The h Bar - 2025-02-13

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naturallyInconsistent

01:21

@Slereah did you make this? can't find the XKCD source

1 hour later…

bolbteppa

02:39

ihes.fr/yvonne-choquet-bruhat

bolbteppa

02:54

@Sanjana From this:

> As we already commented, the superfield Y is too big. It has way more fields than we expect from the representation theory of Section 2.3. This is because Y is not an irreducible representation. It can be reduced to something smaller. The question is: how?

> Second, note that it contains many more fields that we might have thought from our analysis in the previous section! The representations on single particle states suggested that there should be a chiral multiplet containing a single complex scalar and a Weyl fermion and a vector multiplet containing a gauge field and a Weyl fermion. Yet the
superfield Y contains a plethora of such fields. We will shortly see how we can impose further restrictions on Y that truncate the number of fields lying within to match our earlier expectation.

Sanjana

@bolbteppa Yeah I know why they do this from a physics POV. I am wanting a mathy POV because physics is like "we considered some example in some other section, I wanna reproduce that. I am looking for something like "These are ALL the things we can consider and we are considering this because" ... idk maybe these are the ONLY things which we can consider after imposing other more natural conditions??

qwerty

03:26

@naturallyInconsistent I think it was modified from xkcd.com/2281

naturallyInconsistent

03:53

Thanks~~

4 hours later…

Ryder Rude

08:04

hi

1 hour later…

Tobias Fünke

09:10

morning

naturallyInconsistent

09:23

mew mew

3 hours later…

Ryder Rude

12:47

do you think some physicists are getting too arrogant? like, claiming to know what reality is

like, physicists don't subscribe to Kant-type ideas where everything we know about the universe is dependent on our mind's features

they subscribe to some naive philosophies, like claiming that a physics model is the ontology

i also see this behavior in computer scientists. too many of them say that the universe is a computer

whatever happened to Socrates's "All I know is that I know nothing" or Newton's "I feel like a child playing on the sea-shore while the entire ocean remains unexplored"

Signor Feynman

13:17

@RyderRude I think that every time this discussion popped up in this chat, the most common opinion is that we try to make predictions about what is observable; "the true ontology" of the universe is not, so I'm not sure where the physics literature actually makes claims about some absolute concept of reality or where it's ever relevant in physics

Tobias Fünke

@SignorFeynman Physics does not, physicists (or scientists in general) might, though. That's however a matter of opinion, and clearly not all are claiming such things. If I had to guess I'd say the majority of physicists has a "converging realist" or "entity realism" POV, although "operationalist" and "instrumentalist" POV are common, too.

I don't know if there are any studies done on this. I'd like to see some numbers

Ryder Rude

@SignorFeynman yes. i don't see physics literature making these claims either. on the other hand, i do see physicists making weird philosophical judgements because of physics models. like, saying that free will doesn't exist. or that consciousness doesn't exist. or that "the universe is a wavefunction" or that "the universe is bunch of particles interacting, and that "explains" everything else"

i also see computer scientists saying that any math that is non computable is fantasy, and also that reality is computers

i think these are naive philosophical judgements which result from not having experience in philosophy

Tobias Fünke

@RyderRude might be true, but on the other hand why would you take these claims serious? I don't think it is worth to discuss every random opinion from random people ^^

Signor Feynman

I don't care what physisicts say if it's outside the realm of physics, i.e. outside of what can be written in a paper

Ryder Rude

@TobiasFünke he is a prominent figure... he is Joscha Bach. Wolfram also says this stuff

i cant remember any other names.

there's Aaronson

Signor Feynman

13:29

Let people talk about anything; take them seriously about their expertise only

Ryder Rude

Aaronson is another computer science guy who thinks that reality is computable stuff

Tobias Fünke

@SignorFeynman this

Signor Feynman

that

Ryder Rude

@SignorFeynman sometimes it becomes misinformation.. like in Carroll's case. he talks in a really convincing way. i think it really convinces the audience into believing naive physicalism.

Carroll takes the "success of science" to mean "success of materialism"

he would say "science is so successful, so ofc one day consciousness would be reduced to materialism"

and he puts it really well into words. a non experienced audience would find no holes in his logic. and he himself finds no holes in it _____

Signor Feynman

On the one hand, a popsci author should make sure to make a distinction between scientific truth and personal belief, on the other hand a well educated subject knows what I said above. You should not take too seriously people talking about other fields, even more so for something that is probably outside the realm of any field

qwerty

13:35

cough michio cuckoo, I mean, kaku

Signor Feynman

Rovelli does that too :P

Ryder Rude

@SignorFeynman exactly. i think it comes across as arrogant when they claim to know stuff, instead of stating it as opinions. i don't take them seriously ofc, but only because I can detect the holes in their arguments

Signor Feynman

His popsci books basically present LQG almost on the same grounds as QM :P

Ryder Rude

also, the audience thinks the physicists or the computer scientist must be right cuz they must be intelligent.... even though they r making claims about philosophy

qwerty

we should probably just stop giving them airtime

it's the cult of celebrity

Ryder Rude

13:39

@SignorFeynman yeah... he titled his book "quantum theory of gravity". i think he did it to counter string theorists tho :P

