The h Bar

0celo7

00:15

"Lipshitz" is an unfortunate name.

NeuroFuzzy

Why?

0celo7

Generally any name that sounds like "shit" is unfortunate.

Icosahedron

Because it doesn't exist.

That's not even a name.

0celo7

There should be a "c" in there, I think.

NeuroFuzzy

ah, well...

0celo7

00:23

Lipschitz

NeuroFuzzy

Jacques Tits

that is my favorite unfortunate name

Icosahedron

@0celo7 Almost every name most likely means something unpleasant in some language, at some point in time.

0celo7

@Icosahedron My name means "little king" in Gaelic.

Icosahedron

Therefore calling that unfortunate is confused.

0celo7

I'm not little though.

Icosahedron

00:25

Though you're a king?

0celo7

We all know that English (specifically the American flavor) is objectively the best language.

@Icosahedron Of course.

NeuroFuzzy

I need to stay off stackexchange and keep working on rep theory

Georgi is a very annoying book.

0celo7

I was planning on reading him over the summer.

Icosahedron

@0celo7 Yes because it's the most logical and efficient language there is.

$3x + 7 = 5$

0celo7

@Icosahedron $x=-2/3$.

NeuroFuzzy

00:29

@0celo7 it could be that there's something wrong with ME. Recently I've had terrible opinions of three separate books I've tried to study through.

0celo7

@NeuroFuzzy There's nothing wrong with you. You're beautiful the way you are. <3

2

NeuroFuzzy

#allmindsarebeautiful

Icosahedron

I like reading books that are way above my level.

It feels like this.

NeuroFuzzy

@0celo7 you know @Danu was trying to find an alternative to Georgi though, right? Speaking of which I was looking at these two books for the summer: springer.com/us/book/9780387798516 amazon.com/…

0celo7

@Icosahedron What the heck are you reading?

@NeuroFuzzy I was eying this.

Icosahedron

00:41

@0celo7 Flipping through hawking and ellis, as a pastime.

0celo7

@Icosahedron It's not a "flip through" kinda book. It's more of a "read page, contemplate deeply, despair over detail, eureka!, next page" kinda book.

Icosahedron

I can understand some of the words.

Btw, is that the end gr book?

0celo7

End?

Icosahedron

final book.

0celo7

No.

Icosahedron

00:47

What is more advanced than it?

0celo7

Straumann is certainly comparable.

Icosahedron

What about penrose?

0celo7

There are books that treat stuff like the Cauchy problem, 3+1 splitting or other things in more detail.

Icosahedron

spinors and spacetime book.

0celo7

@Icosahedron He has quite a few books.

That's not a GR book.

Icosahedron

00:48

apparently it is

0celo7

I know there is a book by John Stuart which is all about spinors in GR.

Then we have the canonical Exact Solutions of the Einstein Field Equations by Stephani et al.

The Mathematical Theory of Black Holes by Chandrasekhar.

It's not like you can read Hawking & Ellis and suddenly know all of GR.

Icosahedron

How much GR do physicists like penrose know?

0celo7

I haven't read his books.

NeuroFuzzy

@0celo7 ie right now in Georgi I'm trying to figure out what means what with how he defines the adjoint representation, where $X_a$, an element of the Lie algebra, and $T_a$, an element of the adjoint rep, has $X_a$ used as both an operator and a state, and $T_a$ used as both an operator and a state.

0celo7

I imagine he knows a lot more than you or me.

Icosahedron

00:51

Really?

0celo7

Yes. He is the author of one of the black hole singularity theorem.

Icosahedron

$3x + 5 = 7$

NeuroFuzzy

which leads to the question: What the hell changes when you do a change of basis! it's terrible especially when other people's notations "ad(x)(y)=[x,y]" make perfect sense and questions like that become easy.

Icosahedron

@0celo7 You should flip through his RTR book, I'm sure you can learn something from it.

0celo7

@Icosahedron No time.

And shouldn't you be learning QM?

Icosahedron

00:54

I don't work on weekends.

I learn other stuff.

