The h Bar

02:26

@Mr.Feynman When wavefunctions are very much spread out, like in metals, the molecular type of Exchange interaction is too strong, and so Hartree approximation would do better than Hartree-Fock, since the latter necessarily has the full Exchange interaction due to Slater determinants

@SillyGoose You can estimate the validity of the assumption. It is very much still valid. Also, to fully understand why the assumption is valid, you would also need to understand cluster decomposition principle, which is surprisingly simple to derive. Sadly, it is never treated as part of an introduction to QFT. Does Schwartz cover it?

@user430580 You must burn in hell for that B

2

@Mr.Feynman Just as that you cannot force a donkey to drink, you also cannot force a person who insists upon not understanding what you are saying.

think_meaning_builds

17 hours ago, by Mr. Feynman

@user430580 or, at the very least, thrown out the window :P

naturallyInconsistent

02:45

@think_meaning_builds and then he himself is thrown out for misspelling miao

think_meaning_builds

Indeed sir.

naturallyInconsistent

I mean, he didn't capture that it is more of meow meow that was always on about Gauß, and even more fanatic than ACM since myow myow keyboard doesn't have that glyph. But that is tolerable; the joke wont work otherwise. Instead, not having miao, is inexcuable miehehehehehe

think_meaning_builds

Lest we forget that I am "That Guy" when I asked ACM if he minded me using ß in ACurioußMind as my new username.

user430580

think_meaning_buildß

think_meaning_builds

03:01

Hmmm 🤔

naturallyInconsistent

@think_meaning_builds off to siberia you go

think_meaning_builds

Whelp, they put Nelson Mandela in prison for 27 years; I guess, I could handle Siberia.

user430580

If you mißuße "ß", you get ßent to ßiberia

3

think_meaning_builds

:D

user430580

BTW did you know that the symbols "&" and "ß" have something in common? Both of them came to be as fusion of two characters, "s" and "z" for "ß", and "e" and "t" for "&"

think_meaning_builds

03:17

TIL, thanks 🙏

user430580

You're welcome :P

think_meaning_builds

I haven't seen "& al" used for "et al" but I guess that's like mixing metaphors.

some human

!i.sstatic.net/UeWC1IED.png?s=16 who is this?

think_meaning_buildß

That's the cover of a book.

user430580

@think_meaning_buildß No, you're not mixing anything, it's just that "& al" is an old and deprecated usage =]

Wow I just noticed you actually changed your username =O nice!

I know your avatar is a cover of a book, but in miniature it looks uncannily similar to the flag of Poland

some human

03:34

spam

it does

@think_meaning_buildß yes.I forgpt that. :embarrasaed-face:

think_meaning_buildß

np

some human

why did you delete that?

think_meaning_buildß

redundancy

some human

why though?

think_meaning_buildß

habit, I guess

some human

03:36

/define redundant

doesnt work on here.

it does on the test chat.

think_meaning_buildß

Not necessarily

some human

my icon is big.

why not?

how do you make a room? I want to test some thigs out.

user430580

I believe you need to have at least 100 points or it won't work

think_meaning_buildß

Right, I forgot about that rule.

some human

oh. I answered one q like a month ago and it has not been seen.

how do i make xp fast? are there mob grinders?

user430580

04:03

You need to visit hot network questions list and answer a question that you know the answer for, you will need a little luck but that's all, the answer doesn't even have to be that good or that long, if you're lucky the question will get lots of views and give you a lot of points. Each upvote is 10 points while downvote is only minus 2, so even a quite bad answer will probably net you a positive gain for points

naturallyInconsistent

04:27

You should just write good answers. Don't grind for xp

NOTE Book

hi

qwerty

yis. xp feels like a silly game :(

user430580

hi

NOTE Book

Please help me with a doubt

It is that if touch two identical charged conductors of any shape and size then charge will be distributed equally or only in cases of spheres?

qwerty

@NOTEBook if anyone wants to answer they will...