Signor Feynman

@qwerty with four characters less, this message would be so mean :P

Ryder Rude

like, string theorists would say "we r the only game in town". So Rovelli isn't playing by the rules either.

qwerty

@SignorFeynman hahaha

Tobias Fünke

lol

qwerty

@RyderRude the "some physicists" in this statement would be the self promoters and wannabe celebrities

unfortunately it's got nothing to do with being a physicist imo

Silly Goose

13:52

@RyderRude i have been told that the modern view is that everything is an effective theory

In the sense that a theory of everything even if extant would be utterly intractable to use to model a metal

Ryder Rude

@qwerty this applies to some like Kaku. But I think some others genuinely believe their ideas but they just make naive philosophical judgements to arrive at them

@SillyGoose right. in this case, TOE itself wouldn't be an effective theory, but everything else except TOE would be

@SillyGoose the effective theory perspective is better. there might be still be some nuance left. like, is the hierarchy of effective structures attributed to objective reality or are they the mind's interpretation of objective reality. but I think physicists wouldn't be interested in this nuance

still, if one isn't familiar with these nuances, one should be more careful and say that their philosophical judgements are merely opinions

_______

fqq

14:34

@qwerty I agree with the criticism that some of Rovelli's book fail to make a distinction between well-established science and LQG, but it's absolutely unfair to group him with Kaku and the absolute nonsense he keeps peddling

And it's a very different issue from "talking about other fields". LQG and QM is very much Rovelli's field, his books are usually well written and correct, but might sometimes mislead laypeople and Sig.F's criticism is fair. Kaku's field is also apparently physics but that doesn't stop him publishing complete bullshit

Eg about quantum stuff

Signor Feynman

14:55

Beware @fqq that I was only talking about pop science books, not Rovelli's serious books about QG. If my memory is not trolling me, I remember him describing the discreetness of spacetime as a fact in a book

1 hour later…

bolbteppa

16:16

Show me a 'nonsense' statement by Kaku and I bet it can be defended

naturallyInconsistent

^perfect rendition of feynman bro as collier was complaining about

ACuriousMind

16:39

@bolbteppa e. g. Aaronson reviews several embarrassing basic mistakes and lack of substance in Kaku's quantum computing book in scottaaronson.blog/?p=7321

DIRAC1930

16:53

@RyderRude I believe that this has become slightly more toned down and I think part of it is due to Eric Weinstein

And I do think he has a point

Oh I thought you were talking about the people who used to talk about String theory like it was as established as describing the real world as QM

Ryder Rude

@DIRAC1930 yeah...i was talking more about physicists using physics to make naive philosophical judgements and not being careful in stating them

@DIRAC1930 Weinstein also promotes his own theory tho

Signor Feynman

17:08

Isn't Weinstein a bit of a crackpot?

Ryder Rude

maybe. i think he has made a theory just to get popular. he doesn't believe in his theory

or maybe he believed in it long ago but not anymore

DIRAC1930

Well he got a PhD from Harvard in a lot of the stuff that is to do with his own theory I think

Also, I would way rather someone who takes their own path even if they might be wrong

I think it should be more encouraged

Ryder Rude

i read some stuff about this theory which sounded shady. like, how he promoted it for years without even releasing it to be reviewed. but I think he has released it by now

@DIRAC1930 yes. it is a good thing. but some of Weinstein's actions looked weird to me.

DIRAC1930

I guess time will tell

I do not understand why he is being so cryptic about things though

Ryder Rude

see this physics.stackexchange.com/a/619971 he apparently took a lot of time to release his theory. maybe he wanted to get popular

Lisi is another guy who has a more honest attempt. like, he put out his theory to be criticised. but he is also called a crackpot

DIRAC1930

17:17

I think Weinstein is unfairly being dismissed a lot of the time. Getting a PhD in mathematical physics from Harvard doing your own original work is next to impossible

And i don't think it happens a lot

Ryder Rude

i didn't know that. it is really impressive

i cant judge these peoples' ideas without having read it. but Weinstein def is capable as a physicist

string theorists keep saying that they r the only game in town and dismiss any other stuff. that deserves criticism

naturallyInconsistent

The chances of reading a crackpot paper from top unis like Harvard, Yale, MIT, Caltech, etc, is a LOT higher than reading a crackpot paper from a 2nd rate uni like Minnesota. Those from the top tier simply aint getting any push back. Of course, 3rd rate and below, there are plenty of crackpottery, but if there aint tolerance for crackpottery at 2nd rate unis, there also should not be any tolerance for crackpottery at top tier too.

bolbteppa

He starts by bitterly whining about the fact Rogan brought him (Kaku) on instead of Aaronson, lamenting the fact that his decades of outreach have done nothing compared to Kaku. Then his first criticism of Kaku is wrong, Kaku is just stating what Google claimed as was a big news story yet Aaronson is trying to blame Kaku for a mistake by google, this is literally dishonest by Aaronson,

whining about Kaku bringing up a famous news story he clearly assumes his readership probably had heard of, without litigating its veracity, illustrates how desperate people get when they bash Kaku.

