The h Bar

Emilio Pisanty

13:01

In that connection, this is a good resource

Richard Feynman - The Character of Physical Law - 2 -The Relation of Mathematics to Physics

►

starting from about minute 15 or so, as I recall

(and that whole playlist is a must-watch anyway)

Sha Vuklia

@Emilio wow!!!

Emilio Pisanty

Or possibly it's the third lecture?

Sha Vuklia

I had no idea there were lectures online

Emilio Pisanty

can't remember it's been online

Sha Vuklia

I thought he only had the transcript online

Emilio Pisanty

13:03

@ShaVuklia Those aren't the Feynman Lectures from the book

those are seven public lectures

Sha Vuklia

ohh okay

Emilio Pisanty

much better than recordings of his course, to be honest, it's much more compact

Yashas

[Free feynman lectures on physics](http://www.feynmanlectures.caltech.edu/)

Sha Vuklia

yay thx @Yashas

Yashas

[test](test)

the chat malfunctioned: doesn't show me links :D

(test)[test]

Sha Vuklia

13:06

I'm reading Goldstein now as a recap for classical mechanics. I think it's pretty neat.

the only unfortunate thing is that we haven't had any vector analysis yet

AccidentalFourierTransform

test

it works for me

Sha Vuklia

so I have to study that on my own

for me too @Accidental

whaaaaattt

did i seriously just got rick rolled in a physics chat? :P

5

Yashas

Emilio Pisanty

@ShaVuklia people.virginia.edu/~ecd3m/1110/Fall2014/… from page 47 or so

Yashas

SE chat bugs are as weird as quantum mechanics

Sha Vuklia

13:07

LOL yea I already found out yesterday

Emilio Pisanty

particularly mid-page 49

0celouvskyopoulo7

I am using $\mathfrak O$ unironically

Emilio Pisanty

(as marked on the page)

Sha Vuklia

thanks @Emilio

0celouvskyopoulo7

wait

maybe I am using it ironically

can I be ironic about doing something unironically?

AccidentalFourierTransform

13:09

anything written by Feynman is a must read

user228700

Has anybody here experienced intense pain at joints/bones due to indigestion?

AccidentalFourierTransform

what did you eat!?

Jaime Gallego

Nitrogen

user228700

@AccidentalFourierTransform Everyday food cooked at home.

AccidentalFourierTransform

can Indians get an indigestion?

you people have a natural resistance to that, right?

0celouvskyopoulo7

13:13

@Kaumudi.H lol

Balarka Sen

@Kaumudi In the ribcage, yeah.

user228700

I've been trying to figure out what's happened but to no avail.

ACuriousMind

@Kaumudi.H That sounds like a case for a doctor.

Balarka Sen

Acid reflux does that.

user228700

@0celouvskyopoulo7 Thank you for ur sympathy.

0celouvskyopoulo7

13:14

@BalarkaSen did you not see my compact surface thing?

AccidentalFourierTransform

:-)

Balarka Sen

Nope.

0celouvskyopoulo7

23 hours ago, by 0celouvskyopoulo7

@BalarkaSen Interesting result of Minakshisundaram-Pleijel: Let $M$ be a compact surface, and $\lambda_j$ be the eigenvalues of the Laplacian. Then $$\sum_{j\ge 0}e^{-\lambda_jt}\sim \frac{\mathrm{vol}(M)}{4\pi t}+\frac{\chi(M)}{6}$$ as $t\downarrow 0$.

user228700

@ACuriousMind I phoned the doctor but she said that she can't see what the problem is, given that I don't have fever.

0celouvskyopoulo7

@BalarkaSen The spectrum of a compact surface completely determines what it is.

user228700

13:15

Just an inability to like, move or do anything. Typing also hurts like hell :'-(

Slereah

How come Reed and whatnot pretend that $\pi \approx \delta /\delta \Phi + \Phi$, but both Rovelli and Haag say it's just $\pi \approx \delta /\delta \Phi $

0celouvskyopoulo7

maybe tag ACM

Balarka Sen

@0celouvskyopoulo7 why do i care

Slereah

@ACuriousMind plz respond

user228700

So nobody, huh? Gah, I have no idea what to do now!

