The h Bar

Danu

16:05

Hi @ACuriousMind

ACuriousMind

16:19

@Danu Heyho

HDE 226868

If I write up an answer and it gets saved as a draft, does that draft ever disappear?

ACuriousMind

4

A: How long do saved drafts exist?

If I return to that question say a week later, will my draft still exist? Drafts will be automatically cleared after a week. Also note if one of your answer is saved in draft and you start a new answer then the old one will be cleared. Reference

HDE 226868

@ACuriousMind Weird. Mine's gone after two days.

Danu

@HDE226868 It has before, for me.

ACuriousMind

@HDE226868 Note that it also disappears if you start another answer.

Danu

16:23

(on that god damn question by Emilio, mind you)

That was not a fun experience.

HDE 226868

@ACuriousMind I only had the one.

ACuriousMind

@HDE226868 You answered a question 17 hours ago.

Any draft from before that will be gone.

HDE 226868

@ACuriousMind Oh, answering a different question? Damn.

Danu

When I see "Fock space is freely generated by", what kind of structure is the Fock space implied to have?

(in what sense is it generated by [...]?)

ACuriousMind

@Danu Depends, what are the things it is claimed to be generated by?

I can imagine both as a vector space and as an algebra

Danu

16:29

By certain operators (implied to be acting on the vacuum)

ACuriousMind

@Danu That's not specific enough. Do those operators generate only 1-particle states or arbitrarily high particle numbers?

Danu

@ACuriousMind Arbitrarily high

If it's not specific enough that's a shame, but that's all the book gives me ;)

But it's implied to be the entire Fock space, not just a fixed particle number subspace

ACuriousMind

Then it's probably meant to be generated as a vector space, however, "freely" is then a bit superfluous as every vector space is free.

Danu

As a vector space, really? That's a bit disappointing :P

I think we also need to form all finite words out of these operators

and the words are not included in the supposed generating set

(also this book is not mathematically rigorous so it may just be imprecise/incorrect)

ACuriousMind

@Danu aha! Now that's more specific

Danu

16:33

@ACuriousMind The operators are $\psi_{-r},\bar\psi_{-s}$ for $r,s\geq 1/2$

(free fermion CFT; Blumenhagen's book)

ACuriousMind

That sounds like generated as a ring/algebra, however, the Fock space is not free - the (anti-)commutation relations have to be imposed, so "freely generated" is wrong.

Danu

^That's what I was thinking

there are nontrivial relations

so how can it be freely generated

Also, I don't quite understand in what sense the space of states can even be a ring? I understand that he $\psi$'s can form a ring, but am I really taking a (tensor?) products of states when I do something like $\psi_{-1/2}\psi_{-3/2}\mid 0 \rangle$?

I guess maybe I am

No, I don't think so actually

:P

ACuriousMind

@Danu Yes, you are. Bosonic Fock spaces are essentially the symmetric algebra on the creation operators, Fermionic Fock spaces are essentially the antisymmetric algebra on the creation operators.

Reading Blumenhagen, he doesn't mean freely generated - he means the fermionic Fock space generated by those operators, i.e. the antisymmetric algebra, not the free algebra on them.

Danu

So I'm supposed to interpret every operator $\psi_{-s}$ as a state?

@ACuriousMind He literally says freely generated

ACuriousMind

@Danu Of course, as the state $\psi_{-s}\lvert 0\rangle$.

Danu

16:39

@ACuriousMind Okay, I guess, though I don't intuitively think about it that way.

ACuriousMind

Likewise, $\psi_{-s}\wedge\psi_{-r}$ is $\psi_{-s}\psi_{-r}\lvert 0\rangle$.

Danu

I think about the modes as things that can create/act on states, not states themselves per se

ACuriousMind

This gives you an isomorphism between the antisymmetric algebra on the operators and the fermionic Fock space.

Danu

Yeah exactly, it's isomorphic

I see that, but it's not "the same" in my mind :P

ACuriousMind

@Danu I know, but that thing's not free. I suppose he used the word to mean there are no "unusual" relations imposed, forgetting that this space is not free in the mathematical sense.

Danu

16:41

@ACuriousMind Yeah, okay.

I was only nitpicking on this because I just learned about free products etc etc

in my algebraic topology course

And this is not it :P

I'm compiling an email with errata/mistakes in the book, which I'll send to Plauschinn once I'm done with this course.

How to best put this...