naturallyInconsistent

Just the other day I was reading / watching something unrelated, and suddenly the topic made a brief detour to how a MIT prof was just publishing a lot of "throwing ideas out there" kind of papers, and something like that would not have been publishable in non-paper-mills if they simply werent a MIT prof

bolbteppa

In other words, because Kaku didn't immediately bog the reader down with poor writing by wasting time explaining the later developments after the big news articles that Google's initial estimate of 10,000 years was criticized and debated (i.e. secretly Aaronson is wining that Kaku didn't cite his blog post about this in the opening of his book to waste the readers time on this tiny detail).

We can get into the rest of it and how tivial it is, basically doesn't pass the smell test if one applies the most basic critical thinking

Kaku says some 'crazy' things that are all defendable, e.g. talking about teleportation etc can be painted as crazy yet even in the past two weeks there was another article about it being done

ACuriousMind

17:34

@DIRAC1930 Using his PhD as evidence of any kind of competence when he explicitly puts himself outside of academia because it wasn't receptive to his ideas is a pretty bizarre move. So his PhD is proof of his competency, but when literally almost every other PhD in his field doesn't even engage with his ideas, that's baseless group think and their PhDs aren't proof of their competency?

@bolbteppa What do you mean "immediately"? Does he clarify later in the book? Uncritically citing a controversial claim as fact is not defensible to me when you pose as an authority on a subject

Ryder Rude

@bolbteppa Kaku also believes in MWI. i think u would say he is wrong there?

bolbteppa

Google made the claim, whether they were right or wrong doesn't matter, it was such a big deal that news articles were written about it, complaining that Kaku didn't delve down the rabbit hole of litigating the details on a famous news story that is a representative of the larger story that supercomputers can do in 200 seconds or 2.5 days or whatever what used to take 10,000 years is bad writing in a lay book

Ryder Rude

i think Aaronson's criticisms are somewhat reaching for straws. The book sounds like a pop sci book and the statements made r not supposed to be technical. so statements like "a classical computer can never do this" are not supposed to be interpreted technically

bolbteppa

It's why people know Kaku and they don't know this bitter blogger

Ryder Rude

the valid part of Aaronson's criticism (assuming it is correct) is that the book is bad, as in, it is titled "quantum computing", but most of the book is just filler about other stuff

oh but there are some technical statements that are made precisely and are flat out wrong. Aaronson has pointed this out

ACuriousMind

17:42

Also, to turn our own hostile rhetoric back on you, it's pretty telling that you picked the one example where he's actually citing someone else rather than just stating nonsense as fact, such as the claim that quantum computers can solve problems classical computers couldn't solve even in infinite time. Why are you immediately jumping to personal attacks?

Ryder Rude

e.g. Kaku says the time a classical computer it takes to factorise the number is $e^N$ which is just wrong

Aaronson says it is supposed to be $\sqrt {N}$

but maybe two or three errors are to be expected, especially from pop sci books. the main valid criticism is that the book is bad because it is mostly about stuff unrelated to its title

ACuriousMind

@Sanjana is this any different from studying the Weyl (=chiral) and Majorana (=real) spinors as subrepresentations of the Dirac spinor representation?

from a math POV the "interesting" thing is just that there are subrepresentations of the algebra under consideration (in my example the Lorentz algebra), and by general arguments subreps/irreps are interesting in the sense of being "basic building blocks" of the representation theory in most cases

DIRAC1930

@ACuriousMind It's not about group think. I was just saying that most PhD's are their supervisors ideas which is usually the only way thats possible since there just isn't enough time (at least in European PhD's). To produce something truly original at a PhD level is apparently quite rare at least in modern times

Also it's not just that. He found the Seiberg-Witten equations or something before Seiberg and Witten. His postdoc supervisor essentially discouraged him and then Seiberg and Witten came out with their version. Seiberg apparantly appologised to him or something on stage at the IAS

fqq

@SignorFeynman yes that was clear

DIRAC1930

And academia isn't receptive to any new ideas in hep-th anyway. You just will not get funding

Except maybe in mathematics do you have that freedom

But I don't know about their hiring practices

ACuriousMind

18:02

@DIRAC1930 Do you have any evidence for this that is not Weinstein's words?

Because that's exactly the kind of story I would make up to show how unfairly academia treats geniuses like me. Not that I believe there isn't a lot of bad stuff happening in academia, but precisely because it is, one has to be careful not just to believe any story that falls into one's preconceived ideas about how academia is bad

bolbteppa

After the first page criticism being absurd, one error on page 2 that the blogger paints as the worst thing ever, another he admits is just a belief, and then he has to go to page 84 to find the next one which is presumably a stupid mistake, oh and because Kaku acknowledged famous physicists instead of these bloggers he is clearly spreading misinformation. This is not exactly damning stuff.

fqq

lol at the personal attacks on aaronson

"these bloggers" lmfao

bolbteppa

realclearscience.com/blog/2022/07/06/…

To me this is embarrassing, he's making an understandable point though I still think its embarrassing

@SignorFeynman He is a full-fledged one

15

Q: Is Eric Weinstein's copyright protection of Geometric Unity in the spirit of Science?