NOTE Book

04:30

ok

John Rennie

05:33

@NOTEBook When you connect the two objects together they are at the same potential so you know V₁ = V₂.

The potential of a charged conductor is given by V = Q/C where C is the self capacitance of the object.

So the charges on the two objects are related by:
Q₁/C₁ = Q₂/C₂

Ryder Rude

06:54

hi

Mr. Feynman

08:07

@naturallyInconsistent Thankies

@naturallyInconsistent I still don't understand this misspelling thing. Isn't it "meow" in English? :P

In Italian it's "miao"

qwerty

if I guess correctly nI spells it Miao to match mandarin

Mr. Feynman

Oh ok

Then in the meme he was speaking English.

Slereah

09:05

@Mr.Feynman 😺🤌

Ryder Rude

i cant think of any consistent definition probability other than that it is a degree of belief

but irl, we conceive of probabilities as representing something which makes predictions about a system

but if the only consistent definition of probability is about personal beliefs, then probabilities can't represent anything objective about a system

but in QM, probabilities are the properties of the system itself

but i can't think of any consistent definition of probability which defines it as a property of a system

cuz we need an infinite number of trials to define probabilities using an objective criterion

e.g. if the probability associated to a property is 0.33, then if there were existed an infinite number of instances, then a third of those would have that property

but there never exist an infinite number of instances of anything. So I can't attribute probabilities to systems themselves

what is the proper philosophy of what probabilities mean in quantum mechanics

Tobias Fünke

good morning and hello everyone :)

Ryder Rude

@TobiasFünke hello

Slereah

Hello

Tobias Fünke

09:21

@RyderRude isn't this the old debate between the frequentist and bayesians?

Ryder Rude

@TobiasFünke yes. I think it is related. But I don't think frequentism is consistent

Tobias Fünke

@RyderRude this seems to be an interpretation of QM already

Ryder Rude

@TobiasFünke yes. I think MWI wouldn't agree with that statement. But I discard MWI, so i don't take it into account

Tobias Fünke

as far as I understand your concerns, they touch the problem of "falsification of probabilistic theories", but there exists much literature about it

@RyderRude how about QBism?

Ryder Rude

@TobiasFünke QBism is strange. I cant re-concile it with QM. If QM probabilities were about beliefs, then the validity of QM would be a matter of opinion. But QM is a predictive theory

I'm trying to reconcile the view that probabilities are beliefs with the view that probabilities make predictions in some objective sense

Tobias Fünke

09:26

The pragmatic "solution" or response to your concerns would be something like: Probabilities (in the frequentist view) is an idealized mathematical concept. But that does not mean that theories which predict probabilities are "useless", because we can still test their predictions

Ryder Rude

@TobiasFünke what would u recommend?

Mr. Feynman

@Slereah Hear me out now: Italians do NOT do that gesture all the time

Slereah

@Mr.Feynman How many percent of the day then

Ballpark figure

Tobias Fünke

@RyderRude What is your philosophy of (classical) statistical mechanics? Do you know the work of Jaynes?

Mr. Feynman

It has a precise meaning, i.e. "What?" or "Who?" or sometimes "Where?"

Slereah

09:27

link.springer.com/article/10.1007/s10670-017-9936-9

bad news

Mr. Feynman

Whenever you have to ask that and want to emphasize it or to say it without speaking :P

Ryder Rude

@TobiasFünke yes, i understand things in a practical sense. But i can't pin down the foundations. It all falls apart when I try to make real sense of it

Slereah

Also I am told that the Sopranos have the accent of dirty Neapolitans, is that correct

Do you have opinions about how they pronounce the gabagool

Ryder Rude

@TobiasFünke I've not read Jaynes. About classical probabilities, my philosophy is that they entirely come down to degree of beliefs. Any success of probability theory in classical realm is only justified by experience

e.g. from experience, i know that a fair coin gives head/tails half of the time. so this is the only thing which justifies the assignment 50-50