0celo7

@NeuroFuzzy I'm in a state of constant confusion trying to muddle through the rep theory in these string theory books.

Icosahedron

(It's a long weekend in canadia, has something to do with queen victoria)

Though it's mostly an excuse to sleep in.

0celo7

I learn something one way and then they make vague as hell statements that completely destroy my knowledge of the subject.

I end up begging @ACuriousMind to explain it, but sometimes he doesn't know either.

(This is obviously bad.)

Icosahedron

@0celo7 If he read books at your rate instead of wasting time on SE, he would literally be god.

NeuroFuzzy

Heheh okay, so maybe Georgi is a good book for you and maybe I just have to get used to it!

0celo7

00:57

I haven't read it!

I will one day. Maybe. Depends on how confused I get.

NeuroFuzzy

oh of course, for the summer I mean

0celo7

@Icosahedron I'm wasting time on here right now.

Icosahedron

@0celo7 Aren't we all?

0celo7

@Icosahedron Pretty much.

I don't want to read the second chapter in Hawking & Ellis, because I know the material, but I also want to see how the masters do geometry.

Icosahedron

@0celo7 Name the last 5 books you have read entirely or mostly.

0celo7

01:00

@Icosahedron Uh

Wald

Uh

Shit, I'm really bad at finishing stuff.

GDI I was reading and you interrupted me

Shoo, go learn QM

Icosahedron

I need to finish cahill ch1.

A lot of it is new to me.

0celo7

You said you looked at Linear Algebra Done Right and it was too easy.

That book is more advanced than Cahill's chapter on linear algebra.

Icosahedron

That's because I was reading linear algebra by insel which is more advanced than axler.

But I only read <10% of it.

(Got boring)

0celo7

@ACuriousMind Holy crap, HE actually provides an example of a non-Hausdorff space.

HE := Hawking & Ellis for future reference.

Icosahedron

How can HE be that advanced though?

0celo7

01:07

Very steep difficulty curve.

Icosahedron

Last year, a postdoc at my university recommended it to me as an introduction, when I only had knowledge of manifolds at the vector analysis level.

0celo7

BBS starts out with the action of a point particle in special relativity and has managed to intellectually rape me.

Just because the prereqs aren't bad doesn't mean you don't need the intuition that comes with a lot of math training.

You should ask that postdoc for a recommendation for an advanced text.

I'm looking to broaden my GR knowledge.

Icosahedron

Most likely lecture notes.

0celo7

@ChrisWhite What is the most advanced GR book that you know of?

Icosahedron

This looks frightening.

0celo7

01:13

I mentioned that a while ago.

It's on my list.

24 mins ago, by 0celo7

I know there is a book by John Stuart which is all about spinors in GR.

Shit, wrong last name.

Sounds the same :P

I will definitely read that, but $55 is a little steep.

amazon.com/…

That's scary.

$100 for < 300 pages is ridiculous.

NeuroFuzzy

01:36

I didn't know john stewart did GR on the side of his TV stuff

user54412

02:11

@0celo7 Can't think of any. My only GR course went Carroll -> MTW -> Wald, and after that we just referenced canonical papers in the field rather than books.

user54412

Note that we decided to focus on numerical relativity, solving the ADM equations and such, and to my knowledge no book has ever been written on the topic.

0celo7

@ChrisWhite My next question was "is there a book on ADM".

Do you have Hawking & Ellis within reach?

user54412

@0celo7 Alas no.

0celo7

I'll just screenshot.

I'm confused by the definition of the curve in curly brackets.

user54412

I'm also confused

0celo7

02:17

@ChrisWhite I'm assuming the curve that's being glued to the sine function is the part sticking out, right?

user54412

that's what I would interpret the diagram as, but I don't see how the braced locus of points relates

0celo7

Ok, let's assume that's a typo.

Why is the curve not an imbedding?

user54412

that would be easier to answer if I knew what the curve was

0celo7

They define imbedding by saying an imbedding means the map is a homeomorphism onto its image.

user54412

how does that arc at the top connect to the mess along the y-axis?

user54412

02:20

or is it not supposed to?

