The h Bar

ACuriousMind

00:13

@SillyGoose There should be a "-" on one of the $v_i$, but otherwise that's just the equivalence between undirected graphs and 1-dimensional CW complexes. This is exactly the cellular boundary map of a CW complex.

@Relativisticcucumber what's the difference :P

I've talked about the von Neumann quote that in math you don't understand things, you get used to them before (e.g. here or here) and I think it is the case that much of "understanding" is just getting used to how stuff actually works (thus retraining one's "intuition") instead of relying on untrained (and wrong) intuition

naturallyInconsistent

00:33

@Relativisticcucumber is it important to tell? Isn't it enough to just celebrate having better understandings of things?

Silly Goose

@ACuriousMind what is the point of the $-$ sign?

Relativisticcucumber

00:54

@naturallyInconsistent well if all one does is get used to things, this is arguably not a productive understanding. i say arguably bc i am arguing with myself if that is even valid or not

Allie

meow

meowing

Relativisticcucumber

@ACuriousMind well can you actually do things with content you have internalized but don't understand? i mean one might say yes bc we are conversing productively in english which is smth we just internalized and i dont even know what it would mean to understand english

Allie

@naturallyInconsistent the vW KE is exact for a one electron system, right?

since square root of electron density is just wave function in that case

Relativisticcucumber

but i have this fear of like being blinded by "knowledge goggles".

Silly Goose

@Relativisticcucumber kant be like: that's all human experience

naturallyInconsistent

00:59

@Relativisticcucumber what is it is a mixture of both? I'm really not trying to argue that it is great to just get used to things, but that it is futile to try to be exacting about all that.

@Allie m e o w ~

Silly Goose

Kant was a proponent of representation theory: "Our knowledge springs from two main sources in the mind, first of which is the faculty or power of receiving representations (receptivity for impressions); the second is the power of cognizing by means of these representations (spontaneity in the production of conceptions)." ;)

Allie

yeah, well he was a real Kant

naturallyInconsistent

01:47

@Allie The literature claims so; I'm not inclined to disagree, but I'm inclined to point out that this isn't useful. I mean, we do not really care about KE term alone, and the difficulty in DFT is not in the KE term either; the difficulty is in handling exchange-correlation, which isn't appearing in one-electron systems.

Allie

I'

naturallyInconsistent

@Allie enter button is just close by lol

Allie

again, I'm talking about OFDFT...

So yes, the difficulty is in the KE term

thats precisely the difficulty

naturallyInconsistent

@Allie are exchange-correlation not a headache in OFDFT too?

Allie

not nearly as much as KEDF

majority of the energy is KE

the idea is to get it at least approachable to KS accuracy so you can take advantage of its awesome O(n) scaling

since you can just use the same XC as you use in KSDFT (provided it is not orbital-dependent...)

anyways, thats why im focusing on KEDF's so much. OFDFT research is mostly in new KE functionals from what i understand, this is the biggest issue

naturallyInconsistent

01:52

Oh yes, you are correct, sorry.

Allie

lul its ok meow

naturallyInconsistent

I forgot that you could just spam XC functionals

Allie

yeah, KE is not so easy unfortunately

but being able to treat 100 million atom systems with DFT is... pretty cool

so im excited to work on this project

naturallyInconsistent

yeppuu

Allie

anyways thanksy

naturallyInconsistent

01:54

mew mew

Relativisticcucumber

@naturallyInconsistent for the first sentence i had the experience of having to read it multiple times adjusting the word that i place emphasis. i feel like an AI when this happens

i think it should read what if it's a mixture of both xD

naturallyInconsistent

@Relativisticcucumber correct lol

Relativisticcucumber

yeah i mean that's a valid point. what i got to is the observation that i feel younger people struggle to follow complex trains of thought, and im trying to understand why this should be so. this seems to be one of the key factors that underlies this phenomena that we "get things" more as our experience grows but i am not sure what the root of this would be really. one possibility is that we learn frameworks for mapping complex thoughts onto something more intuitive (i.e. we learn to model)

but still the process by which we learn to access these models / this more abstract way of thinking is mysterious to me. i think even not all people do this well even if they age, so it can't be just about getting older, but something active must be done to activate this type of thinking

so i wonder what this is

naturallyInconsistent

@Relativisticcucumber I'd not exactly agree with "younger people struggle to follow complex trains of thought". I think older people are worse at it than younger people.