0celouvskyopoulo7

13:16

@BalarkaSen Because it's interesting?

ACuriousMind

@Slereah I don't know anything about the wavefunctional representation, really

Balarka Sen

why is it interesting

user228700

@BalarkaSen Man, you really couldn't care less, could you? Didn't even bother to capitalize the "i" :-P

Slereah

quite unfortunate

I guess it's time to ask PSE

0celouvskyopoulo7

@BalarkaSen Because the eigenvalues of the Laplacian determine the topology, regardless of the metric

AccidentalFourierTransform

13:17

what canonical algebra do they use?

Balarka Sen

@Kaumudi i'm just being honest :P gimme a reason to care and i'll

0celouvskyopoulo7

it's about as interesting as Gauss-Bonnet

AccidentalFourierTransform

$[\delta+\phi,\phi]\neq 1$

no wait

hmm

Slereah

$[\phi, \phi] = 0$

as u well know

Balarka Sen

@0celouvskyopoulo7 How does it "determine the topology"? It gives a topological constraint on the manifold to admit a Laplacian with a given spectrum. But why do I want to have a Laplacian with a given spectrum?

ACuriousMind

13:19

@Slereah it makes for a nice question, I think

You might even be lucky, someone like Valter Moretti might know

0celouvskyopoulo7

@BalarkaSen If I give you the eigenvalues of the Laplacian on a compact surface, you could in theory tell me which surface. If you don't think that's neat, ok.

Slereah

I'm fairly sure those two representations aren't unitarily equivalent

Balarka Sen

@0celo I might, it might be neat, I just don't know the Laplacian story well enough.

to appreciate it

0celouvskyopoulo7

It's not a fundamental result

But there's a long standing question in analysis: Can you hear the shape of a drum?

For compact surfaces, the answer is yes.

Balarka Sen

Oh.

It relates to that?

Slereah

13:22

That's the one

0celouvskyopoulo7

@BalarkaSen Yes, the harmonics of a drum are the eigenvalues of the Laplacian on it.

Slereah

Wait, actually Reed also mentions $\pi \approx \delta / \delta \Phi$

what's the difference between the two

Balarka Sen

@0celouvskyopoulo7 Interesting.

Phase

@0celouvskyopoulo7 what about a spherical drum

AccidentalFourierTransform

there is a factor of $i$ that looks suspicious there

Slereah

13:25

Apparently the difference might be that in the other rep, the vacuum state is just $1$?

AccidentalFourierTransform

something about hermiticity

0celouvskyopoulo7

@Phase That's a compact surface

Slereah

While in the "standard" one, it's a complicated thing

Phase

Wait so

Slereah

Ah, I see

Phase

13:26

You could have a spherical drum?

Slereah

It's two different Hilbert spaces

0celouvskyopoulo7

@Phase Probably not, the question is more philosophical in nature than practical

Slereah

$\pi \approx \delta / \delta \Phi$ is for the classic $L^2(\Bbb R^n)$

0celouvskyopoulo7

maybe refrain from calling QM classic

Slereah

While the more complicated one is for $L^2(\Bbb R^n, d\mu_k)$

for some measure

Phase

13:27

@0celouvskyopoulo7 well, drums just make sound by the surface vibrating up and down, wouldn't a spherical surface still somehow have states where the surface can oscillate?

Slereah

I think the measure is just the Gaussian measure

Phase

It would be hard to produce though

Slereah

Now the question is

@yuggib why were you bothering me about this

0celouvskyopoulo7

what did yuggib do?

