The h Bar

Silly Goose

00:10

@qwerty no counter example in mind. Just like i feel like i am unfamiliar with even proving that say something like some configuration space X is really a manifold

Relativisticcucumber

@ACuriousMind hm. Is there a way I can get to a more general claim? I am hoping for a claim about the energy of two electrons just in a gas for example I believe.

Hi @SillyGoose

Silly Goose

Spiderman meme @Relativisticcucumber

ACuriousMind

@SillyGoose The configuration space is generalized positions. A position is something in $\mathbb{R}^n$, and so a space of "generalized positions" should look locally like $\mathbb{R}^n$, i.e. be a manifold.

Silly Goose

Well okay maybe i should say something like $ISO(1,3)$

ACuriousMind

@Relativisticcucumber What kind of general claim? I don't even know what "singlet" or "triplet" states in a gas are supposed to be, since gas particles are free and not bound states with angular momentum relative to the centrum of the binding potential

@SillyGoose A Lie group is a manifold because you claim it's a group of continuous transformations, i.e. transformations that can be parametrized locally by $n$ continuous (real) parameters, i.e. a manifold locally described as $\mathbb{R}^n$.

Silly Goose

00:14

Well i mean say we didnt know it is a Lie group

@ACuriousMind although i guess this does offer an example of a simple way to see why it can be seen as a manifold, which is nice

ACuriousMind

@SillyGoose How are you defining this group, then?

Silly Goose

Well let’s say “isometries of $\eta$”. So sure it’s certainly a group. But then we should have to prove it is Lie, which would require proving it is a smooth manifold first as well. Barring theorems that simplify the process.

I guess i have a hard time thinking about manifolds because they are defined by quite a lot of data relative to topological spaces or groups or algebras or vector spaces

ACuriousMind

@SillyGoose In the general case where we have an arbitrary pseudo-Riemannian manifold $M$ with metric $g$, the statement that the group of isometries is a Lie group is the Hilbert-Smith conjecture.

Silly Goose

Separately from a blog lol: “Are you smoking weed? Ashcroft and Mermin published the worst book in solid state physics in the history of humanity. Full of typos and errors, mistakes, and BSing. I can totally see how they fooled you into thinking this is a good book. Wake up society!”

ACuriousMind

But for Minkowksi space $\mathbb{R}^n$ it is much simpler: Just exhibit the Poincaré group as a subgroup of $\mathrm{GL}(\mathbb{R}^{n+1})$ and use standard results about $\mathrm{GL}(V)$ being a Lie group and closed subgroups of Lie groups being Lie groups.

Silly Goose

00:22

Hm okay

My faithful friend GL(V)

qwerty

@SillyGoose "wake up solid-state-sheeple!"

ACuriousMind

@SillyGoose I disagree with this characterization: A manifold does not carry a lot of data, it's just a submanifold of some $\mathbb{R}^n$.

Yes, the modern abstract definition is different, but the embedding theorems prove this is all it is.

Silly Goose

@qwerty i know the last line is hilarious

@ACuriousMind isn’t this a self-referential definition 0.o

ACuriousMind

@SillyGoose No, it's not. Historically all manifolds were considered to just be "nice" subsets of $\mathbb{R}^n$ until the more abstract definition "won". The embedding theorems then showed the two notions are ultimately equivalent.

Relativisticcucumber

@ACuriousMind pls just end my suffering and murder me

Then u can all eat me for nourishment

like baby spiders

ACuriousMind

00:30

@Relativisticcucumber I'm not a hitman

Relativisticcucumber

No u got it wrong

I’m not offering u money

ACuriousMind

also I would advise touching some grass if mere physics provokes such despair :P

Relativisticcucumber

Like weed?

ACuriousMind

@Relativisticcucumber I'm also not a hitman pro bono

Relativisticcucumber

Since ur a man of morals what if I make u a better offer

Hypothetically I could say Murder me or I’ll murder 10 babies

ACuriousMind

00:33

@Relativisticcucumber I meant "go do some other stuff" (cf. Wiktionary), but I guess weed works, too.

qwerty

oh no. cucumber trolley problem

Silly Goose

Hbar’s trolley problem

en.m.wiktionary.org/wiki/touch_some_grass#English Lol have you heard the pronounciation

pronunciation

Relativisticcucumber

I have tried. Sadly all I can do is lay in despair or look at tag urself memes

I really hit a rock bottom at this point

ACuriousMind

@SillyGoose lol

qwerty

@SillyGoose i snorted

Allie

00:35

mew

qwerty

gotta link direct to the audio file next time

ACuriousMind

@Relativisticcucumber The difficult part about realizing the trolley problem is not getting anyone to pull the lever, it's to put someone into the position where their only options are to pull it or not.