Relativisticcucumber

true but what i mean is that there seems to be a very strong limitation on what kids can handle in terms of thoughts, at least i have experienced this with calculus and physics in high schoolers versus uni students. and small kids also seem to get confused quite fast, even the bright ones. this leads me to think there is some average fundamental limitation

naturallyInconsistent

02:08

@Allie oh, miao miao was reading a review's table of data and suddenly there was an absurdly good DFT result, only to realise that the caption said:

> The exact-DFT result quoted from Ref. [61] is calculated from the exact exchange-correlation potential obtained by reverse engineering from the exact Hylleraas solution. So, its accuracy only reflects the accuracy of the Hylleraas solution that must be known in advance, in contrast to the accuracies of all other methods which are genuine and real. We quote the exact-DFT result just to remind the reader of the scope of DFT, which should be the target of improved approximations.

Relativisticcucumber

i think this goes for some older people as well, but i am curious about what "lifts" this limitation

Allie

probably just brain development

Relativisticcucumber

i think maybe it can be like we learn by observing, so maybe we acquire enough knowledge to understand the abstract arguments put in front of us, then we engage and learn and then eventually gain the ability to do this ourselves

Allie

i dont think at all its a specific hard limitation

i just think kids brains arent fully formed yet so they cant handle the most complex thoughts

Relativisticcucumber

but still smth is missing here so idk. i need to think about this

naturallyInconsistent

02:09

@Relativisticcucumber The opposite is true. I've never had difficulty teaching my younger students calculus. But needless to say, miao miao has a very rigorous yet smoothed out treatment that maximised their ability to follow the story.

The initial bits are very applied. Not at all abstract. But they'll get it, if you hand-hold them through the algebra.

Relativisticcucumber

hm interesting. i find there are certain things i can do to check and i realize the students actually dont get it. bc if i do some ode problem and i say the integration constant is c, then we end up with $e^c$ then i say ok constant is $k = e^c$ then i use $k$ then they become very confused

naturallyInconsistent

Actually, the main difficulty is in algebra; students are extremely averse to using algebraic notation for their own work and thinking processes, and it is that, that is hindering calculus understanding.

Relativisticcucumber

so this tells me they dont actually understand what's going on or else they'd be fine w this manipulation

but wdyt ab this?

naturallyInconsistent

@Relativisticcucumber see, your problem here is not calculus, but algebra, again

Relativisticcucumber

well i think it means they dont get the concept of this constant

like if they think it must be c then they are missing the point, no? /

same for today i was doing series and the canonical problem i have is that students hate when u change the dummy index

naturallyInconsistent

02:13

The only time when students really don't like miao miao, is when at age 10 or 11 miao miao insists that they do everything in algebra; they might do it once in any other form, but will redo it in algebra. Once they are familiar with algebra by age 13, they are ready to do calculus at age 14-15.

@Relativisticcucumber and this is yet another algebra problem. Look, my students might take some time to understand that I did a swap and get used to it; I'd give them the whole 5 minutes they need to convince themselves that everything makes sense, but they can follow the argument themselves and will not need more hand-holding nor myow time to explain how.

Relativisticcucumber

hm interesting. i somehow feel that my students are like memorizing the methods but not truly getting it -- i hope i can improve this. to be fair right now im limited to TAing/tutoring so i have to basically just supplement the prof/teacher's approach. i am eager for the day that i will get more say in the presentation style

bc for the hs students that i tutor, im 100% certain their teachers do not even know what they are teaching bc the methods they employ are just bogus sometimes. so this really hinders the progress i can make

like one of my students came to me and she can do a problem like finding what a geometric series converges to but when i ask her to define a series she says she doesn't know bc they didnt go over it. i was like ??? how even

and she is a v good student so its not even her fault so its just like i feel bad for the students

Silly Goose

i wonder how hard it is for children to learn category theory

Relativisticcucumber

02:50

@SillyGoose did u ever use those stupid toys where you put the shapes into the box

Allie

yeah thats a stupid toy, kids should have to turn the sphere inside out without creasing

Turning a Sphere Outside In

►

oh i sent the completely wrong one LMAO

yeah do not watch that....

naturallyInconsistent

03:15

@Relativisticcucumber It might not even be the case that the teaching is bad. Most of hoomanity would completely blank out the abstract definitions that are mentioned once at the start of the topic and never again.

Allie

meow

naturallyInconsistent

m e o w ~

Allie

03:40

learning is hard sometimes

i hope im learning well

Allie

04:00

@naturallyInconsistent i have another pregunta.... >,<

i shoiuld really go to bed but i do want to know

bestie

naturallyInconsistent

didnt realise pregunta is just question...

Allie

ok, so...