On page 67, we read that in the Neveu-Schwarz sector, the Hilbert space is the "Fock space freely generated by \psi_{-s},\bar\psi_{-r} for r,s \geq 1/2". However, the fermionic Hilbert space is actually not the free algebra generated by the \psi_{-s}, \bar\psi_{-r} in the mathematical sense of "free", since there are nontrivial relations (antisymmetry!) that have to be taken into account.

Similarly, the Hilbert space of the free boson (see the bottom of page 55) is not the "Fock space freely generated by j_n, \bar j_m for n,m \geq 1" in the precise mathematical sense.

You think this is decent?

added [Note: Mathematical nitpicking!] in front :P

@ACuriousMind I guess that one could say the "freely generated fermionic Fock space"

ACuriousMind

@Danu It's fine

@Danu That's...silly.

Danu

@ACuriousMind I think Blumenhagen likes throwing in "cool words" every now and then

but he doesn't really care about mathematics as far as I can tell

My questions are already out of his comfort zone and I think they're quite basic :P

Mike Miller

17:00

when someone says that instantons are non-perturbative phenomena, is this something like saying that the defining equation is ill-posed? that slight modifications of the metric will lead to vastly different solution sets, but that we can still extract "perturbation-in-metric-invariant" data?

Danu

@MikeMiller In physics, we often to perturbative expansions around the "classical" solutions

Mike Miller

I do not know what that means. I'm looking at part 1 of this answer

(In particular, what are you expanding/perturbing?)

Danu

When one says "non-perturbative" in QFT contexts, it means that it's a solution which is not detected by a perturbative expansion

@MikeMiller Typically, we're looking for expansions of n-point correlators (does that word sound familiar to you at all?)

ACuriousMind

@MikeMiller It's more that they're invisible to physical perturbation theory. That assumes a small coupling $g$, and the instanton contributions are typically $\propto\exp\left(-\frac{1}{g}\right)$ in the "perturbative expansion" (cf. nlab). Additionally, perturbative theory also expands around a classical vacuum solution, so seeing the influence of other vacuum solutions on the sector you are perturbatively investigating is...difficult

Mike Miller

@Danu: No.

Danu

17:07

@MikeMiller Expectation values (in the vacuum state, or whatever else we expand around I guess) of products of the fields appearing in the Lagrangian

Mike Miller

Here's specifically how I'm interpreting it. If I have a carefully chosen path of metrics $g_t$, I can consider the instanton moduli space for each $t$. Suppose each moduli space is 0-dimensional. Then it's entirely possible this is shaped like a parabola: on the left end there are two solutions (one "positive" one "negative"), at $t=1/2$ there's only one (those two solutions "smashed together" and for $t>1/2$ there's none

Danu

I love how this is like... the perfect example of "incommensurability"

A path of metrics on what?

Mike Miller

So that if one tries to expand around $t=1/2$ one has trouble. (I'm thinking here of the metric like an initial condition, though I'm admittedly really changing the operator.)

A compact 4-manifold. :)

Danu

@MikeMiller So this would be... the gauge group?

Mike Miller

The ASD equation on a compact 4-manifold has as input a gauge equivalence class of connections on (say) an $SU(2)$-bundle, and as output $F_A^+$, and I'd like that to be zero. "$F_A^+$" depends on the metric on the 4-manifold.

Danu

17:10

@MikeMiller What is the ASD equation?

Mike Miller

@Danu: To you, I think that's space. I think $SU(2)$ is what you call the gauge group. What I call the gauge group is the group of fiberwise automorphisms of the bundle, which is really really big (infinite-dimensional).

ACuriousMind

@MikeMiller: The "non-perturbative" has nothing to do with the behaviour of the instanton equations, or anything with the shape of their moduli space. It is entirely physical terminology that refer to them being invisible to physical perturbation theory (which in this case also has nothing to do with perturbing initial conditions or something).

Danu

@MikeMiller You want to do physics on a compact 4-manifold? Ah...

The most simple setup in physics terms is to fix the spacetime to be Minkowski space ($\Bbb R^{1,3}$)

Mike Miller

@ACuriousMind: OK, fair enough. I don't really understand why that answer is so popular then, since I don't really understand what a mathematician gets out of it. :)

Danu

@MikeMiller HNQ effect?