I don't have a "kill Relativisticcucumber" button I could just press to stop you :P

qwerty

relativistic squid game

ACuriousMind

I haven't watched that :P

Silly Goose

Apperently lemma has a separate meaning from its mathematical: en.m.wiktionary.org/wiki/Wiktionary:Lemmas

Relativisticcucumber

00:41

@ACuriousMind thank u for giving me a purpose

Relativisticcucumber

01:03

@ACuriousMind ok im ready to be serious. im having trouble formalizing what my state of interest really should be rigorously. i mean these two electrons are under the influence of some potential since they are confined to a general region, but i am confused how to think about the energy landscape in this situation. specifically it seems as tho this is being treated as a two level system with singlet and middle triplet where singlet is the ground state but im trying to figure out how to see why

ACuriousMind

@Relativisticcucumber is the potential assumed to be spherically symmetric? There's really not enough information here to tell what situation you're considering

Relativisticcucumber

@ACuriousMind there is a graph in a paper and in a text that shows that as i adjust the potential to bring two electrons together, we move from a situation where there is a triplet state as the ground state ($T_-$) to a state where the singlet is the ground state. this potential does not seem to be spherically symmetric.

im under the impression that i should understand why this is bc i dont see the text or the paper explaining why this is so i think it must be obvious but i am not seeing it

ACuriousMind

@Relativisticcucumber If the potential is not spherically symmetric, then the generators of angular momentum do not commute with the Hamiltonian, and so the ground state is not (at least not in general) an eigenstate of angular momentum. So the usage of "singlet" and "triplet" does not make sense to me in this context with the information so far.

Relativisticcucumber

@ACuriousMind bah hm i see what you are saying

but surely there must be some way to rationalize this hmmm

ok i will go back and read again

qwerty

01:28

@ACuriousMind necropost but i think this about myself all the darn time

Relativisticcucumber

I FOUND A HAMILTONIAN

thank GOD

leave it to experimentalists to not put the hamiltonian in the paper -.-

qwerty

@Relativisticcucumber i find experimental papers so hard to read compared to theory

in general it seems like they assume the reader knows a lot more background than theory papers do

Relativisticcucumber

@qwerty yes. the thing is it makes me curious how the authors understand this thing. i mean they put graphs of an energy landscape but they dont provide a hamiltonian so where do they think it comes from? am i just missing smth idek

i think they maybe think i the reader should just know it idk

yet they put things like "electrons are fermions"

???????

what is this assumed knowledge

qwerty

@Relativisticcucumber i think for like, the big collab papers, it's almost like they assume the reader is already in their field or a group working on pretty much the same thing

in which case a new student would have an advisor or postdoc explaining the background and context somewhat

Relativisticcucumber

true this prob only harms the people in the process of entering. i feel it can be used as some kind of hazing

@qwerty one would think but the thing is

qwerty

01:35

and everyone else they assume who is interested in the technical details, they think they know

it's not very friendly to someone working alone in an adjacent field

Relativisticcucumber

ok so this prof ive been taking a class w i was like "im interested in working w u" he was like ok lets do my process. so i did the interview and it went well. then he gave me a paper and said "read it and lets discuss"

so i read it and came to chat and i asked if i could ask him some questions and he said, let me start. then proceeded to go at me with question after question

not letting me have more than 5 seconds to think

then he was like "come back if you can do better"

qwerty

oooft that's awful

Relativisticcucumber

so he was not willing to explain the details XD

qwerty

uhhh. run

Relativisticcucumber

i was just shocked bc i was like ok if u wanna do a paper test, sure fair game, but could you at least have told me that bc to me a discussion requires dialogue xD

qwerty

01:37

you are a brilliant person - don't let those people haze you

2

Relativisticcucumber

so now im trying to understand every details so i can prove that im not stupid

thing is now i dont know if i even wanna work w the man i dont wanna be a person who cant handle criticism g

but im very afraid lol

@qwerty thanks ;,)

ACuriousMind

@qwerty I'm working on a rant preliminarily titled "Invariance, covariance and all that" that examines properly the relationships between symmetries, coordinate changes and the confusing ways in which the average physics texts uses those notions. No, there is no ETA :P

qwerty

@Relativisticcucumber as someone who once worked with someone (not for my phd) who was extremely judgemental like that, RUN

Relativisticcucumber

@qwerty oh no

but it could be that i am the problem

qwerty

your advisor is someone who you should feel like supports and bring out the best in you

Relativisticcucumber

01:40

bah

qwerty

cucumber, you are, as Herr F put it, "ACM's favourite student": it is obvious to all in hbar that you are a good student. you are definitely not the problem.

