The h Bar

0celo7

12:00 AM

Try?

I just did.

Sir Cumference

I'd say the only useful sciences are biology and applied physics

And biochemistry

0celo7

chemistry in general probably

Sir Cumference

Maybe

0celo7

@BalarkaSen Should I do QM or topology homework

Sir Cumference

But even so, theoretical physics can be insanely interesting. Sure, you can't make much use out of the constituents of the entire Universe, but most people have a genuine curiosity to understand the Universe

That's what philosophy and religion are here for

0celo7

12:02 AM

what are you on about

Sir Cumference

Point is: astronomy and theoretical physics are useful in that regard

Balarka Sen

Sorry, was afk.

Sir Cumference

All right, now I need someone who knows GR pretty well

Balarka Sen

@0celo7 I don't really want to check it right now, partially because it's 5 in the morning. Sorry.

@SirCumference I do pure math.

@0celo7 Topology.

@0celo7 We'll see about that after the WWIII starts.

Sir Cumference

@BalarkaSen Give it a year or so

Trump might be president

Balarka Sen

12:06 AM

Yup.

And with all these terrorist activities already...

0celo7

@BalarkaSen that's much harder though :(

problem 1 was done in class lol

(QM homework)

2physics

@BalarkaSen May I ask a question?

Balarka Sen

Sure.

0celo7

Huh?

The mistake is that it's not Hermitian, wtf is this "time dependent problem" he's on about

2physics

about numbers

not a question actually cuz I just found the answer lol

user218912

12:17 AM

@0celo7 can the kronecker delta raise and lower indices?

2physics

I was thinking if we can have a system of just rational numbers. I mean imagine we just use rational numbers. but then I realized that something like trigonometry produces irrational nos again

Balarka Sen

I mean, that's a vague question. What does a "system" mean? $\Bbb Q$, the set of rational numbers, is a fine set by itself. If you want to impose further structure on it, then you'll soon have to add irrationals.

0celo7

@IceLord I won't respond to bad questions.

@BalarkaSen QM homework is nice, two problems were fully solved in class.

Balarka Sen

E.g., if you want your "system" - whatever that means - to contain a root of $x^2 - 2 = 0$, you automatically add an irrational $\sqrt{2}$.

So not even trigonometric functions are necessary at this point. It all depends on what you want to do with your system.

user218912

@0celo7 how is that a bad question?

user218912

12:20 AM

because I need it to contract with another tensor.

user218912

is that illegal though?

2physics

yea. you imagine we only have Q. but when you for example want to find the length of the hypothenus of a triangle which its sides are equal to 1, it faces you with an irrational no to find it

Balarka Sen

Sure

Note that even $\Bbb R$ is not a "system" in that sense, as it doesn't contain any solution of $x^2 + 1 = 0$.

So you extend to $\Bbb C$, the complex numbers.

there's a theorem that it's as far as you can go up. namely, fundamental theorem of algebra

2physics

I was thinking somehow light speed is similar to irrational numbers. because probabably you cant find it exactly

user218912

@0celo7 ur mean

user218912

12:22 AM

:(

2physics

@BalarkaSen yup

Balarka Sen

Alright, it's crack of a dawn here and I should sleep

2physics

ok. good night

I mean sweet dreamssss

user218912

@0celo7 it would still not be hermitian if you remove the last term right?

0celo7

@IceLord Because it is.

You don't understand what contraction is, clearly.

user218912

12:34 AM

@0celo7 explain please :(?

0celo7

1:04 AM

@IceLord Nah.

Try explaining to me why you can contract

I'll tell you if you're right or not.

Sir Cumference

1:51 AM

I just realized

Monkeys made it to space before we did without even trying.

0celo7

@ACuriousMind halp

@SirCumference ...what

Sir Cumference

@0celo7 google.com/…

0celo7

so?

Sir Cumference

So technically the animal kingdom beat us in the space race

Using our technology, nonetheless. Clever.

DanielSank

@2physics @Sanya and others: I wrote my latest paper by putting the TeX source on github. This allowed myself and my two collaborators to simultaneously work on various parts of the paper, review each others' changes, and organize our work via the github issue tracker system. This was incredibly efficient and pleasant.

I wonder if Word could support such a workflow.

dmckee

2:15 AM

@0celo7 You set the energy of the initial state (AKA the mass of the parent nucleus) to the energy of the final state (the sum of the masses of the neutrons and heavy fragments plus the KE of the neutrons plus the KE of the fragments). Done and dusted.

Sir Cumference

@BernardMeurer Please tell me that's a reference to what I'm thinking of

user218912

2:28 AM

@SirCumference you're implying humans aren't animals and are not part of the animal kingdom?