Slereah

He was the one telling me that $\pi \approx \delta / \delta \Phi$ was not Proper

0celouvskyopoulo7

13:32

@Phase I don't think there would be a way to make it vibrate evenly

I'm not sure

girlphysicsmajor

1 3

Phase

@0celouvskyopoulo7 I imagine different parts would vibrate differently, if you want the entire surface to vibrate in some way

0celouvskyopoulo7

@ACuriousMind Jeez, what happened there?

ACuriousMind

@0celouvskyopoulo7 You know that we generally don't discuss specific suspensions in public.

Slereah

What is girl physics

0celouvskyopoulo7

I don't know, but there seems to be a deleted comment thread that's the origin of all of this

AccidentalFourierTransform

13:38

web-beta.archive.org/web/20170503034938/https://…

0celouvskyopoulo7

"I went to undergrad at MIT and grad school at Caltech. I get the feeling nobody here even has a degree in physics. :)"

I'm too stupid to post memes

Phase

Chrome wont even let me view the page

Fawad

:37134404 put ! Before URL to send that linked images

Phase

"Your connection is not private" joy

0celouvskyopoulo7

"Particle physics has failed since the 70s. Sorry to hear you were one."

sick burn

Phase

13:41

Can someone send me a transcript?

Or images or smthn

0celouvskyopoulo7

@AccidentalFourierTransform Is it letting you expand the comment thread?

AccidentalFourierTransform

nope

0celouvskyopoulo7

quickly

it will be deleted

Phase

thx bby

AccidentalFourierTransform

@Phase lol, why do you even use virgin

they are the devil

Phase

13:43

Well I'm at a Premier inn for a few weeks

If I had a choice I'd be on any other provider

Can someone go to Grad school and somehow not learn about Four vectors?

AccidentalFourierTransform

wat is dat

Phase

Grad school?

Idk but I assume its like a masters program in Europe

AccidentalFourierTransform

hmm

Phase

Undergrad surely would still force you to Learn four vectors

for SR

0celouvskyopoulo7

You don't know what grad school is?

It's a PhD program

AccidentalFourierTransform

13:48

I WAS ASKING WHAT IS A FOUR VECTOR

0celouvskyopoulo7

@AccidentalFourierTransform a 4-dimensional vector, clearly

do you not know relativity theory?

AccidentalFourierTransform

ಠ_ಠ

<|>

Phase

It's only relativity theory because it doesn't agree with reality

ACuriousMind

@AccidentalFourierTransform Is that...really necessary?

0celouvskyopoulo7

@ACuriousMind This is obscene.

Phase

13:51

Tesla is the future

Koolman

@Kaumudi.H Thanks , but we already had a talk

Slereah

Haag has a heuristic argument for the non-unitary equivalence of QFT but I'm not sure I get it

Leaky Nun

People, please don't misuse flags

@ACuriousMind hi

0celouvskyopoulo7

@LeakyNun Testicles are hardly appropriate for chat.

Leaky Nun

@0celouvskyopoulo7 alright, sorry

Phase

13:53

@0celouvskyopoulo7 testicles is a contentious topic it seems

0celouvskyopoulo7

Don't what

Slereah

He says that for some Fock space representaiton $n = (n_0, n_1, ...)$, $(n^{(1)})$ and $(n^{(2)})$ are equivalent if they only differ by a finite number of particles, and then... I dunno

Phase

Can't remember who but someone went on a bit of a rant about how it's only ok for some users to talk about them or something

Koolman

@Kenshin hello , how was your trip :-)

0celouvskyopoulo7

@Phase Daniel Sank; John Rennie.

Phase

13:55

@0celouvskyopoulo7 ok maybe "cant remember" was just a censor

rip

Slereah

the argument

0celouvskyopoulo7

@Slereah are you talking to yourself?

@NateStemen You have an unfortunate surname.

Phase

I've had a realisation:

Slereah

@0celouvskyopoulo7 I am only if you people don't answer

Rude

Phase

For like, 50% of the time, "The h bar" is just another maths.SE chat, but a topology specific one

0celouvskyopoulo7

13:56

I will help you with GR, not this

ACuriousMind

@Slereah What does "differing by a finite number of particles" mean?