Relativisticcucumber

LOL not after hbar trolley

but thank u for the kind words

i have much to think about

qwerty

i am very annoyed at all the judgement that we internalise from these people. we spend months or years trying to prove ourselves worthy to them

when we are young, and we take their words too much to heart, but they're supposed to be older and wiser and we freaking admire them

ACuriousMind

@Relativisticcucumber Without that last response, I might have interpreted this charitably simply as some awkward interaction that got off on the wrong foot. But "come back if you can do better" without offering you much more detailed assistance on how to be better is just a failure of mentorship.

qwerty

we think that their positive judgement is somehow worth more because they are "discerning"

and we get to be accepted as part of their inner clique where we sit around and laugh at the guy down the corridor who doesnt know GR

the truth is just that it's simply unkind, it drags everyone down instead of lifting up everyone to perform at their best

I feel like I see this even at times here - when ACM has to remove messages - there's still damage done. people stop wanting to ask questions, people aren't encouraged to do better

Relativisticcucumber

01:47

hm now im starting to think twice about this

because i am thinking now that to succeed in research i will rely on mentorship from my advisor so this is kind of raising a red flag

qwerty

talk to his current and past students privately, off the record, if you can.

2

they will know his personality and the situation better

Relativisticcucumber

idk i just dont trust myself to form opinions its so hard to judge a situation that involves oneself

@qwerty true thats a good idea

qwerty

and the same goes for any potential mentor

ACuriousMind

@Relativisticcucumber If you don't form your own opinions, you let others form them for you.

4

Relativisticcucumber

@handan_toddler this happened like this wkd so yes i think they have been

qwerty

01:53

for the past students - try to find any that left the program, any that are now postdocs - if you really want to be thorough

the postdocs may have a positive bias, and those who left may have a more negative bias

ACuriousMind

@handan_toddler If you have nothing constructive to add to the discussion, just be silent.

DIRAC1930

02:10

In QFT why do people not just consider two different field operators, one for positrons and one for electrons? Why do they combine the expression into one field operator? If one considers two different field operators, the Hamiltonian comes out correct

ACuriousMind

@Relativisticcucumber Experimental papers are (or, at least, historically were) often under (from the viewpoint of a theorist, strange) constraints of space, i.e. they need to put their essential findings into X pages, where X is often very small compared to all the figures and descriptions of experimental setup they need to present.

Also they are often tightly embedded into a web of preceding papers, much more so than many theoretical works which feel a compulsion to at least pretend to develop a subject from some ab initio standpoint. I say this not as a value judgement, but it's also my experience that experimental papers tend to be much more dense to understand than many purely theoretical works.

DIRAC1930

My reason for asking this is that its not clear why people use the expression $\hat{F} = \int \mathrm{d}x \hat{\Phi}^\dagger f^{(1)} \hat{\Phi}$ where $f^{(1)}$ which is derived from having field operators of the form $\hat{\Phi}^\dagger= \sum_i \hat{a}^\dagger_i \psi_i^*$

And only seems to work for operators of the form $\hat{\Phi} = \sum_i a_i \psi_i + \hat{a}^\dagger_i \psi_i^*$ etc. because the cross terms cancel

Relativisticcucumber

@ACuriousMind yeah i am definitely seeing this. kind of a shame too bc this thing that ive been thinking ab for days i finally found the ham and then just plotted the energies on mathematica and got smth quite like the paper in like 2 min so its just like BAH. also then it makes it so clear why smth is the case -- no need to concoct some convoluted story :PPP

but now i know to expect this

DIRAC1930

Why do all books seem to show the non-rel case, then assume the rel case is the same when the field operators have a completely different form

ACuriousMind

@DIRAC1930 Given your recent lines of questioning, I think you might enjoy the first few chapters of Scharf's Finite Quantum Electrodynamics. The latter sections of the book deal with the technical implementation of Epstein-Glaser renormalization, but the first half seems to me to be to exactly the kind of building up the notion of fields from the particle theory that you are looking for, only carried out carefully and rigorously.