I've seen 2 definitions for the non-interacting kinetic energy in KSDFT, i want to kinda understand their connection and how theyre the same

so the first one of course is $\sum_i \langle \phi_i | -\frac{1}{2}\nabla^2 | \phi_i \rangle$

just directly calculating the KE from the KS orbitals

naturallyInconsistent

Yes, that $\frac12$ is really $\frac{\hslash^2}{2m}$ with $\hslash=1=m$

Allie

Now, I should say i derived the KS equations by minimizing the energy functional $E[n] = T_s[n] + \int v_{ext}(\mathbf{r})n(\mathbf{r})d\mathbf{r} + E_H[n] + E_{XC}[n]$

subject to the constraint that the KS orbitals be orthonormal

sound right?

naturallyInconsistent

Cannot remember the details, but it does sound correct.

Allie

04:11

My confusion lies with the other definition, $T_s[n] = \min_{\Psi \rightarrow n} \langle \Psi | -\frac{1}{2}\nabla^2 | \Psi \rangle$

naturallyInconsistent

Of course, the $T_s[n]$ not actually being a functional of the density $n$ is a pain in your neck right now.

Allie

In other words, the minimum KE of any N-electron wave function that produces the electron density n(r)

I understand how this comes about if you were to minimize E[n] for a given n, since the other 3 terms are fixed for a given n, but $T_s$ is the only one that depends on your orbitals

sorry, that should say the minimum KE for any non-interacting wave function

OH, i think i get it.........

I was gonna ask why the minimum KE of any non-interacting N-electron w.f. producing a given electron density n(r) happens to also be the KE of the KS orbitals, since you have a potential v_KS there

but I realized because you have the electron density fixed, the contribution from the potential is fixed, so you basically only are changing the KE when you vary the KS orbitals

naturallyInconsistent

people.chem.ucsb.edu/metiu/horia/OldFiles/115C/KH_Ch4.pdf

I think you are trying to be too mathematical about this. For HK theorems HK1 and HK2, you have exact mathematical equivalence. However, they are talking about exact, interacting, electrons. The KS DFT is a complete swap and there is very little that is realistic.

Kohn–Sham equations

The Kohn-Sham equations are a set of mathematical equations used in quantum mechanics to simplify the complex problem of understanding how electrons behave in atoms and molecules. They introduce fictitious non-interacting electrons and use them to find the most stable arrangement of electrons, which helps scientists understand and predict the properties of matter at the atomic and molecular scale. == Description == In physics and quantum chemistry, specifically density functional theory, the Kohn–Sham equation is the non-interacting Schrödinger equation (more clearly, Schrödinger-like equation...

Allie

lol

naturallyInconsistent

It is openly admitted that KS stuff are lies, and the various links to Koopman's theorem is trying to tell you that, indeed, they are lies.

We don't even know the error bars of those approximations.

Don't be too uptight about them. It will make your life hell.

Allie

04:25

are you talking about results from KSDFT in general?

naturallyInconsistent

I am saying that the transition from the mathematically exactly correct HK to the mathematically nonsensical KS DFT is well known to be nonsense, but it is tolerable because the whole of KS DFT is built on top of comparing to experiment, and this makes its errors tolerable.

Allie

i mean, how is it mathematically nonsensical

KSDFT is formally exact

naturallyInconsistent

none of the transition is mathematically justified, but the errors are constrained by choices of parameters by experiment. It is bad, but it is not toooooo bad.

@Allie Well, we cannot prove that the non-interacting bit is "formally exact" either.

Allie

yeah because that part is nonsense

naturallyInconsistent

I mean, have you checked what "formally exact" means there?

Allie

04:28

im talking about the overall process of KSDFT

if you have the right XC functional youre golden

in any case, i understand why youre telling me not to focus on the non-interacting KE, but this is entirely the focus of my research: recreating the non-interacting KE without the use of orbitals

naturallyInconsistent

But even if you have the correct XC functional, given to you by a soul trade with the devil, you will not be able to obtain anything else from there because Koopman's theorem implies that the individual KS eigenfunctions and eigenenergies are nonsense.

Allie

@naturallyInconsistent i have the exact XC functional on a floppy disk somewhere in my closet...

naturallyInconsistent

@Allie No, I'm not asking you to stop your research. I'm trying to tell you that if you are looking for a mathematically sensible treatment of the topic, you will not be able to find one, because it doesn't exist. However, this also means that if you simply dream up some functional, you can try it and see if your thing works. Maybe they'll give you a Nobel prize for a good dream.