Tobias Fünke

@RyderRude I suggest to read his papers and work

Mr. Feynman

09:30

@Slereah Yes 100%

Ryder Rude

classical theories are deterministic, so probabilities can't represent any property of the system itself

@TobiasFünke i will check it out

Slereah

What is the stereotype of Neapolitans

Mr. Feynman

(Of course I'm joking about sopranos) :P

@Slereah There are good and bad stereotypes D:

Slereah

Bit weird that the mob boys all talk like neapolitans considering the mafia is generally associated with sicily

but maybe it's a Jersey thing

Ryder Rude

@TobiasFünke unrelated, but do u prefer any interpretation of QM or do u think we need QM+GR to solve the measurement problem?

Mr. Feynman

09:32

@Slereah Mhhh, the typical mob accent is sicilian as far as I know

But to be true there are many mobs in Italy, in southern Italy especially and none of them is lesser, just the Sicilian one is more linked to stereotypes

Slereah

Although to be fair part of the plot of the Sopranos is that when they go to Italy, even the Italian mobsters treat them like a bunch of rubes

Mr. Feynman

They also have different names

They call the Sicilian one "Cosa nostra" ("Our thing"), the Calabrian one "' 'Ndrangheta" and the Neapolitan one "Camorra"

Tobias Fünke

@RyderRude I am to a lage extent an "instrumentalist" or "anti-realist", and in particular I see QM only as a toolbox, to which I don't attach more meaning that I have to. It is an easy and cheap escape lol. But of course I also think about interpretations...that being said, I don't have a favorite one; depending on the situation I have to analyse I take the best of all worlds lol

Mr. Feynman

So when you hear a Neapolitan accent it's supposed to mock Camorra

Slereah

> In the city of Newark, New Jersey, the Italian criminals were divided into two ethnic factions; the "Sicilians" and the "Neapolitans".

I guess that explains it

Mr. Feynman

09:36

But then again, over time I realized that even though the difference in accents is wild to us here, abroad they don't seem to notice it and Italians sound all the same to them

Ryder Rude

@TobiasFünke i think, for currently accessible experiments, the instrumentalist view is great for experimental physics. measurement problem is more of a theoretical problem about currently non-accessible experiments

Slereah

Well same as all stereotypes really

Same thing with French stereotypes

Americans do not know about the various French regions :p

It's all Paris, just like Parisians believe

Ryder Rude

because, in principle, one needs to make well defined what one means by instruments

as in, it should be part of the theory how instruments behave just like how anything else behaves

Mr. Feynman

@Slereah Yes, it's definitely the same thing. It's very surprising to me, and it also happens on a smaller scale: in different cities of the same region people have a different accent and those of that region can tell, while those from other regions tend to have a harder time doing so

Slereah

Stereotypes also have quite a large inertia

Still stereotypes about French people and onions like they're thinking about the early 20th century onion sellers in the UK

Mr. Feynman

09:39

The funny thing is that on a regional level you can hear some degree of similarity at least, while on a national level, the accent is so wildly different that it's almost surprising that we can sound the same in intonation

Slereah

Or about striped shirts like they're thinking of Marcel Marceau in the 50's

Mr. Feynman

@Slereah What about baguette

Slereah

That one's fair

Baguettes are great

Mr. Feynman

I mean carrying it under your armpit

Slereah

I mean how else would you carry it

That shit is long

Mr. Feynman

09:41

I've also heard about people laying it on the metro seat, with the exposed part touching the seat D:

Slereah

Not something I've seen

But I'm sure some people do :p

Mr. Feynman

Ewww

Slereah

I've been in the US once

finding good bread there is quite hard

What a wasteland

Mr. Feynman

(I've seen people drop a slice of ham on the street, pick it up and eat it here)

naturallyInconsistent

@Mr.Feynman yes, meow is in English. But miao miao iz not English

Slereah

09:44

Five seconds rule

naturallyInconsistent

@qwerty correct

Slereah

Fortunately with the cultural hegemony I can recognize all the dirty US accents

The greatest Chicago accent

►

Mr. Feynman

@naturallyInconsistent Hey, I know another Chinese word

naturallyInconsistent

yay~

Mr. Feynman

傻逼

Slereah

09:48

wan wan sui

naturallyInconsistent

@Slereah once, in Amsterdam, miao miao basically ate only baguette for lunch for a while. Wonderful~

@Mr.Feynman describing whom?