The definition of the Dirac field there is little more than a repackaging of the c/a operators for the Dirac Fock states, not some assumption dropped from above

DIRAC1930

02:20

Thanks I'll check it out

Why do the books with all the secrets use a weird notation :p

Allie

mew

Silly Goose

@Relativisticcucumber more data points to my theory

ACuriousMind

@DIRAC1930 I think Scharf is better than Weinberg in that respect, but...yeah, there seems to be a trend that if you do QFT differently from the usual mainstream intro, you also have to choose at least one weird notation convention :P

qwerty

@ACuriousMind xD can't wait to read it

handan_toddler

@Allie meow

feeling any better?

👀👂

Allie

03:55

ehh im alright

thanks for asking

handan_toddler

04:11

np 👍

Allie

07:11

hey girls

John Rennie

only an app can make 1 million mistakes in a second (although students have tried to best this)

There speaks the voice of experience :-)

Allie

meow

i dont like reading off a computer screen

but this book is $200

so i will read off the computer screen

hi user

User1865345

07:36

Hey.

@JohnRennie i don't know why they even had to ask that in the first place? Wasn't it evident? Seriously?

@Allie Do you have departmental library access or sort of like that?

Allie

no i go ot a super tiny school

User1865345

I see.

Allie

i am the only person who does computational chemistry, faculty or student, so they definitely dont have books on DFT lol

User1865345

🥺

John Rennie

@User1865345 When I was student in the 1970s I had teachers tell me that electronic calculators would make me stupid because I would forget how to do basic arithmetic. These days everyone uses calculators and I haven't noticed students getting any more stupid than they were in my day.

Allie

07:40

i think the difference is that everyone learns how to do arithmetic without calculators

John Rennie

Obviously ChatGPT is rather different from a calculator, but I don't think that's a reason for a blanket ban on its use by students.

Allie

i dont know, the way kids use chatgpt is not the ideal way wed like them to

User1865345

@JohnRennie I cannot blame your instructors here. They had genuine reasons to fear.

Allie

i say kids but i guess students

when i was tutoring i had kids ask me to look over work that was clearly written entirely by chatgpt

it used organic chemistry words but it did not make 1 bit of sense :P

John Rennie

@Allie It's early days and we don't know how tools like ChatGPT are going to work out.

I agree it would be a bad idea for students to rely on LLMs in their current state, but who knows how thiongs are going to work out in the next decade or so?

User1865345

07:42

In my early undergrad days, we had to work with Biometrika. My then instructors back in their days had to calculate Pearson curves with that; took hours.

Allie

it is way too god damn cold in my room

this is getting ridiculous

User1865345

We still had those big machines in the underground storage room. Those weren't calculators but they were only used for these stuffs.

@JohnRennie see this

handan_toddler

old adages like garbage in garbage out don't change though

User1865345

21

Q: How did past mathematicians feel about giant computations? Did those who saw the advent of computers get jealous?

A bit of a soft question. Did past mathematicians ever reveal what feelings they felt as they did a massive computation by hand? Did they hate it? Did they wish that they didn't have to? Might they have even loved it? Did any of them see computers rise and rise, and regret spending time on tedi...

@JohnRennie I have no problems with LLMs. But students nowadays rely blindly on these as if these are some oracles.

2

This attitude has to change.

2

Allie

exactly

User1865345

07:46

@Allie heaters? 😱

Allie

parents wont allow it

User1865345

🥶

Do you have those warming blankets?

I mean those electric ones?

Allie

no,. maybe. should get one

User1865345

Please. Get those things. Would make your life easier.

John Rennie

@User1865345 Yes I agree that we, everyone - not just students, need to learn how to use LLMs so they work to our advantage and not our disadvantage. But isn't that the point of the question?

handan_toddler

07:48

Everybody wants to waste their time looking for the royal road.

User1865345

My previous hostel dorm room was cold like a morgue. Those things halped me survive (funny that there was a morgue nearby, lol).

@JohnRennie hm. I see your point.

@JohnRennie, how is the cold back at your place?

John Rennie

@Allie Buy a cheap children's (i.e. small) sleeping bag and slip your legs into it while you're sat at you desk working.

I swear this saved me from frostbite when i was an impoverished student huddled in my garret :-)

User1865345

@JohnRennie 👏🏻

@TobiasFünke 🤞🏻👍🏻👏🏻

John Rennie

@User1865345 The UK is currently panicking because a few cm of snow are forecast to fall.

