Indeed they lose a lot in the translation :(

Really? I didn't know that

I never noticed it was translated

Ewww. No wonder it sux

Mostly into British English

What's your favorite GR book?

Which is hard to understand even for the British :D

I prefer the originals.

@ACuriousMind Is there a "simple" proof that all 2-dimensional manifolds are conformally flat?

@ACuriousMind My hand-wavey proof is that in two dimensions the curvature only has one degree of freedom.

@0celo7 Um, I'm not sure, but isn't this just the observation that the metric has three components, and the two coordinate rescalings + Weyl trafo allow you to choose all three?

@ACuriousMind That argument is used in string theory because the brane action has these symetries.

But what does that have to do with the general case?

Why would the usage of it in string theory mean it is not valid for the general case?

Ah

I just moderated a chat flag a moment ago in which someone seemed to have threatened Sabertooth. That is rather disconcerting.

@ChrisWhite That's why I offered the \bigg( as an alternative.

@0celo7 Well, to be "conformally flat" means there is a conformal map such that the curvature vanishes. I think your handwavy argument is the right argument

(With time, you might notice that though I know the lingo, I don't actually know all that much differential geometry)

@ACuriousMind I figure this is a common "ailment" of physicists.

@0celo7 Probably true

@ACuriousMind Does the Weyl anomaly have anything to do with GR? $\langle T^\alpha{}_\alpha\rangle=-cR/12$ looks suspiciously like the traced Einstein equations.

@KyleKanos "Threatened" as in an actual real world threat? Perhaps that should have been flagged for moderator attention rather than spam/offensive

It was slightly more hypothetical (what if I came to your house & cut off your mom's head), but that definitely needed some attention.

Hopefully my valid flag did something useful

@0celo7 Not that I know. But since the EM-tensor is the variation w.r.t. metric, it is not really surprising that this looks like Einsteins equations, is it?

@ChrisWhite Man, of course I saw your comment right as I woke up from my nap. Now I have to learn something else again today.

@KyleKanos That's very disconcerting.

BTW, I don't know with whom exactly it was, but we had a discussion about time reparametrization and zero Hamiltonians. I found the (classical) answer: If the chosen phase space variables transform as scalars under time reparametrizations and the time reparametrizations are a symmetry, then the Hamiltonian indeed vanishes at least on the constraint surface (i.e. the surface on which all solutions to the e.o.m. lie).

@ACuriousMind Where did you find that answer?

@0celo7 Quantization of gauge systems by Hennaux/Teitelboim

@ACuriousMind :: looks sceptically :: You read a book?

Yes. Since gauge theories are one of my prime interests, I want to understand them in depth. And that's the authoritative reference on them.

So far, I am loving it

@ACuriousMind I'd add it to my to-read list, but that has spiraled out of control.

A chronic problem for me

E.g. I had no idea that gauge theories essentially arise when the Legendre transformation to a Hamiltonian is degenerate, leading to us having to keep constraints to actually reproduce the correct solutions to the equations of motion, and that the fact that these are also gauge symmetries of the action is rather derived from a Hamiltonian point of view

I agree, to-read lists are next to impossible to control.

Too many interesting things to read!

@KyleKanos I'd appreciate your opinion: is this question of engineering type? I have no idea of which condenser he/she speaks, but maybe it's just ignorance from my part.

@0celo7 I'm not sure if it is a good book for self-study. They use a lot of algebraic terminology and concepts and assume you know them - as well as extensive parts of classical and quantum mechanics.

@ACuriousMind Perhaps, but they don't come about in similar ways at all. That's why I asked if there is some relation. If there is, it isn't obvious.

@ACuriousMind Hardly any graduate texts are good for self-study, hence my need for lecture notes.

(Currently reading 3 sets of string theory notes.)

@Sofia A condenser concentrates the light in a microscope

There are very few good textbooks to independently self-study out there :(

@ACuriousMind Aaaa! So, you saw my question about that post. Is it O.K.? Or it's engineering? What you say?

@infinitesimal Zee's gravity book is good because he is such a good writer. (he also assumes virtually no prerequisites)

Srednicki has a full solution manual out there.

@Sofia I think it is on-topic. It asks for the physical reason why the resolution is maximal for a particular lens configuration. It's not as theoretical as most of our questions, but that's not a bad thing.

Even if you supplement them with the Internet there will still be gaps.

@ACuriousMind I hardly remember optics.

That's where a prof is needed.

@infinitesimal The purpose of self study is not to get a university-level education, however.

Hello, everybody!!! Is someone good at optics here?

@infinitesimal Oh, profs also leave giant gaps

They just also teach you not too worry too much about that ;)

@0celo7 how are you with optics? Are you good at that?

@Sofia I know some stuff about gravitational lenses.

I have no interest in any other kind of optics.

@infinitesimal are you good at optics?

The only optics I know are the ones sitting on my nose

Aaah I see, we have returned to the topic of having the "right to a textbook" ;) @ACuriousMind

@ACuriousMind No contacts?

@ACuriousMind what you say? Since which age?

@0celo7 Not for me, I have a form of heterophoria for which there are no contacts, as far as I know

I'm not sure I could bear poking the finger with a contact into my eye, anyway

Contacts aren't worth the trouble

The mind's eye is far more interesting

;-)

@infinitesimal abstrusegoose.com/508

@acur most excellent

@ACuriousMind That sucks.

I'm at the age where all my siblings lost their 20-15 vision and had to get glasses/contacts.

@0celo7 Oh, I really don't have a problem wearing glasses

My left eye is losing distance vision.

FML

I don't know, I really don't see anything bad about wearing glasses. Unless you choose ugly ones :P

It's just one more thing to worry about.

spikedmath.com/562.html

I like the one about the first five chapters :D

And then they complain about students not having proper foundational skills.

@infinitesimal I wish authors dedicated a page in the intro where they tell you exactly what material you need and provide titles and chapters for said material.

That would indeed be helpful.

But they rarely ever do.

@0celo7 I don't know... there is no other undergrad course on mechanics here and we basically only covered the first half of Arnold mathematical methods of classical mechanics. I see it the other way around - "university-level education" is the minimum! All the useful stuff is indep. study

@NeuroFuzzy But the interesting part of Arnold is the second half!

I KNOW!!! :(

+ the 200 pages of appendices

Arnold has a book on ODEs

I found it in the library by accident yesteday

I went to the ODE section and just happened to pull it off the shelf

@StanShunpike I think he has two

@StanShunpike "Geometrical Methods in the Theory of Ordinary Differential Equations" & "Ordinary Differential Equations"

w/ geometrical methods being more advanced

@NeuroFuzzy cool I hadn't seen the other

@StanShunpike actually I don't really know what the geometrical methods book covers

It was interesting. Unlike the other ODE books Arnold seemed to be most interested in physics

I only browses like 6 so not a large sample size

@0celo7 Okay, so let me see if I understand a point about SR. So in SR, unlike Galilean, there is no notion of absolute simultaneity. But, what does that mean for predicting events between interacting particles? Like, how can describe the interaction between two particles if they have independent notions of time?

@NeuroFuzzy one of the things I hate about studying on my own is that I learn everything in a very haphazard manner.

BUT on the flip side, I have the freedom to study whatever I want and at any pace

@Danu do not have "day job" in QM myself. have been intrigued by QM computing possibilities for over ~1½ decade. great to see some of it materializing. yes by his profile noticed DS is working at the martinis lab. would surely be interesting to hear more sometime. the other major entity in the race is dwave