The h Bar

dmckee

12:25 AM

@0celo7 I couldn't tell you the difference if they took turns beating me with long hooky-s-things...

0celo7

12:49 AM

@ACuriousMind It seems I've forgotten why $SO(3)$ is not simply connected.

How does one show this?

ACuriousMind

@0celo7 Because you can give an isomorphism $\mathrm{S^3}/\mathbb{Z}_2 \to \mathrm{SO}(3)$ (e.g. through quaternions), showing that it has a simply connected double cover $S^3 = \mathrm{SU}(2)$, but simply connected covers of a simply connected thing are just (copies of) the thing itself, so SO(3) is not simply connected.

0celo7

@ACuriousMind Is there an intuitive reason why we have to divide by $\mathbb{Z}_2$?

ACuriousMind

@0celo7 A quaternion and its negative define the same rotation

Alfred Centauri

@ACuriousMind along with W balls and all?

ACuriousMind

(You have to look at how quaternions define rotations for this, of course)

0celo7

12:54 AM

Yes, I don't know much about $\mathbb{H}$.

Is there a way to understand this without quaternions?

ACuriousMind

@AlfredCentauri Yes, although I really don't know whether I should expect an SU(2) theory to behave like the SU(3) theory if we cannot see confinement rigorously for the latter. I think the usual confinement argument relies only on the fact that the gauge group is non-Abelian, though.

@0celo7 One way or another, any explicit proof of this that doesn't use any other machinery will boil down to simply giving the isomorphism by Euler-Rodrigues, I think.

It's really annoying to find the connectedness of something explicitly because it is a topological property that isn't seen well in coordinate descriptions.

Alfred Centauri

@ACuriousMind any idea at what temperature-density deconfinement ("lepton-W plasma") would occur?

ACuriousMind

@AlfredCentauri This answer claims the SU(2) confinement scale lies "far below" the Higgs SSB scale. I cannot access the linked articles, the claim that a confining SU(2) looks much like a SSB-Higgs SU(2) at low energies sounds strange to me, but might very well be true.

No idea where you would see the analogue of the quark-gluon plasma, though

@0celo7 Qiaochu Yuan does it without saying "quaternion", but I don't think you'll find his argument more straightforward. The fundamental group of SO(3) is particularly annoying in this respect because the non-simply connectedness of SO(N) for N>3 follows from it by induction (if you know a bit about fundamental groups/homotopy).

0celo7

1:21 AM

I get that $SU(2)=S^3$. $S^3/\mathbb{Z}_2$ is the three-sphere with opposite points identified, right? @ACuriousMind

Is it also true that $S^2/\mathbb{Z}_2$ is $SO(2)$?

ACuriousMind

@0celo7 Yes, you can also write $S^3/\{\pm 1\}$ if you want to stress which kind of $\mathbb{Z}_2$ we mean.

@0celo7 No, $\mathrm{SO}(2) = \mathrm{U}(1)$ is just the circle $S^1$.

It is an interesting factoid that $S^1$ and $S^3$ are the only n-spheres that can be made into Lie groups

0celo7

Do I recall correctly that $S^3=SO(3)/SO(2)$?

ACuriousMind

@0celo7 Nah, it's one higher, like $S^n = \mathrm{SO}(n+1)/\mathrm{SO}(n)$

(The $\mathrm{S}$ is actually optional, works the same for $\mathrm{O}(n)$)

Danu

Oh man, I just saw it was Friday and was totally shocked

...but it's only Friday "tomorrow"

ACuriousMind

Until now, I could not have told you what weekday today was :D

Danu

1:29 AM

oh glorious ridiculous spring holidays

0celo7

@ACuriousMind My Google research returns only quaternionic arguments.

I demand something alternative.

Zeidler mentions it early on in the historical introduction, so hopefully he explains it later on.

ACuriousMind

Most of these group theory facts are rarely explained by the people who use them :P

0celo7

The fact that I'm on page 150 and am still doing introduction is ridiculous.

@ACuriousMind The whole point of this set is to be mathematically rigorous.

Danu

Also if you're reading 150 pages in 1 day I doubt you're properly reading it (no offense meant)

ACuriousMind

@0celo7 Have you looked at advanced math? Mathematical rigor does not mean that you show every well-known fact, or that you do every tedious computation

0celo7

1:36 AM

I read the 70 page excerpt on Springer before today.

Danu, this is all review. Particle phenomenology and whatnot.

ACuriousMind

The amount of "The diagram obviously commutes" where a rigorous proof of that takes about 10 pages is ridiculous, for example. (But it is really obvious)

0celo7

@Danu Currently reading about spin sums. For the fifth time.

Forgive me for skimming.

This is BS. Who the hell writes $\mathbf{B}'(\mathbf{x})\mathbf{m}$ for the directional derivative $(\mathbf{m}\cdot\nabla)\mathbf{B}$?

He's just making up notation now, @Danu.

0celo7

1:55 AM

@ACuriousMind Is there an $SU(6)$ flavor symmetry for the quarks? If yes, it's only approximate, right?

@ACuriousMind Is "strong isospin" the same as the isospin in particle diagrams?

