The h Bar

0celo7

12:01 AM

@NeuroFuzzy What is $H|0\rangle$?

NeuroFuzzy

12:25 AM

@0celo7 $H$ is the imagined inverse of Dirac's procedure that goes from the hamiltonian to the path integral.

0celo7

What

I mean the Hamiltonian

what are you talking about

NeuroFuzzy

Well when he writes down the Lagrangian densities for fields, things such as "what kind of space does $|0\rangle$ live in$ and "can you actually define a Hamiltonian from this" aren't clear. (right, because "H" is an operator but "L" is just a density on $q,\dot{q}$ space.)

I thought you were criticizing the rigor. But anyways

0celo7

uhh

NeuroFuzzy

$H_J|0_J\rangle=E|0_J\rangle$.

0celo7

No no, I mean when there is no source

NeuroFuzzy

12:30 AM

Oh, then it would be $H |0\rangle=E|0\rangle$ with $E$ the energy of the vacuum. Which, as I'm approaching it, I just treat as a formal symbol/undefined

since I expect infinities.

0celo7

What the heck is the vacuum then

This is a problem I have with Zee

He never says what the heck $|0\rangle$ is...

NeuroFuzzy

@0celo7 I think you could write it down in the quadratic case

it would just be a superposition of field configurations

0celo7

What

What is the definition of $|0\rangle$

NeuroFuzzy

@0celo7 I'm correct in assuming you're not going to accept "the lowest energy eigenstate of $H$"?

0celo7

No, why should it have a lowest?

NeuroFuzzy

12:36 AM

but that's what it is. If you want, discretize space and make space finite

0celo7

And why should there be one lowest, assuming there is one at all?

NeuroFuzzy

then apply nonrelativistic quantum mechanics

Lol, that's when you break out assumptions like keeping the case quadratic

I don't think that line of questioning is useful. And yeah, if you had a Lagrangian like $-\phi^2+\alpha \phi^4$ you would have other minima.

but for the quadratic case it's all well and good. For phonons in 1D the ground state is something like $e^{-\phi_1^2-\phi_2^2-\cdots}$

0celo7

That's not a state...

NeuroFuzzy

@0celo7 Nitpick. Surely you know what I mean. $\langle \{\phi_1,\cdots \phi_N\}|0\rangle\sim e^{-\phi_1^2-\phi_2^2-\cdots}$

0celo7

I dont know what those $\phi$s are

NeuroFuzzy

12:44 AM

In what I'm referencing, the 1D phonon case, they're supposed to be interpreted as displacement from equilibrium on a 1D lattice

displacement of particles

0celo7

Ah, I finally sat down and proved that the tangent bundle is always an orientable manifold.

Wonderful.

NeuroFuzzy

@0celo7 Sorry if I'm not being clear. I'm talking about something like this physics.ucsd.edu/~mcgreevy/w15/130C-2015-chapter03.pdf section 3.2.1

0celo7

Took me a year

Balarka Sen

...

On a serious note, good job.

How did you do it?

NeuroFuzzy

I'm totally fine with imagining the continuum limit of that, even though $(L^2)^{\otimes \infty}$ is hard to grasp.

0celo7

12:46 AM

@BalarkaSen I explicitly calculated the determinant of the transition functions.

It didn't take me a year to do it, btw

Balarka Sen

Ugh

0celo7

I heard that first a year ago, and just today sat down and worked through it.

NeuroFuzzy

Ugh I have to read stuff for my final tomorrow

I have to force myself off stackexchange...

0celo7

@BalarkaSen I know there's a fancy exact sequence argument

NeuroFuzzy

QFT is way more fun than political science :(

0celo7

12:48 AM

@BalarkaSen Do you want to see my calc?

Balarka Sen

Sure.

0celo7

Let $\{(U_\alpha,\mathbf x_\alpha)\}$ be an atlas for $M^n$

We get charts on $TM$ in the standard way: $\mathbf y_\alpha:U_\alpha\times\Bbb R^n\to TM,(x_1^\alpha,\dotsc, x_n^\alpha, u_1,\dotsc, u_n)\mapsto (\mathbf x^\alpha(x),u_i\partial_i^\alpha)$, where $\partial_i^\alpha=\partial/\partial x^\alpha_i$.

summation implied.

Balarka Sen

Yes

0celo7

Let $(p,v)\in \mathbf y_\alpha(U_\alpha\times\Bbb R^n)\cap\mathbf y_\beta(U_\beta\times\Bbb R^n)$.