Anyway, I think we have had enough discussion: you should go sneeppuu, and miao miao needs to restart computer; this restarting might drop meow meow off the face of the Earth, but alas, it needs to be done.

Tobias Fünke

06:29

@Relativisticcucumber yeah, by definition of a natural science it cannot. to what extent a theory is "real" is a matter of debate/personal interpretation... but sure, you can ask those questions, and these can give motivations for specific theories or so...but in the end you just shift the "why" to the next level (and even then you don't know if the theory is "true" or "real").

for this special example, I recommend Wigner's essay about the unreasonable effectiveness of mathematics in the natural sciences.

@Allie Is your question about the KS equations settled now?

@naturallyInconsistent well, there are a lot of researchers, especially mathematical physicists, who make DFT, to some extent, completely rigorous (Lieb, for example, made huge contributions)

ACuriousMind

07:08

@SillyGoose in general it's so that the square of the boundary map vanishes; I agree this is not obvious in 1d

@Relativisticcucumber I mean if you understood the exact nature of this process you'd understand how to build true artificial intelligence :P

@Relativisticcucumber I think this phenomenon is largely a consequence of most standardised testing methods being unable to differentiate between "understanding" and memorization, but we use it as a proxy for understanding, and so you get a lot of people that on paper should understand something but really they just memorized the parts of it necessary to (minimally) beat the tests

If you put a metric on something, people start optimising for the metric, not for what it is supposed to measure

qwerty

07:30

@ACuriousMind humans wanna follow geodesics?

ACuriousMind

Yuuuup

qwerty

(Human) nature is thrifty in all its actions

Ryder Rude

i put emphasis on understanding

humans should live a life of meaning and meaning comes from understanding

Tobias Fünke

OTOH, as von Neumann (?) said: you don't understand mathematics, you get used to it :p

one might replace mathematics with any subject hehe

qwerty

7 hours ago, by ACuriousMind

I've talked about the von Neumann quote that in math you don't understand things, you get used to them before (e.g. here or here) and I think it is the case that much of "understanding" is just getting used to how stuff actually works (thus retraining one's "intuition") instead of relying on untrained (and wrong) intuition

correct :p

Tobias Fünke

07:37

haha

yes, I agree with ACM. Understanding means to a large extent, especially in highly "abstract" sciences, a retraining of "intuition"

Ryder Rude

or even stopping to care about having an intuition. shifting goals

qwerty

i dunno about retraining so much as developing

Tobias Fünke

similarly as in martial arts, where you have to learn certain techniques and maybe do not the "intuitive" thing (sorry my English is bad, especially in the morning, so I cannot phrase it properly right now haha)

@qwerty both, I'd say

Take SR. The human intuition is that of absolute time, but that's not what experiments tell us

Ryder Rude

yes. it is impossible to talk about SR without spacetime diagrams

qwerty

@TobiasFünke any schoolchild knows that times goes slower when you're bored ;)

Tobias Fünke

07:41

hehe

I cannot argue this

qwerty

actually that would be a fun one for early childhood development, i bet theres already studies on time perception in preschoolers...

i wonder what they would say

Tobias Fünke

hmmhmh

qwerty

about whether the notion of absolute time taught (by learning to read clocks etc)

Ryder Rude

i think I read somewhere that time was not thought of as absolute before Newton tried to enforce it

but this seems wrong. i thought about time as absolute

qwerty

iirc some cultures don't have notions of absolute time

Ryder Rude

07:44

depends on the notion. i have a hard time imagining that some cultures lack a notion of "what's happening on jupiter right now"

the idea is "what's happening on place x right now". this kind of thought should be universal across cultures

i think the absoluteness of simultaneity is intuitive

naturallyInconsistent

@TobiasFünke I am not denying that there will be wonderful people doing amazing work on DFT, but I am saying that DFT, as of now, is still an uncontrolled approximation, and we should never deceive ourselves in trying to deny that it is not an approximation. The functionals have been proved to exist but are not found; they are widely suspected to be of incredible complexity.

Ryder Rude

08:00

i also think that the absolute simultaneity notion is useful for survival in wildlife. e.g. a prey animal has to calculate what the predator is doing at the moment and vice versa

animals have to operate as if there is an absolute plane of simultaneity

Herr Feinmann

08:12

I was wondering: if your objective is to just learn more physics and mathematics, is research really the best path to do it?

