The h Bar

4:00 PM

@RyderRude What I do know, is that if you are asking it in such a way, then it is clear that you are not even attempting to treat it with the nuance that it would require.

Ryder Rude

I havent studied books in detail. Im just going by the stuff that people from these countries say

I mean... what they say about what is taught

Japan is infamous for not teaching bad stuff

naturallyInconsistent

@RyderRude I suppose we should celebrate the rare occasion that you state an unequivocally true statement.

;P

Ryder Rude

But Japan didnt even win. This is more of a case of "ruling state writes the history". More neutral accounts can be found on wikipedia, I guess. But it's very hard to know who is unbiased :P

The internet is a good anti-thesis to "history is written by winners"

But the internet is full of bias too. I just wish that someone could just give unbiased views

I think chatgpt is a good start in that direction

ACuriousMind

absolutely not

Ryder Rude

Chatgpt pulls its stuff from the internet but it aggregates all views

naturallyInconsistent

4:10 PM

@RyderRude But this is already sufficient an evidence for you to refute your earlier non-nuanced take

@RyderRude Have you not been on the main site? Have you not seen the quality of the answers that ChatGPT gave to the questioners that later pushed them to us?

ACuriousMind

the idea that there even is such a thing as an "unbiased view" is questionable - mostly people who insist on their views being "unbiased" just want to shield themselves from criticism

elementary facts can be right or wrong, but once we come to views, to aggregation and presentation of facts, there is always choices being made where to put the focus or what to mention first and what last etc., and those choice introduce "bias"

Ryder Rude

Yes, chatgpt still seems very biased toward the popular viewpoint. I just like the aggregation aspect. U r right that there is no such thing as an "unbiased view"

naturallyInconsistent

It might be fun to ask those extremist experimentalists to give a presentation of classical mechanics in a way that is purely experimental and not at all theoretical. It will be an achievement if they can get past the millennia milestone of advancing past Medieval physics.

@RyderRude Flat Earth seems quite popular right now

Mr. Feynman

I think that renormalization is the most difficult thing I've ever encountered

The more I read the less I understand

ACuriousMind

@Mr.Feynman that's entirely normal for this topic :P

Ryder Rude

4:18 PM

Have you tried the effective field theory view?

Slereah

I think it's weird that renormalization is mostly taught for QFT and statistical mechanics

Two topics already pretty complicated on their own

naturallyInconsistent

@Mr.Feynman I found that it was useful to learn some asymptotic analysis, because that helps make some sense of what it is we were trying to do in renormalisation

@Slereah Two topics complicated for basically similar reasons

Ryder Rude

In EFT, we no longer deal with infinite bare stuff becuz we make a cut-off to the theory

naturallyInconsistent

@RyderRude In CPT the renormalisation is taken right from the start so that there is no bare quantities either

Ryder Rude

Lemme google cpt

ACuriousMind

4:20 PM

it's causal perturbation theory

Ryder Rude

Oh. I havent learned this approach yet.

ACuriousMind

or "Epstein-Glaser renormalization"

Ryder Rude

Yes. U mentioned this one

I havent studied physics in months. I should try again

I got too much into philosophy :P

naturallyInconsistent

@RyderRude shaken by this blatant display of introspection

Shikhar Chamoli

4:39 PM

Hello everyone, can someone tell why usually only first order diffraction is considered in the bragg's x ray diffraction.?

Mr. Feynman

@ACuriousMind normal but not normalized...

@naturallyInconsistent like for the problem of asymptotic series and perturbation theory?

@RyderRude that's what I'm subscribing to :P

naturallyInconsistent

Oh, you know that the basic perturbation theory is asymptotic? _Good_
But I really just meant to study asymptotic series of stuff, even just, say, Airy function. Very nice to learn about.

@ShikharChamoli fine structure constant is tiny.

Mr. Feynman

@naturallyInconsistent I know in the sense that I've been told it. For the time being I'm content with the handwavy explanation for why asymptotic series provide information

Right now I'm more concerned with Lie Groups and G-bundles

Once again the ACM singularity has replaced the Slereah singularity and I've crossed the EH

naturallyInconsistent

@Mr.Feynman It is just very crazy that we keep finding good results from abusing mathematics

@Mr.Feynman hmm, are there asymptotic expansions of them...

