team very upset that they've been doing machine learning for ages and now all people want from it is to generate corporate speak :P

Slereah

Learning differential cohesion is tough because half the articles are in category theory and the other half is in type theory

I'm not good enough to do the translation in my head

also sometimes it's category theory and sometimes it is $\infty$-category theory

Trickier to deal with

qwerty

@naturallyInconsistent it's fine for generating drafts of code imo because it's efficient and it's easily testable. but it clearly cannot replace documentation written by a human who knows the actual purpose of a script

naturallyInconsistent

@qwerty ive not included a judgement claim in that comment miehehehe

qwerty

:)

Slereah

13:39

One thing I am particularly confused by is the notion of term rly

If you have a term $x : T$ in type theory, what does it mean on a categorical level???

qwerty

hbar is so cosy. like this description maggieappleton.com/cozy-web

Slereah

The usual translation is that if you have $x : T \vdash f(x) : S$, that's a morphism $f : T \to S$, but then what does it mean for an empty context

Like what does the unit type $\vdash \ast : 1$ mean, categorically

User198

1.) Momentum is the generator of translation $\{f,p\}=\frac{\partial f}{\partial q}$

$q$ is the generator of momentum, but from the Poisson brackets, I get it with the $-$ sign: $\{f,q\}=-\frac{\partial f}{\partial p}$ by definition. Is it correct than to say that "$q$ is the generator of momentum" or should I now say that the "$q$ is the negative generator of momentum" or sth like that? It bothers me that both expressions are not the same, but we talk like they are. Or am I missing something?

2.) Momentum in CM: $\{\cdot,p\}=\frac{\partial \cdot}{\partial q}$

in QM $\hat p=-i\hbar\nabla$ its similar.

What about $\{\cdot,q\}=-\frac{\partial \cdot}{\partial p}$ in QM, is there expression akin to the momentum one in QM?

Slereah

@User198 That is the position operator in the momentum space

User198

@Slereah Ok thank you

ACuriousMind

13:53

@User198 The minus sign is irrelevant when talking about "generators"

you can multiply a generator by an arbitrary non-zero real number and it still generates the same one-parameter group of transformations

just different values of the parameter correspond to different transformations when you change the generator

also, it's "generator of translations in momentum", not "generator of momentum"

@Slereah isn't the unit type just a/the terminal object in the category of types?

at least in the basic functional programming way I understand type theory, the unit type is the terminal object and the empty type is the initial object

Slereah

@ACuriousMind Yeah I think the "normal" thing is $\Gamma \vdash \ast : 1$, ie any context [object] has a morphism to it

But what about the empty context?

Empty context is technically a valid one, as far as I know

ACuriousMind

I don't really know what context means in this context, sorry

Slereah

in this what?

ACuriousMind

:)

Slereah

A context is a list of formulas

ACuriousMind

13:57

if the contexts are your objects, isn't the empty context just the empty type in my langauge?

Slereah

You'd think so, but from what I could find no

Although I'm not 100% sure

ACuriousMind

so your "unit type in the empty context" is not the morphism from the initial to the terminal object?

Feynmate

Whenever I read "LLM" I can't help but think of TTM (Tank Top Master) from OPM

ACuriousMind

@Feynmate It's funny that you spelled out TTM but apparently assumed everyone knows what OPM is :P

Slereah

TTM is the double tangent bundle

Feynmate

13:59

Good point

ACuriousMind

OPM = One Province Minor

Feynmate

(you both)

One Punch Man

ACuriousMind

ah, I suspected anime :P

Silly Goose

@TobiasFünke oh lol i see. Is your chemical potential grouped into $\epsilon$?

Tobias Fünke

@SillyGoose I work in the canonical ensemble

Feynmate

14:01

TL;DR: This average guy gets bored of normal life and starts training. His training consists of 100 push-ups, 100 sit-ups, 100 squats and a 6.2 Mile (10km) run, a banana and no air conditioning for three years. So he becomes bald, but also so strong that he can one-shot everything with a punch

Silly Goose

Oh i was computing in grand canonical

Feynmate

@TobiasFünke does the salary fluctuate?

Slereah

Although really to be fair the comic is barely about OPM after a while :p

Feynmate

That's when you drop it :P

Tobias Fünke

@SillyGoose well, then the result is basically in every textbook

Slereah

14:02

Which I guess is inevitable, if they focused too much on him it would get boring

Tobias Fünke

@Feynmate classic FM, once again :d

Slereah

Just wins every time

Feynmate

Honestly, it got boring when they started talking about the other fodders

Silly Goose

But im a bit confused. I mean the partition function for non-interacting particles generically factors, so computing the PF in GCE is kind of not bad. But every resource I’ve seen takes some semiclassical limit to analyze the chemical potential and etc

Feynmate

I only wanna see Saitama punching people

ACuriousMind

14:03

@Feynmate Okay, I can suspend my disbelief for the "gets super strong" part, but why is baldness a necessary consequence here???