Research in academia of course

DIRAC1930

@HerrFeinmann I'm starting to think no lol

Ryder Rude

@HerrFeinmann i think research is about learning one aspect of physics really well and even contributing to it. if u r going for variety in knowledge, research does not contribute to that

DIRAC1930

However I imagine if you're doing your PhD in America, 7 years will give you enough time to learn what you want on the side but I don't know

If your PhD is 3 years, you end up feeling guilty for not working on the problem you need to solve to get your PhD lol

But then again, you probably learn more physics and mathematics compared to finding a job and have multiple tabs open lol

Herr Feinmann

08:29

I don't think it's just about time. Research is heavily focused on a single topic or a list of heavily related topics, so even if you devote more time to physics, you spend 100% of that time on a specific argument. Of course that is how expertise works, still I don't know if I see myself happy to work on the same thing for a while

qwerty

@HerrFeinmann yeah i was coming to similar conclusions when applying to postdocs

Herr Feinmann

You do learn more physics and mathematics but still related to that branch, like maxing out only one stat in an RPG

I always thought: after I finish my master's I will spend time filling the gaps and learning about the things I couldn't learn here because of time. The result is that my friend started a PhD and I see him heavily focused on his work 24/7

qwerty

there's risk involved to do new things compared with established knowledge as well; it's not like youre being efficient with learning. often you're doing grunt work to get out the pubs as well.

DIRAC1930

This Christmas break, was the only time I got to learn what I wanted to learn for the entirety of the last academic year

The rest was just focused on solving a problem for my PhD

Ryder Rude

i think people who want to contribute new knowledge should do research

Herr Feinmann

08:34

Also, there are so many things that worry me: some advisors can be very - uhm - stubborn and you may end up being published in a paper that you are not 100% convinced about, that is really scary for me

Say, for example, that you realize after some time that your advisor is a crackpot

Ryder Rude

do advisors force u work on their own stuff

qwerty

@HerrFeinmann yeah uh something like this happened to me :p

i sorta alluded to it on here before

i think if you get out of a phd and decide you want to continue, there's perhaps less risk of that in e.g. a postdoc

Ryder Rude

does it kill reputation if the ideas u published are wrong

Herr Feinmann

@RyderRude Basically, yes. You can't go there and say what to do. Of course, you may say your opinion. Whether that is considered relevant depends on the advisor, I guess. Nonetheless, what I mean is that yoru advisor may choose a direction of research that you do not consider proficient and you would be forced to follow that too

What if that "stains" your career?

DIRAC1930

I mean, you can check their papers before hand

qwerty

08:37

you just got to push on through

Herr Feinmann

@DIRAC1930 Mhhh, I'm talking about something happening in the middle of your PhD

@qwerty Yeah, probably you just have to live on :'(

Ryder Rude

@HerrFeinmann what do u get to choose? do u get to choose the broad research topic like whether u want to research mathematical QFT or Standard Model? do u also get to choose the specific problem within the broad topic? or do advisors choose both the problem and the solution direction?

qwerty

@RyderRude it depends on the advisor and program

Herr Feinmann

Well, between mathematical QFT and SM there is already enough difference that it may mean choosing a different advisor in the first place

qwerty

there's no rules except the ones your advisor makes up :p

Ryder Rude

08:40

yes. i think advisors are categorised according to the broad research topics. so u have some control over choosing advisors. but once u choose an advisor, do u get to choose a problem within the topic?

qwerty

and i guess the institute might have guidelines, but they are usually... guides.

Ryder Rude

or does the advisor choose both the problem and the solution approach

Herr Feinmann

I'll give you an example of what I mean. Let's say your research area is X. Then, after discussions and publications, your advisor gets interested in Y. You think that Y is just a blind alley, but you end up having to spend your time on it

Ryder Rude

does X refer to a problem? like u signed up to work on the problem of position basis in QFT, but ur advisor latter became interested in the Haag's theorem

both are problems within mathematical QFT

naturallyInconsistent

It is usually more that the advisor chooses you or not, especially if their research area is exciting / competitive / rich

Herr Feinmann

08:43

@RyderRude I think the position basis in QFT may be too specific, but yes. Let's say that's the case

Ryder Rude

i think advisors can decide whatever they want, based on this discussion. they can change the solution approach or even the problem itself

and their specific problem approach can be crackpottery. I understand now

Herr Feinmann

And if your advisor ends up being a crackpot, you'll always be a guy who did a PhD with a crackpot D:

Ryder Rude

does ur phd research topic decide the direction u research in after phd?

naturallyInconsistent

@HerrFeinmann you can at least hope, with good chances, that your crackpot advisor is not so big of a deal that international news cares.