Mr. Feynman

@naturallyInconsistent I feel way too uncomfortable with that and that's why I define QFT magic

There is a preface to some notes of a course by Schuller that I really appreciated

> Theoretical physics is all about casting our concepts about the real world into rigorous
mathematical form, for better or worse. But theoretical physical doesn’t do that for its
own sake. It does so in order to fully explore the implications of what our concepts about
the real world are. So, to a certain extent, the spirit of theoretical physics can be cast into
the words of Wittgenstein who said: “What we cannot speak about [clearly] we must pass
over in silence.” Indeed, if we have concepts about the real world and it is not possible to

@naturallyInconsistent are there? What I care about right now is to understand gauge transformations properly

naturallyInconsistent

4:57 PM

@Mr.Feynman I do not think I would be too helpful in this

Ryder Rude

please listen to the jigglypuff song if you havent :P

Silly Goose

5:17 PM

okay i think i have been getting a little bit lost in the sauce :P i think i have it philosophically backwards to expect precise physical content from precise mathematical content. it seems i should get a good grip on physics first and foremost and then learn its precise formulation in math

naturallyInconsistent

@SillyGoose YAYYYY

Silly Goose

:-)

Mr. Feynman

5:30 PM

@naturallyInconsistent Most people I've talked to in person don't think this would be helpful :P

naturallyInconsistent

lol

Silly Goose

what is the meaning of symplectic: what conceptual meaning does the presence of the word symplectic imbue into things

wikipedia says it is a literal translation of "complex" from another language

but it obviously is not used to just mean complex as in complex numbers; e.g. a symplectic vector space from wikipedia is not a vector space over the complex fild

naturallyInconsistent

I have a lot of headaches over that too.

Silly Goose

D:

naturallyInconsistent

Life was so much simpler when I could draw vectors representing what my momentum was.

ACuriousMind

5:35 PM

@SillyGoose Have you read the Weyl quote on the origin of the name here?

naturallyInconsistent

Now I have all these mathematical machinery of tangent bundles, cotangent bundles, but everybody just wants to do the whole "you can use this maths" and not actually motivate them in a way that we can see why we ought to do so

Silly Goose

@ACuriousMind so is the meaning of braided together meant here?

ACuriousMind

@SillyGoose no, Weyl is talking about the line complexes from algebraic geometry

Silly Goose

so then i shall not understand what symplectic means for a while huh xD

ACuriousMind

and "complex" there is used as a noun meaning something like "bundle"

naturallyInconsistent

5:38 PM

And then after I understood some tangent bundles and cotangent bundles, suddenly we get thrown fibre bundles without any explanation of how to align them. How to think about parallel transport in them

ACuriousMind

@SillyGoose no, it's more that the name doesn't really have anything to do with what it denotes in modern times

Silly Goose

oh

ACuriousMind

Weyl first encountered the symplectic group when dealing with these line complexes

Ryder Rude

Differential geometry is the prettiest math subject ive ever seen

Slereah

It has the benefit of being geometry

So you can kind of draw it

Mr. Feynman

5:40 PM

@RyderRude and the most intuitive one at least for basic DG

Ryder Rude

It just sooo squishy and cute with bundles and stuff lol

Mr. Feynman

In constrast to Functional analysis which feels so techical ewww

naturallyInconsistent

@RyderRude it ends up giving me most angst because most calculations are still in centuries old maths

Mr. Feynman

What do you mean?

Ryder Rude

@Mr.Feynman yes, it's so advanced yet so simple

naturallyInconsistent

5:41 PM

@Mr.Feynman is this for me?

Mr. Feynman

@naturallyInconsistent Yes

Ryder Rude

It's like the best refinement of the geometry ideas that we have come up with after centuries

Historically, dual vectors were not regarded as their own thing

But we have refined these ideas so much now to have the most convenience

ACuriousMind

@SillyGoose Names generally are historically interesting but not very enlightening. In this case the connection ends up being that these line complexes have vanishing antisymmetric forms, and symplectic geometry is based on an antisymmetric form, so Weyl named the latter after the former and switched to Greek to not confuse everyone with a double meaning of "complex"

naturallyInconsistent

@Mr.Feynman After doing a bit of GR, and thus having tensors, and later DG, I wanted to do some computation of problem solutions. Then I realised that the centuries old maths that are plastered all over physics, wiki, and so on, are working in terms of vierbeins, and so you cannot apply the tensors or DG toolkit without first translating everything

And then you have to have some way to communicate your answer solutions to students, and that is yet another headache

Slereah

I'm afraid in geometry you have to juggle like 20 different formalisms

naturallyInconsistent

5:44 PM

@Slereah GA claims to be the one formalism to rule them all.

Ryder Rude

What is GA

naturallyInconsistent

it is supremely beautiful, but I never managed to make heads or tails of their GTG

@RyderRude oh, nooo, do you really want to touch this black hole?