Physicist spillover? :P

Mike Miller

17:14

ASD = anti-self-dual. $F(A)$ is the curvature of a connection $A$ on the $SU(2)$-bundle. There is the Hodge star, and I want $F$ to be anti-self-dual: $*F(A)=-F(A)$. Define $F^+(A)$ to be $(*F(A)+F(A))/2$. Then the equation is just $F_A^+=0$.

The metric-dependent thing here (actually, only conformal class dependent) is the Hodge star.

@Danu You want to do physics on a compact 4-manifold. I just want to do PDEs. :)

Danu

Anyways, yeah, as ACM said, this has nothing to do with instantons being "non-perturbative"

@MikeMiller No, I want to do it on a non-compact one :P

ACuriousMind

@MikeMiller The answer illustrates one of the most important appearancs of smooth non-analytic functions in physics, namely the partition function is non-analytic in the coupling constant due to instanton contribution. The physicist calls the non-analytic part "non-perturbative".

Danu

But I guess I am liable to use the 1-pt compactification at any time for convenience ;D

@ACuriousMind That's also a funny way of looking at it, I guess.

alarge

I thought this (pdf) was pretty cool (modeling instruments; SIGGRAPH). Here's a video.

Danu

If it's non-perturbative it does not appear in a power series expansion -> non-analytic

Mike Miller

17:18

Fair enough.

John Duffield

17:59

@HDE226868 : the gin-clear ghostly elastic solid is the correct analogy. That's why there's a shear stress term in the stress-energy-momentum tensor. And understanding gravity is not philosophy, it's physics.

Hitesh Pathak

Hey Is it right to think that newton had not himself thought about inertial frames of references It was us who introduced this idea and established the first law as definition of inertial frames

Danu

@HiteshPathak Perhaps a question for History of Science and Mathematics?

Hitesh Pathak

Yeah !

But I guess that Newton really meant his laws with respect to a frame of reference fixed to earth Am I right ??

Danu

I don't really know. You can easily find his original texts (at least the Principia) online, so you should be able to find without too much effort whether he considered inertial frames or not.

Hitesh Pathak

Perhaps he considers a frame that is moving with constant velocity with respect to what he calls the ABSOLUTE SPACE

HDE 226868

18:10

@JohnDuffield Physics does not answer fundamental "Why" questions, like "Why is the value of $G$ what it is." That question boils down to something like that.

Hitesh Pathak

but its so vague to have abstract mental.concepts like that of absolute space Mach critises it good

John Duffield

HDE 226868 : but it does answer fundamental "why" questions such as Why does light curve? and Why does your pencil fall down? People who tell you that it doesn't, and that such answers are mere philosophy are people who don't know the answers.

Probably because they've never read the Einstein digital papers.

HDE 226868

I'm not going to get dragged into that. You have a terrible habit of bringing every single discussion you get into back to Einstein's writings.

Kyle Kanos

It took me a minute to realize that I still have Duffy blocked, so I was reading the above words and wondering what I was missing.

HDE 226868

@Danu Fun fact: The magnetic moment has historically been defined differently than the modern version, according to Wikipedia. It leads to a factor of 2 difference.

Hitesh Pathak

18:15

@JohnDuffield perhaps it answers not really why a pencil falls but more that HOW in way it falls ..I think so that the quest for why is endless..

I meant HOW, in what way the pencil falls

HDE 226868

@KyleKanos If I had pinged him, would you have seen my message, then? Perhaps there should be a chat feature to remove the confusion.

Danu

@HDE226868 I guess this has to do with the correction by a factor 2 in the transition Schroedinger -> Dirac equation?

when was the definition changed?

Kyle Kanos

@HDE226868 I do see your message. It's just that I've not been on all that much, so I've forgotten all about it

But now I see his gravatar all minimized

HDE 226868

@Danu Strangely enough, no. The "older" one starts from$$\mathbf{\mu}=\frac{1}{2}\mathbf{r}\times\mathbf{j}$$while the "newer" one starts from$$\mathbf{\mu}=\mathbf{r}\times\mathbf{j}$$

Magnetic moment

The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of electric current, a bar magnet, an electron (revolving around a nucleus), a molecule, and a planet all have magnetic moments. The magnetic moment may be considered to be a vector having a magnitude and direction. The direction of the magnetic moment points from the south to north pole of the magnet. The magnetic field produced by the magnet is proportional to its magnetic moment. More precisely, the term magnetic moment normally refers to a system's magnetic dipole...

Bloody LaTeX.

The magnetic moment pseudovector is defined differently.