@Slereah none of us here should be an emperor

Mr. Feynman

@naturallyInconsistent Me

As I understand it's the chinese equivalent of baka

naturallyInconsistent

@Mr.Feynman you don't fit it; at least here, there are way better candidates

correct

Mr. Feynman

@naturallyInconsistent But, uhm, can't it be used jokingly?

naturallyInconsistent

it is mostly used jokingly

Slereah

09:54

I appreciate the Chinese music

"美国兵是废货" American Soldiers Are Trash (Anti-American Song)

►

Important messages

imbAF

https://physics.stackexchange.com/questions/1846/soliton-mechanics
In the derivation of the equation of motion why is it like that instead of:

$ml^2 \frac{d^2 \phi_i}{dt^2}+ mgl\sin\phi_i + D(\phi_{i+1}-\phi_i)+D(\phi_i-\phi_{i-1})$? Can anyone explain ?

Mr. Feynman

Do you mean for the sign?

Quoting your equation @imbAF this sign?
$$D(\phi_{i+1}-\phi_i)\color{red}{+}D(\phi_i-\phi_{i-1})$$

imbAF

Yes, but I noticed he takes the opposite sign euler lagrangian

Mr. Feynman

I don't understand.

In any case, you sign is wrong. It should be a minus.

The relevant term in the differentiation is the potential energy $\frac{D}{2}\sum_i (\varphi_{i+1}-\varphi_{i})^2$

You have two terms involving $\varphi_i$, which are the only relevant ones when differentiating: $\frac{D}{2}(\varphi_{i+1}-\varphi_{i})^2+\frac{D}{2}(\varphi_{i}-\varphi_{i-1})^2$

naturallyInconsistent

10:22

@Slereah that was quite the laugh

it is as stupid and funny in its original language

qwerty

@Slereah to be fair, as i have linked before: visualcapitalist.com/wp-content/uploads/2023/02/…

Mr. Feynman

Ah, imbAF left

Mr. Feynman

11:16

@think_meaning_buildß No, actually "that guy" is any user pointing that out in such a moment, I wouldn't disrespect you or anyone by using "that guy" instead of the proper username :P

Qmechanic

@TobiasFünke : Ha-ha. For completeness, you should link to the IMDB page for actor David Cross on your profile page :)

3

Mr. Feynman

If Qmechanic becomes a regular user of the hBar too I will get a tattoo of their favorite quasisymmetry

4

qwerty

@Mr.Feynman you weirdo :p

Mr. Feynman

Thanks :D

qwerty

here I am, logging on to hbar for a nice, relaxing sunday night... and the first thing I read is your parasocial stanning :P

Mr. Feynman

11:31

I'm scared to google what that is

qwerty

urbandictionary.com/define.php?term=Stan

Parasocial interaction

Parasocial interaction (PSI) refers to a kind of psychological relationship experienced by an audience in their mediated encounters with performers in the mass media, particularly on television and on online platforms. Viewers or listeners come to consider media personalities as friends, despite having no or limited interactions with them. PSI is described as an illusory experience, such that media audiences interact with personas (e.g., talk show hosts, celebrities, fictional characters, social media influencers) as if they are engaged in a reciprocal relationship with them. The term was coined...

Mr. Feynman

Oh, then yes.