Nate Stemen

@0celouvskyopoulo7 really, never heard that...

0celouvskyopoulo7

@NateStemen remove the t

Nate Stemen

@0c

nah not seeing it

sorry man

0celouvskyopoulo7

do you not know what that is?

Slereah

13:57

@ACuriousMind I'm guessing if $n^{(1)} - n^{(2)}$ is $\neq 0$ only in a finite number of places

Nate Stemen

nah never heard to it

0celouvskyopoulo7

strange, ok

you will one day

then you will think of me

Nate Stemen

omfg...

ACuriousMind

@0celouvskyopoulo7 Ew. Please don't deter newcomers to this chat like that :P

@Slereah Yeah, I'm reading the screenshot you posted

0celouvskyopoulo7

What's wrong with what I said?

Nate Stemen

13:59

@ACuriousMind right?

0celouvskyopoulo7

@Slereah How does one pronounce your last name, anyway?

ACuriousMind

@0celouvskyopoulo7 I can't find anything right with it.

@Slereah What are the $\Psi_{(n)}$?

Slereah

@ACuriousMind $(0,0,...,0,\psi(x_1,x_2,...,x_n), 0, ...)$

Leaky Nun

@ACuriousMind do you have interesting integrations?

ACuriousMind

@LeakyNun Sorry, but I don't understand the question - what's an interesting integration, and why might I have one?

@Slereah Uhhhhh...could you elaborate?

Slereah

14:01

Wait no

Let me check

ACuriousMind

I mean, $\Psi_{(n)}$ is a vector for a sequence $(n)$. I'd bet it's the one created from the vacuum by applying each $a_k$ $n_k$-times

Slereah

"Let $\Psi_n$ denote the normalized state vector corresponding to the occupation distribution number $(n)$. These vectors form a complete orthonormal basis"

Leaky Nun

@ACuriousMind oh sorry, wrong ping

0celouvskyopoulo7

@ACuriousMind I don't aim to be right.

Slereah

$$a_k \Psi_{(n)} = n_k^{1/2} \Psi_{(n - \delta_k)}$$

0celouvskyopoulo7

14:03

@Slereah ...proof?

ACuriousMind

@Slereah Ah, yes. Then I understand the argument

Slereah

Ah, I think $\Psi_{(n)}$ doesn't denote a specific state

Just "the state with distribution $(n)$"

Where $(n) = (n_1, n_2, ...)$

ACuriousMind

That is a specific state :P

Slereah

sure, but it could be any state

for a choice of $(n)$

ACuriousMind

Basically, what he's saying is that an irreducible representation of the $a_k$ is already given by choosing any $\Psi_{(n)}$ and taking the space spanned by all the other vectors created from it by applying $a_k$ or $a_k^\dagger$ to it.

Slereah

14:06

Oooh

And the usual QFT state we pick is the vacuum, isn't it?

ACuriousMind

Yep

Slereah

And I do know that for the study of topological defects, we pick the defect as the "background" state

So that's why that doesn't really work here

ACuriousMind

(Or you could pick any other state with $(n)$ in the same equivalence class. The point is that applying the $a_k$ only creates $\Psi_{(n')}$ states where $(n')$ is in the same equivalence class as the original $(n)$)

Slereah

But what about "infinite" operators made from them, such as field operators

Or exponentials of it or such

ACuriousMind

We're just talking about representations of the CCR, not about fields at this point.

Slereah

14:09

Alright

ACuriousMind

The second part of your screenshot is really neat. I never realised that one might encode a fermion state as a single real number between 0 and 1

Slereah

Representing quantum states as vectors in $\mathfrak l^2$ fell out of favor

I'm not sure why

0celouvskyopoulo7

I wonder how long I can keep a book without the library getting mad

oh nice, you can renew book loans online

user228700

@Koolman Ah, OK :-)

Slereah

Haag's argument for interacting theories is that for different values of the coupling constant $g$ of a field, the vacuum has to depend on $g$ (since its energy will vary with it), and if we had the same Fock representation, then $\Omega_g = \Omega_0$

Phase

14:23

Question: how do we even know that we can generate the conditions for fusion in such a way that there's an energy efficient way to do it?