In (Dr.) Eric Weinstein's Geometric Unity: Author’s Working Draft, v 1.0 he has a footnote on the first page: The Author is not a physicist and is no longer an active academician, but is an Entertainer and host of The Portal podcast. This work of entertainment is a draft of work in progress whic...

etiquette science academic-freedom

"This work of entertainment"

Literally burst-out-laughing level stuff, oh man

Tobias Fünke

19:17

0

Q: Upper bound of ground state by variational method

In many quantum mechanics books (such as Bransden) they prove that this method always gives an upper bound by saying: Let's say $\phi $ is our trial function and $\psi_{n} $ are the complete set of orthonormal eigenfunctions of our Hamiltonian. In Bransden it is stated that we can always expand $...

quantum-mechanics schroedinger-equation hamiltonian variational-principle ground-state

Does anyone understand what OP is talking about?

I have a vague idea...

controlgroup

I don't really get it either. The top answer (+1 right now) seems applicable and hasn't been commented "wrong" yet, so maybe that's it??

ACuriousMind

@TobiasFünke I think OP is just unaware of the spectral theorem?

Tobias Fünke

I really don't know

could be true. but then again, I've linked a related question

and they said it did not help at all

I think they might misunderstand the theorem itself and how in practice it is used

their terminology is too confusing for me

ACuriousMind

Like, they seem concerned that the eigenbasis of the Hamiltonian is finite even if the space is infinite. This can be either because a) they don't know about the spectral theorem b) they are concerned because they've learned that the Hamiltonian might have continuous spectrum for which the "eigenbasis" in the strict mathematical sense might indeed be finite

I've left a comment trying to coax this out of them

now I just hope I don't get responses from uninvolved commenters who will point out the thing about continuous spectrum, which will bring us no closer to what OP means :P

Tobias Fünke

@ACuriousMind I was SO close to do it haha just kidding

yes, I see your point--but that should've been cleared in the answer of the post I've linked, no?

ACuriousMind

19:25

I understand the urge all too well :P

Tobias Fünke

perhaps it was not stated clearly enough there (for the purpose of this question here)

ACuriousMind

@TobiasFünke Askers will not read the answers to the posts you link as duplicates. They just read the question and then get upset that the question is not the same as theirs :P

Tobias Fünke

ah :d that could indeed be the case

ACuriousMind

you have to very explicitly say something like "it's not the same question but the answer should clear your confusion" or something like that

I've been there :P

Tobias Fünke

yeah

"Edit 3: I didn't know "complete set of eigenfunctions" implied it was infinite. I thought it meant that our set had a complete set of set of (commuting) observables."

ok

ACuriousMind

19:28

that just kicks the can down the road because I can't tell what the second part of the statement means :P

Tobias Fünke

yeah :d

but I guess part of the problem is the physicists in using "complete basis"

I mean why emphasize with "complete" -- a basis is a basis... although one might mean to emphasize the difference between Hamel and Schauder bases? or what?

ACuriousMind

@TobiasFünke It's just physicists not being mathematicians :P

Tobias Fünke

lol

ACuriousMind

Physicists don't think about words in terms of formal definitions, so they see nothing wrong with a pleonasm like that

imbAF

Can anyone help me understand this weird thing that is going on with my calculation, where clearly some mistake must be made:
Lets have a=(E,0,0,E), b=(m,0,0,0), c=(E' * * E'cos\theta), d=(m,0,0,0) the * is a placeholder for whatever value.
If you do the following dot product (ab)(cd)=2m^2EE'
If you do the following one: (ac)(bd)=EE'(1-cos\theta)m^2 right?

How scalar product doesn't give same result when changing places of the four vectors ?

ACuriousMind

19:41

@imbAF Why should it give the same result?

imbAF

isn't inner product commutative ?

ACuriousMind

It is but that's irrelevant to your question.

If you write your expression carefully using the inner product notation $\langle -,-\rangle$, you are claiming that $\langle a,b\rangle \langle c,d\rangle = \langle a,c\rangle\langle b,d\rangle$ should be true. Commutativity of the inner product is $\langle a,b\rangle = \langle b,a\rangle$ and does not allow you to derive that (false) equation.

imbAF

I did not derive it. I encountered in something I am solving 4 four vector multiplication, and since I can write it in component notation using lorentz indices , I thought of shifting terms around

but, apparently the result changes

ACuriousMind

Index notation does also not allow you to arrive at that false equation :P

imbAF

Yes it's wrong since I get the wrong result

ACuriousMind

19:48

I don't understand why you would just assume something should be the case when you have no reason to believe so, i.e. have not derived it. Math does not work by just assuming things are true based on vague ideas. Either you can prove an identity (or point to a proof in the literature) and it's true or you can't prove it and it's false.

imbAF

derive what exactly?

that I have 4 vectors scalar multiplying each other?

