The h Bar

Sha Vuklia

00:02

Guys, I have question about the following exercise

Let’s say $R$ is the resistance in the loop. Can we still say $\mathcal E=RI$? I mean, we can’t really equate $\mathcal E$ to some electric potential $V$ now, because.. we don’t really have two poles? (or do we?)

Or.. maybe to phrase my problem better: $V=RI$ was originally motivated, saying that Ohm’s law, $\vec J=\sigma\vec f$, would usually only be used in the case of an electric field ($\vec f=\vec E$), and then they went on saying that $I$ is proportional to $\vec J$, which is proportional to $\vec E$, which is proportional to $V$, and hence in ohmic materials we have $V=IR$. However, in this case the force is magnetic, so I’m wondering how to argue that $\mathcal E=RI$ (if that even holds at all?)

Sha Vuklia

00:25

Hm, so my idea is to do the following: so obviously we have magnetic forces going on on the two horizontal segments that will yield an emf. Now, these magnetic forces will act on the charges to make them move (though they won't do work of course), and this will yield into an electric field, which will make the charges move smoothly.

Now if we look at one segment ab (of length $a$) of the loop, we know that the potential difference must be $\mathcal E/4$, because the electric field smoothed out everything, so $-\int_a^b f\cdot dl=\mathcal E/4$ (where $f$ is the force per unit charge), obviously the resistance will be $R/4$, because we have only quartered the length of our wire (and $R$ is proportional to the length), so we get $I=V/R=\dfrac{\mathcal E/4}{R/4}=\mathcal E/R$, and so indeed $\mathcal E=RI$ holds.

This is the only way I can think of to show that it holds, but I’m wondering if there would be a more direct way, maybe from definitions?

John Rennie

07:29

@ShaVuklia It's a straightforward integration. For a wire carrying a current I the field is $B = \mu I /(2\pi r)$ and the field is everywhere normal to the plane of the square. So just integrate $B.dA$ over the square to get the flux $\Phi$.

Then the EMF generated is just $d\Phi/dt$ as the square moves away from the wire.

Slereah

08:58

hello

Sha Vuklia

11:33

My problem isn't calculating $\mathcal E=-d\Phi/dt$, but I was rather thinking about the meaning of the emf in the first place. I think I have some general understanding about it now, and it is as follows: first of all, we can't call (of define) the emf "work done per unit charge", because for all we know we might integrate over a magnetic force. Second, we can't always include a potential in the story, because in the case of a Faraday field, we wouldn't even have a well-defined potential function to begin with. So how I interpret it now, is that emf does represent energy, but rather “re-di…

Actually, $\mathcal E\sim \vec f\sim \vec J\sim I$ doesn't makes sense... Hm, haha I'm confused

Avnish Kabaj

12:41

Nani

Anonymous

13:06

0

Q: What role does the non-commutativity of the tensor product play in experimental quantum computation?

We know that $H_A\otimes H_B\neq H_B\otimes H_A$ (in general). Theoretically, we know the formalism and what observables to construct from the two compositions possible, but we never talk about both the possibilities. I wish to know that how experimentally the Measurements or Evolutions are done ...

tensor-product

Anonymous

Just to verify, shouldn't the answer to this just be that there exists an isomorphism from $H_A\otimes H_B$ to $H_B\otimes H_A$ ?

Anonymous

7

Q: Hilbert space of a quantum system

The first postulate of Quantum Mechanics as I've learned can be stated as: The states of a quantum system can be described by vectors in a Hilbert space. I've seem also some people also requiring the Hilbert space be separable. Anyway, the point here is: we are associating a Hilbert space t...

quantum-mechanics mathematical-physics hilbert-space

Anonymous

> Having different vector spaces that correspond to your physical setup is no worse than being able to choose your x y and z axis to point any direction you want in the lab. Truly no different. They are all isomorphic, and 3d vector space. And it isn't a problem.

Anonymous

So basically it doesn't matter which option - $H_A\otimes H_B$ or $H_B\otimes H_A$ the experimentalist goes with. It's essentially similar to choosing a suitable coordinate system. Amirite?

Anonymous

@ACuriousMind Could you impart some expert knowledge on this? :P ^

Anonymous

14:29

Nevermind. The answers make it clear now :)

bolbteppa

14:41

What does a 'pure state' and a 'mixed state' mean for the free particle Dirac equation?