Tobias Fünke

@SillyGoose as I said, in the GCE the partition function of the QHO should be derived in any reasonable textbook

Feynmate

@ACuriousMind This one is actually WebComic--->Manga--->Anime just FYI

Tobias Fünke

we can discuss later, just ping me. I have to go again, but I will read later!

Slereah

@ACuriousMind Too much testosterone? :p

Feynmate

@ACuriousMind I think it's quite intentional to have such irony. An average guy does a tough but normal training (with some funny details like the air conditioning) for three years and he gets so strong that a punch of his blows away a storm

Silly Goose

14:04

@TobiasFünke my confusion though is that several papers, e.g. by ketterle, use approximations of the partition function when seemingly an exact answer should have been readily available

ACuriousMind

@Feynmate I'm confused about the genre here. Is it (partly) a comedy?

Slereah

OPM has a similar issue to God Man I suppose

ACuriousMind

in a comedic story I can buy this

Slereah

Slightly overpowered

Feynmate

@ACuriousMind In my opinion, yes. It's a comedic story. Hardcore fans might want to read too deep into it and claim otherwise, though

Pretty much like ST people claiming to have the final theory of the universe :P

Slereah

14:06

The comedy mostly stems from Mr. One Punch Man mostly being a hapless dude

He's not super smart

Feynmate

Then the story is played upon paradoxes. The setting is that of a society endangered by ever-looming monsters, which are antagonized by the heroes of the Hero association. Even if the protagonist is by far the strongest, he is considered a second class hero because of unlucky coincidences, causing more famous heroes to be considered responsible for his heroic acts

Like when Hilbert stole GR (JK y'all)

Slereah

Restarting the entire universe is his main move I guess

Tanishq S

hello! I am a highschooler and I've recently had this question in my exam: `Assertion (A): Magnetic field lines around a bar magnet never intersect each other.
Reason (R): Magnetic field produced by a bar magnet is a quantity that has both magnitude and direction.

A) Both assertion and reason are true, and the reason is the correct explanation for the assertion.
B) Both assertion and reason are true, but the reason is not the correct explanation for the assertion.
C) The assertion is true, but the reason is false.

I was wondering if the reason is a correct explanation or not, many on YouTube say its not, but I was thinking that it seems to link to the fact that Magnetic fields are vector fields, which seems to be a correct reason?

qwerty

14:25

@TanishqS I saw your closed question. Did you look at the question that Vincent Thacker linked?

User198

@ACuriousMind Oks thank you

Tanishq S

@qwerty Yes I did go through it, and I understand that they not intersecting, but I want to know if it is reasonable enough to say that the reason is a correct explanation or not...

ACuriousMind

this is the kind of exam question I hate :P

Silly Goose

Education be like: the assertion is true but the reason is false

Tanishq S

@ACuriousMind That's the reason I am seeking help because it feels as if it could be based on the perspective of the examiner...

ACuriousMind

14:35

You can argue both A) and B) depending on how narrow/broad your idea of an "explanation" is and there's no "correct" answer, just the answer the test writer wants to hear

Silly Goose

Actually more like the assertion is false and the reason is false

Tobias Fünke

@SillyGoose can you please link to the paper? Are you totally sure that they use the GCE? Their BEC work is often in harmonic traps, no? So the number of particles should be conserved?! I cannot help you further without seeing what exactly you mean here.

Silly Goose

@TobiasFünke i am using gce with the understanding that we will fix the chemical potential via constraining expected number of particles to be the actual number of particles in the system

as is done e.g. to quickly derive the BE distribution

Tobias Fünke

15:11

ok. and what are your results for the GC partition function and the chemical potential? @SillyGoose

I mean the standard form of the GC PF for bosons is in all textbooks. Did you arrive at an analytical expression for the HO?

Sir Cumference

18:19

@ACuriousMind Reminds me of how "flux" and "flux density" get mixed up depending on the person

Tbh if astronomers were able to put their foot down on the meaning of "planet", I feel like they should be able to create standards for other terminologies too

Well, maybe it's just because "planet" seems like such an important term to everyone

ACuriousMind

@SirCumference I'm not sure what you mean. Stuff like "flux" or the radiative terms you cited isn't exclusive to astronomy, those terms are used in a lot of other contexts, too

Sir Cumference

Ah yeah, that's true

ACuriousMind

while "planet" always refers to the astronomical context, so it's the astronomers who set the standards around its "official" meaning

Sir Cumference

Maybe we should just leave it up to the mathematicians to come up with all the terminologies

They usually seem to avoid these kinds of naming conflicts

Rigorous bunch

ACuriousMind

nah, they managed to make it so that "manifolds with corners" are not necessarily "manifolds" :P

Ryder Rude

18:42

i feel people who only learn olympiad skills have a shallow view of physics

and math

these subjects r not games

i am feeling better now

Tobias Fünke

@RyderRude nice :)

@RyderRude I don't know... many of those brilliant people also end in academia as researchers... But of course, solving very specific problems is only one skill needed for success in academia/science.

Ryder Rude

18:59

@TobiasFünke yeah.. Tao was also in the IMO, apparently. there r correlations

but someone who only does the olympiad stuff has a shallow view of physics and math

but maybe that is what they like

Tobias Fünke