0celo7

No clue.

I guess it attaches to the peak of an oscillation.

user54412

I guess it's an immersion of R^1, so there should be two endpoints, so maybe they're not supposed to connect?

user54412

@0celo7 agree

0celo7

Well what does that actually mean? I've always viewed this stuff intuitively, but this is a counterexample for when intuition fails.

Wald says this condition means the curve does not come arbitrarily close to intersecting itself.

user54412

hmm

0celo7

02:26

Perhaps there is some weird stuff with the oscillation going on, since $\lim_{x\rightarrow 0}\sin(1/x)$ DNE.

@ChrisWhite Page 431.

user54412

well, Wald doesn't seem to think this is an important counterexample, since he excludes the homeomorphism condition from his definition

0celo7

It might be important for HE, which contains all the proofs omitted in Wald.

user54412

okay, let's agree as to what the picture is -- I'll say the arc on the top stops at (0,1) (the image of $-\infty$)

user54412

then any neighborhood of (0,1) contains points in the curve from far away (images of points past 1, or wherever the transition to $\sin(1/x)$ occurs)

user54412

this feels like it violates a separation axiom of some sort

0celo7

02:38

But if the curves are joined smoothly, how can you connect the top arc to the oscillation, which has no limit?

Wait.

user54412

I don't think they're joined there. They're clearly joined on the RHS, and this is the image of R^1, not S^1

0celo7

Nvm

@ChrisWhite Ok.

But they come arbitrary close to intersecting?

After all, the sine function will go arbitrarily close to (0,1).

So how does Wald's intuitive explanation follow from the definition?

user54412

Well, the image of the curve, with the inherited topology from R^2, is not regular, since any open neighborhood of (0,1) will intersect the closed set formed by the entire sinusoidal nonsense. I think.

user54412

Whereas homeomorphisms should preserve topological properties. Maybe.

0celo7

@ChrisWhite Agreed.

@ChrisWhite Maybe agreed.

Seems good enough for me, lol. I'll return to ask you or ACuriousMind again if I need to really understand this better.

user1667423

04:30

In conceptual terms, which is the more fundamental quantity, the electric susceptibility or electric permittivity (1 + Xe = er)?

NeuroFuzzy

06:35

@user1667423 Neither!

It's just a first order approximation of polarization as a function of the electric field. But polarization could depend on a whole lot of things, or could be a more complicated function of $E$.

So it's not really fundamental in the first place...

ACuriousMind

11:36

@0celo7 What do they give as an example? I've only ever run into non-Hausdorff spaces as spectra of rings.

ACuriousMind

11:58

@ChrisWhite Yes, a homeomorphism should map a regular space to a regular space - simply because the image of two open disjoint sets must again be two open disjoint sets.

Jim the Enchanter

13:27

@Icosahedron :::2 days later::: What did you need me for? And for shame! Yesterday was a Canadian holiday and you were trying to get me to work on that long weekend?

And not just any long weekend, the long weekend in Canada that is nationally recognized as the official one for drinking an entire 24-pack of beer

Danu

14:06

@0celo7 It fails to be a topological embedding (and therefore isn't a smooth embedding---the relevant notion for smooth manifolds)

(imbedding is archaic spelling... I think)

This is also discussed in e.g. Lee's book

In general, making precise why exactly something fails to be a topological embedding is not easy

Examples 4.18-20 of Lee's book give an idea of what type of stuff you should be looking for.

It seems you guys were already on the right track

David Z

15:20

Chat session coming up soon, I suppose? (40 minutes)

I don't think I can make this one. I'm about to leave the office and the internet access from home has been very bad lately.

Jim the Enchanter

@DavidZ I won't mind if you miss this one. It's not like we pay you to be here for them anyway

Danu

Chattitychitchat

0celo7

@Danu It's either archaic or the British spelling.

@ACuriousMind HE defines the exterior derivative component-wise, instead of the more elegant definition as the unique nilpotent degree 1 antiderivation.