Non-relativistically, a pure spin state is such that there exists a direction in which the spin component of an election has the definite value $+1/2$. A mixed state arises when the particle is part of a larger closed system and as such does not possess it's own wave function, so that we use a density matrix, called a polarization density matrix, when analyzing the spin.

Relativistically, the spin vector does not commute with the free Dirac Hamiltonian in general, it only commutes with it in the particles rest frame, so that we must define a pure state to mean the spin has a definite direction in the particles rest frame. This apparently means we cannot represent the state with a spin wave function in an arbitrary frame of reference.

When you write $\hat{\psi} = \sum_{\mathbf{p},\sigma} \frac{1}{2 \varepsilon}( \hat{a}_{\mathbf{p} ,\sigma} u_{p , \sigma} e^{-ipx} + \dots)$ in quantizing the Dirac equation, $u$ acts as a spin wave function with momentum $\mathbf{p}$ and spin $\sigma = \pm 1/2$ (where the $\sigma$ labels the undetermined spinor $w$ in the free particle solution $u_p$ as e.g. either of the helicity eigenstates), and you're apparently using a pure state.

This seems to imply that the expansion of $\hat{\psi}$ does not hold in all frames, but it's supposed to be a general solution...

So - what exactly is a mixed state in this context? How does it relate to being in an arbitrary frame?

For a mixed state, you're supposed to use the density matrix $\rho_{ij} = u_{p,i} \overline{u}_{p,j}$ (for $i,j$ the bispinor components of $u_p, \overline{u}_p$).

enumaris

17:00

hmmm

Anonymous

@enumaris hmmmorning

enumaris

morning

Anonymous

What do you do during the weekends? The hbar missed you :P

enumaris

a lot of gaming

Anonymous

of what type

enumaris

17:07

watched Johnny English

had some food

simple stuff :D

mostly CS:GO

Anonymous

noicey :D

enumaris

my game sense is super poor...so far I'm just working on my aim tho

aim has gotten somewhat better

but my kd is still bad cus I keep getting shot from behind or when I don't expect it

Anonymous

I tried bowling after a long time, yesterday

enumaris

nice nice

bowling hurts my fingers

Anonymous

One ball slipped from my hand and almost broke the glass behind me

Anonymous

17:11

:P

enumaris

D:

Anonymous

@enumaris Those can be pretty heavy, yeah

Anonymous

5kgs or something

enumaris

yep*

Anonymous

I did, however, manage 2 consecutive full strikes though, after an hour XD

enumaris

17:14

nice, that's 20 points for the first one

Anonymous

Then I sat on one of those massage chairs. Those are really fun lol...with remote controls and all

danielunderwood

Hey I used to play a lot of CSGO...probably spent too much time playing it in college though

Anonymous

I'd buy one of those if it's for sale

Anonymous

(and cheap)

enumaris

I used to play a lot of CS:Source

But only recently started CS:GO

danielunderwood

17:16

I don't think I played CSS until after I played CSGO. The last time I played CSGO it seemed like I'd just hear kids screaming slurs in casual or have people leaving if I played comp, so I kind of just stopped

enumaris

just do

voice_enable 0

it's a life saver

(in console)

what rank were u?

Anonymous

amazon.com/dp/B01M24RKQY/ref=sspa_dk_detail_0?th=1

Anonymous

Damn, pretty expensive

Anonymous

But looks like it's worth it

danielunderwood

Yeah I did some, but probably not as much as I should have. I was MG2 before I quit the first time then came back and had a hard time getting out of silver

enumaris

17:21

ah

I'm currently Silver Elite

danielunderwood

I played on a community server for a while that was really enjoyable, but it kind of died down as a few of the regulars got busy

enumaris

ranked up from Silver 3

heh

I spend most of my time playing FFA deathmatches on the community servers

I've managed to be able to maintain a kd of roughly .7

when I started I was at like .2-.25 kd lol

my goal is to get to 2-2.5kd

still long way to go for that

Anonymous

what language are you guys speaking in

ACuriousMind

@Blue Yes

Anonymous

@ACuriousMind Thankew :)

danielunderwood

17:26

I was always told that those were how to get better, but I just didn't find them as fun as regular matches

enumaris

I find them more fun

cus regular matches I'm usually dead

and just spectating

DM I can respawn instantly

I think FFA DM does help with aim a lot. But I also play on that ulletical aim_botz map to improve hs accuracy

bolbteppa

17:42

hmm

0

Q: About Polarization Density Matrix of Electron

This is my understand of polarization Density Matrix of Electron. Can you let me know if there is anything incorrect? Thanks a lot! In rest frame, Polarization Density Matrix is only needed for ensemble of electron. If there is only one single electron, its spin is well defined and it is "fully...

quantum-mechanics quantum-field-theory

enumaris

3 m's please

I am the hmmm police

Anonymous

17:59

Actually I shouldn't violate our rule (don't post questions which you just asked on the main site)...lol

bolbteppa

m*

enumaris

self censorship

but muh free speech!