Ryder Rude

Do u mean Geometric Algebra

naturallyInconsistent

Yes

Ryder Rude

I dont think it brings the full power of tensors

Its just differential forms pretty much

naturallyInconsistent

5:46 PM

It does

Ryder Rude

Differential forms already hav the wedge product

But GA does bring this "geometric product"

It seems very cool

naturallyInconsistent

Mind you, it is somewhat trivial to incorporate all these things. It is just that you will have a mixture of things when you play with it

ACuriousMind

geometric algebra is what happens when a bunch of physicists rediscovers modern linear algebra and geometry :P

Ryder Rude

I see clifford algebra as a distant cousin to real numbers, complex numbers, quaternions, octonions, etc

Slereah

Is it the dual of algebraic geometry

Ryder Rude

5:48 PM

GA does claim to be better than the latter, by subsuming complex numbers

ACuriousMind

@Slereah sadly not

Ryder Rude

But i still think all numbers have their own geometric use. GA is just one of them number systems

It is wrong to think of complex numbers as subsumed in GA

GA is like grassman algebra on steroids

But i would very much like to learn the motivation to generalise the exterior product into geometric product

Geometric algebra has a division. I think it makes division possible by having the dot product around too.

What would be the exact equivalent of the geometric product stuff in standard differential geometry?

naturallyInconsistent

@ACuriousMind lol, but no. mathematicians are not likely to add scalars to matrices.

@RyderRude it just does not exist.

Ryder Rude

Tensors allow for arbitrary linear maps of any number of indices. So i dont think GA brings the full power of tensors

Silly Goose

is the adjoint representation a formal way to have elements of your lie group transform elements of its lie algebra into other elements of its lie algebra

naturallyInconsistent

5:58 PM

@RyderRude Just have each index come with Cartesian product of GA elements. The result is a monstrosity but it would still work.

ACuriousMind

@SillyGoose Not sure what you mean by "transform"

Silly Goose

does replacing with the word "send" make it better?

ACuriousMind

what I'm trying to say is that I don't understand the question: Yes, the adjoint representation is an action of the Lie group on its algebra

but I don't know what you mean by it being "a formal way to have..."

Ryder Rude

@naturallyInconsistent this is a good idea. But it's like a generalisation of usual GA?

Silly Goose

okay i think that answers the question i was just asking about what the jist of an adjoint rep was

Ryder Rude

6:02 PM

GA also gives us some geometric interpretations of bivectots, trivectors, etc

naturallyInconsistent

@RyderRude Yes, but it is a trivial, natural extension. It is not like tensors of many many indices are able to avoid being labelled as anything but grotesque

Ryder Rude

Like a trivector is an oriented volume but it is shapeless i think

And it has a pseudoscaler for the biggest wedge product. This stuff is similar to differential forms. But the geometric product is very pretty

Rotation algebras like complex numbers, quaternions, etc only work in 2,4,8,16 dimensions. But GA works in all dimensions

naturallyInconsistent

I also admire the beauty, but until we can reliably do basic computation of problems we get in physics, it is a problem

Like, because of the very nice textbook by Hestenes, I can solve, say, projectile motion problems in GA in perfect generality and much faster than other methods. But it is the integrals of E fields that I really want done.

Integrals of the various vectorial, bivectorial, etc quantities appearing in modern physics, especially in curved spacetime (really, just curvilinear flat space is already headache enough)

Silly Goose

i dont know if you recall me asking but apparently there is this fraction term in the derivative of the exponential of a matrix w.r.t. to the variable the matrix depends on @naturallyInconsistent :0

naturallyInconsistent

@SillyGoose Oh, sounds like the derivative in the denominator that appears when you study Euler-Maclaurin summation formula

Mr. Feynman

6:12 PM

Is geometric algebra related to algebraic geometry?

naturallyInconsistent

@Mr.Feynman not at all

Ryder Rude

Minkowski had considered using quaternions for spacetime becuz they squared to -1 lol

Mr. Feynman

Damn I hate that name swap thing

Ryder Rude

Would've been very badass for quaternions if that worked out

naturallyInconsistent

@RyderRude there was an entire generation of physicists who had been taught that as the gospel

Ryder Rude

6:14 PM

Lol

They seemed like match made in heaven : SR metric and Quaternions

More Anonymous

what did they do??

Mr. Feynman

@naturallyInconsistent translating is sure one of the worst problems between Math people and Physics people

Roughly, it's like Physics people can barely speak a language properly and Math people pretend to not understand even those few words :P

ACuriousMind

@RyderRude what do you mean "if that worked out"? it's not particularly widespread or useful, but there are reformulations in terms of quaternions, see e.g. physics.stackexchange.com/a/28806/50583

@MoreAnonymous see meta.stackexchange.com/q/389359/263383

naturallyInconsistent

@Mr.Feynman maths people will violate all conventions.