When I first joined the site, analytical mechanics was my favorite topic and I would always find qmechanic's answers (I intentionally spelled it lower case, for this is what the username used to be back then) about it

qwerty

I also liked analytic mechanics... maybe because it was the least demanding subject 😅

naturallyInconsistent

@qwerty surely that was before you realised that so much of it is written vaguely?

and then finding out from ACM that a lot of vague statements raised to mysticism status are really just badly written

Mr. Feynman

@qwerty It was the most demanding back then: I was in my second year :P

qwerty

11:44

@naturallyInconsistent I don't know what to say! What introductory/undergraduate level topic in physics isn't vaguely written? Also there's so many books out there. Arnold certainly would satisfy most demands for rigour.

naturallyInconsistent

@qwerty oh no no no no! Arnold is definitely the opposite of what rigour looks like...

qwerty

@Mr.Feynman I struggled with most other topics much more than mechanics; it remains what I am most comfortable with...

@naturallyInconsistent really?? it's written for mathematicians and I have heard more than one maths prof praise it...

Mr. Feynman

@naturallyInconsistent I would dare to say that holds for most Russian math books: they deal with advanced topics but they tend to be less rigorous than the math I know :P

naturallyInconsistent

I suppose, compared to most of the other standard textbooks for analytical mechanics as used in physics, Arnold is using much more mathematical notation than usual.

qwerty

@Mr.Feynman eyes so it's not just the russian physicists, it's the russian mathematicians too??

naturallyInconsistent

11:48

@Mr.Feynman miao miao was also thinking of whether to just assert that problem with the entire Russia style, but yeah, that stereotype is not for show

@qwerty correct.

Mr. Feynman

@qwerty They are one and the same, my friend

Which isn't bad per se for physics, it's more practical and - uhm - appliable?

I have this russian book about differential equations and calculus of variations separating variables like it's nothing (I'm talking about ODE), like physicists usually do

naturallyInconsistent

It does mean that there is a niche unfulfilled: a mathematically rigorous introductory textbook on classical and analytical mechanics suitable for a first or second year mathematical physicist

qwerty

go write it, nI!

naturallyInconsistent

I'm not going to write it. I have my hands full with the textbook on QFT skipping QM.

Mr. Feynman

Instead, in my real analysis course we briefly discussed - basically hinted at - separating variables in ODE and we had to deal with like three different types of solutions depending of the domain of the integration constant (which is not $\mathbb{R}$ for a general non linear ODE) and a simple equation took PAGES of calculation

@naturallyInconsistent Actually, Valter Moretti did it :P

naturallyInconsistent

11:52

And to write that, I'm already needing to write an introductory textbook on classical mechanics that uses the most natural units that miao miao found

Mr. Feynman

And it was recently translated

naturallyInconsistent

@Mr.Feynman ooooooHHH

Mr. Feynman

@naturallyInconsistent Who's the monster who uses units?!

The free particle lagrangian is $\mathcal{L}(q,\dot{q})=\frac{\dot{q}^2}{2}$

qwerty

Me, natural units are kinda annoying

if you're working with different stuff

domains

Mr. Feynman

The mass is always one.

qwerty

11:53

set everything =1, then we dont have to solve anything

ACuriousMind

I wouldn't call Arnold "non-rigorous", but it's definitely Russian :P

qwerty

go home, everything is solved and perfectly beautiful. the answer is 1

naturallyInconsistent

@Mr.Feynman There are two masses that are natural to set to one. There is the electron mass, and the Dalton. It is difficult to figure out which one to pick.

@qwerty fine structure constant isn't 1

Mr. Feynman

Classical mechanics is math, no electrons, no particles, no masses :P

NO PHYSICS.

naturallyInconsistent

And if it were, then we might well be unable to find QED.

qwerty

11:55

@naturallyInconsistent i'm being sarcastic :P

naturallyInconsistent

@qwerty the reply is also sarcastic

qwerty

MIAO

Mr. Feynman

HONK

naturallyInconsistent

M I A O ~

But when it came down to some simulations, it turns out that it is quite important to pick electron mass rather than the Dalton to be 1, because it is easy for electrons to go relativistic while still having non-relativistic nuclei.

qwerty

alright people (and cats): what exactly is 1) non-rigorous and 2) Russian about Arnold?