(we're calculating the chart overlaps now)

Then $(p,v)=(\mathbf x_\alpha(q_\alpha), D\mathrm x_\alpha (v_\alpha))=(\mathbf x_\beta(q_\beta), D\mathrm x_\beta (v_\beta))$, for some $q_\alpha\in U_\alpha, q_\beta\in U_\beta, v_\alpha,v_\beta\in \Bbb R^n$

Then $\mathbf y_\beta^{-1}\circ\mathbf y_\alpha(q_\alpha,v_\alpha)=(\mathbf x^{-1}_\beta\circ\mathbf x_\alpha(q_\alpha),D(\mathbf x^{-1}_\beta\circ\mathbf x_\alpha)(v_\beta))$

that's hard to type, Jesus

@BalarkaSen believable so far?

Balarka Sen

Yes, but you're done, no?

0celo7

12:56 AM

yeah, the Jacobian of that is $(D(stuff))^2$.

Balarka Sen

Derivative of that is positive because derivative of the transition functions downstairs is positive.

0celo7

I guess you have to "prove that"

@BalarkaSen downstairs?

Balarka Sen

On $M$.

0celo7

The manifold is not assumed to be orientable

Balarka Sen

But of course.

0celo7

12:58 AM

What

The tangent bundle is always orientable as a manifold, that's what we're showing.

Balarka Sen

Yes, orientability of $TM$ is independent of $M$, I am being dumb

0celo7

Do you see what the determinant of that thingie is

Balarka Sen

Can't say I do.

0celo7

If you break it into blocks, you get $D(\mathbf x^{-1}\circ\mathbf x)$ as the diagonal two blocks

Balarka Sen

Yeah.

0celo7

12:59 AM

The top left block is the derivative of the transition function wrt the $x$ variables

The bottom right is the derivative of the transition functions wrt the $v$ variables

But it's linear in $v$, so you just get back the derivative

Then one of the off-diagonal blocks is the derivative of the transition functions wrt. the $v$ variables, which is zero

the other block does not matter

Balarka Sen

Ah

0celo7

when you take the determinant you get $(D(x^{-1}\circ x))^2$, which is clearly positive.

Balarka Sen

Right.

I was worrying about the off-diagonal blocks, but as you said, of course that's zero.

0celo7

you just need one off-diagonal block to be zero, too

Balarka Sen

True

0celo7

1:02 AM

(which is the case here, the other one will not be zero)

The next thing is to prove rigorously that $T(M\times N)\approx TM\times TN$.

I've always taken that for granted

Balarka Sen

That's quite clear.

0celo7

Is it?

The tangent space thing does not imply that immediately.

Balarka Sen

Just write down a tangent space wise decomposition, and show that it's also smoothly varying

0celo7

That's the part I'm concerned about

"smoothly varying"

Bott & Tu seems to be fine, btw.

Balarka Sen

@0celo7 Write down a bundle isomorphism locally.

0celo7

1:10 AM

@BalarkaSen Sure, it's the details I don't know. I'm not too concerned with that right now though

Trying to understand the "compact vertical cohomology" of vector budles

Balarka Sen

No idea about that.

0celo7

Me neither

What time is it where you are

Balarka Sen

6:43AM

I have turned into a complete nocturnal creature, yes

0celo7

@BalarkaSen Why don't you get that small Ricci flow book so we can discuss

I'm thinking about giving it a good skimming

Balarka Sen

What is the book?

I am not sure if I have background

0celo7

1:14 AM

Skipping some of the algebraic geometry they use, of course

amazon.com/Sphere-Theorem-Graduate-Studies-Mathematics/dp/…

Hmm, I think you do have to know some Riemannian geometry

But you can pick it up quickly I imagine

It's more geometrical than the analytic "Hamilton's Ricci Flow"

Balarka Sen

Sounds like too much work, and not quite in my list of interests.

0celo7

I'll check with my advisor to see if he's read it

If he has, I'll likely get it

I'm 99% sure I've seen it next to his desk.

Balarka Sen

You should tell me about the Poincare-Hopf theorem.

0celo7

I didn't read about it in GP, I read about it in Milnor's other book

the diff topology one

Balarka Sen

Sure, Milnor's diff top is a concise, but good book.

I like it.

0celo7

1:21 AM

And in Morse theory he relates it to the homological Euler characteristic

I didn't understand the details there, of course.