DIRAC1930

I mean you can always ignore your advisor lol

naturallyInconsistent

08:46

rip marvin

Herr Feinmann

Well, people won't throw eggs at your house, but if you apply somewhere for a PostDoc, you may be rejected (?)

naturallyInconsistent

@DIRAC1930 you cannot ignore your advisor when they withhold your degree

DIRAC1930

Oops, I should probably email my advisor lol

Ryder Rude

but this discussion is really orthogonal to ur initial question. even if everything in research turns out right, u would still be working on one problem for long

it does not encourage variety in learning

but if u want to contribute things instead of learning, the current discussion is useful as a risk-reward analysis

qwerty

@HerrFeinmann well, if you manage to extricate yourself and do your own thing, actually people end up acknowledging your scientific integrity... but yes, it's a tricky situation that is not recommended for mental health or career

Herr Feinmann

08:50

I don't know how much that could affect me. I already refuse to answer question I'm not sure about in daily situations, imagine how much publishing something like that could destroy me :P

qwerty

@naturallyInconsistent degree is usually fine actually if you have enough work done - that is usually handled on the university level, the problem is reference letters, connections, recommendations... that sort of thing

naturallyInconsistent

@HerrFeinmann Well, that does not mean that your own research would have no choice but to also be crackpot. You could restrict your own research details and outcomes to stuff that you can prove to be correct.

Herr Feinmann

I guess you mean later on, after finishing the PhD

naturallyInconsistent

@qwerty they can straight up deny your research contributions and make it such that you cannot prove that you have enough work done. I'm not saying this as a hypothetical.

qwerty

@naturallyInconsistent ooft

Ryder Rude

08:55

u also have to consider the financial risks. Would u be depending on research for personal finances?

Tobias Fünke

@HerrFeinmann Doing a PhD usually makes you focusing on a very very narrow topic. If you want a better general understanding, I'd say it is probably not the best option

Herr Feinmann

I guess what I want is freedom to do what I want :P

Ryder Rude

i can write a flow diagram : (are you interested in A learning, or B contributing) ---> (are you okay with financial risks in academia)---> (are you comfortable with the risk in having chosen a bad advisor)

the third question should be answered based on a probabilistic analysis

Herr Feinmann

Why can't we make a hBar research group?! AAAAAAH :P

4

Tobias Fünke

@HerrFeinmann that depends on your advisors/program. but then again, if I had to bet I'd guess that 99.9% of PhD students do research in a (very) narrow field

Ryder Rude

08:59

if the answers are B, Yes, Yes, then u are into research. but u should analyse the situation more

qwerty

hbar is already more interesting and helpful than my actual research group meetings ever were back in the day

Ryder Rude

@qwerty did you leave research

Tobias Fünke

I am currently reading a paper from someone closely related to my field, and he quotes/says: "Education at its best is understanding what others have already
understood. Research at its best is understanding what no one else
has yet understood, so there is no clear roadmap for research. Some-
one (maybe Einstein) once said “Research is what you are doing
when you don’t know what you are doing.” The condensed matter
theorist John Ziman said “Basic research is what you are doing when
you don’t know why you are doing it.” However, usually, you are

qwerty

if you want freedom to do what you want then a) be independently wealthy and b) experienced/educated/smart/whatever enough to lead an interesting research program

naturallyInconsistent

@qwerty Sooooo many people were screwed over. They screwed their careers, their families' lives, the poor student (whose career history looks soooo dodgy), the university president, a friend's professorship, etc.

Ryder Rude

09:02

@qwerty Wolfram tried to do this :P

he is ignored by academia

but tbf his ideas were crackpot until recently when he started working on the specifics

qwerty

@naturallyInconsistent ughhhhhh :( i feel so bad for them

did the uni try to cover it up too?

naturallyInconsistent

@qwerty dont worry, the guy who caused all that, also did not get a good ending.

Herr Feinmann

@qwerty Great advice. I'll start gambling to gather money

naturallyInconsistent

@qwerty they kept quiet, hoping that the problem will just disappear from public consciousness. It hadnt, but they also hadnt needed to come clean on it either.

Herr Feinmann

It is time to learn Poker

"Näherung des mittleren Felds" why is is capitalized?

Is it some grammar rule of German?

Tobias Fünke

09:15

what exactly do you mean?

the syntax is indeed correct

Herr Feinmann

Felds :P

It was in the middle of a sentence and I saw it was capitalized (I do not understand German) so at first I suspected it was a personal name

Tobias Fünke

yes. das Feld =the field (nouns are with a capital letter)

Herr Feinmann

I see

Tobias Fünke

des Feldes is the genitive (is this the right word)?