Ryder Rude

@ACuriousMind wow i may vomit :P

ACuriousMind

6:18 PM

if what's going on behind closed doors is any indication, this is the smallest SE fuck-up you're going to see in the coming weeks

Silly Goose

in that derivative of the exponential, am i meant to understand the middle term (to the right of exp(X) and to the left of dX/dt) as a map acting on dX/dt?

naturallyInconsistent

@ACuriousMind The answer in there is mathematically correct but does not use quaternions correctly. It is a very well-known thing that the correct way to implement rotations in quaternions is the much simpler formula than whatever is presented, and boosts are trivial too.

ACuriousMind

@SillyGoose don't things in formulae always act on what's to the right of them unless otherwise indicated?

Silly Goose

i suppose that is true :)

although, what is the meaning of $1/\text{ad}_X$?

ACuriousMind

it's the inverse of $\mathrm{ad}_X$

a good way to understand what's going on in Lie theory is to just think about everything as matrices

Silly Goose

6:24 PM

okay can i also safely take $e^{-ad_X}$ as $1/e^{ad_X}$?

hm then so is this what the expanded form looks like

also i guess i have never internalized this: does 1/(thing) usually denote the inverse of (thing)?

Charlie

Presumably especially in situations in which "1 divided by X" isn't defined

If I was reading something about groups and for a particular group $(G,\circ)$ an author wrote $1/g$ with $g\in G$ I would definitely interpret that as notation for the inverse element, $g^{-1}$

ACuriousMind

@SillyGoose it's more common to write $\text{stuff}^{-1}$ for things that can't literally be divided, but $1/\text{stuff}$ is the same

Charlie

Mathematical texts are generally careful about introducing notation like that but anything goes in physics so the notation is likely to just mean whatever it makes sense for it to mean without further comment :P

Silly Goose

hm i see tbf to this text i only opened it up since wikipedia cited it for this formula heh

Silly Goose

6:48 PM

Hm actually what i expanded must only be true for abelian groups

Mr. Feynman

I once got mocked in the MSE chat for using the weird ass notation for an operator :P

Amit

I remember my Linear Algebra lecturer telling us... "how do you guys write your inner products? Oh yeah...", and then she mockingly continued the comma in an $\langle , \rangle$ expression that was on the board into a vertical line, lol. But I took it as a joke, I don't think there was any real "mockery" involved

Mr. Feynman

@SillyGoose you can find a proof of this formula in guess what book, chapter 5 :P

Amit

@RyderRude changes from purple to brown, and now this, the vote buttons... I'm not sure I can take another change

I'm too set in my ways

Mr. Feynman

7:03 PM

@naturallyInconsistent I think that Math people tend to be right about that kind of stuff

More Anonymous

@naturallyInconsistent I thought it was us physicists who use black magic as a substitute of math

naturallyInconsistent

@Mr.Feynman Absolutely not.

Mr. Feynman

@Amit what about @Relativisticcucumber becoming jigglypuff?

Amit

@Mr.Feynman omg right, I saw it earlier today and I think I suppressed it! :D

naturallyInconsistent

@MoreAnonymous It is much more common for people who realise that they do not fully understand something, to be more careful to follow conventions about things

Mr. Feynman

7:06 PM

@Amit Tbh my first trauma was the first time ACM changed his propic (since I was here)... Then I found out he does it kinda regularly so I got used

@naturallyInconsistent What kind of conventions are you talking about though? Math books tend to be consistent with themselves. Physics books are full of ill-defined notation or ever changing notations

Amit

I guess it's different when people do stuff willingly too. But the Identicon thing and the Vote thing are both events that just happen there in the block universe

Silly Goose

@Mr.Feynman what book :0

naturallyInconsistent

OMG I was just struggling with Georgi Lagidze and it turns out, he was poisoned by Khan academy ibb.co/HzZgsT5

Silly Goose

my tea finally came >:D

naturallyInconsistent

TEA~~

Silly Goose

7:21 PM

i can now confirm that gyukuro is delicious

naturallyInconsistent

yay~

Mr. Feynman

@SillyGoose The book I always mention when it comes to Lie groups, i.e. Hall

Silly Goose

ah!

you know i was looking for it in hall originally

i now know to cf chapter 5 :)

i was looking in chapter 3

Mr. Feynman

Lie Algebras

Silly Goose

apperently gyukuro has like 160 mg caffiene in a 5g dose; all condensed in a 100 ml cup of tea :)