Basically, given a vector field that has no zeros, you can scale it down to a unit vector field

Balarka Sen

So, do you want to go through the statement/proof with me? I have Milnor with me if it helps.

0celo7

On an $n$-dimensional manifold $M$, you get in this way a map $v:M\to S^{n-1}$

@BalarkaSen Let me grab a copy of Milnor from the library (I'm in it)

Balarka Sen

If not, it's fine. Otherwise, can we start a bit later? I got some stuff to get done.

0celo7

Ok

So you study the degree of that map

And we should assume $M$ is compact for Milnor's proof to work

Balarka Sen

My manifolds are compact :P

0celo7

1:26 AM

Wonderful :D

Balarka Sen

Thanks, I'll ping when I am free.

0celo7

Oh shit I have homework to do

Balarka Sen

That's what I am doing, coincidentally :P

0celo7

The library has a wonderful hardback of this book

I am jealous of the hardbacks they have

lucas

1:57 AM

@knzhou Hi

@knzhou All of us make mistake sometimes. If we don't forgive each other, we cannot live happily.

0celo7

What's the point in living if we cannot hold grudges

no_choice99

understanding the universe

i.e. study physics

that's the goal.

0celo7

that's a terrible reason

no_choice99

I've learned to live with it

0celo7

I'm starting to despise physics

no_choice99

2:09 AM

"trying to understand the universe". the best thing I could live for

you may need a break, but you'll come back

0celo7

Doubtful

It is a fundamental disagreement

no_choice99

I tried reading sci-fi the other day (I, robot from Asimov), it's extremely low level compared to physics

I don't know if something better than physics exists

0celo7

Mathematics.

Engineering.

no_choice99

try your way out of physics. oh yeah math...

math is also "serious enough"

0celo7

@BalarkaSen I'm done, ready whenever you are

no_choice99

2:12 AM

maybe even computer science

0celo7

(if I don't write back I'm on the toilet, printing something out, or walking)

peterh

@no_choice99 It was written in a 60s or in the 70s for young guys who didn't have any contact with the physics until then. Now they are maybe engineers and physicsists. On my opinion, popularizing science is very important, more important as the scientific accuracy.

no_choice99

enjoy your break @0celo7

@pereth

Balarka Sen

@0celo7 Sorry, don't think I am going to have much time this morning, I remembered I had more work to do than I thought at first. I'll get back to you after school.

0celo7

Ok

no_choice99

2:13 AM

it was written in the 50's I believe. yeah, he completely mispredicted the future (I don'T blame him at all for that) but the basis of the book from which the stories are built are shaky IMO

like the 3 fundamental laws of robotics which aren't well defined IMO

0celo7

Are they consistent with ZFC

no_choice99

and this stuff I cannot allow

what's zfc

knzhou

@lucas Hi!

no_choice99

I was pushed toward that book. extremely disappointed. I am about 15 pages from the end

lucas

@knzhou :-)

no_choice99

2:15 AM

my next book is going to be a textbook for sure

knzhou

Don't worry, all is forgiven. :P I dip into this chat room for a minute at a time, so I tend to not see messages until much later.

no_choice99

read the first page of a solid state book vs the 1st page of asimov'S book is like day and night

lucas

@knzhou Thanks a lot! You are so kind! :-)

no_choice99

I've heard a lot of physicists praise sci-fi from asimov because the book "makes somewhat sense", I didn't find this in "I, robot". ok, it's only 1 book and I should try others from him... but i won't try one of his book anytime soon

peterh

@no_choice99 It is funny to see, how Asimov's world mirrors the technical level of his era. For example, the robots were analogous machines and logical contradictions could cause physical harm in their brains.

no_choice99

2:19 AM

analogus machines? hmm but their brains were positronic (without more details)

peterh

@no_choice99 Well, the particle physics wasn't his strength. First the positronic brains, he probably didn't know the annihillation. Second, somewhere in a later novel he wrotes about a virus what contains radioactive isotopes in its DNA.

no_choice99

i don't really know how to interpret a positronic brain

it's sci-fi so I don't blame him if he ignores annihilation

but he never defined "harm done to humans" for instance.

to me the laws of robotics are a bit shaky, not really well defined and the whole book is based on them

that is why i really didn't enjoy the book so far.

peterh

@no_choice99 As I know, he was biochemist, and nuclear physics was a new thing at the time, probably he didn't take any course from that. It is also very interesting to see, how he overestimated the speed of the technological development.

no_choice99

yeah i don't blame him at all for that

I can understand it. and I can just add a 300 to 400 years in all dates in the book to make it a little bit more realistic ^^ it's not the problem

but the laws of robotics are too vague

program a robot so that they obey vague laws.... I can't grasp this

it makes no sense to me

peterh

@no_choice99 Btw, if our current robots would be already on the level, as Asimov thought realistic for the 80s, these problems (what is harm, what is human) could be also hard for them. Some border cases are hard even for us.

no_choice99

2:24 AM

yes

peterh

@no_choice99 But they wouldn't die while mist is coming from their heads, they would do only silly things.