Herr Feinmann

if it means "of (the) fields", yes

Tobias Fünke

09:18

and then you can leave the "e" out, i.e. write des (mittleren) Felds, instead of Feldes

Felds here means of the field, yes (not fields), I would say

Herr Feinmann

I had a glimpse of the nightmare that German grammar is :P

Tobias Fünke

:D

if you had a plural (fields) you would write something like "Näherung der mittleren Felder"

btw: what are you reading?

Herr Feinmann

The book from yesterday :P

Hugo Reinhardt

I'm comparing another sections to my other references

DIRAC1930

Btw you may not want to continue after your PhD
Your priorities are very likely to change once you reach your late-20s

Tobias Fünke

ah ok. Have fun :)

(lol, this sounds too mean, was not intended)

DIRAC1930

09:29

Does anyone collect old physics textbooks

qwerty

@TobiasFünke tobias you never sound mean :p

DIRAC1930

Like 50s and before

Tobias Fünke

@qwerty haha

qwerty

Dec 5, 2024 at 15:52, by Relativisticcucumber

tobias is like a teddy bear

Ryder Rude

is it harder to get popular physicists as ur advisor

Tobias Fünke

09:31

<3

@RyderRude depends

Arjun

Hi

Tobias Fünke

morning

Ryder Rude

hi

Herr Feinmann

@TobiasFünke How does that sound mean?! lmao

the meanest reply a human being can give is "something lol". The lower case "lol" is just bullying

qwerty

@HerrFeinmann hmm lol

Herr Feinmann

09:39

okay.

Arjun

I was reading Landau today and have stumbled upon the following,in his 2nd volume,pg 27 he speaks about the energy of a free relativistic particle,he says unlike a classical free particle whose energy is arbitrary upto a constant,for a relativistic free particle it is fixed and is given as $\gamma m c^2$ I was wondering what would change if we add an arbitrary constant to the above energy since EOM's would be the same regardless.

qwerty

hehehe

Arjun

Maybe we want the energy of free space(where there are no particles present) to be zero and since energy is the component of a four vector, this would nicely lead to it being zero in all inertial frames(ofcourse momenta are taken zero as well),Is this the reason or there is something else?

Ryder Rude

@Arjun sorry I'm not sure now

Arjun

It's okay : )) ,see landau vol 2,page 27 he speaks about it there :p

Ryder Rude

09:44

i will check it out

we also want to satisfy $E^2=p^2+m^2$ in relativity

Landau does not justify his claim too much

the closest justification i can think of is that, in non rel physics, the energy of a particle is the sum of kinetic and potential, and it is the potential energy that is defined upto a constant. as a consequence, the particle energy is defined upto a constant

in rel physics, the potential energy becomes field energy. it is not considered a component of particles energy. and the particle energy is the formula $\gamma mc^2$

DIRAC1930

@JohnRennie Was doing your degrees in Cambridge a magical experience?

John Rennie

@DIRAC1930 It was the best six years (three undergrad, three PhD) of my life!

I guess I must have been lucky because I hear stories about how bad other people's experiences have been, but mine were absolutely fantastic.

DIRAC1930

10:07

Glad to hear, It looks like it would have been completely magical

John Rennie

I had spent all my life up to the end of my degree being told what to learn, and when I started the PhD it was the first time I got to choose what I wanted to learn. That was the most amazing part of it.

I did have a project to do, i.e. a long term goal, but I felt that how I achieved it was down to me to plan. Though in retrospect I think my supervisor was quietly giving me stealthy nudges in the right direction.

Tobias Fünke

hehe

good job of your advisor, no?

John Rennie

I think I didn't appreciate him as much as I should have!

Herr Feinmann

@Arjun I'm not sure I understand the question

John Rennie

I suspect he needed superhuman patience to deal with the 21 year old me :-)

qwerty

10:12

@HerrFeinmann i hope i didn't joke too hard btw :(

Herr Feinmann

Oh, come on :P

I'm just forgetful because I'm reading 4 books at once D:

qwerty

haha phew xD

@HerrFeinmann 3 in German?