That's pretty much my only nit-pick so far.

Eh, I also don't think they motivated the introduction of a the connection very well. That's passable, considering this is a collection of geometry results and not for teaching.

Terry Bollinger

15:53

Greetings and felicitations, I hope everyone is well.

Hmm, speaking chattily, this is not a very chatty group so far... :)

user54412

just munching on some food here

Terry Bollinger

I'm listening to Infected Mushroom on Pandora. It sounds like, well... an infected mushroom, but in a nice way...

0celo7

Reading.

Terry Bollinger

So, I was wondering (I don't expect answers): How much of the Standard Model can be translated one-to-one into manifolds in higher dimensional spaces?

0celo7

My immediate thought is that spin is a 3-d thing.

vzn

16:06

@TerryBollinger hi (all). isnt this related to string theory?

Terry Bollinger

I'd say 4D, specifically in quaternion space H.

@vzn Argh, you're right, I hadn't even though of my question that way...

user54412

@TerryBollinger Are you asking if we can explain our physics by appealing to "simpler" theories in more dimensions, or are you asking if our models just "work" in higher dimensions?

ACuriousMind

You'll have no direct notion of "spin-s" fields for a single number s, so you need to figure out what to do with your fermions

0celo7

Considering the standard model is a model, what do you want to model?

ACuriousMind

But the gauge and scalar field can directly be carried over into other dimensions, no problems there

Terry Bollinger

16:07

@ChrisWhite Not simpler -- exactly equivalent.

vzn

do not know a lot about strings but do they cover "deformations of space" somewhat similar to manifolds?

Terry Bollinger

@ACuriousMind Referring to H for spin?

vzn

how does SM interrelate to space/ geometry?

ACuriousMind

Except that the renormalization behaviour shifts, and I think it will become either super-renormalizable or non-renormalisable.

0celo7

@vzn The standard model describes forces geometrically using the language of bundles.

ACuriousMind

16:09

@TerryBollinger What do you mean "referring"? You'll have to say how the fermion field transforms under your higher-dimensional Lorentz group, how does H help with that?

user54412

@ACuriousMind Should I think of that the same way I think of magnetic fields being weird in higher dimensions?

Terry Bollinger

BTW, I wasn't thinking string theory, just whether the math of the SM has a manifold representation.

vzn

how does SM interrelate to GR? does GR "deform" the spaces that SM refers to?

Terry Bollinger

@vzn Answer that well and I think you get a Nobel?

vzn

lol ok...

ACuriousMind

16:11

@ChrisWhite I think not. The "magnetic weirdness" is because the dual of the two-form field strength isn't a two-form field strngth anymore, the "spin weirdness" is because the representations of the isometry group are no longer essentially controlled by SU(2)xSU(2).

user54412

@vzn Well, the SM is local AFAIK, and GR is locally nothing special...

Terry Bollinger

@ChrisWhite I'd have to go back to my notes, but magnetic fields are very "3D", whereas electric is a bit more gnarly and requires 4D. Ask me what I mean by that and I won't even be able to tell you... :)

ACuriousMind

@vzn The SM knows nothing of GR. It is ordinary QFT in ordinary Minkowski space

vzn

doesnt GR work with "manifolds"?

or something like it?

Terry Bollinger

@ACuriousMind Interesting!

ACuriousMind

16:13

@ChrisWhite The action of the SM is not invariant under general coordinate transformations, and if you (try to) make it so, it becomes "QFT in curved spacetime" which is a lot weirder than ordinary QFT.

Terry Bollinger

@vzn Big problem with GR is that it is nothing but geometry. Makes it hard to quantize.

user54412

@ACuriousMind I wouldn't be surprised if there were a category theory way of seeing those as the same :P

0celo7

@ACuriousMind Speaking of magnets, I completely forgot to read your chat comment on the hypersphere.

ACuriousMind

@TerryBollinger Oh, quantizing is not actually the real problem. The problem is that the quantization is non-renormalizable.

Terry Bollinger

@ACuriousMind Heh! And that causes no problems?