I don't know when this started; I'll probably ask on HSM.

Danu

@HDE226868 It's probably not that interesting :P

HDE 226868

18:22

@KyleKanos Ah.

Danu

Also, I guess it's just to get rid of the inconvenient factor 1/2

I wonder where it came from...

@KyleKanos wow hey long time no see!

Kyle Kanos

@Danu Hi

How goes it?

Danu

How are you liking your new job?

Hitesh Pathak

Do anyone know how we can say that all interactions or forces can be broken into the fundamental forces

Danu

Any use for your stochastic analysis? ;)

HDE 226868

18:23

@Danu I've asked about an obscure coefficient used in one formula for mass loss rates from red giants. That's uninteresting. :-)

Kyle Kanos

@Danu It's actually going great. I sit next to my boss's boss's boss, who's a really cool guy.

I've not yet needed stochastic calculus any, but most of what I'm doing doesn't actually involve that

Danu

@KyleKanos Lol!

Kyle Kanos

And I've not yet met my actual boss yet; he works out of NYC while I'm not there

Danu

@KyleKanos Okay.

Is the job interesting intellectually?

Kyle Kanos

I had to fix some VBA (Excel spreadsheet macros) this week. That was....interesting, I guess

@Danu Oh yeah, definitely

Danu

18:26

@KyleKanos Nice!

What kind of stuff are you doing?

anything mathy?

Kyle Kanos

Most of the math I've done is PEMDAS & exponentials

But I'm currently a "fixer of things"

Danu

That easy?

Hmm...

Kyle Kanos

Someone's got some mostly-working code that needs tweaking in efficiency, so I do that

Danu

So what kind of stuff is interesting at the job?

Kyle Kanos

@Danu The people for sure. Traders and (some of the) quants are among the more interesting people I've met

Danu

18:28

I thought you'd be doing some quant-ish stuff

Hitesh Pathak

Is anyone interested in discussing Mach's principle here..

Danu

@HiteshPathak I think it's purely of historical interest (and not very interesting in that respect either)

Kyle Kanos

@Danu I am, just not stoch. calc. stuff (because there's more than just SDEs to finance)

Danu

@KyleKanos So I guess you're mostly doing coding stuff

Not like developing algorithms

Kyle Kanos

Well sometimes developing algorithms is coding ;)

But, like I said, I'm mostly fixing things that otherwise work fine

I think it's just a "get my feet wet" phase before they start getting me into more stuff

Danu

18:32

aight

Kyle Kanos

I missed out on a training program over the summer (didn't get the job until late August), and I think had I been around for that I'd be doing more SDE-related work (the other people who were in attendance for that are doing such SDE work)

Danu

Ah, okay.

Well as long as you're happy it dun matter much

Btw, how come you're suddenly returning to chat? :)

Kyle Kanos

I was in last night b/c wife was at a party and I was bored at home

Hitesh Pathak

You won't believe in my university I don't have anything related to multivariable calculus in First semester but in mechanics we have gravitation and work energy all using concept of gradients and curls..
Only I know how I am managing..

Kyle Kanos

In now because wife is away shopping and some of the kids are down for naps

(i.e., also bored)

Steelers don't play until 8:15p EST tonight, so got nothing to do until then.

Danu

18:35

We're your last resort, eh ;)

Hitesh Pathak

And then they say we promote understanding among students this sucks

alarge

@Danu That's a bit of a simplification: At the highest level you have a formula you want to solve, then a step down is a discretization that leads to "an algorithm". Implementing the algorithm may require a lot of other algorithms and decisions (e.g. how to invert a matrix?). Finally you might need to look at how to make the algorithms run efficiently with the hardware you got (and/or to indeed decide what HW to run on).

Danu

@alarge I don't nkow the first thing about that type of stuff ;)

HDE 226868

@HiteshPathak Math sometimes lags behind physics. I'm in a similar boat.

John Duffield

18:53

@HDE226868 : Einstein explained gravity saying concentration of energy in the guise of a massive star conditions the surrounding space altering its metrical properties and that light curves because the speed of light varies with position. No problem if you don't want to get dragged into that, but please don't pontificate about nobody understanding gravity, or that such understanding is philosophy rather than physics.

Danu

@JohnDuffield You're fulfilling his prophecy ;)

John Duffield

@HiteshPathak : the how and why of that falling pencil is very straightforward. Just apply the wave nature of matter.