Mr. Feynman

11:58

So, in my opinion it's not really non-rigorous: as ACM said it's Russian. So your question is condensed to a single one

Let's now address the other point

Your typical math book tends to be very precise, making sure to shed light on every relevant passage and to always work using more systematic methods instead of intuition (unless it's an example or so). Arnold uses heavy weaponry but it doesn't strike me as pedantic, not as much as a normal math book would be

I'm sad when we talk about Arnold, because my Arnold got hurt because of my bad book parenting

naturallyInconsistent

Reminds meow meow of my prof describing why he could not read Schwinger. Schwinger had a text that is called "Source Theory" that he kept claiming to be equivalent to QFT. My prof said that Schwinger would go on and on with some elegant derivation, lots of maths, and then suddenly the argument will go "It would be nice if we have so and so property" and then just use the property as if it were true or proven. (I think, in essence, it is being wished to be true.) After many years, someone

proved from Schwinger's source theory a prediction that directly differs from QED, and that finally put that thing out of its misery.

Mr. Feynman

Look what my neglicence caused

naturallyInconsistent

You can fix it, you know? Other than ironing it, you can pay to turn it into hardcover.

Mr. Feynman

Yes, I have it in Italian, after all it's a translation anyways :P

qwerty

@naturallyInconsistent how is this similar to arnold?

naturallyInconsistent

12:06

If you are ironing it, use a towel or something so that you don't ruin the cover.

Mr. Feynman

@naturallyInconsistent I would never do such thing to a book of mine

Wait, does the hardcover look any good?

naturallyInconsistent

@qwerty No, I am not saying that there is any similarities there. Just saying that it reminded meow meow of the anecdote.

qwerty

oh

naturallyInconsistent

@Mr.Feynman Well, you know how libraries do their hardcovers? You can pick and choose which type of hardcover you want.

Mr. Feynman

Wait, the starred message is dangerous, I will NOT get a TATTOO

naturallyInconsistent

12:08

@qwerty sorry for being misleading there. Miao miao never proceeded past the front bits of Arnold, because, again, the treatments that do symplectic geometry tends to be "these maths are useful" and not interested in motivating why, and miao miao needs the motivation for those particular bits of maths.

qwerty

most paperbacks won't have the correct kind of binding to last long/withstand stress as a hardcover

it would be for looks only

naturallyInconsistent

@Mr.Feynman Now you must miehehehe

Mr. Feynman

@qwerty Tell that to Editori Riuniti who prints most of its books in paperback

I have a nice-looking Landau 1, while Landau 2 and 3 smell like garbage

(I just wanted to be dramatic, they smell like an old library and I like it)

naturallyInconsistent

Sigh, the cute ppl have just left.

qwerty

I have uhhh a bunch of Indian edition textbooks which were much cheaper from when I couldnt afford all the standard western market books. basically printed on phone book paper, the pages were so thin

naturallyInconsistent

12:11

And it is time to go get dinner

ACuriousMind

@qwerty It's hard to define - this branch of Russian (Soviet, really) math/physics has a vibe to it that's very different from the "Western" math. Part of it is definitely not being as enamoured with the Bourbaki-style definition-theorem-proof structure, and skipping tedious details with less fuzz. If one compares Arnold to something like Abraham/Marsden from around the same time, the difference is striking.

Mr. Feynman

@naturallyInconsistent I'm still here thank you very much

qwerty

@naturallyInconsistent WHAT ABOUT Mr F and I??

naturallyInconsistent

@qwerty Miao miao got some books from there too. Miao miao calls them printed on toilet paper.

@Mr.Feynman I'm saying my room

@qwerty Not hbar

qwerty

we are in your room. on your screen ~~

naturallyInconsistent

12:12

Goldstein and JD Jackson on toilet paper are still wonderful

@qwerty lol ok yall cute

qwerty

:3

naturallyInconsistent

Now I wonder when is the next time somebody stays over

qwerty

@ACuriousMind I've not read Abraham/Marsden! Would you recommend?