Sir Cumference

@IceLord True, true

user218912

wow.

Sir Cumference

I mentioned my realization in another chat btw

I got the response "i'm not necessarily one for political correctness but it seems kind of racist to call the Russians 'monkeys'"

user218912

link?

Sir Cumference

Don't remember, it was this morning. Might've been on space exploration or some other science chat

user218912

2:30 AM

@SirCumference wait so you think humans are somehow special compared to other animals?

Sir Cumference

@IceLord Well we managed to fuck up our entire planet

I'd say that separates us from the other animals

Both technologically and intellectually

user218912

why?

Sir Cumference

We're the only ones both smart enough to figure it out and dumb enough to do it

0celo7

@SirCumference proof?

Sir Cumference

@0celo7 get out of here

Trump supporter

0celo7

2:34 AM

bold, bold claim

"fucked the planet"

Sir Cumference

I can't begin with this

there is no saving you if you believe climate change is a myth

0celo7

That immediate strawman

Nice!

Sir Cumference

Sigh...all right, what do you have to say?

0celo7

Nothing, you just keep going

Sir Cumference

@0celo7 I...I...stop

@0celo7 This is not nothing

DanielSank

2:38 AM

@SirCumference I would disagree. Humans are animals.

user218912

@DanielSank disagree with who?

Sir Cumference

@DanielSank Icelord said that

DanielSank

@IceLord Oops, pinged wrong person.

fixed

Sir Cumference

@DanielSank I...I never said they weren't

DanielSank

Then I retract my comment.

0celo7

2:40 AM

I'm not an animal

user218912

@SirCumference uhhh yes you did

Sir Cumference

@IceLord Quote?

user218912

by saying that you implied that they are not animals.

user218912

otherwise how could the animal kingdom beat us when we're part of it?

DanielSank

@IceLord Actually, he did not.

@IceLord I could say "My family beat me to the ice cream store".

Sir Cumference

2:40 AM

And when you mentioned humans being animals, I said "True, true"

DanielSank

That doesn't mean I don't regard myself as part of the family.

Hello @KaumudiHarikumar. How is your studying?

user218912

@DanielSank fine.

Sir Cumference

@DanielSank Huh, good analogy

Anyway, how are y'all?

0celo7

Got too much to do

user218912

@SirCumference did you go to university/college this year?

DanielSank

2:42 AM

@SirCumference It was a natural one, since the animal kingdom is a sort of family.

Sir Cumference

@DanielSank True

DanielSank

Animals are amazing!

Sir Cumference

@DanielSank Got a favorite?

DanielSank

@SirCumference You have to ask?

Sir Cumference

Guessing octopus...

Yeah...

0celo7

2:43 AM

how'd you guess that?

DanielSank

Other good ones: chameleons, polar bears, monarch butterflies.

Sir Cumference

@0celo7 I'm omniscient

user218912

@0celo7's favourite animal is an ocelot.

user218912

am right?

0celo7

No

Sir Cumference

2:45 AM

@0celo7 Schrödinger's cat?

0celo7

@SirCumference What?

user218912

that's not a species of cat.

0celo7

I'm not a nerd.

Sir Cumference

What are you doing on this chat then?

user218912

^

0celo7

2:46 AM

I ask that all the time

@DanielSank How do I actually use the Heisenberg EoM to solve for the time-dependent operators?

Like, I have $$\frac{d S^x(t)}{dt}=\frac{\omega}{\mathrm i\hbar}[S^x(t),S^z]$$

But what then!?

Ah

$S^z$ commutes with the evolution operator.

user218912

@0celo7 why is there an $\omega$ on the numerator?

DanielSank

@IceLord Because @0celo7 made a mistake.

0celo7

I did?

DanielSank

The better question is why is there an $\hbar$ in the denominator.

0celo7

Because that's what the Heisenberg EoM is?

$A'=(i\hbar)^{-1}[A,H]$.

DanielSank

2:54 AM

@0celo7 Uh huh, and what are the dimensions of each side of that?

0celo7

@DanielSank hbar over time.

So, energy?

DanielSank

@0celo7 Wat?

$A'$ has dimensions of...?

Oh wait a second. What are the dimensions of $S^x$ in your land?

0celo7

action

DanielSank

k

0celo7

@DanielSank Check Shankar page 490 if you don't believe me

DanielSank

2:56 AM

Sorry, I was reading $S^x$ as $\sigma_x$.

user218912

@DanielSank do you have to set $\hbar = 1$?

DanielSank

@IceLord Nooooooooooooooooooooooooooooo

0celo7

lel

@DanielSank ok.