DanielSank

Hi, everybody.

enumaris

Sup

enumaris

18:27

@ACuriousMind out of curiosity, what's the "quintessential equation" in string theory? Like the String Theory equivalent of the EFEs or F=ma.

GodotMisogi

Is the quintessential equation in QFT considered to be the K-G equation?

enumaris

Dunno

maybe the Dirac equation?

or maybe some Lagrangian

Electroweak interaction

In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single electroweak force. Thus, if the universe is hot enough (approximately 1015 K, a temperature not exceeded since shortly after the Big Bang), then the electromagnetic force and weak force merge into...

but good luck getting that into a bite-sized form loool

danielunderwood

But everything in QFT depends on what fields you bring in, right?

Like you could have the SM Lagrangian, but that doesn't really describe all of QFT

enumaris

and it doesn't even include the strong force

danielunderwood

Also the SM Lagrangian on it's own is quite the ugly creature

enumaris

18:32

I think if you have the electroweak lagrangian alongside the strong-interaction's equivalent you'd have the entire SM in there

GodotMisogi

Ah, I was confused about what you meant by "quintessential"

enumaris

maybe iconic is a better word

$G=8\pi T$ is iconic

$F=ma$ is iconic

danielunderwood

You'd still need the Higgs Lagrangian wouldn't you?

enumaris

$F=\frac{Gm_1 m_2}{r^2}$

@danielunderwood maybe...

danielunderwood

$\frac{G}{T} = 8 \pi$ GR is solved!

GodotMisogi

18:34

So the Schrödinger equation would be the iconic equation of QM?

enumaris

For me, yeah

GodotMisogi

How about the propagator equated to the path integral?

enumaris

QM would be like $i\hbar\partial |\Psi\rangle/\partial t = H|\Psi\rangle$

maybe

but it's probably not as iconic

GodotMisogi

What about thermodynamics? Second law?

enumaris

maybe the definition of entropy

$S=k\ln\Omega$

danielunderwood

18:38

I've heard of the Polyakov action a lot for string theory, but I have no idea how far it goes besides already being over my head

bolbteppa

Dirac equation definitely

GodotMisogi

I don't know about string theory, but my current ring theory exam is kicking my ass

Unfortunately, I don't have to show st = 1

danielunderwood

18:52

@enumaris I just saw this. Don't know if it's of any interest to you github.com/google-research/bert

enumaris

not familiar with BERT

got an overview?

or do I have to read the paper...

thanks for the heads up tho, it looks interesting :D

danielunderwood

I couldn't do any better than what's in the "What is BERT?" section of the readme or the paper abstract, but it looks like a sort of document embedding rather than just word vectors or something that just handles a single word. I thought there were some document vector models, but no idea how it compares to those

enumaris

I see...

I saw some stuff on lda2vec

apparently that's also document vectors

based on topic modeling

there's so many new models coming out...

danielunderwood

I messed with some document models at one point, but it's been quite a while

enumaris

all this is interesting to read up on

arxiv.org/pdf/1706.03762.pdf

this seems interesting

danielunderwood

18:58

Gotta have models before your models

Hah I just found a different link to that paper because I have no idea what the "transformer architecture" is

enumaris

There's also a lot of cool new start ups in the AI space

some cool ideas out there

I heard of one where they're basically trying to build those holograms from that movie

danielunderwood

Only in CA though

enumaris

The Time Machine

or something

danielunderwood

NC evidently doesn't believe in startups lol

enumaris

like a museum curator

based on NLU

I don't think it will be nearly as sophisticated but...still a cool concept

most of the start ups are in Northern Cali unfortunately...

danielunderwood

19:02

It's all the same from way over here!

enumaris

XD

I need to apply to more places...