Allie

i have a somewhat stupid question

but it keeps coming up and im confuzzled

User1865345

07:52

@JohnRennie wow. I do love snow. But not when they block the doorways.

handan_toddler

@Allie askaway

Allie

so i get what theyre doing, minimizing the energy with respect to the density, while constraining that the density integrates to exactly N electrons

User1865345

@TobiasFünke that is indeed true. We at stats haven't gotten a single cracpot post, plausibly because there doesn't exist any.

Allie

But usually when I've seen lagrange multipliers, the mu is also varied as part of the minimization

here the derivative is only with respect to n(r). and the grad student who is helping me also says that mu isnt varied

so im just confused where mu comes from in that case

User1865345

There is no scope for any crackpot ish handwavy science fantasy stuffs unlike in physics, which is the more famous cousin among the other subjects.

Allie

07:56

@User1865345 i have a theory that everything actually has a 100% probability of occurring because parallel universes and you cant prove that they dont

(just kidding)

User1865345

@Allie I don't know the premise of MWI. But it seems mostly it is exaggerated by science fantasy stuffs.

Allie

i am not a physicist so yell at me all you want if im wrong, but from what ive heard its not useful as a theory because you cant really prove or disprove it

so maybe it is true but what bearing does it have on the world we live in and how could we even know

User1865345

I see. You are way more physicist than I am though 😄

Allie

TOBIAS.

Tobias Fünke

morning

Hi Allie

Allie

08:01

My bestie

good morning (it is 3 am!)

User1865345

Hello.

Allie

physics.stackexchange.com/questions/788014/… heisenberg XXX model? this sounds like some kinda strange physics-based porno

sorry...

bad joke

someone say something and air out the silence

User1865345

@Allie name is dope though, no doubt.

handan_toddler

::crickets::

Tobias Fünke

@ACuriousMind are you serious? :p do you post it here on SE?

User1865345

08:05

@Allie 😆

Allie

so nobody knows where mu comes from :(

Tobias Fünke

@Allie hehe, I made a meta post about it a while ago, because the thread got a lot of views

@Allie what do you mean?

$\mu$ is the Lagrange Multiplier

Allie

oh i asked a question above :3

Tobias Fünke

yeah, I am referring to this question :p

Allie

i get that, but is mu not varied during the minimization?

Tobias Fünke

08:08

no, why do you think so?

Allie

if its not, where does mu come from? do we have to summon Lagrange from the dead and ask him?

Tobias Fünke

that's just basic Lagrange multiplier business

Allie

just from waht i remember you also vary mu. i guess this speaks to my inexperience with classical mechanics

Tobias Fünke

khanacademy.org/math/multivariable-calculus/…

aah

now I understand what you mean

Allie

that one literally varies the lagrange multiplier!!!!

Tobias Fünke

08:10

you mean to take the (partial) derivative with respect to $\mu$?

yes, sure

Allie

yes tahats exactly what i mean, i do not need khan academy

sorry that was mean LOL

Tobias Fünke

but this just gives you the constraints

Allie

right that makes sense

Tobias Fünke

if you take the derivative of your example with respect to the LM, it will give you the constraint of $\int n(x)\, \mathrm dx =N$

Allie

i just wanted to make sure that you are also minimizing with respect to mu, even if you do it in a separate step

Tobias Fünke

08:11

yes, sorry, I completely misunderstood :/

Allie

yeah that makes sense. okay, so there was a miscommunication between me and my grad student. glad im not crazy

no no worries at all i appreciate your help as always :3

Tobias Fünke

08:30

^^

Allie

ok this book has gotten hard

i have a feeling i need to study statistical mechanics

Tobias Fünke

@User1865345 lucky you! :d

Allie

OVERWHELMIN G

Tobias Fünke

@Relativisticcucumber that does not sound very constructive, and also unfriendly...

@Allie mhmhm you think so?

most thinks are at $T=0$, no?

Allie

well i know i need to at some point but i think i need to do it like, sooner than i expected

hush

User1865345

08:35

@Allie another aspect of self-studying when you realize you need to go through another thing to understand this thing. After some cycles of that, you forget where you began from. That's fun!

Tobias Fünke

hehe

Allie

its fun but i guess im a little scared

because i really want to start on my research project and do well on it

User1865345

@TobiasFünke boring subject has its benefits though. 😄

Allie

and i worry they are going to think im uncapable and too slow and not a good fit for the group

but also im doing the work for free on my own time so maybe that shouldnt be a worry, idk....

User1865345

Self studying requires time and patience. At least that is my experience. You can't haste anything for good results.