ACuriousMind

@0celo7 In pure QCD, there is an SU(2) global symmetry that mixes up- and down-type quarks. It is not a symmetry of the electroweak theory/Standard Model, though, since flavour changing processes exist there.

0celo7

So how does the SU(3) u, d, s symmetry work in the SM?

ACuriousMind

@0celo7 Strong isospin usually refers to the approximate symmetry between proton and neutron, for example, but it really depends on who's using it. People working more with the weak force will tend to use "isospin" for the $\mathrm{SU}(2)_L$-charge, which people working with the strong force will say "isospin" for that approximate symmetry.

0celo7

@ACuriousMind :: sigh :: Isospin is an overused term.

ACuriousMind

@0celo7 Ah, the u,d,s symmetry doesn't work, the electroweak coupling terms do not respect it. It's exact in the strong sector, though, which is why one calls it an "approximate symmetry" in situations where the weak force is truly weak, and hence neglegible.

ACuriousMind

2:23 AM

Has this question been posted somewhere outside of SE recently? I've had upvotes trickling in over the last two days or so, and now a user from another site suggested an edit. I find it hard to believe this is coincidence.

0celo7

How do we know if we have a situation where the weak force is really weak?

dmckee

@ACuriousMind I don't know, but the title of the question always annoys me. I know that people get told that, and I know that it is not an unreasonable interpretation at the pop-sci level, but it gives people the feeling that they know something and that thing is wrong.

Danu

...just as all pop-sci

it means well, it just sucks

...okay maybe that's a little harsh

ACuriousMind

@Danu Weren't you telling me not to hate on non-science a few hours ago? :P

Now you're hating on almost-science, much better! ;)

Danu

If you're gonna do it, do it right!

ACuriousMind

2:30 AM

@dmckee I understand your annoyance, but as an SE title, it's actually quite good, isn't it, because that is exactly the kind of phrasing someone who doesn't know the answer would choose?

Danu

So pop-sci is worse than no-sci, in some sense.

@ACuriousMind "It fits the SE model well"

dmckee

@ACuriousMind Yeah. I don't actually have an urge to edit it away, because you are absolutely right about that.

I have an urge to find the guy (or gal) who told the OP that and just shake them and scream.

That's different.

ACuriousMind

@dmckee There'll be a lot of people to shake then. I remember at least one of my physics teachers and two chemistry teachers telling me (and the class) the same thing.

dmckee

@ACuriousMind Yes. A futile mission.

Kyle Kanos

@ACuriousMind It, for whatever reason, popped back up in the HNQ.

ACuriousMind

2:44 AM

@KyleKanos I see. Weird.

vzn

@JamalS hi saw your comments, are you in IB? in US? what do you mean "risk a too-complicated paper being rejected"? would be interested to see that list that the MIT math prof has. fyi here are many top math topics from recent years.

see also the se math blog

math.blogoverflow.com

user54412

3:14 AM

@Jiminion Blasphemy! More seriously, though, is why Kepler and not Tycho? All Kepler did was fit his favorite model to Tycho's data, which was by far the best astronomical data that had ever been gathered. (Yes I'm resurrecting this conversation)

user54412

I suppose Newton-Kepler-Tycho are the paradigmatic example of everyone remembering the theorist, some people remembering the observer, and very few even knowing who the instrumentalist is

Danu

3:34 AM

Reading up on Kepler a bit more, it really doesn't seem like he did anything more significant than Newton

user54412

@Danu My understanding (though I haven't fully researched this from multiple sources or anything) is that Tycho was aware of Kepler's heliocentric proclivities and didn't want his data falling into Kepler's hands when he died. Kepler took the data anyway.

Danu

Also, it appears Tycho kinda died before his main work got even near to fruitful application in the hands of Kepler

Meh, Kepler simply got hired to complete Tycho's work, so yeah...

user54412

I still think Newton's was the key insight into the whole thing: without extending the Earthly concept of inertial frames into the Heavens, the whole question of geocentric vs. heliocentric models didn't make any physical sense. It was speculative metaphysics at best.

Danu

I like how you capitalized Heavens :P

And yeah, I think Kepler was mostly an amazing geometer, working on fitting astronomical data

user54412

We tend to think "oh those silly geocentrists, adhering to the wrong theory for 2000 years" when actually there wasn't any scientific distinction between heliocentrism and geocentrism until ~1600s, and certainly there was no empirical evidence in support of one over the other.

user54412

3:41 AM

@Danu Is there a term for adapting the writing style of people you're thinking about?

Danu

Hah, there should be

I want to ask this on English Language & Usage now

although, last time I went to their chat, I met some extremely unpleasant individuals

user54412

@Danu My understanding is Gauss was the master of that, like he was at many things.

Danu

Gauss really revolutionized geometry itself though

user54412

At some point I want to work through his algorithm for determining a planet's orbit from just a couple observations.

Danu

which Kepler certainly didn't do

I'd rate Gauss much higher than Kepler

I'd almost say he was like the Newton of mathematics

but mathematics is much too big a field to make such statements

user54412

3:45 AM

German question: Is Gauss spelled Gauß in German?