It was 2, now it's 4. I didn't know that I had to check that.

Which I did

ACuriousMind

@imbAF You do not have "4 vectors scalar multiplying each other", that's exactly why I wrote the equation in different notation to make that clear

you have two inner products, which take two vectors each as arguments. The result of an inner product is a real (or complex) number, and then you multiply those two resulting real numbers as real numbers

imbAF

yes

Tobias Fünke

the OP uses "same (or different) Hilbert space" over and over

mhmh

DIRAC1930

Does anyone have a book like Heitler's Quantum Theory of Radiation but going into things like non-linear extensions etc.

ACuriousMind

20:04

@TobiasFünke yeah, there is some fundamental misunderstanding here that has nothing to do with the variational method

DIRAC1930

@imbAF How is your group/representation theory coming along?

ACuriousMind

classic XY problem but OP has come so far from the origin of their actual problem that they have difficulty describing it in terms of which we would have a shared understanding

Tobias Fünke

it seems so

imbAF

@DIRAC1930 Ok to a degree. I am continuing with Voigt or what is his name. But because I am doing QFT during the week, programming 2 days of the week, only the weekend days I try to read one chapter from the book and 1 lecture on Differential geometry, which I found online (suggested by someone). So, while slowly, I think that by the end of may i will have the book finished, or those parts I care about

DIRAC1930

There's an absolute classic called Group Theory and Quantum Mechanics by Van Der Waerden. It uses the standard notation of QM and it is more straightforward

It treats the relationship between representations of SU(2) and SO(3) in all details

imbAF

20:15

Only those two ?

or other groups as well

DIRAC1930

It goes through all of rep theory and its applications to QM

imbAF

I am also interested in a flashed out explanation of group theory in general and not particular to a group. Ofc eventually I want to know more about a particular group, but I'd like to have a good understanding of generality

Ok

@DIRAC1930 that it shows the applications in QM that is good

ACuriousMind

it's from 1932, not really commonly recommended as an introduction to modern audiences (DIRAC1930 loves these old texts but I feel compelled to point out that is not the majority view)

imbAF

A while ago I posted a particular instance of the book that I am reading on the topic

DIRAC1930

It was updated by Van der Waerden in 1974 and it reads like a very modern textbook

Woit's book is a bit tough as a first introduction to rep theory

imbAF

20:20

I will stick with it but

DIRAC1930

It has some insights you cannot get anywhere else

imbAF

There are instances that the book

is unclear

I had a discussion a while ago about a particular instance

care to discuss it? Simply because you are someone who was read the book

DIRAC1930

I found that also

imbAF

my discussion ?

DIRAC1930

As in I found it unclear in certain places

imbAF

20:22

Ah

Just one thing, to confirm my understanding

When we say group G acts on set M

what really happens, is that a group S, that is a homomorphism of G, acts on set M

ACuriousMind

A group cannot be "a homomorphism"

Tobias Fünke

this does not make much sense, and as far as I remember that was not the issue

imbAF

A group homomorphism from G to some other group S

ACuriousMind

That's not a complete sentence

The statement you're probably trying to make is that the definition of "$G$ acts on $M$" is that we have a group homomorphism $\phi$ from $G$ to the group of functions from $M$ to itself, so that the "action" of any $g\in G$ is given by applying the function $\phi(g)$ to (elements of) $M$.

If you want you can call the group of functions from $M$ to itself $S$, but it's not "some other group" it's very specifically the group of functions from $M$ to itself (or some subgroup of it, depending on the context, like the continuous functions)

Loong

@PM2Ring Be-7 would be the best guess for a peak around 477 keV from an environmental sample.

DIRAC1930

20:34

I don't think studying group theory formally will help much

What you really need is the basics of representation theory

Loong

There can be interference with the Compton edge of Cs-137, though.

What was the new NAA question?

imbAF

@ACuriousMind I am confused if $\phi$ is the result of a homomorphism as you said, how it can't be considered as a group?

I mean in the wikipedia that is how it's framed

ACuriousMind

@imbAF I do not understand the question, in my notation above $\phi$ is the group homomorphism, not "the result of a homomorphism".

A function $f : A\to B$ is not "the result of a function".

imbAF

But that is what group homomorphism is isn't it? A relation of some sort, for lack of better words, between two groups

at least, according to wiki

ACuriousMind

It's not a "relation of some sort", it's a function (or "map") between two groups obeying certain axioms (that we usually paraphrase as "preserving the group structure").

imbAF

20:38

A mapping

ACuriousMind

I have no idea where you're getting these vague phrases from. Math is about precise definitions.

imbAF

you think I am, on purpose, doing this? Like, I know the accurate word, but for some reason I refuse to use it?