AccidentalFourierTransform

:(

Slereah

@Phase look at the sky

Phase

But that's an immense gravitational field, my question is how do we know that we can create suitable conditions without needing more energy than we'd get out the fusion itself

AccidentalFourierTransform

I dont believe in the sun

Slereah

Well then we do not know!

Although with recent progress I think it's doable

we're getting pretty close to sustainable fusion

Phase

14:25

@AccidentalFourierTransform why not?

0celouvskyopoulo7

@Slereah Uh, I don't believe I've ever seen the sun in the night sky.

Phase

@Slereah reassuring

@0celouvskyopoulo7 God are you dumb? it gets colder and turns into the moon.

AccidentalFourierTransform

have you ever seen the sun?

I dont think so

0celouvskyopoulo7

And you haven't either.

Slereah

"This conclusion is usually referred to as Haag's theorem"

Don't play coy, Haag

You can just say it's yours

0celouvskyopoulo7

14:26

@Phase If I flag this you will get suspended.

Phase

Really?

0celouvskyopoulo7

I am talking to you as per @ACuriousMind 's instructions

@Phase Yes

But I am not supposed to flag without asking you to stop

Phase

I guess I should start using those upside down question marks

0celouvskyopoulo7

I have severe PTSD

Phase

I'm sorry for shaming you for your lack of Astrophysics knowledge, and the sun-moon duality of quantum mechanics

I've checked my flat-earth privilege

0celouvskyopoulo7

14:28

good

Phase

؟I respect your feelings؟

Slereah

"This means that the fields in an interacting theory are more singular objects than in the free theory and we do not have the canonical commutation relations."

nooo

ACuriousMind

@0celouvskyopoulo7 Why would you flag it? Don't just tell people "you'll get suspended", tell them why you would flag it in the first place.

0celouvskyopoulo7

He called me dumb

That's Not Nice

Phase

Yeah, I'm gonna flag you for not saying why you'd flag me

Get banned

0celouvskyopoulo7

14:29

go for it.

AccidentalFourierTransform

physics.stackexchange.com/help/badges/21/tumbleweed

Slereah

Yeah but no tattletales

AccidentalFourierTransform

can I get suspended for writing ω?

ACuriousMind

@AccidentalFourierTransform As you noticed, that depends on the context (as with most things). :P

0celouvskyopoulo7

yep

ACuriousMind

14:30

@AccidentalFourierTransform congrats :P

Phase

$$\mathbf{O\omega O}$$

AccidentalFourierTransform

$|ω\rangle$

it was a shitty question anyway

Slereah

it does look like a butt

Phase

@Slereah $|)\rangle$ nah

fuck

Slereah

The standard way to write a Hilbert ray that isn't $\omega$ is $\psi$

ACuriousMind

14:32

@Slereah Honestly, what did you expect?

Slereah

@ACuriousMind who knows

Can't the QFT people just switch to distribution algebras

Like sensible individuals

Then they can write all that without any problem

What is the equivalent of that problem in the non-relativistic statistical QM, by the way?

Since it's also infinitely many degrees of freedom

AccidentalFourierTransform

NRQM typically has finitely many d.o.f.

$2N$, where $N$ (fixed) is the number of particles

Slereah

Not if you have infinitely many particles

AccidentalFourierTransform

well in that case you have Haag as well

Slereah

Also you mean $2Nn$ with $n$ the dimension :p

AccidentalFourierTransform

14:37

I just reabsorbed the $n$ in the number $2$

Slereah

that's not a lot of dimensions

Or it's a very large $2$

AccidentalFourierTransform

$$\Huge 2$$

arxiv.org/abs/1705.00626

> We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field.