Danu

the progress in physics was nice and linear in the beginning

Yes, Gauß and Graßmann

user54412

I had a German math prof who did that, and it took me a while to figure out who he was talking about

Danu

this is exactly what I went to the English Language & Usage chat for

Kyle Kanos

I thought Germans were trying to stop using ß

Danu

literally precisely this

I'm editing a script for a course I took

since I'm at LMU, the teachers of course wrote Gauß

I was wondering whether I should keep it like that or make it Gauss

...the question started a fight in chat, and I ended up having to temporarily suspend one of the users lol

Kyle Kanos

3:47 AM

I'd vote Gauss

Danu

Classic American ^^

user54412

I wouldn't object to the letter except for the fact that it's clearly a β

Kyle Kanos

I am classy & an American, so yes ;)

Danu

Classic $\neq$ classy

in fact classy is a proper subset, but oh well

Anyways, I'm keeping the $ß$ (btw it looks better in $\LaTeX$ font)

Kyle Kanos

What command do you use for it in latex?

Danu

3:49 AM

\ss

which is hilarious in some sense

Kyle Kanos

Ah

Makes sense

user54412

@Danu btw I've had less than pleasant experiences with some of that crowd too

user54412

One thing I never figured out about tex is how I'm supposed to put weird letters in the middle of words

user54412

like Gra\ssman clearly doesn't work

Danu

Gra{\ss}mann

...yeah, it sucks

Kyle Kanos

3:53 AM

$Gra{\ss}mann$

Not accepted

user54412

@Danu I like how you copied my misspelling

Danu

damn you

$Gra{\ss}mann$

heh, lemme check which packages

Kyle Kanos

It works on my Latex, not here though

Danu

oh ok

it's jsut mathjax being poor-mans latex

Kyle Kanos

Looks like GraBmann though

Danu

3:55 AM

nawww

Kyle Kanos

My mother didn't realize it made the S sound and thought Großmutter was pronounced "grob-mutter" (English mutter, not German moo-ter)

Danu

lmao

Kyle Kanos

I informed her the correct pronunciation, but she instead insisted on being called Nonna (which is Italian, even though we aren't)

Danu

The Dutch version is better

Oma

(this also works in German, btw)

Kyle Kanos

I seem to recall mentioning that one to her too

But she had already decided on Nonna

Danu

4:01 AM

kk

Kyle Kanos

This was also like 7 years ago

Shortly before her oldest grandkid could speak

Danu

Man, it's so late

5 AM

the holiday feels are real :)

Seventh Stitch - Tin Pear (HQ full track)

►

Sofia

Dear @glance , I was quite upset with the problem of the anti-commutator of the fermions. So, I didn't have patience and I placed a question. It was a long debate and all sort of answers that I didn't feel satisfied with them. The one who indeed made light was Mark Mitchison. I understand that he has experience with the fermions.

ACuriousMind

4:35 AM

Ah, I found the culprit that revived the old question

user54412

5:24 AM

Aha! There's a Vim Stack Exchange!

2

user54412

(except I don't really know what their long-term plan is -- unlike emacs, vim doesn't have infinitely many modules written for it, implementing everything in a text editor that should never be implemented in a text editor)

David Z

5:56 AM

1

Q: Simple Relativity Question

I have a simple question in foundation SR that I hope someone can clarify. Given a mirror of length l travelling at a relativistic speed wrt a 'stationary' frame of reference containing two laser lights spaced l apart as well. If the mirror were not moving at all, the laser lights can be fired s...

special-relativity

Anyone know, or can find out, what that's a duplicate of? (It's gotta be something)

Follow My Proposals

@DavidZ Hi!

DanielSank

6:28 AM

@Danu: Well, I just don't think morality as it is used in most conversations if particularly well defined. It seems to usually mean "acceptable under my personal criteria for how I want everyone else to behave."

(agreeing with you)

Jiminion

@ChrisWhite Kepler found the 3 laws. He worked the data. I thought Kepler added some of his own data to Brache's. Plus he was basically homeless. With the 3 laws, I think someone would've probably figured out the inverse square law. Liebnitz was also working on calculus. Now, I've been wondering if Mars happened to have a more circular orbit, perhaps they would think the orbits were not ellipses. That would have been bad, as it would be an incorrect analysis that would muck things up.

Eka

6:55 AM

@alarge @Neuneck
Thanks for your reply.. But i am specifically looking for nature letter archive because some of the papers in nature letters are very interesting.. Like X-ray generation using scotch tape.

JamalS

8:58 AM

@vzn The IB, yes, but not in the US.

alarge

@Eka Why letters specifically? I've subscribed to the RSS feed of Nature for some years now, and can tell you that I've never noticed a difference between articles and letters in skimming through the feed (for example, STAP cells generated both an article and a letter). I can also tell you that I understand probably 1% or so of the titles of the papers. Are you sure you're not looking for something like Nature News instead?

glance

10:11 AM

@Sofia well ok, but I don't understand what your problem is with my answer. Did you see the last edit?

@Sofia (I'm answering to this message)

0celo7

12:16 PM

@Danu That's really experimental.