ACuriousMind

@qwerty Another aspect is a greater focus on computation and examples - theorems are stated and proven in both cases, but the Soviet style is often much more intermixed with exercises and examples than an equivalent Western text, while the Western texts emphasize proofs more. It's tempting to blame again Bourbaki.

naturallyInconsistent

I would have very much preferred intermixing with exercises and examples; Arnold was very much not that.

ACuriousMind

12:18

@qwerty It's the book if you're interested in mathematical Hamiltonian mechanics

naturallyInconsistent

Instead, Greiner was very very very very readable

@ACuriousMind but it seems to be a book you read after you are already functioning in Hamiltonian mechanics?

ACuriousMind

@naturallyInconsistent Hm? Arnold is full of examples.

They're just often very tersely formulated

naturallyInconsistent

I found it really really difficult to read

I see, that might be why

qwerty

@ACuriousMind I knew that about the Soviet physicists firsthand, but I had no firsthand interactions with Soviet mathematicians. I also did standard maths instead of advanced maths which focused a lot on computations rather than proofs. So it was something I never learned to read or get comfy with tbh; I would not have the palate to tell the difference between Soviet maths and Western maths. Physics was easy to tell.

ACuriousMind

I'm personally not a big fan of Arnold's style, either

naturallyInconsistent

12:21

Arnold is a very hit-and-miss. There are some of his writing that is lucid

Sadly, not very much of it is lucid

Greiner series was a great find

ACuriousMind

@naturallyInconsistent not necessarily; a mathematician trying to learn Hamiltonian mechanics could definitely start there

naturallyInconsistent

@ACuriousMind Ah yeah, of course. But I'm never interested in that direction; most of humanity arent going to be able to understand things that way

ACuriousMind

for physicists I generally recommend learning the physics version first and then reading the math :P

naturallyInconsistent

lol submitted that just before ya

qwerty

Lanczos has a place close to my heart. It's probably not the best book, but there are sections which try to explain things other books don't. it was the first physics book I read after a 1 year of being unable to do or think about physics. It really felt so nurturing and soothing and really helped reignite my spark

naturallyInconsistent

12:27

yay

qwerty

:66598480 that's the one!

naturallyInconsistent

@qwerty amazon.com/Variational-Principles-Mechanics-Dover-Physics/dp/…

qwerty

yep

naturallyInconsistent

hmm, can't get it to expand bigger when it is a reply

oh, it doesn't expand even if it is not a reply lol

I'm kinda eagerly waiting for you to try deeper topics

like, stat therm, E&M, and quantum

qwerty

I started writing notes on quantum at the start of the year, but it got put on the backburner

I think I mentioned I was following Dirac

naturallyInconsistent

12:34

Oh, that's a cute book

Many cute theorems and their proofs. But it is a bit out of the way to read.

qwerty

actually around the same time I started on some notes titled Dynamical Systems, which ended up poking a bit at statistical physics too right at the start, because it sets the stage with the correct kind of structure. the book I referenced was by Radu balescu, I think it might be a bit obscure. I never finished reading it

naturallyInconsistent

its ok, nothing is to be rushed now

ACuriousMind

@Slereah We can conceive of the Poincaré group not only as the group of isometries of Minkowski space but also as the group of transformations between the coordinate systems of inertial observers in it. Is there a concept of the group of transformations between the coordinate systems of inertial observers in a general spacetime? (It's definitely not the group of isometries)

Slereah

@ACuriousMind what do you call the coordinates of an inertial observer here

ACuriousMind

That would be part of the question :P

Mr. Feynman

12:42

@ACuriousMind What is the difference between the two ways to see the Poincaré group here?

Slereah

An observer defines a timelike vector at a point and around that you can define the kinematic group associated to this vector I guess?