Herr Feinmann

The German one is for emergency. I use chatGPT to translate (it does a better job than translators) and figure it out, so it takes a lot :P

Arjun

@HerrFeinmann I was asking the following:Why energy of a free particle arbitrary up to a constant in classical mechanics, whereas absolute in relativistic mechanics(ofcourse for a free particle)

Herr Feinmann

Just eng books

qwerty

10:20

@Arjun i had a semi-related question with some linked questions on the main site, but i dont think they will be that helpful for you... i have some vague ideas but not enough to want to say anything ;p

Herr Feinmann

@Arjun I would say that you should see it this way, you can still add an arbitrary constant to your energy, it's just that the relativistic energy is defined in a way such that $E(p=0)=mc^2\neq0$. When you take the nR limit you of course recover the classical kinetic energy but since the zero is not the same as the conventional one in classical mechanics, you also have that term, irrelevant for the EoM

Arjun

@qwerty Any insights/Ideas from your side are a welcome in this regard :p

Guys I've been SEing and found the following answer by Luboš Motl

21

A: If energy is only defined up to a constant, can we really claim that ground state energy has an absolute value?

In non-relativistic and non-gravitational physics (both conditions have to be satisfied simultaneously for the following proposition to hold), energy is only defined up to an arbitrary additive shift. In this restricted context, the choice of the additive shift is an unphysical, unobservable conv...

what do you think he means by the "energy" of the minkowski space?

Ryder Rude

he means vacuum energy. the total energy when there is no matter and fields around

i don't see any contradiction with setting the vacuum energy to non zero. it is only the differences in energy that are measurable

one can add an arbitrary constant to the Lagrangian density and then apply Noether's theorem to get expressions for energy-momentum four vector upto an arbitrary constant. Is this incorrect?

but he is right that, in gravitational contexts, one can't add arbitrary constants

qwerty

10:36

well this was my question physics.stackexchange.com/questions/838651/…

there's a bunch linked as well that are sorta on the same sort of vague theme

of what you're asking, but i dont know that it's helpful

Herr Feinmann

@Arjun as I told you the zero of energy in the presence of a potential is still irrelevant in SR, the point is that the dispersion relation that you choose is not the exact energy that corresponds to the usual non relativistic kinetic energy. You could do this upside down and start with a $E'=E-mc^2$ energy in special relativity for a free particle, if that makes you feel better

You shouldn't worry about absolute energies until you get to general relativity

Slereah

I think it's sad that the big list questions are forbidden on PSE

They're always the best threads on MSE

qwerty

@Slereah big list?

Ryder Rude

10:54

@Slereah what questions

Slereah

74

Q: A bestiary about adjunctions

What is your favourite adjoint? Following Mac Lane philosophy adjoints are everywhere, so I would like to draw a (possibly but unprobably) exhaustive list of adjunctions one faces in studying Mathematics. For the sake of clarity I would like you to follow a general scheme, a very naive example of...

That sort of thing

1647

Q: Visually stunning math concepts that are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are both accessible (easy to explain and understand) and mathematically beautiful. What are some other concepts like these?

soft-question recreational-mathematics education big-list visualization

374

Q: Collection of surprising identities and equations.

What are some surprising equations/identities that you have seen, which you would not have expected? This could be complex numbers, trigonometric identities, combinatorial results, algebraic results, etc. I'd request to avoid 'standard' / well-known results like $ e^{i \pi} + 1 = 0$. Please wr...

soft-question big-list

Highly illegal here

Ryder Rude

opinion based questions

Slereah

Not even necessarily opinion based

Just not focused on a specific answer

I don't know what misery gut ruling the site has forbidden them

Ryder Rude

what could one ask in physics

what are some spacetimes with peculiar properties

Slereah

Sure

Your imagination is the only limit

I'd rather have that than more questions about spinors

Ryder Rude

11:00

mathoverflow has some physics discussions like this

but maybe not exactly

qwerty

@Slereah complain on meta SE :p

Ryder Rude

mathoverflow is too technical

"what are some fun time travel techniques allowed by known physics"

Slereah

I don't even know who runs this site, de facto

qwerty

irresponsible to have such lack of SE civic knowledge

Slereah

It is a secretive cabal

I'd propose to rule the site myself but that would involve reading a lot of posts

Ryder Rude

11:33

i have been thinking about the unreasonable effectiveness of mathematics

ACuriousMind

@Slereah it's you! (please do your review queues :P)

Ryder Rude

one answer to the unreasonable effectiveness of mathematics is to imagine the universe itself as a piece of mathematics, like a cellular automata structure. one can, e.g., re-formulate classical physics this way

qwerty

@Slereah all the marxist talk is just a façade for your dreams of dictatorship, right?

Ryder Rude

perhaps this answers all of the questions, except for "why is the universe like this". questions like this can be ignored

but I am also looking for more sophisticated answers, like within Kantian idealism where we almost claim nothing about the nature of the outside world

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