0celo7

12:30 PM

Bass Modulators - Music Is My Life (Full) [HD]

►

is where it's at.

@Danu I think I've figured out what's happening. Zeidler is explaining the physics in the first part of the book (which I already know) and then the mathematics later (which I don't know). Although it's interesting that he's discussing spontaneous symmetry breaking before introducing quantum fields or Lagrangians.

0celo7

12:46 PM

@ACuriousMind Zeidler defines force as the manifestation of the curvature of the fiber bundle.

Danu

1:04 PM

@0celo7 Isn't it great?!

@0celo7 Afraid this is really not my thing

ACuriousMind

1:16 PM

@0celo7 Okay, that is a bit more general than my "it's the gauge symmetry" because it also directly includes GR, but in all other cases it's just the statement that forces from from gauge symmetries (...or gauge symmetries from forces, perhaps?)

0celo7

@ACuriousMind Is the pion thought of as a force carrier in the standard model or just in the nuclear effective field theory?

ACuriousMind

@0celo7 The latter.

The non-effective Standard Model doesn't really have a pion, strictly speaking.

0celo7

@ACuriousMind Strictly speaking?

From a standard model point of view, how do nuclei stay together then?

ACuriousMind

@0celo7 Well, through the pion :P

The Standard Model is the high-energy theory - the pion appears as a condensate when you go under some energy threshhold

But the composite particles don't really feature in the Standard Model as such - they're either condensates or resonances

0celo7

So you can't have high energy pions?

ACuriousMind

1:25 PM

(Don't ask me what a resonance exactly is, I don't know)

0celo7

@ACuriousMind What's a condensate exactly?

ACuriousMind

@0celo7 I prefer not to answer that question. The energy scale describes the "average" energy of the system, not the energy of a single object, so I'm careful about interpreting what "low-energy effective" exactly means.

@0celo7 A condensate appears because something acquired a vacuum expectation value.

(Yeah, that doesn't sound very specific, either, but it is all that happens)

0celo7

@ACuriousMind Well that explains why the Higgs is called a condensate.

ACuriousMind

Yep. The pion appears because $\langle \bar \psi \psi \rangle$ for $\psi$ some quark field isn't zero below some scale, if I recall correctly

Could be chiral symmetry breaking that happens there, but I'm not sure off the top of my head

0celo7

1:41 PM

@ACuriousMind So we don't have nuclei at GUT energies?

ACuriousMind

@0celo7 No, that is far above the deconfinement scale, I think. Just a bunch of quarks whizzing around there - "Quark-Gluon plasma". It's a bit more subtle in reality because the density of particles and some other things also play a role, but essentially, if you turn up the energy, sooner or later stuff starts falling apart.

0celo7

Quark pairs, right?

Or are they free at GUT energies?

(I'm unfamiliar with confinement.)

ACuriousMind

@0celo7 No pairs, just quarks.

It's a bit trickier because the things you can observe have to still be gauge invariant = have no color charge, but the quarks as particles aren't bound in pairs/triples anymore

0celo7

@ACuriousMind So how does that work?

ACuriousMind

Ask the quark-gluon plasma people, I'm no expert on that, all I know is that it works. This high energy physics is only accessible in colliders and other rare events, anyway - trying to imagine a "world" at that scale is probably not a good idea.

0celo7

1:50 PM

@ACuriousMind Colliders can reach asymptotically free energies?

ACuriousMind

@0celo7 (De-)confinement is not asymptotic freedom. The former is a statement about phase transitions, the latter is a statement about the running coupling. One does not imply the other

And confinement is really not well understood, only on unphysical lattice models.

0celo7

What does asymptotically free mean then?

I was under the impression it had to do with confinement.

ACuriousMind

@0celo7 That the (gauge) coupling goes to zero at high energies, essentially.

0celo7

@ACuriousMind I know that, but what does that imply?

ACuriousMind

@0celo7 Uh, that the theory becomes free at UV energies?

No interactions

0celo7

1:55 PM

Is confinement an interaction?

ACuriousMind

@0celo7 No interaction = the interaction terms in the Lagrangian become neglegible

Confinement is a phase transition that is related to the coupling strength, but confinement is more than just "strong coupling"

0celo7

Isn't confinement an interaction? Perhaps you can see why I got it mixed up.

ACuriousMind

It has to do with how the "force" between two particles scales, which depends on more than just a single coupling strength.

And confinement is not an "interaction" in the sense that there'd be a term in the Lagrangian that is the "confinement term"

It's a phase transition

Of course you can say that water freezing is an interaction, but that's not the essence of what freezing is

0celo7

I'll read up on RG either in Zeidler or finally finish Weinberg.

ACuriousMind

I have no idea how relevent RG for this is, because I only have a very vague idea of how renormalisation works, and I never needed it in the particle physics and QCD lectures where we discussed this stuff

0celo7

2:04 PM

All I know is that Weinberg discusses quark confinement in his RG chapter. The problem is that I don't understand RG the way Weinberg presents it.