TestPilotDoc

16:15

Have you seen any new computer visualization techniques for H, or higher Clifford spaces, for example,"Visual Complex Analysis" referred by Penrose in The Road to Reality"?

JamalS

@TerryBollinger Well, if you want to compute physical finite quantities such as cross sections and branching ratios, then non-renormalizability is a problem.

Terry Bollinger

@JamalS It's a problem, yes. If you can't renormalize... ouch in many ways.

vzn

@TerryBollinger yes that seems to be one of the acknowledged big open problems of the field how to mesh relativity ("very big") with quantization ("very small") but not sure if it has been formulated ("reduced") as a math problem yet, & shows up with eg black hole study in particular....

ACuriousMind

@ChrisWhite Wouldn't surprise me, either ;)

Terry Bollinger

@TestPilotDoc I came up with a physical design for a quaternion "slide rule" multiplier. It's kind of fun. There are many interesting ways to view H multiplication.

vzn

16:17

& there are theories & maybe even experiments about gravity being quantized afaik, under development....

TestPilotDoc

I think I saw that as a mathematica demo?

ACuriousMind

@vzn Yes. Those theories are mainly string theory and loop quantum gravity.

No experiments yet, though

vzn

@ACuriousMind actually there seem to be early attempts

eg Experimental Search for Quantum Gravity / Hossenfelder

Terry Bollinger

@TestPilotDoc Really? I never have found an equivalent slide rule for H. Do you have a ref?

@ACuriousMind Is it absolutely necessary to quantize gravity? I've always assumed so, but could a theory somehow dodge the need and instead leave gravity off by itself? (I can't see how... gravity has energy after all...)

vzn

experimental search for qm gravity / Nordita

> Many approaches to quantum gravity that rely on discretizing space-time or that describe gravity as an emergent phenomenon violate Lorentz-invariance.

have long thought/ conjectured gravity is an "emergent phenomenon"... great to see some alignment on that

TestPilotDoc

16:22

Not H but related? demonstrations.wolfram.com/ComplexSlideRule

Complex Slide Rule

Terry Bollinger

@TestPilotDoc Somewhere I have an image of a drawing of an H slide rule... looks sort of like a ring on a ring.

John Rennie

@TerryBollinger Not strictly true. Yang-Mills theories are also geometrical. The problem is that GR is wrong sort of geometry.

ACuriousMind

@TerryBollinger Well, from the usual reductionist standpoint of physics, it is necessary to get a theory which has both QFT and GR as certain limiting cases (or at least from which both QFT and GR can emerge in some sense), and this is what is meant when broadly speaking about "quantizing gravity".

TestPilotDoc

google/see: f(x) program also Needham's book mentioned above: Visual Complex Analysis

ACuriousMind

No one expects that we will be able to "quantize" gravity in the same way we did the rest of classical physics (because that's what gives us a non-renormalizable QFT, among other issues)

user54412

16:27

@ACuriousMind That argument... always seemed off to me. What does it even mean for QFT and GR to be limiting cases of one theory such that the union of the two is not the theory we're looking for? Indeed, how do you even count how many separate theories you have?

vzn

> "...from the usual reductionist standpoint of physics..."
maybe part of what needs to be rethought or maybe even (eventually) [gasp] abandoned!

Terry Bollinger

@ACuriousMind I guess I'm inadvertently questioning the faith premise that all forces must unify at high enough energies. Seems very Nascar. What if gravity really is different?

ACuriousMind

@TerryBollinger No unification of gravity with the other forces happens in e.g. the string theory approach (as far as I understand it). This is not about making gravity the same as everything else, this is about having a theory that is able to deal with both gravitational and quantum effects.

vzn

@TerryBollinger agreed. maybe gravity is inherently related to low energies/ separation of mass/ space & is meaningless in a big bang universe-concentration scenario.

ACuriousMind

@ChrisWhite Well, right now, what if my spacetime is horribly curved (e.g. around a black hole) and I ask what happens if I do HEP experiments there? Can the "union" of QFT and GR answer that?