Allie

08:37

i understand that, its more about whether the group will. i hadnt been able to work on research OR studying for months because grad apps swallowed all of my time

User1865345

@Allie why would they? I don't think they evaluate in such a botched way.

Allie

but i think they should, hopefully. they are very nice people

User1865345

@Allie exactly

@Allie most of the recruiting faculties are good. You can trust on that fact.

Allie

i just really do want to do well on this project. it is very exciting

Tobias Fünke

yeah, try to don't worry too much

User1865345

08:38

Recruiting process takes into account different factors.

Allie

i guess yall are right. i dont wanna rush it

User1865345

@TobiasFünke exactly. I have seen people do appreciate if the incoming students have the zeal of self studying. Not a sole factor. But can be good plus point.

Tobias Fünke

yes.

User1865345

@Allie do what you are doing. Don't worry too much.

Allie

@TobiasFünke have u read Tuckerman stat mech?

Tobias Fünke

08:40

@Allie nope

Allie

dang it

Tobias Fünke

I think the most important point is that a student is motivated, and is able to understand what the goal is, and what they have to do in order to reach it, no?

3

User1865345

Exactly.

Tobias Fünke

Of course, some kind of mentor/advisor will help with that

and help to reach the goals

User1865345

Yes

Allie

08:41

i am definitely motivated, sometimes its hard to tell how much i have left to learn. right now it seems like a LOT

Tobias Fünke

and I think Allie is motivated :) so... no worries for now

User1865345

🥳

Tobias Fünke

Yeah, I understand. Give it some time. In a few months, in half a year or in a year you will look back and can be proud what you achieved

User1865345

I have seen students of all types. ultra bright to average. But there was one thing common: they were eager to do something and super motivated.

Perseverance and stubbornness. These are the keys.

2

Tobias Fünke

yeah

User1865345

08:44

@TobiasFünke yeah. Year later Allie will be in different place remembering h bar. 😇

Tobias Fünke

hehe yes

Allie

thank u guys :3

i will let everyone know as soon as i get decisions back.... hopefully sooner rather than later

User1865345

Anyways you folks enjoy your day. I have some chores to do and call off later.

Allie

ok have a good day!

User1865345

@Allie 🥳

Ohh and have some good sleep @allie.

Allie

08:46

i will try. i really want to get on a better schedule

Tobias Fünke

sleep well

and see you around

Slereah

10:00

I like how the longer I work on some latex document, the weirder the import section gets

qwerty

10:27

mathstodon.xyz/@johncarlosbaez/113652794327730499

> ""Ptolemy was essentially using Fourier series 1500 years before Fourier."... Funny how "epicycle" sounds bad but "Fourier series" sounds good.

slereah this baez post seems like your sorta thing

handan_toddler

10:39

@User1865345 students are always going to look for the magic of garbage in, gospel out.

that's just human nature

naturallyInconsistent

@ACuriousMind @Relativisticcucumber @qwerty this is very very very very true. Many journals have tight page counts and it is sooooo difficult to squeeze what you want to say into them. It might have made sense back when everything was printed, but now it is so egregious, since we just download PDFs.

handan_toddler

M I A O ~

naturallyInconsistent

@DIRAC1930 That's because your underlying assumption is completely false and not possible to work with. Few textbooks cover this, but when they do, they are very very good. It is, however, not very difficult to see why it is necessarily so in general, and not just a quirk of the fields we care about.

@handan_toddler M I A O ~

Slereah

@qwerty Not exactly a new observation!

qwerty

@Slereah lol the main post was about britannica being Wrong xD

indeed i thought you might have seen it but i was reminded very much of you

> The Alfonsine Tables, which the Brittanica is complaining about above, actually computed planetary orbits using Ptolemy's method, developed way back in 150 AD. This method uses just 6 circles and 6 epicycles - nothing like Britannica's ridiculous claim of between 240 and 360 epicycles.

naturallyInconsistent

10:55

@qwerty that's nothing mysterious. The "alchemy" that became respectable, is now called chemistry. When they originally were using epicycles, they had no idea what they were doing, and were applying ever more complicated band-aids to their broken theories. We now understand what Fourier series do to the analysis of problems, and so we are perfectly allowed to use them.

@Allie the grad student is wrong. What is happening is that we vary this Lagrange multiplier separately and it trivially obtains the constraint equation, and thus there is no need to write it out. It is implicit in your solving procedure. I think you had already worked this out with Tobias in the later comments

handan_toddler

@Slereah working on your blog?

naturallyInconsistent

@handan_toddler kinda curious what comments of yours got the axe

handan_toddler

accompanied by an ensuing double suspension

time to return to Siberia

naturallyInconsistent

11:27

by handan walking?