DanielSank

I was mistaken. @0celo7's equation is fine.

user218912

I still don't understand why there is an $\omega$.

DanielSank

2:58 AM

@IceLord He implicitly wrote the Hamiltonian as $\omega S^z$.

Sir Cumference

Guys, we've been funding space travel wrong this whole time. This guy's got it right:

kickstarter.com/projects/1553181191/…

0celo7

@DanielSank yeah

user218912

@DanielSank oh okay.

0celo7

dmckee

Worth keeping in mind George Carlin's wisdom on the matter of "saving the planet":

0celo7

3:00 AM

@DanielSank So now just solve the coupled equations?

dmckee

> "The planet is fine. The people are f%@$ed!"

user218912

@0celo7 I don't get that why is there an $\epsilon_{ijk}$ there?

0celo7

@dmckee That's exactly what I had in mind.

@IceLord You do not belong in a QFT class at all.

Sir Cumference

I'm pretty sure both everything on the planet's fucked

as well as the people

@0celo7 Jeez, you don't mince words

user218912

@0celo7 well I'm in one so deal with it.

dmckee

3:02 AM

Which is, of course, exactly why we shouldn't be messing things up any more than necessary until we figure some stuff out about how planetary ecosystems actually work: i'd like my hypothetical descendants to have a working ecology to live in.

DanielSank

@0celo7 Why do you ask questions like that?

0celo7

@IceLord I don't have to deal with it.

@DanielSank What?

DanielSank

You don't need the help. Are you looking for a psychological crutch because you're afraid of spending time going in the wrong direction?

0celo7

Yes.

DanielSank

@0celo7 Oh, well then I decline to help. You're better off training your psyche to deal with the uncertainties of problem solving.

user218912

3:03 AM

2 mins ago, by IceLord

@0celo7 I don't get that why is there an $\epsilon_{ijk}$ there?

user218912

explain pls?

user218912

someone

DanielSank

@IceLord Look up the wikipedia article on the Pauli operators.

user218912

oh

user218912

:(

DanielSank

3:06 AM

@IceLord Why frowny face?

user218912

because I should have known that.

user218912

bare with me guys I'm basically learning/relearning QM while I'm taking QFT.

DanielSank

@IceLord That sounds unpleasant.

Why not take QM?

user218912

because it doesn't fit with my schedule.

DanielSank

@IceLord That sounds ill advised.

user218912

3:12 AM

I'm learning all of the required QM on the side though by myself.

user218912

by the end of the QFT course I'll know both QFT and QM well.

user218912

ideally.

DanielSank

@IceLord I can't imagine absorbing a meaningful amount of QFT without already understanding QM reasonably well. Best of luck to you.

user218912

@DanielSank I know the basics, enough to understand QFT.

user218912

I mean

user218912

3:13 AM

I did once read shankar front to back

user218912

but I did it in 30 days so I don't remember much.

user218912

dw it will work out, i'm trying my best and reading up on anything I don't really understand.

0celo7

@DanielSank It worked out, I just had to compute a matrix exponential.

user228700

@DanielSank Hi :-) The studying is going alright. Bit confused about Fourier's law at the moment; posted a question just now. How are you doing?

DanielSank

@0celo7 Fortunately, exponentiating spin ops is easy :)

@KaumudiHarikumar I'm doing very well. Link to your question?

0celo7

3:18 AM

@DanielSank Yeah, but I don't know if I would have been able to do it without previous knowledge

DanielSank

@0celo7 Bah! They square to the identity.

0celo7

@DanielSank Sure, but someone (Shankar) had to tell me that!

user228700

0

Q: Fourier's law and time taken for heat transfer?

Fourier's law states that "The time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area." A mathematical description of this law is given as $dQ/dt=-KAdT/L$ However, we may write $dQ/dt=mCdT/dt$ to obtain $mCdT/dt=KAdT/L$ ...

0celo7

I wonder if there's a direct way to solve the ODE without matrices

user228700

Might seem a little primitive, but please bear with me as I plough through thermo. for the first time in detail.

DanielSank

3:22 AM

@0celo7 You used matrices?

@KaumudiHarikumar Allow me to edit it, briefly.

0celo7

@DanielSank Ok, there is an easier way to do this.

I probably learned it in ODE and forgot

but I learned this method in LA, so it's all good

DanielSank

@0celo7 You could just straight up recognize your two equations as those of circular motion in phase space...

But sure, whatever floats your boat.

0celo7

@DanielSank how is that derived?

DanielSank

@0celo7 Uh, I mean, if I say $dx/dt = -y$ and $dy/dt = x$ then you should immediately recognize that as motion in a circle in the $xy$ plane.