ACuriousMind

I know confinement by way of lattice QCD + Polyakov loops. No RG involved, but you have to go through the trouble and understand how the gauge theory works on a lattice (and then you see confinement only in the "wrong" limit of the lattice, too)

0celo7

@ACuriousMind God, so much information, so little time. I'm struggling here. I don't know if I want to stick with learning QFT better or continue with GR/Cosmo or tackle CFT/Strings.

ACuriousMind

@0celo7 There's a reason there are so many subfields, y'know? ;)

0celo7

@ACuriousMind If I stick with learning more QFT I think I'll have to learn more math than the other paths.

The string theory books and lecture notes I have are not that advanced.

Sofia

2:21 PM

@glance first of all I removed the minus. I dislike minuses, and anyway, it can't be said that your answer is wrong. There is only one thing that I suggest that you'd better remove from it. You say that the anti-commutation relations proved themselves in predicting averages for single particle. But we have here to manipulate with two particles. Well, if I miss what you mean, maybe you'd clarify this point. But there is another thing (I continue).

ACuriousMind

@Sofia You should stop approaching the Fock space notation with your insistence of identifying individual particles in individual states. The entire point of the Fock space is to fully recognize that we cannot track indistinguishable particles, and hence use a formalism that doesn't even try - that of the creators and annihilators. The annoying phase factors appear everywhere, but they work out just fine. There is nothing deep to be learned from them.

0celo7

@ACuriousMind Aren't (overall) phase factors unobservable and hence irrelevant? (I don't know the exact context, mind you.)

Sofia

@glance The user asked what he did wrong in his calculus. He didn't ask for other calculi which prove the anticommutation relation. The type of calculus he did, he may need to do in other situations, and if something is wrong in it, he needed to know. Nobody gave a clear explanation as Mark gave. And it is that when we apply $C_a C_b^{\dagger}$ it's as if we rotate the system by 2\pi. He gave such a formula in his answer.

ACuriousMind

@0celo7 Yes, of course, but this is essentially about different conventions how to define the fermionic Fock space. Because the operators anticommute, you have an annoying amount of minuses you have to consistently deal with. If you aren't careful, you can incur relative minuses, which then lead you to wrong conclusions.

0celo7

@ACuriousMind I made it to Part II of Zeidler! :D "Analyticity"

Yay @ hopefully new material

Sofia

2:35 PM

@0celo7 we have some sort of Berry phase here. The phase is important when you have to do superpositions of branches of the wave function that underwent different evolutions.

ACuriousMind

@Sofia Not a Berry phase, because Berry phases are something related to a local U(1) phase symmetry. This is just the spinorial nature of fermions.

Sofia

@ACuriousMind Aaaa, yes? Thank you.

@ACuriousMind for all the Gods in the sky, this utility renders me mad. I wrote you a comment, but it doesn't pass.

ACuriousMind

@Sofia It is possible that it is too long, chat only allows "short" messages

Try posting it in several pieces

Sofia

@ACuriousMind : but about individual fermions I completely disagree. I explained that about the singlet. It is exactly because we trace the individual fermions (arranging them in a certain order in a product), that the phase -1 appears when we interchange the fermions. Yes, we interchange the two individual fermions.

@ACuriousMind what we do when we interchange the two fermion in the singlet? We attribute to fermion 1 the spin of fermion 2, and vice-versa.

0celo7

@ACuriousMind How does the residue theorem work if $f(z)$ has a pole of order 2, for example. ("Analyticity" is a review of complex analysis, which I really need.)

Sofia

2:49 PM

@ACuriousMind you see, we cannot keep track experimentally of which one is 1 and which one is 2, but "they know", and when we interchange them they signalize to us that they "know", by the -1 phase.

ACuriousMind

@Sofia The exchange is not a physical operation. The idea that "wavefunctions are antisymmetric under exchange" comes purely from the way a spinor behaves abstractly. Mark also said this in a comment to you, and this is exactly the source of the trouble here - you think of the exchange as a physical operation, when it is not, it's just something that makes wavefunctions that correspond well to anticommutativity/slater determinants

@0celo7 Only poles of order one contribute, this is why it is so powerful.

0celo7

@ACuriousMind Neat! I'll have to look for the proof.

Oh, you just Laurent expand, right?

ACuriousMind

@0celo7 Basically, yes

0celo7

Then deform the contour around the poles.

ACuriousMind

@Sofia The fermions don't know which of them is which, either - that is the entire point of what we are doing! You are not doing something physical when you talk of "exchanging" them because they are indistinguishable.

Sofia

2:53 PM

@ACuriousMind Ooooh! You Kantian (or Popper? - about this one I never read). My teacher in the school told us that physics you do first of all without formulas. And I fully subscribe. Physics is a science of nature, of phenomenology.

0celo7

@ACuriousMind How useful are topological charges in QFT? Is the mass shell a topological charge?

Sofia

@0celo7 what you stay there with QFT? Come and give a hand of help!

ACuriousMind

@Sofia Heh, yes, I'm very much on the Popperian side that all science can ever do is predict results. I don't demand of my formalism that it corresponds to anything physical, just that the results are physical

0celo7

@ACuriousMind He defines a topological charge $Q$ by $$\frac{1}{2\pi i}\oint f(z)dz=Q$$

The mass is a residue of the propagator, right?