ACuriousMind

No, I am confused where you are getting these phrases from that are not anywhere (like claiming I said something about $\phi$ being "result of a homomorphism" when I didn't use the word "result" anywhere)

the moment I thought you were doing this on purpose I would stop talking to you entirely :P I am just pointing out that part of doing mathematics is about using the terminology according to its definitions and not making up phrases that are not technical terms because that makes you extremely hard to understand

imbAF

For the last time, if I had the knowledge you have,then I would be able to realize that using the word "result of..." is wrong, I don't have that knowledge. So, idk why I am stating the obvious

ACuriousMind

@imbAF But if you want to get useful help here you have to explain yourself - I didn't say "$\phi$ is the result of a homomorphism". But you asked me a question that claimed I said that. If you don't explain to me what you mean by that, i.e. what part of what I said you interpreted as saying that, I can't give you any useful response! The problem isn't that you would be "wrong", the problem is that I can't even tell what you mean.

Loong

20:47

@PM2Ring If it's an activated sample, it could also be Eu; but you would see many other peaks then.

imbAF

@ACuriousMind Can I point out, that you saying : " it's very specifically the group of functions from $M$ to itself", to me sounds as if this specific group is related to the set(S in this case) and not to the the group homomorphism of G. What I am trying to say is. If you'd switch the set from M to N. In this case would you, considering the initial group G, via group homomorphism have $\phi$. The same \phi which was the group homomorphism, when the considered set was M ?

If my question doesn't make sense or is unclear, I am sorry, but that's the best I can do

ACuriousMind

@imbAF Perhaps we need to be more explicit in the notation. Let's call the group of functions from a set $M$ to itself $F_M$. That is, any $f\in F_M$ is a function $f: M\to M$. Then my $\phi$ is a function $\phi : G\to F_M$ that is a group homomorphism between these two groups. This is "a group action of $G$ on $M$" (or at least one of equivalent ways to phrase it).

You're now asking me about a different set $N$. Since $\phi$ is not a function to $F_N$, it is not an action of $G$ on $N$.

imbAF

Ok I understand this

The source of my confusion was :

I thought that $\phi : G\to F$ and not $\phi : G\to F_M$

So, once you had $\phi : G\to F$, you could consider any arbitrary set N_i

But your notation makes it clear that it's not like that

I hope you can understand my confusion and it's not unclear what I was considering

ACuriousMind

well, at least once you were more specific I could figure out that the problem lay somewhere in that area

I'll not claim that I understand how you got into that confusion but that's not your fault :P

imbAF

I'd like to say how, because that might show my misunderstanding

DIRAC1930

21:04

Btw a big reason why I use a lot of old texts is probably because of my educational background. A lot use the same sort of language and arguments based on intuition that comes more naturally to me. Once the basics are understood, then it can be useful to use a more mathematically precise book that can sometimes go deeper

imbAF

The definition of group action (wiki):
In mathematics, a group action of a group G on a set S is a group homomorphism from G to some group (under function composition) of functions from S to itself. It is said that G acts on S.

I didn't know what group homomorphism is. So I go to group homomorphism, and the definition is:
In mathematics, given two groups, $(G,*)$ and $(H, \cdot)$ a group homomorphism from $(G,*)$ to $(H, \cdot)$ is a function $h:G\rightarrow H$ such that for all $u$ and $v$ in G it holds that $h(u*v)=h(u)\cdoth(v)$

@ACuriousMind As you can see when the group homomorphism is given, you have a map from one group G to H, and no set of any sort is taken into consideration

So I apply this to the definition of group acting

which means, that $\phi$ is a group homomorphism of G, is separate and has nothing to do with the set we consider, S in our discussion

Tobias Fünke

21:20

@ACuriousMind Reading now carefully again the comments, it seems that OP is asking about the domain of the Hamiltonian?

ACuriousMind

21:32

@imbAF It's fine, but I'm not sure I have anything useful to add here, sorry. Perhaps the problem is trying to learn from Wikipedia - for math it's a very useful starting point or reference once you know a sizable amount of math, but it's not structured in a way that makes understanding mathematical concepts from the ground up accessible

@TobiasFünke at this point all I can say is: Maybe :P

imbAF

@ACuriousMind I agree with the last part

Tobias Fünke

yeah, also they left a comment under the answer they've linked to. (but there again, I think they mix concepts and definitions etc.)

ACuriousMind

yes, perhaps the problem is they think the Hamiltonian is only defined on "part" of the Hilbert space. But it still remains unclear if this is the rigorous kind of nitpicking about unbounded operators being only densely defined or a fundamental misunderstanding about the concept of operators and Hilbert spaces

imbAF

ACM perhaps I have asked you this, but did you read a particular book to have an understanding on group/representation theory ?

ACuriousMind

I took abstract algebra courses (which taught me group theory) and a course on representation theory of Lie groups from the mathematicians (well, the latter was technically in the physics department but it was taught by a mathematician).