0celo7

Uh, nope.

DanielSank

3:29 AM

@0celo7 :|

0celo7

and even if I did, I wouldn't know the actual solution for $x$ and $y$

without doing that matrix exponential, that is

@DanielSank how do you see that that's circular motion

DanielSank

@0celo7 Well, the dumb way is to solve it once and then never forget it because it's so useful.

0celo7

Sure

DanielSank

The other way is to picture it in you mind for a moment.

@KaumudiHarikumar I can't give a particularly good answer to your question, but I would point out that cancelling the dT on each side is not particularly rigorous mathematics :)

0celo7

@DanielSank I'm having a hard time seeing that the solution there is a circle

DanielSank

3:34 AM

@0celo7 Stat out on the x axis.

The diff eq. says you should start moving up.

user228700

@DanielSank Thanks for editing it :) Oh, OK.

DanielSank

Now you're a bit up, so the diff eq. says you get a little bit of leftward motion.

0celo7

no I see that

DanielSank

@0celo7 if you're on the positive y axis, the diff eq. says to move left.

It's a circle...

0celo7

I'm having a hard time seeing that $$S^x(t)=S^x(0)\cos\omega t-S^y(0)\sin\omega t,\quad S^y(t)=S^x(0)\cos\omega t+S^y(0)\sin\omega t.$$ is a circle

user228700

3:35 AM

I had a discussion with @JohnRennie a few days ago, I believe, about this very same issue of cancelling the terms on both sides but the situation was different then.

DanielSank

@0celo7 Well, that's a circle alright.

0celo7

@DanielSank Oh, there's a typo.

DanielSank

perhaps

@KaumudiHarikumar Can't comment on that ;)

0celo7

$$S^x(t)=S^x(0)\cos\omega t-S^y(0)\sin\omega t,\quad S^y(t)=S^x(0)\sin\omega t+S^y(0)\cos\omega t.$$

ok it's clear if $S^y(0)=0$, I agree.

DanielSank

@0celo7 Very good.

0celo7

3:37 AM

but from that right there...not so much

user228700

I had asked him about cancelling $dT$ on one side and $T-To$ on the other, but it turned out that we can't do that 'cause while $dT$ is an infinitesimally small quantity, $T-To$ is finite.

0celo7

@KaumudiHarikumar Really pedantically $dT$ is a one-form...

"infinitesimal" has no meaning in standard analysis

user228700

@0celo7 Do you have the time to elaborate? I don't understand...

0celo7

@KaumudiHarikumar I have time, but I doubt you want to hear, honestly.

Oh wait, wrong context

DanielSank

@0celo7 Any chance you can explain it in a way that's useful for a recent high school graduate?

user228700

3:40 AM

@0celo7 Uh, what's that supposed to mean..?

0celo7

(I just looked at the question)

@KaumudiHarikumar In $dy/dx$, $dy$ and $dx$ have no meaning by themselves.

DanielSank

@KaumudiHarikumar Oh heavens, don't worry about one-forms. @0celo7 is going to drag you through a hell of mathematics that's far more advanced than what you need here.

@0celo7 Correct!

0celo7

@DanielSank No, no I won't.

DanielSank

Very good.

0celo7

I've calmed down.

DanielSank

3:41 AM

;)

0celo7

My girlfriend has taught me some things...

DanielSank

@0celo7 Very good.

user228700

@0celo7 Okay, but sometimes, my textbooks cancel them like they are...

0celo7

@KaumudiHarikumar The "canceling $dT$" can indeed be made precise.

DanielSank

Ugh, yes, books do that. It's somewhat irresponsible.

0celo7

3:41 AM

It's called the "change of variables formula for integrals"

DanielSank

@0celo7 Interesting point of view.

But that can't work with pde's right?

0celo7

@DanielSank Well, it's how you get $\int \frac{dy}{dx}dx=\int dy$ without "canceling $dx$"

user228700

@0celo7 Should I look this up or will I be sent down the rabbit hole of Wikipedia?

0celo7

@KaumudiHarikumar No, don't look it up.

DanielSank

@0celo7 I'm not even sure what that means.

Looks like integration by parts to me.

0celo7

3:44 AM

@DanielSank There is a rigorous way to solve separable ODEs

DanielSank

@0celo7 Indeed.

0celo7

What's a nice separable ODE?

$x'=x$ is good.

DanielSank

Yes I remember this from my analysis course now.

@0celo7 wait.

Can you use functions instead of variables?

0celo7

@DanielSank Sorry?

user228700

So, um, that's all about my question? Alright, I'll wait for someone to answer. Thanks, guys.