Secret

12:42

1

Q: Connections between the path integral formulation and the Fourier transform

I am just learning abut the Path integral formulation and it seems to me that there is a connection, at least conceptually, to the Fourier transform. In the Path integral formulation we sum over all possible paths a particle can take between two points. Each path contributes with a phase factor d...

quantum-field-theory fourier-transform path-integral

That the action is just some waves but more complicated sounds like an attractive interpretation

Arjun

13:07

I was reading this answer on SE physics.stackexchange.com/a/273647/304878, in this answer prahar says the Lorentz transformation connected to the identity (invariance of intervals)should be continuous,why is this a physical necessity?Also what are orthochronous Lorentz transformations?(I don't know any advanced maths :'(

I was reading the above answer linked to a question that I asked on SE physics.stackexchange.com/q/838856/304878

Tobias Fünke

@Arjun orthochronus just means that it preserves the time direction.

proper means that it preserves also the orientation

Arjun

@TobiasFünke Oh I see,the guy who linked the above answer to my qn said causality is preserved because the transformation is orthochronous

Tobias Fünke

2

Q: Orthochronous condition - Lorentz transformations

I'm trying to learn by myself some special relativity. By reading online I've come across the fact that Lorentz transformations are rotations on a 4D spacetime with a Minkowski metric. A rotation $\Lambda$ must preserve lengths, therefore, for a generic 4-vector $\vec{x}$: $$ \Vert\Lambda \vec{x}...

special-relativity symmetry group-theory time-reversal-symmetry

here it is explained in more detail

Arjun

13:25

@TobiasFünke what does orientation mean here? The time axes coincide?

Tobias Fünke

reading the comments under your question, let me note that: the proper orthochronus Lorentz transformations are not all Lorentz transformation, there are different ones, too

Lorentz group

In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry: The kinematical laws of special relativity Maxwell's field equations in the theory of electromagnetism The Dirac equation in the theory of the electron The Standard Model of particle physics The Lorentz group expresses the fundamental symmetry of space...

regarding continuity, you should check (matrix) Lie groups or so

Arjun

@TobiasFünke @TobiasFünke This seems so advanced :' (

Tobias Fünke

no, it means orientation of space

Arjun

@TobiasFünke ok

Tobias Fünke

it is quite well explained/summarized in the Wiki article

Arjun

13:31

@TobiasFünke Are there any physical arguments(without going into advanced maths) as to why for time-like events causality is preserved?

Tobias Fünke

@Arjun by orthochronus transformations?

by construction

sorry, I have to leave now. perhaps someone else can help you (I am anyway no expert in this)

Arjun

@TobiasFünke ciao,thank you for the links!

Arjun

13:51

My question boils down to why only orthochronous Lorentz transforms matter(that is what landau is seeming to imply)

ACuriousMind

14:22

@Arjun It depends on what context you're talking about, but if you're talking in terms of frames/observers, then a non-orthochronous transformation flips the time direction. But in reality we do not have observers for whom time runs backwards compared to others.

naturallyInconsistent

@Secret The question is just too far off wrong, but yes, it is an interesting thing that had been explored.

Arjun

@ACuriousMind Ok can we derive from the two postulates of relativity why this has to be the case for frames/observers?

Or is it just a fact of the world that has to be taken as a given?

ACuriousMind

@Arjun I don't know what the "two postulates" of relativity are :P

Arjun

1)All inertial frames of reference are identical in terms of laws of physics and 2)there exists something that has the same speed in all frames is what I meant

ACuriousMind

but the argument for why those observers don't exist is that the orthochronous Lorentz transformations are the ones connected to the identity. If you start in one frame, the only other frames you can reach are those with transformations connected to you since all physical motion is continuous -

you could track the frame you're in at every instant of time, and there would have to be a transformation between that frame and the starting frame, and the closer the instant is to the starting time, the closer that transformation needs to be to the identity.

so, sure, in principle you could posit that there are strange observers "born" with the property that time runs backwards compared to others, but you can't take an observer and do some continuous physical motion to them to reverse their time direction

naturallyInconsistent

14:36

oh lol the conversation is here. miao miao left a comment on your post

ACuriousMind

...I didn't know there was a post :P

naturallyInconsistent

@Arjun @ACuriousMind here is the link

Arjun

@ACuriousMind physics.stackexchange.com/q/838856/304878 this..