Terry Bollinger

16:31

@vzn Given the complexity of universe, I lean towards fractal complexity that has reductionism at its root, but expresses itself in diverse broken symmetries. (Eh? I'm not even sure what I just said... :)

@TestPilotDoc Thanks I'll take a look.

Q: If classical space and time are both emergent properties of QM, I wonder where that would place gravity?

user54412

@ACuriousMind Why indeed wouldn't it?

user54412

If the large curvature breaks things, then the small curvature must be qualitatively wrong too, even if only by a small amount. How is it wrong, though?

vzn

@TerryBollinger my thinking is that gravity is inherently associated with the separation of mass and space which happened long after the big bang (where they were nearly fused/ undifferentiated).

ACuriousMind

@ChrisWhite It...just can't. The derivation of scattering amplitudes (and indeed the very definition of a particle state) in QFT needs Minkowski space. The LSZ formalism just breaks when you have a different metric. (and also, you get again problems with fermions, but one can do things to have fermion fields living on cirved spacetime)

Even doing QFT against a classical background metric that isn't quantized is very difficult if it is far from Minkowski, and its interpretations are...very unclear - vacuum and particle become very fuzzy notions.

Terry Bollinger

@ACuriousMind Is that related to Dirac's complaints about curved space being incompatible with QM?

vzn

16:39

right now it is hard to figure out what emerges from what, but definitely reductionistic approaches (which have gotten physics very far and can be long venerated for that) are increasingly at odds with emergentist approaches.

the entire "intellectual architecture" of physics is in many ways reductionistic and (overly, at times) compartmentalized.

user54412

@ACuriousMind Is this because you're looking for asymptotically free particles to anchor your calculations?

ACuriousMind

@TerryBollinger I am not familiar with Dirac's specific argument

Terry Bollinger

@ACuriousMind "Lectures on Quantum Mechanics", well worth a look.

@ACuriousMind BTW, which character is your new icon?

ACuriousMind

@ChrisWhite Yes. In Minkowski space, there is a uniquely specified set of creation and annihilation operators and a unique free vacuum. There is no such thing in other spaces, even flat FRW space already has infinitely many different choices.

Jim the Enchanter

@TerryBollinger HK-47 from star wars: KOTOR

Terry Bollinger

16:43

@JimtheEnchanter Thanks!

0celo7

@ACuriousMind You've been studying QFT in curved spacetime this semester?

ACuriousMind

@0celo7 Yes, attending a seminar on it.

0celo7

I remember asking for notes, are there none?

user54412

@ACuriousMind Ok, but let me continue prodding. Is this really necessary? I mean, pure GR is also easier in asymptotically flat spaces, but I'm not concerned by the general lack of global quantities in weird spaces, because all my physics is local and hyperbolic and evolving predictably from Cauchy surfaces, etc.

ACuriousMind

@vzn I don't understand how an "emergentist" approach is at odds from the "reductionist". Being a reductionist doesn't mean that you deny that properties can be emergent. Doesn't "emergent" mean "This property is not visible in the reductionist description, but only appears once you [do this limit/iterate it often/average in this way/whatever]"?

@ChrisWhite Without the notion of asymptotic states, you...really can't do much. If you don't know what "the vacuum" is, it is unclear what the averages of observables one might calcuate e.g. by the path integral are. What state should we identify with the "experimental vacuum"? Is there even a well-defined Hilbert space of states. You just have no way to connect your math to anything physically observable.

Terry Bollinger

16:52

@JohnRennie "wrong sort of geometry"... elaborate briefly?

John Rennie

11

Q: Can all fundamental forces be fictitious forces?

After reading many questions, like this and this, I wonder: is it possible to consider also the other fundamental forces, the electroweak interaction and the strong interaction or ultimately the unification of these, to be fictitious forces like gravity in the framework of general relativity? ...

Terry Bollinger

@JohnRennie Excellent, thanks!

John Rennie

Except that GR isn't a Yang-Mills theory. If it was we'd have quantised it by now and a lot of string theorists would be looking for jobs.