ACuriousMind

@Sofia: (cont'd) If you think that science should correspond to more, that's fine. The problem is that the Fock space formalism you are tackling here is not designed with that in mind - it corresponds to my idea, and not yours. I don't know if there is a formalism that satisfies you, really.

@0celo7 That's a weird definition of a topological charge, but I guess no one ever had a good one, anyway

0celo7

2:58 PM

@ACuriousMind What is your definition?

Sofia

@ACuriousMind I lost you.

0celo7

And Zeidler is weird anyway, he defines the Laplace transform with an i in the exp.

Sofia

@ACuriousMind "is not designed with that in mind". Which "that"?

ACuriousMind

@Sofia Your idea that physics is phenomenology first. It's a pure formalism, and not the kind of formalism you want for the way you think about physics.

@0celo7 A topological charge is something that's invariant under homotopy :P

(Which contour integrals are, indeed)

0celo7

Exactly!

So how is that weird? In the context of complex analysis, it makes sense.

Sofia

3:02 PM

@ACuriousMind Whaaaaaaat? Physics is a science of phenomena. If you don't understand a phenomenon, how do you want to put it in formulas? Well, you can understand it partially, try a theory and check it by experiment.

@ACuriousMind but basically you need some understanding, and the formulas bring you to more facts, so - you need more experiment and you'll understand more.

ACuriousMind

@0celo7 Yeah, but you'll have to redefine it as soon as you get to other "topological charges"

0celo7

@ACuriousMind He writes it a little weird. He calls $Q$ a topological charge, but doesn't define it as a topological charge. He then mentions it has to do with homotopy.

Sofia

@ACuriousMind the engineer that built you house didn't understand phenomenology? Ayyyye, a catastrophe would happen in that case.

ACuriousMind

@Sofia The only way I understand phenomena is if I can write down a formula that allows me to predict them. If you cannot predict, you do not understand. And mincing words does not lead to quantitative predictions.

(This is the essence of "Shut up an calculate")

0celo7

@ACuriousMind What is the interpretation of the winding number $$w(f)=\frac{1}{2\pi i}\oint\frac{f'(z)}{f(z)}dz$$

Sofia

3:05 PM

@ACuriousMind "mincing"! what's that?

0celo7

He says it has something to do with the number of times the image curve $f(C)$ goes around the origin?

What does that mean

Like for $f(z)=z^n$ we have $w(f)=n$. What does this $n$ mean?

ACuriousMind

@Sofia Oh, sorry, I misused a figure of speech. I meant that talking doesn't produce predictions, calculating does.

@0celo7 Well, $z^n$ maps the $n$-th part of the unit circle to the entire unit circle, and so maps the entire unit circle $n$-times onto itself. One says that this map "winds" the circle $n$ times around itself, therefore.

0celo7

@ACuriousMind "$n$-th part"?

ACuriousMind

@0celo7 One of the pieces if you divide it into $n$ equal pieces

0celo7

@ACuriousMind I'm probably being dumb, but I don't see how it maps part of the the unit circle into the whole unit circle.

ACuriousMind

3:10 PM

@0celo7 Think about what raising to the $n$-th power does to $\exp(\mathrm{i}\phi)$.

Sofia

@ACuriousMind you know, there is a saying in my country "what was first, the hen, or the egg". If the hen was first, from what was it born, and if the egg was first, who hatched it? We'll never end our argument.

0celo7

@ACuriousMind Oh.

@Sofia It's chicken in English :)

Sofia

@ACuriousMind however, to a child, how do you explain some phenomenon? By formulas?

@0celo7 and what is "mincing"?

ACuriousMind

@Sofia I know. I'm not even saying that you're wrong. I say that the modern formalism of physics is designed to work my way, and not yours. The Fock space notation does not carry the phenomenology you want it to carry.

0celo7

@Sofia You "mince" onions or chives. Cut into small pieces, essentially.

IDK how that keeps happening.

ACuriousMind

3:13 PM

@0celo7 I said "mincing words", but looking it up I realized it didn't mean what I wanted it to mean

Sofia

@ACuriousMind Your way not mine? Prove it!

0celo7

@ACuriousMind I'm assuming my definition is correct.

ACuriousMind

@Sofia No, I don't bombard them with formulae, I tell them Lies-to-children.

Sofia

@ACuriousMind Don't mock my words! I am not mocking you!!!!!!!!!!!!!!!

ACuriousMind

@Sofia The fact that I am not troubled by the notation while you are is a good indicator that it works my way more than yours, isn't it? ;)

@Sofia I did not mock you, Lies-to-children are indeed what I would tell them

0celo7

3:15 PM

@ACuriousMind Thomson's Modern Particle Physics follows this principle. Undergraduate QFT, never again.

ACuriousMind

The bonmot "You don't understand math, you get used to it" is also true for physics, to some extent.

Sofia

@ACuriousMind I don't tell them lies. I tell them whatever I can present at their level, and for the rest I say "you'll understand in the school". So, I give them some simple ingredients.

ACuriousMind

@Sofia Oh, did you not click the link under lies-to-children?