> The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then c…

neat

Slereah

Neat indeed

it's always hard to find good stuff for the full Pauli Fierz action

since it's infinite and nasty

AccidentalFourierTransform

no, its massless I think

the gauge-fixed massive graviton propagator is awful

its half a page long

Slereah

lol

Enough Haag for now, I should tidy up the flat

Phase

14:43

You know that user

who did the whole "physical entity" "fourth dimension" and "straight A's at MIT"

I think this might not be their first account

Look at this

0celouvskyopoulo7

Such accusations carry a serious penalty.

Phase

I said I think, and the link seems to be unnaturally similar to the other user

The other user also posted essentially this question twice on their "girlsciencemajor" or whatever account

It's just fishy is all I'm'a sayin

AccidentalFourierTransform

and you suggesting that girlsciencemajor is JD?

0celouvskyopoulo7

NO

Phase

Wait who's JD again?

Is this the guy who's voldemort?

0celouvskyopoulo7

14:46

Voldemort

ACuriousMind

@Phase We do prefer that you raise such speculations (if you think you have evidence) as a custom mod flag and not in public. It's not really constructive to accuse other users of sockpuppetry in public.

Phase

nice

oh, sorry I didn't really know there's a system for it.

How do I submit this flag?

ACuriousMind

There's no "system" in any specific sense, but in general, many concerns you have about the site that you feel you might want to bring up here actually either belong into a meta post or a custom mod flag.

Phase

Oh ok, nevermind then

John Rennie

@AccidentalFourierTransform: well I thought it was funny :-)

Phase

14:48

It's not that serious it just seemed too uncanny to not point out at least, given how it's also suspended

but I'll zip now

ACuriousMind

@Phase You'd just flag any post of either of the users with a custom flag explaining what the issue is.

AccidentalFourierTransform

@JohnRennie what's it?

Slereah

the question is, if I pick an arbitrary Fock state and use the usual CCR of the ladder operators, can I work out QFT in general?

a bit vague but I'm not quite sure how to express it

AccidentalFourierTransform

go review the rules of differentiation. — ILoveMath 11 hours ago

John Rennie

@AccidentalFourierTransform your, erm, emoticon

0celouvskyopoulo7

14:51

of course you did

John Rennie

Did you get suspended for it, or was the post just deleted?

AccidentalFourierTransform

ah, the ω!

YES I WAS SUSPENDED BUT I WOULD DO IT AGAIN

Phase

Sorry, what happened?

Is this post still around?

ACuriousMind

Jeez, why is everyone so keen on drama today? Chill out, people.

John Rennie

@AccidentalFourierTransform I had never seen that emoticon before and I have to confess I laughed out loud, which is not my usual response to the physics chat.

0celouvskyopoulo7

14:54

sick

@ACuriousMind I think you know why.

Phase

It's not for the sake of drama, I just want to know what the emoticon is. Also, @ACuriousMind what's the deal with this should I try and edit it or just flag it

AccidentalFourierTransform

no, my figurine is legless

0celouvskyopoulo7

@Phase It was a man with large testicles.

Slereah

What is this... figurine... doing in my... house???

Phase

@0celouvskyopoulo7 Well there we go

AccidentalFourierTransform

14:55

2

look what you did

0celouvskyopoulo7

I don't know why people think such things are funny

ACuriousMind

@Phase Uh...you should edit it if you think the end result will be on-topic, otherwise you should flag it.

@0celouvskyopoulo7 I have genuinely no idea

John Rennie

it was a / followed by a lower case omega (presumably the unicode character ω) then a \
It looked uncannily like a logogram of a spectacularly large pair of testicles. Try typing it and you'll see.

0celouvskyopoulo7

$\Upsilon$

Phase

What's the protocol for actually changing questions by editing

This is all I could think of that would even partially make it valid

Changed wave to field and stuff

Also missed typos, corrected them now

Fawad

14:59

@ACuriousMind status-declined

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