ACuriousMind

::twitches::

5

HDE 226868

@JohnDuffield Ah, I see you're still good at twisting words. Besides, I'm clearly not to only one who agrees that there was a lot of philosophical implications at work there.

John Duffield

@HDE226868 : I'm not twisting words. Gravity is straightforward. If you don't understand it ask a question and I will explain it. But not now. It's Saturday night, and I'm off out.

HDE 226868

18:57

@JohnDuffield I never said nobody understands gravity - the answerer wrote that.

> Relativity is clueless about what attracts two objects towards each other in the first place.

Rather, something like it.

@JohnDuffield Your explanations are historically rejected by others.

End. Of. Discussion.

0celo7

Wtf does the wave nature of matter have to do with anything lol

Can someone please explain what a quantum effect has to do with classical gravity

@ACuriousMind you're a quantum guy

ACuriousMind

@0celo7 No. Because it has nothing to do with it.

0celo7

What did Einstein have to say on the matter

If it has nothing to do with it, where is @JohnDuffield getting the idea that they are related??

Danu

@JohnDuffield Lolololol

Hitesh Pathak

19:16

Can.anyone give a link to download principia motte's translation

Danu

@HiteshPathak We're not a download service :P

Bernard Meurer

Quick question in case anyone knows: What kind of force is more likely to cause a glass plate to crack? Compression, traction...

TanMath

20:12

Hello @MarkMitchison you there?

@DanielSank you there too?

ACuriousMind

@TanMath: How often are they going to have to tell you to just say whatever you want and they'll respond to it when/if they can/want?

TanMath

@ACuriousMind i'd like a "live" conversation... that is why...

Danu

@TanMath Well, get over it

It's quite annoying at this point

TanMath

anyway...here is the question @DanielSank @MarkMitchison ...Why won't my open quantum system for the FMO complex, site 3 population decrease and converge towards zero? I want a physical reason...I have reviewed the code and it seems there is nothing wrong with the code...I am probably missing something

Here is the code:

Bernard Meurer

@TanMath Wouldn't you feel you might be abusing of other people's good will to help? Your code is horribly large to run, and you didn't even go through the trouble of following PEP8 with it. I'm not a physicist nor a professional programmer; but I feel the solution to your problems lie in your responsability, and not on others.

dmckee

20:25

No one is going to believe that your code is bug free (even if it is) without (at a minimum) a full coverage test suite.

Because we've all discovered multiple bug in code we were sure was bug-free in the past.

Bernard Meurer

There's no such thing as bug free, you're just using the wrong system to find the bugs :p

Danu

@dmckee That one course on numerical methods I took...

THE SEMICOLONS!!!!

3

Bernard Meurer

Hahahahaha

ACuriousMind

I still don't know whether that one code I wrote a while back was just buggy or if the simulation technique was fundamentally flawed somewhere. Then again, I wasn't particularly interested in finding out after I passed the course with it, anyway...

Bernard Meurer

Are you sure it wasn't a feature?

ACuriousMind

20:31

@BernardMeurer No, that's kinda the issue. Maybe it was working perfectly but the "expected" result wasn't actually what one should've expected, especially since there was another paper on that that didn't see the "expected" behaviour, either.

Bernard Meurer

@ACuriousMind When I can't fix it I usually adapt the project to the results

Danu

@BernardMeurer Or the other way around... ;D

Bernard Meurer

Hahahaha @Danu I usually find altering the project as more honest though

dmckee

For code that I'm basing my career on, I write test suites for the low lying stuff and add a test for every bug I find and fix. Mixture of unit test and regression tests. And yes, that means there are often more lines of test than of deliverable.

Bernard Meurer

I feel your pain. I like it when the test takes a day and a half to run and the whole period is just an emotional rollercoaster

It will work -> This is broken -> I think there's no salvation -> It might be working -> It's working! -> It's just broken isn't it?

(@dmckee)

dmckee

20:39

I try to follow the test-driven design people. My test are typically fast, only a few times the build time.

There is one exception: I had a Monte Carlo code were I couldn't think of a way yo text a particular fact beyond exhaustive trials.

Since I was test that something didn't happen more than one in a million, the test runs ten million trials for each of six conditions.