Since kinematic groups are typically constructed around a specific choice choice of timelike translation

qwerty

@naturallyInconsistent yeah I haven't touched those notes for months, I hope I don't just stop learning and writing. I think hbar is helping though: I feel very grateful for everyone here - in particular you, ACM, Mr F, slereah and silly goose. I honestly have not felt this much physics camaraderie since my undergrad days and it's very lovely

ACuriousMind

@Mr.Feynman Well, none in the case of Minkowski space :P

Slereah

And I think part of the point of a kinematic group is that the spacetime structures involved are all invariant under it

Mr. Feynman

@ACuriousMind Mhhh but you made at least a conceptual distinction if the question arose (?)

Slereah

12:44

Since they're constructed typically as the invariant tensors of G structures

You can also have coordinate systems that are appropriate for G structures, ie the integration of them

ACuriousMind

@Mr.Feynman The conceputal difference is that the group of isometries does not relate all the observers in the general case - you can have spacetimes with very little isometry, but I don't think that means there are fewer inertial observers in those

Slereah

And the local equivalent of that is the 1-integration, like for Riemann coordinates

That should apply for any such group

ACuriousMind

so I'm fishing for some formal notion of this "relation between inertial observers" in the general case

Mr. Feynman

@ACuriousMind Oh ok, that makes the question more clear to me

The correspondence between group of isometries and inertial coordinate transformations is accidental

Slereah

Presumably for any integration of a G structure you have a family of observers related by spacelike translation

Which are the "at rest" observers in those coordinates

So with tangent vector equal to the timelike basis vector

Ryder Rude

12:48

@ACuriousMind hi. to be able to talk about transformations between inertial co ordinates in general spacetimes, we need to define the set of inertial co ordinates in general spacetimes. i think there is no good notion of "global co ordinate systems" that are inertial

like, for the same observer, u can choose multiple co ordinate systems that are locally inertial

the only unique co ordinate u can associate is the time co ordinate

ACuriousMind

@Slereah So what I was thinking about is that "inertial systems" in general could be Riemann normal coordinates where the time-like coordinate vector aligns with the tangent to the observer's worldline, and then the group in question would be translations + the Jacobians of the coordinate transformations between those coordinate systems

Ryder Rude

i think space co ordinates cannot be uniquely associated to an observer

Slereah

The observer is also associated with an initial point and frame, course :p

@ACuriousMind yeah that sounds reasonable enough, plus the Jacobians preserving whatever tensor of the kinematic structure

ACuriousMind

(of course all this "locally" at the moment)

Slereah

You can extend them a little using geodesics

By "a little" I mean several light year

ACuriousMind

12:53

but you don't know of any reference where something like this is discussed?

Slereah

Nothing specific I think?

You can check the bibliography of my thing on spacetime measurements I guess

overleaf.com/read/jxvqwttqdrbj#518a5d

Plenty of papers on that general notion

Mr. Feynman

@Slereah it's getting too practical now, chill out

ACuriousMind

alright, time to figure out how much effort I'm willing to invest in this random thought :P

Mr. Feynman

You can do like me. Get a notebook and write it for later

Later is anywhere in your future

Ryder Rude

@ACuriousMind this defines the notion of local inertial co ordinates. But different observers would in general not reside in the same part of spacetime. So one cannot talk about meaningful transformations between their co ordinate systems

as in, the transformation would largely depend on arbitrary choices

in Minwkoski spacetime, one is able to define these transformations despite the fact that the observers don't reside in the same part of spacetime

Mr. Feynman

12:58

I think ACM knows that, it's not what he's asking :P

Slereah

iopscience.iop.org/article/10.1088/1751-8113/47/43/435202

ACuriousMind

@Mr.Feynman I do that (electronically), I have folders full of random stuff I wanted to write and never got past the outline :P

Slereah

That one is pretty cool specifically for observers

Ryder Rude

i think it has to do with the existence of some unique time slicings in Minwkoski spacetime

Slereah

But it is GR oriented

Although I think it would generalize to most groups

Ryder Rude

12:59

@Mr.Feynman i think they r asking for co ordinate transforms between inertial observers in general spacetime...

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