They didn't follow any particular book but the content is standard in the sense that I didn't learn anything you wouldn't find in any commonly recommended mathematical references on the topic

imbAF

21:39

I don't know what to do honestly. Do I start with linear algebra and then find a book about representation theory

or jump straight to group and representation theory

I am uncertain

Signor Feynman

You may want to learn from a book about Lie Groups and representation theory

ACuriousMind

I feel unqualified to recommend anything because it's clear you learn very differently from me

Signor Feynman

You're not interested in algebraic groups and representation theory is very broad

imbAF

And the book would be?

@ACuriousMind differently how?

Tobias Fünke

Well, as I've pointed out several times already: One should first "master" the "basics", before going to more advanced topics

just my two cents

Signor Feynman

21:41

@ACuriousMind I imagined you plugging a usb pendrive in your head

imbAF

@TobiasFünke That would mean linear algebra?

@SignorFeynman lmaooo... Matrix ACM

Tobias Fünke

I've suggested that in our last discussion, yes.

imbAF

You are right. I need to refresh my memory about linear algebra

And then jump to group theory

Tobias Fünke

@ACuriousMind yeah... never mind. I really do not get what they understand and what not. I guess they somehow vaguely heard of "domain problems" and now have some misconception about the variational theorem

well, you should at least be very well familiar with all concepts related to vector spaces: bases, linear maps/operators/functions and so on

PM 2Ring

@Loong They decided it was probable Be-7. I advised them to post their question as a question, but they didn't do that, and their answers are deleted, so it's not easy to communicate with them. Here's their main NAA question:

> I'm also looking for the identity of the 477 keV line. I don't think it's a calibration error.

Here's a sample of one of my spectra

keV - peak71.9 - 8574.2 - 13583.9 - 121238.4 - 131294.9 - 103300.2 - 30351.7 - 250477.7 - 393511.2 - 273583.3 - 78609.6 - 190662.1 - 165910.8 - 74964.3 - 64969.3 - 1071120.4 - 1171237.9 - 711460.8 - 613

Be-7 has a limited half-life of 53 days. Therefore, finding this line in environmental samples that were collected more than ~500 days ago, should be impossible.

Oops. That list got mangled. Let's see if this works...

keV - peak
71.9 - 85
74.2 - 135
83.9 - 121
238.4 - 131
294.9 - 103
300.2 - 30
351.7 - 250
477.7 - 393
511.2 - 273
583.3 - 78
609.6 - 190
662.1 - 165
910.8 - 74
964.3 - 64
969.3 - 107
1120.4 - 117
1237.9 - 71
1460.8 - 613

qwerty

21:51

@naturallyInconsistent was this avi Loeb by any chance?

ACuriousMind

@imbAF In every aspect :P On one hand, I mean just that you just seem to have much less formal mathematical education than I had at comparable points in my physics education (I'm not trying to blame you, I have no way of knowing how much influence if any you could have had over this), which makes it difficult for me to relate (clearly the solution to just learn all the math in record time is infeasible :P).

On the other hand, you often ask questions where I think that if you don't understand that, you can't possibly have understood the other things you say you understand. I'm not saying you're intentionally being difficult or anything, just that I can't understand you most of the time. The way these things are structured in my head are so different from the way you structure them we have difficulty communicating about them.

That's probably not anyone's fault either but it means I don't really feel qualified to be able to make recommendations to you how to learn specific topics - clearly what I find clear and obvious and helpful is cryptic and unhelpful to you a lot of the time.

imbAF

Yes, the only math provided during my bachelors was Hoehe Mathematik I , II, III, which helps f all for the things I want to know

Tobias Fünke

do you study physics?

imbAF

I am aware of my fragmented understanding of physical phenomena and limited math knowledge. Limited toolkit

ACuriousMind

@SignorFeynman unfortunately USB was not such a universal standard as it is now so I have like a dozen different sockets

Tobias Fünke

22:02

@imbAF that's just normal, I'd say

I agree with what ACM says. You should find out how you learn and understand things, and try to "apply" this to e.g. math and physics

of course, this is a non-trivial endeavor

on the other hand, let me assure you that I had and have much problems with math and physics, too

at some point you will feel that you got a certain basic understanding, and got to know the way you learn things appropriately. and then everything runs much smoother, so to say.

imbAF

An issue I have is that, whatever is being discussed in physics, I need to try and visualize the situation described or considered. And that takes a toll on me, because if I am unable to attach what is being described whether with words, formulas or math, to a physical situation I simply cannot operate. Because if I know the situation at hand, sometimes my intuition has helped me get out of the probelm

@TobiasFünke I am waiting for that day. On parallel I am doing linear algebra, diff. geometry and re-reading QFT notes, some given to me by ACM

And trying to visualize the meaning of the lagrangian density that corresponds to $\pi^-\rightarrow \mu^-\nu_\mu$ is kinda super hard to do

as an example

ACuriousMind

Oct 27, 2020 at 18:13, by ACuriousMind

reminds me of that joke about how mathematicians visualize 3d space - they first visualise an n-dimensional space and then let n=3

imbAF

How do you visualize past 4 xD ?