DanielSank

3:45 AM

I remember being very confused about this stuff because physicists like to write variables where they mean functions.

@KaumudiHarikumar Did you study calculus yet?

0celo7

@DanielSank $x:\Bbb R\to\Bbb R$ is a function

DanielSank

@0celo7 I'm ok with that.

user228700

@DanielSank Yep. What I learnt might be equivalent to an A.P calculus in the U.S I believe...

0celo7

here $t$ is the variable

So the equation is $$\frac{dx}{dt}=x$$

DanielSank

@0celo7 So we're saying $(Dx)(t) = x(t)$?

0celo7

3:47 AM

or $$\frac{1}{x}\frac{dx}{dt}=1$$

@DanielSank exactly

DanielSank

Ok.

user228700

But in all my studying, it always seemed OK to cancel these things this way...

DanielSank

@KaumudiHarikumar It is in some cases.

0celo7

now integrate both sides...$$\int \frac{1}{x}\frac{dx}{dt}dt=\int dt=t+C$$

DanielSank

As a rule of thumb, don't do it if you have more than one variable.

In your case, you have dT/dL and dT/dt.

0celo7

3:48 AM

Now, it's possible to change variables in that left integral so $$\int\frac{1}{x}\frac{dx}{dt}dt=\int\frac{1}{x}dx=\ln x$$

user228700

Right. And that works all the time(God, I hope it does)?

0celo7

@KaumudiHarikumar Probably.

I can check my analysis text for the precise theorem

DanielSank

@0celo7 I don't understand this.

0celo7

@DanielSank What about it?

DanielSank

(I understand it at a basic level, but I'm trying to remember how this really works)

0celo7

3:50 AM

@DanielSank Oh...do we need to go back to what $\int \cdots dt$ means?

DanielSank

@0celo7 We might.

0celo7

@KaumudiHarikumar It's about to get ugly.

DanielSank

It shouldn't. I remember making sense of this exact issue in a way that wasn't ugly.

Ah yes.

I get it.

0celo7

If we're defining the Riemann integral, it will get ugly.

DanielSank

@0celo7 What? No.

user228700

3:51 AM

OKAY! I'll come back later then (:P)

DanielSank

@KaumudiHarikumar No no, we're good.

@0celo7 has given a very good illustration.

Never mind my old man's slow brain.

0celo7

list_things_I_never_thought_I'd_hear ++

DanielSank

@0celo7 Oh, come off it.

Yes, @0celo7's illustration shows the steps which lead to "cancelling" the dt.

Thanks @0celo7.

Ahhhhh yes. And if we try to do this for @KaumudiHarikumar's problem, we'll end up with functions of integration, instead of just a constant of integration, I think.

0celo7

> Let $I , J$ be closed intervals, $h$ a primitive of an admissible function on $I$ with $h(I) \subset J$ and $f : J \to \Bbb R$ continuous. Then for all $x_1,x_2 \in I$ $$\int_{x_1}^{x_2}f(h(\xi))h'(\xi)d\xi=\int_{h(x_1)}^{h(x_2)}f(y)dy$$

DanielSank

Hence the naive cancelling doesn't work.

0celo7

3:54 AM

That's the rigorous canceling theorem.

DanielSank

@0celo7 Well, yes, you just restated your example in fancy language.

user218912

math is boring

DanielSank

@IceLord False.

0celo7

@DanielSank Agreed, but @KaumudiHarikumar wanted to know when exactly she can do it!

user228700

Wow. MathJax doesn't work for me so now I'll copy and paste all that math into a new question so that I can see what you've written and then I'll come back and tell you if I've understood.

DanielSank

3:55 AM

@0celo7 Yes, now you should show how it works with a PDE.

user218912

@DanielSank unless there's physics involved

0celo7

@DanielSank Can you give a simple example please?

DanielSank

31

Q: Does the drunk man fall off the cliff? (a random walk problem)

A drunk man stands with a cliff one step to his left. He takes steps randomly left and right. Each step has probability $p$ of going left and probability $q=1-p$ of going right. Each step is the same size. If allowed to randomly step indefinitely, what is the probability that the drunk falls off...

mathematics probability

0celo7

Without a billion constants preferably

DanielSank

@0celo7 Ehhhh, probably not. I don't have paper...

0celo7

3:58 AM

@DanielSank Ok...what am I trying to show?

DanielSank

@0celo7 Mostly that the cancelling you just illustrated doesn't work with PDE's because the "constants" of integration turn into functions of integration.

At least, I think that's what happens.

0celo7

Sounds reasonable!

DanielSank

'morning, @JohnRennie.

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