@no_choice99 Asimov were also quite optimistic. There is no plan or even trace that a First Law would be inserted into the robots. Actually, the task of the most well known robots, the military drones of the U.S. military, is to kill humans. And there is fast development on humanoid military models, too.

no_choice99

true @peterh yes I've heard of the nsa's skynet's program

the one that could kill or did kill humans based on a machine learning analysis of terrorist behaviors in humans in pakistan or so

with a high false positive rate

peterh

@no_choice99 Once I've heard a university professor, pridely explaining, that his son is working on such a military project. It didn't seem so, if he had any ethical problem with it. I've seen only a fater being pride for his sons "result".

no_choice99

this is ridiculous

0celo7

@peterh Are you German?

peterh

2:33 AM

No, .hu :-)

I can understand Paul Erdos in original .-)

no_choice99

hungarian?

peterh

Yes

Why?

you?

no_choice99

viktor toth wrote a blog post about the skynet program i think, he was born in hungary. he's one of the guys who solved the pionneer anomaly ^^

0celo7

@peterh Freedom.

peterh

It is a hungarian name. Many are working in the US and in West Europe (I am also in Germany) in R&D things. It is the current largest problem of the government, they can't pay enough for them to remain home.

no_choice99

2:35 AM

check this out spinor.info/weblog/?p=7589

c u guys im done for today

peterh

@no_choice99 I check. Good night! (Or afternoon, in the USA)

vzn

3:07 AM

in theory salon, 4 hours ago, by vzn

ruby statsample/ multiple regression setup / Tmachine blog

does anyone work with python sci comp/ statistics? wondering how it compares...

@peterh ?!? "ethics"? what are you, an alien? unamerican? $$$ is all that matters :P

0celo7

Correct.

vzn

@no_choice99 somewhat of a fan myself. fyi he had a phd in biochemistry. his writing maybe has not aged as well as some other writers eg dick or orwell etc. ... also his predictions on economics are way off, the idea that robots would save ppl workweeks is laughably erroneous. but he was far from alone on that one. (jetsons, anyone? etc)

@0celo7 aka GDP :P

peterh

@vzn It was a Hungarian prof in Budapest, reaching an U.S. military development project is a very hardcore thing there. The problem is, that this project... well...

vzn

@peterh lol sssh! or the men in black will show up o_O

0celo7

@vzn Nothing is more important than GDP.

vzn

3:15 AM

@peterh US warma$hine out of control since atom bomb over ½-century ago :(

0celo7

@vzn Watch your mouth.

peterh

They aren't a danger for us, because we aren't an enemy for them.

We are slaves for them.

Resource.

vzn

← just bought new feynman bio from caltech bookstore few wks ago, reading it, highly recommend it

@peterh all humanity is an "enemy" of the warma$hine :P

peterh

Btw, what Asimovs maybe largest mistake was: he thought, our Frankeinstein-complex is hard. No, it isn't. It is quite negligible compared to our urge to kill eachother.

vzn

@0celo7 whats wrong, are you on the take?

0celo7

3:18 AM

On the take?

peterh

Thus, the world leader in the robot development is the U.S. military, and their robots surely won't contain any similar as the First Law.

vzn

@peterh its not hypothetical or a future scenario, they already have extremely high-tech/ lethal robots "advancing" as we speak in more ways than one vzn1.wordpress.com/2016/07/15/…

see that you pointed that out above

@no_choice99 try daniel wilson, he has some writing & a recent fiction compilations, bought it, on my to-read pile, have read some of his earlier books, very hilarious

peterh

Jihadi John was killed to show, that the drones are killing the bad guys. But the truth is, the drones are killing the enemies of the U.S., and these and the bad guys are different sets, with some intersection.

vzn

@peterh (in 0celo7ian terms...) its all f*** ed up, its all a huge clusterf ***

0celo7

4:04 AM

DJ KAHLED ALBUM WOOOOOO

@vzn when have I said that?