@naturallyInconsistent you say that only this transformation is physically accessible, is there a deeper reason to it?

naturallyInconsistent

What part of that is contentious enough that you have to ask?

DIRAC1930

@naturallyInconsistent Which textbooks cover this

Arjun

14:51

@naturallyInconsistent I'm somehow missing to see how this is a necessity since I could simply flip the sign of a time interval and it would still not violate the identity,since the identity is from where landau inferred that time interval has to be positive

naturallyInconsistent

I dont remember. I have read a bit too many textbooks before my prof made the main track make sense, and so it is now one big frankenstein mess in my head

@Arjun How would you do an experiment to flip this sign?

Arjun

@naturallyInconsistent I'm genuinely confused,so it's an empirical fact?

naturallyInconsistent

@Arjun no, no, I'm saying that you are reading it way too mathematically. Landau is just meaning the orthochronous Lorentz transformation when he said Lorentz transformation. That is a very standard statement swap

Arjun

15:23

@naturallyInconsistentOh, I might be stupid for asking it but why orthochronous transformations? Is that the only observed one since I don't see how the postulates imply the transformations between frames is orthochronous

Tobias Fünke

1 hour ago, by ACuriousMind

@Arjun It depends on what context you're talking about, but if you're talking in terms of frames/observers, then a non-orthochronous transformation flips the time direction. But in reality we do not have observers for whom time runs backwards compared to others.

doesn't this answer your questions?

naturallyInconsistent

@Arjun the postulates do not imply. We, however, can only access stuff that are continuously connected to the identity. This leaves us in the orthochronous subgroup

Arjun

15:56

Okie so for two time like events happening in one frame the transformation leading to a frame in which the order of the events is reversed is not continuous and hence physically not plausible?

@ACuriousMind So for me to go from one inertial frame to the other the corresponding transformation should be continuous?

@TobiasFünke I was going through his second comment(the one after this) and had some difficulty wrapping my head around it

ACuriousMind

@Arjun No, that's not what I said - there is no meaning to a single Lorentz transformation being "continuous". What I mean is that if you change your frame, then you do so by rotating or accelerating to a different velocity, and we can track your frame compared to $t=0$ by some rotation $R(t)$ and your velocity $v(t)$. The Lorentz transformation into your frame at time $t$ is then $\Lambda(t) = R(t)B(v(t))$ where by $B(v(t))$ I mean the boost into the frame of velocity $v(t)$.

$\Lambda(t)$ is continuous and $\Lambda(0) = 1$. This is the formal meaning of $\Lambda(t)$ being "connected to the identity". You can show that the Lorentz transformations connected to the identity - i.e. the possible values of $\Lambda(t)$ - are exactly the proper orthochronous transformations.

Arjun

16:12

@ACuriousMind Thank you so much,this clarified a lot of details : ) ,Now may I ask how $\Lambda(t)$ could be shown to be orthochronous :p

ACuriousMind

@Arjun In matrix form, you can generally show that Lorentz transformations $\Lambda$ have either ${\Lambda^0}_0 \geq 1$ or ${\Lambda^0}_0 \leq -1$. This means $\mathrm{SO}(1,3) \to \mathbb{R}_{\leq -1} \cup \mathbb{R}_{\geq 1}, \Lambda \mapsto {\Lambda^0}_0$ is a well-defined continuous function. Since the identity matrix has its 00-th component as 1, it lies in the preimage of $\mathbb{R}_{\geq 1}$ under this map,

and this is a different connected component of $\mathrm{SO}(1,3)$ than the preimage of $\mathbb{R}_{\leq -1}$ (otherwise the map would not be continuous). So all matrices connected to the identity must have ${\Lambda^0}_0 \geq 1$.

The intuition for this argument is that a continuous path cannot "jump the gap" between ${\Lambda^0}_0 = 1$ and ${\Lambda^0}_0 = -1$ - it would have to pass through 0 (intermediate value theorem), but that's not in the Lorentz group, so there are no paths in the Lorentz group that connect the negative with the positive side here

Silly Goose

16:38

isn't it misleading to correspond time-reversal to something non-physical. in geometric optics, time-reversal is used to conveniently obtain a solution from a given one that is too realized in the real world.

ACuriousMind

what

DIRAC1930

16:56

The original paper by Pauli and Weiskoff is here archive.org/details/earlyquantumelec0000mill/page/188/mode/2up for anyone interested

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