Lie-to-children

A lie-to-children is a simplified explanation of technical or complex subjects as a teaching method for children and laypeople, first described by science writers Jack Cohen and Ian Stewart. The word "children" should not be taken literally, but as encompassing anyone in the process of learning about a given topic regardless of age. It is itself a simplification of certain concepts in the philosophy of science. Because some topics can be extremely difficult to understand without experience, introducing a full level of complexity to a student or child all at once can be overwhelming. Hence elementary...

It's exactly what you say.

The term lies-to-children is intended to make clear that the simplified explanations are actually wrong, strictly speaking.

Sofia

@ACuriousMind the word "Lie" is wrong - "simplification" would be better.

@ACuriousMind Now what essentially said Popper that you so much stick to that? What he said?

0celo7

TIL "The Collected Works of Gauss" has at least 10 volumes.

@Sofia Not telling the whole truth is usually taken to be synonymous with lying.

Sofia

3:22 PM

@ACuriousMind , @0celo7 , I am a system analyst, of course I mince things. I built and debugged industrial computer systems, and real-time. How shall I not mince things? And there is nothing to regret.

ACuriousMind

@Sofia Well, Popperian science is simple in principle: There is no empirical truth, any statement that is broad enough to make predictions can also, in principle, turn out tomorrow to be false. Statements that make the same predictions are equally true or false. We accept as scientific theories those that make the most predictions and have not been falsified.

0celo7

@Sofia I'm sorry, but why would you regret anything?

@ACuriousMind In one of your posts, you wrote something like, "Theories are never proven, only not disproven."

That's a nice piece of wisdom.

Sofia

@0celo7 Because the Curious Mind says that something is wrong with this.

ACuriousMind

This view of science gets rid of all the annoying debates about "What does it mean?", "Why?", of all the interpretation debates, and so on. There is no meaningful content in "interpreting" a theory, if you get predictions, it doesn't matter what you think about its ontology

0celo7

@ACuriousMind Many people don't think like this. I can tell my classmates all about particles being excitations in fields and being representations of the Lorentz group and all they ask is why.

ACuriousMind

3:26 PM

I know, because most people never waste a thought in their entire life on the question "What does it mean for something to be true?"

But it is the starting point, the very fundament of science. How could you say you know something what you do not even know how to distinguish truth from falsehood

Jimdalf the Grey

@0celo7 Not telling the whole truth usually means telling part of the truth but connotatively leaving out important or meaning-altering details; however, what is said is still technically true. Lying usually means telling something that is not what the teller believes to be true. So I don't think they're synonymous. Both can be a form of deception, but not telling the whole truth is not synonymous with lying. (Although, technically, if you are lying, you must not be telling the whole truth)

ACuriousMind

And that is what science does - like Feynman said, "The sole arbiter of scienfic truth is experiment". Stuff you cannot test experimentally is not even wrong

Sofia

@ACuriousMind our talk goes as debates that sometime I see in my country among politicians. Politician A says about politician B: He (i.e. B) lead a politics not honest, and etc. etc. If I could make me heard by A I would ask him. Why not honest? Prove!

Jimdalf the Grey

@ACuriousMind Yay, my whole field is not even wrong

ACuriousMind

@JimdalftheGrey Add an in principle, there ;)

(I at least hope that there are in principle predictions cosmology makes, right?)

Jimdalf the Grey

3:29 PM

usually untestable predictions

Sofia

@ACuriousMind Formulas may cheet you (elude).

Jimdalf the Grey

or at least ones where the technology to conduct tests is well over a century away

ACuriousMind

@Sofia I'm here, you can ask me :) You want me to prove that current science indeed proceeds as I say? That I cannot, because there are scientists who disagree with me.

@JimdalftheGrey Yeah, that's enough for "in principle testable"

0celo7

@JimdalftheGrey You have a point.

ACuriousMind

Cosmology is thus in a state of "we don't know", which is very different from "not even wrong"

0celo7

3:31 PM

Does observational cosmology fit in the scientific method?

Sofia

@ACuriousMind Aye!! You can't prove because there are scientists who disagree? Truth depends on who is in the neighborhood?

0celo7

i.e. can we get reproducible results?

Jimdalf the Grey

We test it by running simulations on a computer and seeing if we like the way the results look. They don't have to correspond to observations made all the time (it's good when they do though). Sometimes it's "Does this sit well with me?" or "Could I use this to come up with other work to do?"

0celo7

So is stuff like cosmic strings where there is absolutely no evidence and not even a need for them at all considered science?

(Maybe there is a need, IDK.)

Sofia

@0celo7 pleas be kind, what means the expression "I am around"? Does it mean that I am in the neighborhood?

ACuriousMind

3:33 PM

@Sofia Yes, because this is about the very definition of truth. I, and many others, follow the Popperian idea of science, and I am very convinced that the overwhelming majority of theoretical physicists would agree with me. But other "scientists" may proceed with a different idea of truth.

Jimdalf the Grey

But what do you expect? When your job is to develop theories about the universe outside of our observable limits, you can't expect that there would be observations we could make

0celo7

@JimdalftheGrey What's a good intro to cosmic strings, anyway?