Bernard Meurer

This one project I was doing just couldn't have short tests. Fast Factorial Functions. Factorial of 10^x being x a bloody large number. Sit and wait forever

dmckee

It about doubled the time for the whole test suite, so that clean build plus test ran to more than twenty minutes. Yuck,

Bernard Meurer

And better hope those 128Gb of memory don't run out

dmckee

@BernardMeurer Yeah. Get some coffee and a book for that one.

Bernard Meurer

I used to study for my finals while testing

got damn good grades that semester

now I'm porting to Python

and I can literally get a plane to another continent and back in between tests

dmckee

20:43

I did put the probabalistic test at the end and have the test suite print our when it was switching to them. So I could run the build in a separate terminal and go back to work when the Monte Carlo tests cut in.

@BernardMeurer So, you need a automated nightly build. Make it check that stuff while you're away from your desk.

Bernard Meurer

@dmckee I still have a tough time implementing a lot of stuff. Just finished high school so most of what I know I gathered by myself, that's a great tip tho!

I was just working with my CPU crying blood from the calculations in parallel

DanielSank

@dmckee We have the tests run whenever someone makes a pull request on our git repository.

It's a pretty nice system for a couple reasons:

dmckee

Yeah. That's good for a distributed environment.

DanielSank

1) Any would-be reviewer can see whether or not something broke.

2) Everyone learns that tests are important (as should @TanMath).

@dmckee You know, the more I do this stuff the more I think the distributed model is good even for a single developer.

dmckee

@DanielSank Sure, but I was always slow to learn the inner working of source control, so setting up a cron job to run the test over night was less work for me.

DanielSank

20:50

@TanMath Nobody is going to help you until you break the code down into smaller pieces and write tests that run in a few seconds.

@dmckee Well yah, that's a good idea too.

dmckee

To do it right you have to think about triggers and stuff. That means reading documentation.

DanielSank

^ Haha well so does cron, you just happened to already know about it.

@alarge Write the client side code in Typescript for ultimate happiness.

If the page is static then you can just serve the typescript along with the html and be done with it.

If you want to get fancy and generate the entire page programmatically in code, use polymer or angular or something like that.

Bernard Meurer

Okay, now I'm lost

DanielSank

@BernardMeurer In what way?

Bernard Meurer

I went to check the 3D printer and upon my return we are talking about typescript and static pages haha

ACuriousMind

20:56

The day everything in this chat makes sense to you is the day you've gone mad.

DanielSank

Uh oh...

Danu

I wish I had a 3D printer

Bernard Meurer

@ACuriousMind I feel there is some deep truth in that

@Danu If you're willing to pay my ticket I'll build you one anywhere hahaha

Danu

@BernardMeurer Build me one?

I think you're in Germany, no?

Bernard Meurer

@Danu I wish, I'm in Brazil for now.

Danu

20:59

@BernardMeurer oh jk

How are you able to build one?

Bernard Meurer

And yes, currently I work operating, building and fixing printers.

Well, find a place that laser cuts wood, buy some parts get some nuts and bolts an arduino and a shield

and you're good to go

also someone who knows how to set up the obscure settings correctly

0celo7

A watched pot never boils. Proof: Apply the Heisenberg principle. One cannot know the position and temperature of a pot at the same time.

Bernard Meurer

@0celo7, good one hahaha

dmckee

@0celo7 Look up the quantum Zeno effect.

Danu

Well the temperature is not fixed if it's not 100% pure H2O, even when boiling.

Bernard Meurer

21:05

I like it here, I almost feel normal

0celo7

Really? I feel stupid here

Danu

fucking great GIFs

Bass

@alarge Javascript (or Typescript) with a HTML5 canvas is the way to go. You could always directly code against the canvas, but depending on what exactly you want to achieve, there might be some libraries that will greatly ease your task. If it's 2D rigid body simulation like Angry Birds, there's the very popular Box2D engine which has been ported to Javascript, but there are also many alternatives.

Danu

more nice pictures and GIFs

Bernard Meurer

@0celo7 that's infinidecimally close to normal

ACuriousMind

21:10

@Danu: How bored are you that you are looking up images creators on Wikipedia?

Bass

for example box2d-js.sourceforge.net/index2.html, wellcaffeinated.net/PhysicsJS, brm.io/matter-js. There are other libraries for 3D or fluid simulation out there, most likely for Javascript too. It really depends on what you mean by 'interactive physics simulation'. For Hawking radiation simulation, you might have to write your own engine :)

Danu

@ACuriousMind very

Reading CFT is so tedious

Bernard Meurer

Is there a unit for entropy?