ACuriousMind

that's the joke :P

imbAF

ACM one small question, without asking further ones. I was reading the following

3

Q: How does spontaneous symmetry breaking (SSB) happen?

I've just finished studying for an exam on the Standard Model (so electroweak theory and symmetry breaking) and I can't figure out how this question never crossed my mind. I'm now studying the QCD chiral symmetry breaking, but I think my question applies to any (physical) SSB. I know what SSB is ...

standard-model phase-transition higgs symmetry-breaking thermal-field-theory

It's a simple thing I want to ask

Symmetry breaking is not something that happens. It's already there. It's something that characterizes the system

It's not as if, because of external factors, this phenomena occurs

It's all present

Am I wrong for saying this?

ACuriousMind

22:14

That statement can be true or false depending on the exact context :P

You can have settings where there is an actual phase transition between a phase with unbroken symmetry and a phase with broken symmetry

And just like the more familiar phase transitions between states of matter this is a real difference. Ice crystals have symmetries that a bunch of water does not (this is a very handwaving analogy please don't take this seriously! :P)

imbAF

Would the lagrangian prior to the phase transition and past it, be on both cases invariant to the same transformation

@ACuriousMind Yeah I got it

ACuriousMind

But it's true specifically for the kind of SSB we discuss in the context of the Higgs mechanism that we don't really talk about phase transitions

we just have a potential (the Mexican hat) and the theory has ground states that "break" the symmetry

imbAF

So then in the context of Higgs is present

@ACuriousMind Yes

ACuriousMind

there's no transition from an unbroken to a broken phase in this basic Higgs mechanism, your theory just is broken (whether there's an unbroken phase somewhere else is irreievant)

imbAF

Yes

So saying SSB is kinda deceiving

I would say

ACuriousMind

22:19

all we're doing is "rewriting" the Lagrangian in terms of quantities that are more appropriate to describe the physics (i.e. you replace the Higgs field with non-zero VEV by the Goldstone bosons which in turn you have to replace by the massive vector fields when the gauge bosons eat the Goldstone bosons etc.). It's not at all simple to understand this and I would say that not even everyone working with this for decades has exactly the same understanding of it

imbAF

Would it be strange to say that I never, until we spoke about SSB, considered the invariance of a state under transformations. When we were introduced to different transformations, and also had a homework exercise, where a bunch of transformations were given, we had to check whether the lagrangian was or not invariant. So to suddenly consider the invariance of a state, which needs to be considered in SSB, I found it weird

ACuriousMind

in contrast to the more basic math topics we've been discussing I'm perfectly content to say it's fine to be confused about the exact nature of all of this for years after you first learn it :P

@imbAF I would be strange to me, yes, but that's just more evidence of our difference :P

imbAF

But how should I have known that invariance can also be discussed in the context of a state?

ACuriousMind

The whole notion of symmetry is about invariance of something - a state, a Lagrangian, an equation of motion - and to me it's bizarre you should consider this concept for the first time in QFT

Tobias Fünke

@ACuriousMind depends. I mean, from a simple QM POV: Why would you expect at first hand that a state should be invariant under some unitary transformation which commutes with the Hamiltonian, for example?!

ah ok, I misunderstood you

imbAF

22:23

But even Noethers theorem, is related to the invariance of the lagrangian, in CM

Maybe perhaps, there's a math section, dedicated to symmetries

ACuriousMind

more concretely to QFT, I would expect you to have learned about Abelian gauge theory (i.e. QED) before SSB, and during Gupta-Bleuler quantization there should have been some notation of the physical states being invariant under gauge transformations, for instance

imbAF

in a broader context than in geometry

ACuriousMind

and in classical mechanics it's a very natural question to ask whether the transformations that leave the action invariant also leave the Lagrangian invariant, and whether those in turn leave the equations of motion invariant, and whether those in turn leave the solutions to the equations of motions invariant

imbAF

@ACuriousMind I don't understand the last part. The rest we did. We didn't really learn about Abelian gauge theory, but we did mention that QED is such

@ACuriousMind I never questioned the later parts. I presume, the invariance of the solutions to the eom, correspond to the invariance of the state, the solution to the SE in QM

Am I wrong?

ACuriousMind

yes, that's the analogy

imbAF

22:29

I also would say since with the euler lagrange eq. one can derive the eq of motion, if the lagrangian doesn't change, then the eom should be the same, and so should the solutions

or no?

Tobias Fünke

Well, roughly: if you have some transformation on paths $\phi$ and $S(\phi x)=S(x)$, then if $x$ is a solution of the ELE, so is $\phi x$ with the accordingly transformed initial conditions (that is obviously not the most general or precise version, but I hope you get the idea).

49

Q: Do an action and its Euler-Lagrange equations have the same symmetries?

Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can it happen that the equations of motion derived by this procedure have different kinds and/or numb...

lagrangian-formalism symmetry action

I think we had this discussion already, no?

imbAF

I see

Perhaps we did, I am not sure

DIRAC1930

23:00

@imbAF Are you familiar with what constitutes a symmetry in non-rel QM?

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