vzn

@0celo7 311! chat.stackexchange.com/…

0celo7

No, clusterfuck.

vzn

@0celo7 chat.stackexchange.com/…

0celo7

See.

vzn

@0celo7 maybe you should go to a concert sometime

vzn

4:42 AM

@peterh just ran across this Neil DeGrasse Tyson Cozies Up to the U.S. Military Machine / alternet... was recently thinking he might make a dream guest spkr around here... o_O

Danu

6:32 AM

@ACuriousMind Sudan university... hmmm

@BalarkaSen I told you already, didn't I? Complex geometry, characteristic classes and more topology.

John Rennie

7:16 AM

@Danu I was born in Khartoum - my father was working there. I've never been tempted to go to Sudan University though.

lucas

Who does do this? A moderator?

John Rennie

Incidentally Michael Atiyah lived in Khartoum when he was a child. Before my time though. We went to the same primary school in Khartoum.

lucas

Morning @JohnRennie

:-)

Danu

@JohnRennie Ψοολ

*Cool

@vzn I don't think he actually is a great physicist (he has like... 1 publication).

@lucas Nope, it's automated (that's why it tweets bad stuff often)

lucas

@Danu Thanks a lot!

user54412

8:55 AM

Perhaps someone can explain what's going on here

3

user54412

3

Q: Is the deformation of spacetime, elastic deformation or plastic deformation?

Is the deformation of spacetime, elastic deformation or plastic deformation?

user54412

The question makes no sense whatsoever, yet it and its 4 answers bring in a surge of upvotes.

user54412

You'd also be hard-pressed to come up with any question for which those 4 could be meaningful responses.

Secret

9:11 AM

@ChrisWhite
We knew that speacetime will be warped under the influence of energy momentum (described by the riemann curvature tensor, and the relation given by the einstein field equation). But is such warping unlike anything we are familar with, thus we cannot say it bends like a piece of clothing fabric, or plaster or some other material

That is, is the warping of spacetime kinda an abstract thing that can only be accurately described using the riemann curvature tensor, without resorting to any type of thinking that spacetime act like some kind of material?

Danu

10:12 AM

@ChrisWhite Very strange indeed

I'm in a mood for conspiracy

John Rennie

10:27 AM

Anyone want a cyclotron?

4

kickstarter.com/projects/1989795590/…

Spoiler: it's not actually a cyclotron

Balarka Sen

@Danu You did, yes. I guess I was asking for something specific, but I suppose you haven't planned yet.

Danu

@JohnRennie that's like... a 10k+ bike haha

@BalarkaSen I know specifically which books, and I've started.

How much more specific would you think?

Balarka Sen

Dunno, it's probably unfair to ask about specific things when one has just started.

Will ask you 2 weeks later :P

Danu

I mean... It'll just be (chapter X from book Y)

I don't know what you're expecting

Balarka Sen

By "specific", I meant "any interesting-looking specific thing from whatever you're studying which you're pondering on right now".

lucas

10:36 AM

@JohnRennie Have you come back to your previous decision (ignoring)?

Balarka Sen

I don't really study stuff chapterwise or cover to cover; rather, I go through a few problems (either exercises from the book or self-ponderings). Not sure if everyone does that.

@ChrisWhite I'd say multiple accounts but that's too big a conspiracy to be real, I think.

lucas

@JohnRennie I don't know which fault have I done after our last conversation. After that time, I just have said you "Hi", "Good morning", etc.

John Rennie

@lucas Hi Lucas, I'm not ignoring you. I often leave the chat page open without looking at it so I sometimes miss pings. If I missed a ping from you I apologise.

lucas

@JohnRennie No need to apologies! I was so worry! Just this. You made my day! :-)

John Rennie

At the moment I have a big programming job to do, so I'm only on the Physics SE intermittently. Basically when the code has started to swim before my eyes and I need a break :-)

lucas

10:51 AM

I think you sleep less. I see you before 05:00 usually.

ACuriousMind

@Danu I fear the answer is much more pedestrian - it was tweeted by the Twitter bot 13 hours ago which attracted some people who have no idea what they're talking about :P

John Rennie

@lucas I start work about 5 a.m. I still get the usual amount of sleep but it means going to bed about 9 p.m. That's why you never see me in that chat after 9 p.m.

lucas

@JohnRennie So, you sleep more than me!!! I usually sleep 5 hours.

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