Anderson's text is on Scribd.

ACuriousMind

The problem is that these epistemological issues are rarely discussed (because many think it sounds "too much like philosophy"), and hence there is a lot of discussion (e.g. quantum interpretations) within science, that, by my definition, isn't science.

As with all things human, the actual reality is far more messed up than the ideal world :)

Jimdalf the Grey

@0celo7 I don't work on quantum gravity. I'm not a quantum cosmologist. I haven't gotten into any detail on cosmic strings yet. I'm primarily an inflationary/early-universe cosmologist. So I can't help you there

Jiminion

@ACuriousMind Donald Knuth does this a lot in his TeX manual.

0celo7

3:38 PM

@JimdalftheGrey What's the modern introduction to inflation? I'm trying to decide what to "specialize" in during my free time.

Sofia

@ACuriousMind aaah! How you took the words exactly from my mouth! Philosophy! Worse!! Sophism!! Black can be proved to be white and white to be black!

0celo7

@JimdalftheGrey And that depends entirely upon what books and notes I can get my hands on.

Anyone here understand Chinese philosophy?

Jimdalf the Grey

@0celo7 the modern introduction to inflation? Hmmmm..... I don't have much in the way of a favourite text reference. But there are some really good references I could link you to. What's your current level of understanding? Got GR under your belt yet?

0celo7

I'd love an explanation.

@JimdalftheGrey Oh yeah. Wald, Hawking & Ellis and Straumann.

In addition to Zee and parts of Carroll and Weinberg.

Sofia

@ACuriousMind may I know, in how many places you are right now?

ACuriousMind

3:41 PM

@0celo7 Let's not get started on Eastern philosophy. They have an entirely different conception of what the self and the mind and the world are, and it is very difficult to even translate their writings properly because the languages are so different.

0celo7

Currently I'm swaying towards rigorous QFT/String theory because I have found so many lecture notes and online resources. @JimdalftheGrey

ACuriousMind

@Sofia Well, I'm in this chat, I'm writing a LaTeX document, I'm occasionally looking at new questions on the site, and I'm also chatting with two other people who have nothing to do with physics :D

So, in about three and a half places, I guess

Sofia

@0celo7 pleeease, to be "around" means to be in the neighborhood?

0celo7

@Sofia I'm not sure what you mean by "in the neighborhood".

I'm no English scholar, but that's not a saying. (It is actually. I need some context.)

Jimdalf the Grey

@0celo7 okay, well I suppose one of the better intros I've come across is arXiv:0907.5424v2

Sofia

3:44 PM

@0celo7 I was around when this strike took place.

Jimdalf the Grey

I already knew inflation when I read that, so perhaps I only thought it was an easier read because of that. But it's pretty good.

Jiminion

Ocelo7 is actually a holographic projection. So he's everywhere, at least bits of him.

0celo7

@Jiminion what are you on about?

@JimdalftheGrey Any other prerequisites besides GR? SUSY?

Sofia

@0celo7 or, I was around when these demonstrations took place.

@0celo7 does it mean that I was near?

Jimdalf the Grey

@0celo7 I don't think you need SUSY. Just GR for this. I think you can also skip the first section, but I'll leave that to you

0celo7

3:46 PM

@Sofia I would take that to mean you were nearby.

Sofia

@0celo7 aha! Thanks.

0celo7

@Sofia Although, an old person could say they were around during the Second World War.

That just means they were alive.

Sofia

0celo7 aha! Thanks.

0celo7

@JimdalftheGrey What's the first section? Looks like boring phenomenology.

@JimdalftheGrey Thanks. A cursory scrolling shows no math I'm unacquainted with.

Jimdalf the Grey

@0celo7 By first section, I mean microscopic origin of structure and the outline. You should definitely read the next chapter with the intro to the BB problems. That sets the stage for inflation and helps it all make sense

0celo7

3:49 PM

@JimdalftheGrey Part 5 is String Theory.

Is String String theory required or explained?

Sofia

@ACuriousMind you wandering spirit, you are probably in the middle of some other deeds now. So, I also go to see some new questions.

Jimdalf the Grey

@0celo7 Actually, I usually only use this up to part 4. Like I said, I'm not a string theorist, so I don't actually go into that section

I assume, like the rest of the text, it introduces you to it

The appendix is also really fun. Give it a read if you're trying to solve physics problems for fun

0celo7

@JimdalftheGrey Sure. I'll give Zeidler a break for a bit.

Jimdalf the Grey

@0celo7 Yeah, this text had a dedicated screen on my computer for most of my master's degree. It's pretty good for the basics of inflation. It doesn't cover some of the more advanced stuff, but it can only be so long

0celo7

@JimdalftheGrey Have you read Weinberg's 2008 Cosmology book? I have a physical copy of it.

I haven't gotten around to reading it though.

Is it worth it to put a lot of effort into that book, or just use it for selected topics?

glance

3:59 PM

@Sofia again, did you see the last edit? I did the exact calculation he asked about

0celo7

@JimdalftheGrey How are these correlation functions defined? Are they just averages? If so, over what?

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