Terry Bollinger

@JohnRennie Is it possible to state briefly what constitutes a quantizable/non-quantizable geometry?

John Rennie

On a non-quantum gravity note: I see lots of "this is a homework question" comments but with no VTC. Is that because we've all run out of close votes?

ACuriousMind

16:56

@JohnRennie One can formulate it very close to one, with the Christoffels as the gauge field analogon. The problem is that the "gauge transformations" also act on the manifold (they're the diffeomorphisms there), but Yang-Mills transformations leave spacetime unchanged.

@JohnRennie I have 8 left, so not running out. Are the comments from <3k or >3k users?

Terry Bollinger

@JohnRennie I almost never close. Ref to examine?

John Rennie

@ACuriousMind >3K. I'm not sure I can easily find an example, but the comments are from people i know to be power users. The last one was from Kyle I think.

user54412

@ACuriousMind This argument hinges on "experimental vacuum" being something observable. If I set up my lab next to a small black hole, will I empirically see such a thing as cannot be explained by QFT on curved spacetime?

John Rennie

@TerryBollinger Erm, yes, but I don't remember offhand. It has to do with mass appearing with a 1/m^2 power in the perturbative expansion. Or something like that.

9

Q: Why is Einstein gravity not renormalizable at two loops or more?

(I found this related Phys.SE post: Why is GR renormalizable to one loop?) I want to know explicitly how it comes that Einstein-Hilbert action in 3+1 dimensions is not renormalizable at two loops or more from a QFT point of view, i.e., by counting the power of perturbation terms. I tried to fin...

general-relativity gravity renormalization

user54412

(poorly formed thought to follow)

user54412

17:02

What if whatever ambiguities you have in interpreting the outputs of theory calculations are resolved by consistently choosing from amongst the ambiguous possibilities for translating your experimental setup into theory inputs?

Terry Bollinger

@JohnRennie Well, it sure ain't homework, but I remain curious: Is there a simple criterion by which a geometry may be ascertained to be quantizable or non-quantizable? I ask only because often such things have simple underpinnings if examined closely. And sometimes not.

ACuriousMind

@TerryBollinger What do you mean by "a geometry"? ;)

John Rennie

@TerryBollinger No idea.

ACuriousMind

@ChrisWhite I think you run into an issue similar to the old view of non-renormalizability, i.e. you need infinitely many inputs. But I'm not sure at all.

Terry Bollinger

@ACuriousMind What John Rennie meant earlier in Yang-Mills vs GR.

@JohnRennie Thanks.

ACuriousMind

17:07

@TerryBollinger Well, John said that Yang-Mills and GR are both "geometrical", and that's true since both can be formulate in similar terms, but if you are asking for criteria about the "quantizability of geometry", then we should be able to first give a precise definition in what way YM and GR are both subclasses of "geometries", and in what precise way they differ.

Terry Bollinger

@ACuriousMind This seems like something that would have been studied...

John Rennie

Yang Mills and GR can both be written in the language of differential geometry, but i'm not sure that makes them similar.

ACuriousMind

^exactly

John Rennie

I don't think there is a simple way to relate the differential geometry description to the renomalisability.

Terry Bollinger

@JohnRennie Which might make the question interesting to study... hmm. Maybe hard, but who knows...

@JohnRennie Isn't renormalizability related geometrically to scalability?

John Rennie

17:11

@TerryBollinger I'm way out of my depth now, but no I don't think so.

The problem arises because in GR you're quantising spacetime by perturbing a flat spacetime.

In Yang-Mills spacetime is just flat and stays flat.

Terry Bollinger

@JohnRennie So it's just because Yang-Mills is embeddable in flat spacetime without losings its properties? Curvature is the issue?

Online image of Dirac Lectures:

google.com/…

ACuriousMind

@JohnRennie Needn't be, you can formulate YM theories on arbitrary manifolds.

But in ary case, the metric is not a dynamical object there.

Terry Bollinger

@ACuriousMind Can you still quantize if you do?