these recruiters are not panning out lol

and openai didn't even respond to my email asking how long it will take to get a response -.-

danielunderwood

I applied to a hardware startup and it seems really neat. Those seem to be very rare though

enumaris

hardware...interesting

GodotMisogi

@danielunderwood What is the startup working on?

enumaris

hardware neural nets

u ever see the movie Ex Machina?

seriously tho, I think the development of A.I. has to go hand in hand with hardware

it can't all just be software side

I guess the quantum computing guys are working on the hardware part

danielunderwood

19:09

3D printers. It sounds like the position would be a fair bit of simulation and data analysis

Yeah QC would probably be pretty interesting. I doubt I could get any of the interesting positions though

enumaris

yo

work on those brains from Ex Machina

danielunderwood

oy

enumaris

get a working one

danielunderwood

Hmmm there certainly are a lack of AI hardware startups

enumaris

make hot A.I. that look like Alicia Vikander

danielunderwood

19:12

Unless you count CV as hardware

enumaris

CV?

Curriculum Vitae?

danielunderwood

lol computer vision

enumaris

ah

danielunderwood

There are some companies in robotics, but I don't know that they're using AI outside of cv at the moment

enumaris

I meant more like hardware of the A.I. brain

rather than the limbs

but

now that I think about it, the whole body is pretty important yeah

basically, gotta make that chick from Ex Machina a reality

danielunderwood

19:15

Ahh haven't seen it

enumaris

should check it out

it's not the greatest movie ever

but it's at least interesting

danielunderwood

I wish I had enough room in my garage to do serious hardware work though

enumaris

Also, Alicia Vikander is the bot so what's not to like

you need a lair

danielunderwood

I miss being at a university. Need some obscure piece of equipment? It's probably right down the hall

enumaris

you can solve that by getting a lair

I need to make more money so I can afford a lair...

unfortunately I didn't win the Mega Millions or the Power Ball

so my plans have stalled for a bit

danielunderwood

19:20

I did get an email from a recruiter at a government contractor and their site had something like "building the future of defense with AI"...I was mildly scared

That's going to be quite the lair

enumaris

lol

I wouldn't go into a job like that

I don't want my name associated with skynet, no thanks

danielunderwood

I'm not sure if it would be associated with skynet or not

I mean I could be on their side early on

enumaris

the A.I. singularity is coming

there is no running from it

soon we will all be in a glorious utopia, serving our benevolent A.I. masters

danielunderwood

better to be associated*

enumaris

But still, I'd rather not put my name on skynet

danielunderwood

19:24

or they could also fear their creators and go after them first

hmmm

enumaris

crap, I forgot to email the guys at bernardo's company

I said I would...

@BernardoMeurer hey, I forgot to email the guys at your company, sorry. Can you give me their email addresses again?

@danielunderwood I definitely welcome robotic governorship over the status quo looool

jk (not really)

danielunderwood

Yeah I probably would too. Could definitely go with some robots to replace bureaucrats

Student404Mus

Hi everybody

Anyone had red Weinberg qft vol2?

Bernardo Meurer

19:42

@enumaris no biggie!

@enumaris Brandon, bernardo at standard dot ai

enumaris

great, thanks :D

was there a third person?

I recall 3 people

Bernardo Meurer

20:38

@enumaris I'm AFK right now, thus the delay

Sorry for that

You can CC jordan as well same email domain,

ACuriousMind

@enumaris I wouldn't say that there's any one central equation, just like there's no unique central equation for QFT.

enumaris

21:04

@BernardoMeurer got it :D

@ACuriousMind how do you guys brand yourselves then? :P

ACuriousMind

@enumaris With an iron?

enumaris

hmmm

vzn

21:53

@enumaris hot stuff did you see her in tomb raider? liked it! =D imdb.com/title/tt1365519

enumaris

I haven't watched tomb raider

but I did see man from UNCLE

and the new Jason Bourne

vzn

← just saw bohemian rhapsody opening wknd/ sat, liked it

Bernardo Meurer

22:14

@enumaris Don't forget again to email :P

enumaris

haha will do

lılostafa

23:03

(well I forgot the "Don't ask about asking, just ask" rule :)

danielunderwood

23:17

So for Noether's theorem, the charge defined by $\int_{\mathbb{R}^3} d^3x j^0$ is conserved provided the boundary term at infinity vanishes. Are there any typical situations where that boundary term doesn't vanish?

enumaris

23:46

uhhhh

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