TanMath

@DanielSank but it is the physics that is messed up...

@BernardMeurer J/K

@BernardMeurer it takes shorter now...

Bernard Meurer

Is it short enough for a mosquito to experience within it's life time though?

Danu

21:19

@BernardMeurer Same units as $k_B$

Bernard Meurer

Was that non-TeX for Boltzmann constant?

Bass

@ACuriousMind re my question from yesterday. If the 3-spinor $(s_x, s_y, s_z)$ transforms as a 4-vector $\left(\frac{vs_z}{c\sqrt{1-\frac{v^2}{c^2}}},s_x,s_y, \frac{s_z}{\sqrt{1-\frac{v^2}{c^2}}}\right)$, then the spin vector (direction of the spin eigenstate) can indeed be parallel to the momentum, right?

ACuriousMind

@BernardMeurer It's TeX, follow the link in the upper right corner of the room to activate it

Danu

@BernardMeurer That was TeX :P

Bernard Meurer

Got it @ACuriousMind!

ACuriousMind

21:22

@Bass 1. That's a 3-vector not a 3-spinor. 2. Parallel it can be, that's what a right-handed spinor has.

Bernard Meurer

But @Danu I mean, you can get antropy in every(?) system right? There's even entropy in computers

ACuriousMind

@BernardMeurer What has that to do with its unit?

Bernard Meurer

I was just wondering all could be measure equally. Entropy sounds like an interesting thing to study

Bass

@ACuriousMind sorry. Of course, I meant 3-vector.

@ACuriousMind don't know what's wrong with what I'm typing. I wanted to ask: .. then the spin vector can indeed be orthogonal to the momentum, right?

ACuriousMind

@Bass Classically, one would think so - for $s_z = 0$ this would be orthogonal to the momentum. But...you shouldn't think like that in the quantum theory - there is no fixed "spin vector", it's components are never all determined on the same state. In the quantum theory, to discuss whether the spin is "orthogonal" to the momentum, you really should be looking at the operator $\vec \sigma\cdot\vec p$.

Bass

21:34

@ACuriousMind There's no fixed "spin vector" but if the particle is in the eigenstate of some spin operator, then this must be related to one specific axis, because the operator belongs to a specific axis, right?

$\vec\sigma\cdot\vec p$ is helicity, right? This is not Lorentz invariant for massive particles, so it's pretty much useless, isn't it?

ACuriousMind

@Bass I'm not sure I follow. Or rather, I don't understand what you're asking.

@Bass Yes.

Bass

@ACuriousMind If you want to measure spin (in NRQM), you have to decide for an axis. Like Stern-Gerlach, where you have to choose the vertical axis of the Stern-Gerlach apparatus. So when you choose a spin operator, you decide along which axis you want to measure spin. Usually you choose $z$, so you get a $z$ eigenstate.

That's what I mean by "spin vector"

It's the 3-vector that tells us the direction of the spin of the spin eigenstate.

Does that make sense?

ACuriousMind

Yes.

Bass

So when we do a boost in the $x$ direction, the electron gets a momentum in pure $x$ direction. But it remains in a spin $z$ eigenstate, right? So, we have an electron with a spin vector that's orthogonal to its momentum.

Now, if we have three electrons, one (red) with a spin vector in the $z$ direction, one (blue) with a bit of negative $x$, and one with a bit of positive $x$.

ACuriousMind

@Bass Yes...in one frame. If you boost it in $z$-direction, the momentum is parallel. For a massive particle it's not an invariant notion.

Bass

21:47

When we do a boost in the $x$ direction, the green vector changes its direction and aligns more closely to the positive $x$ axis. Similarly, the blue vector rotates to align more closely to the negative $x$ axis.

@ACuriousMind oh really? Then 0celo7 was right..

and if you boost in the $x$ direction?

ACuriousMind

@Bass In that frame, the spin is orthogonal. I already said yes to that.

Bass

@ACuriousMind Yes but isn't that invariant? If we $x$-boost the lab frame vector $(0,0,0,1)$ (red vector in the image above), it stays $(0,0,0,1)$ in other frames.

why is it in that frame only?

ACuriousMind

@Bass Uh, why would that be invariant? That spin vector is not invariant under $z$-boosts.

Bass

@ACuriousMind $x$-boosts. Not $z$-boosts.

ACuriousMind

It's invariant under $x$ and $y$-boosts. So what?

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