Amit

7:31 PM

so one cup (~230ml) gets you above the recommended daily intake, lols

naturallyInconsistent

But this is superbly misleading. One does not eat the dayum tea leaves, so that most of the caffeine will be thrown away with the leaves

This is unlike covfefe, because the powder suspension will be ingested

Silly Goose

i'd like to do a caffiene test on this cup

it certainly is packing a punch right now to me XD im feeling real awake

@Amit good thing it is extremely expensive compared to any other japanese green tea :P really will keep my consumption of it in check

naturallyInconsistent

You are not awake until you jitttteeeerrerrrererererere

Amit

yes, @naturallyInconsistent, makes sense. maybe that's why they also write that caffeine content of tea can "vary wildly"

Silly Goose

i have not jittered for a very long time :P i can drink coffee a few hours before bed time and still sleep these days

Amit

7:37 PM

the best jitter is what you get after a week or two of caffeine abstinence

naturallyInconsistent

my family aint very affected by caffeine. my dad just goes to bed after an espresso

Amit

that's weird... although I know that I have an irrational dread of drinking coffee in the evening as well, so any sleep deprivation effect it would have will be partly psychosomatic

Slereah

Just switch to cocaine

naturallyInconsistent

it is amusing to me that my colleague has to avoid tea from 2pm onwards, and I have to keep finishing his tea for him if he doesnt finish in time

Amit

lol @Slereah... that would definitely nullify any psychosomatic component :D

naturallyInconsistent

7:42 PM

(we brew a huge pot every time)

@Slereah GR: expansion of consciousness, without the abuse of substances!

Silly Goose

@Mr.Feynman do you know if hall ever explicitly talks about the inverse of the adjoint maps?

ACuriousMind

@SillyGoose Don't get stuck on that part, the entire thing in the middle is just a power series, cf. Wikipedia

Silly Goose

Hm well actually. So say we're dealing with $SU(2)$ as the Lie group. then, we have an $H \in \mathfrak{su}(2)$. Let $U \in SU(2)$. Then, $\text{ad}^{-1}_U H$ is actually just $U^\dagger H U$, right? Since $U = \exp(-it\Lambda)$ and $U^\dagger = \exp(it\Lambda)$

ACuriousMind

@SillyGoose yes

Silly Goose

and this special case of the inverse adjoint comes from unitarity of elements of SU(2)

ah excellent so it works out nicely for this application :P

Mr. Feynman

7:51 PM

@SillyGoose I don't think so :/

Honk

Silly Goose

HONK

Mr. Feynman

@ACuriousMind educated guess: three days from now you will be elected supreme general governor of the SE network

ACuriousMind

@Mr.Feynman the first terrible decision just dropped in public

5

Mr. Feynman

@ACuriousMind Alright, that's definitely not something you would decided if you were elected dictator :P

I hope that doesn't affect the quality lf the posts significantly

ACuriousMind

Ha. Ha. Ha.

Mr. Feynman

8:08 PM

*would have decided

@ACuriousMind If that's replying to the message about the quality of the posts, well I'm scared :P

Amit

Delta J to Delta tea is jitter! sorry, late joke

Mr. Feynman

What do you think about this? Unless there is some policy restricting mods to express themselves against decisions, in that case never mind

ACuriousMind

@Mr.Feynman I'm following a lot of parallel discussions on this and also I'm very angry at how SE dropped this on us, but generally I intend to honor our extremely uncontroversial local policy that computer-generated content is not welcome on physics.SE.

5

Silly Goose

is there some result to simplify the thing on the LHS? (the RHS are my attempts)...

In particular, to simplify it to be in a nice form to differentiate w.r.t. to a single $\theta_i$

oh oops the first thing on the top RHS should have a minus sign in the commutator

okay ignore the RHS completely i think those are just wrong :P

Mr. Feynman

8:51 PM

@ACuriousMind well, although it is not welcome, your action s as mods will be somehow restricted for the new policy. OTOH, Physics is luckily one of those fields where detecting AI bullshit is much easier than many others

@SillyGoose what are you trying to do?

Sorry for the double message

Amit

9:14 PM

I think there's one very big problem with the new voting buttons. They may draw more attention, but it's much harder to see that you already voted, and people can easily be confused and undo their votes by accident because of that imo

2

Actually on Physics.SE it isn't so bad. On Math.SE my votes are nearly invisible to me lol

the bottom pair is Physics.SE

Silly Goose

9:43 PM

@Mr.Feynman I'm trying to find the gradient of linear entropy where the $\hat{\rho}$ is a time evolved (2x2) state by an arbitrary (2x2) hamiltonian

the gradient w.r.t. the parameters parameterizing the arbitrary ham

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