I need to go back over the Dirac stuff...

ACuriousMind

@TerryBollinger Not in general, no, same issue as above and more apply. In 2D one can quantize (and exactly solve the partition function), but that's because there are no particles in pure 2D YM.

Terry Bollinger

I am now itching to go back over an examination of Feynman's renormalization arguments. I recall thinking at the time "is that all this is?", but I don't even recall why, other than that there seemed to be a simple scaling issue involved. Hmm.

Must be going gents, it's been delightful as always.

John Rennie

17:22

Bye. I'm off too.

vzn

@ACuriousMind (oops got sidetracked) emergentist science is in its infancy across all areas of science (not limited to physics, although in some ways its a pinnacle there). after centuries of reductionism in science, its not gonna turn on a dime. it is not easy to characterize yet, the overall shape is not yet clear. one might point to "big data" as one of its aspects. it will likely be a very longterm theme/ shift of the entire 21st century.

there have been very longterm (past) hints of emergent properties in physics... gravity, QM, etc, it is quite common... the original perplexity on the foundations/ interpretations of QM relate to it...

TestPilotDoc

Terry, that was f(z) at lascauxsoftware.com

not x as in typo

vzn

re emergentism, a nice example (kinda from physics, ie chemistry, kinda not) is the human body. eg, crosscutting diseases like cancer cannot be entirely understood by just looking at individual organs or cell types. and looking at the "big picture" seems necessary to understand it. reductionism has succeeded to some degree, ie/ aka "lets not throw out baby with bathwater"...

user1667423

17:44

@NeuroFuzzy Understood. Do you know where I can find a list of examples for constitutive relations between the electric field and polarisation density for nonlinear materials?

@NeuroFuzzy Also, I assume the integral expression in en.m.wikipedia.org/wiki/Electric_susceptibility (section dispersion and causality) is the most general way to describe the relationship between polarisation and electric field. Is this correct?

Jim the Enchanter

18:37

What's the most polite way to say "The way you pose your question makes me think you have no idea of the actual science behind this and are just coming up with arbitrary personal theories with arbitrary predictions. You would definitely get a better reception and better quality answers if you could add more background that shows you know what you're talking about."

Danu

@0celo7 Today we did some really cool stuff in Riem. geom.

@TerryBollinger Lol... why?

user54412

@JimtheEnchanter No one ever proved there was a polite way to say all truths.

Danu

@TerryBollinger If you're looking for similar stuff... you could Glitch Mob

@ChrisWhite Lame mathematical response alert: There is no way to say all truths, period!

Jim the Enchanter

@ChrisWhite A "most polite" way isn't necessarily polite. It could still be rather nasty, but if there exists a way of grading levels of politeness, there must be a most polite way

Icosahedron

@JimtheEnchanter The main reason for it is our beloved queen victoria that is no longer with us for more than a century. $3x+5 = 7$

Danu

18:44

@TerryBollinger I'm really not sure what you're trying for here... Of course you can talk about vector bundles and stuff... and Urs Schreiber has a lot more where that came from!

Jim the Enchanter

@Icosahedron I don't follow. What does 2/3 have to do with Victoria day?

Icosahedron

@JimtheEnchanter Read this log, and this log

Danu

@vzn Lol

In these days it's kind of a trivial statement to say that classical physics is emergent

Icosahedron

I found a hyperlinked and searchable V.I. Arnold book, finally.

@JimtheEnchanter Do you follow now?

Jim the Enchanter

@Icosahedron Apparently you were trying to denote sarcasm about queen victoria by using a random equation

Icosahedron

18:52

Completely.

Jim the Enchanter

Might I add that there was no real room for sarcasm in what you said. Unless you were sarcastic about her being beloved. But that's so minor that using a sarcasm identifier kills it

Icosahedron

I tried.

Jim the Enchanter

And how on Earth is an arbitrary equation a better indication of sarcasm than something like: :::he said, sarcastically:::

Icosahedron

Ask Ocelot.

Jim the Enchanter

I will if he uses that on me

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