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12:31 AM
hello
::echos back hello::
it's quiet in here.
 
1:03 AM
@DanielSank what? Already did!
 
1:25 AM
AdS has $\mathbb R^n$ as a cover yes
 
2:00 AM
Is inertial mass an emerging property?
 
2:10 AM
@ACuriousMind what on Earth is this sentence supposed to mean?
 
@ACuriousMind "Es möge $\vartheta(x,y,z)=\vartheta(\tau)$ eine in $T$ und auf dem Rande $S$ von $T$, kürzer in dem Bereiche $T+S$, erklärte beschränkte, integrierbarge Funktion bezeichnen"
I can decipher most of that except for the shorter part and the erklärte part
@Slereah probably full of crank math anyway
 
It's Petrov!
Of the Petrov classification
Not some crank
0
Q: First descriptions of ultrastatic spacetimes?

SlereahWhat's the first appearance of ultrastatic spacetimes (that is, spacetimes with a metric of the form $ds^2 = -dt^2 + h$, with $h$ a Riemannian metric)? The oldest reference I can find on the topic is Fulling's 1977 paper "Alternative vacuum states in static space-times with horizons", but from th...

plz halp
 
@Slereah is that stronger than static?
 
Yes
 
2:24 AM
why
 
The timelike Killing vector is constant
 
constant in what sense?
you can always adapt coordinates to a Killing field and make it constant
 
Constant norm
It has some nice properties
For ultrastatic spacetimes, null rays basically follow optical paths
you can just extremize the distance using Fermat's theorem
 
 
4 hours later…
6:31 AM
Fog at −4 °C; I should stay at home today.
 
We have a storm on the way. There are currently flood warnings in force!
 
it's 22 C here now; I feel it's the coolest day after summer. I really hate the desolate atmophere. I wish it's like summer every day here.
 
7:02 AM
@JohnRennie is that ophelia? Or had that already passed?
 
7:26 AM
@EmilioPisanty Storm Brian
 
7:53 AM
Here it rained yesterday for the first time in about a month
 
I tested that beamsplitter and it works pretty well
I need to make a support for it though
 
@EmilioPisanty Pfft - Ophelia was the nicest day I've ever seen in any October
 
 
1 hour later…
9:28 AM
@JohnRennie it was a partial success I guess
 
How was it?
And how did you cook it? In a skillet?
 
Yeah. I forgot to use butter. It dawned on me when it was too late.
It was ok. Not as good as standard Schnitzel
 
Butter isn't essential, but it makes the schnitzel richer.
Hmm, should we uppercase German nouns when using them in English ...
 
It looks more like fried chicken than Schnitzel. I have to look up an actual recipe. There must be a trick for making the coating
I put them in flour, then egg, then flour again
 
I think that's all my Mum does.
 
Just dip the beaten out chicken in egg yolk then into a disk of flour.
 
Oh I used the whole egg
 
Maybe it's the whole egg. Now I think about it I'm not sure.
@0celo7 that looks about right, but I would have cooked them more to get a browner finish.
 
@JohnRennie it wasn't getting any browner!
I made two rounds and the second ones just started burning but were still white. It was strange.
 
Oh well. Maybe try using butter next time? Or just not bother and stick to what you know you like :-)
 
9:38 AM
@JohnRennie I'll reheat the leftovers in butter
I have to go to VA in a few minutes to prove I'm still alive. Fucking bureaucracy
 
On a Saturday?
 
@JohnRennie I can't very well go on a day trip out of state during school
 
VA = Virginia?
 
Yeah
 
Voter registration? Or some such thing? Why would Virginia care that you're at college out of state?
 
9:44 AM
I stupidly let my driver's license expire which is legally equivalent to dying
 
Ah :-)
 
That's why I'm up at an ungodly hour
Gotta get there early
 
@JohnRennie What value of $R$ should I take in Arrhenius equation?
 
@Abcd 8.31 isn't it?
 
@JohnRennie Yes, I used that but then I got the right answer $\times 1000$.
 
That's the correct value for $R$ so the error must be somewhere else.
 
Let me share the question (PS: It's very easy.)
$\ln k_1 = \ln A - \dfrac{Ea_1}{RT}$
$\ln k_2 = \ln A - \dfrac{Ea_2}{RT}$
We want to find $Ea_1 - Ea_2$
$\therefore \ln\dfrac{k_2}{k_1}\times RT = Ea_1 - Ea_2$
Which yields $9,491$ instead of $9.491$
$k_2 = 2 \times 10^{-2} $ and $k_1 = 5 \times 10^{-4}$, $R = 8.3$
Is there any error @JohnRennie?
I don't think so...
$T = 310 K$
 
10:16 AM
Why did someone star my timelike killing vector
It is not very memorable
 
@Abcd I get 35.5kJ/mol
 
@JohnRennie It's correct (because you will have t subtract from 45 after that). But how is my method wrong?
to*
 
You say Which yields $9,491$ instead of $9.491$, but $9491$ is correct isn't it?
I suspect you're mixing up kilojoules with joules
 
@JohnRennie how can 9491 kJ be correct?
 
$9491$ joules is correct
 
10:22 AM
@JohnRennie Yes obviously... But doesn't my method yield the answer in $kJ$
12 mins ago, by Abcd
$\therefore \ln\dfrac{k_2}{k_1}\times RT = Ea_1 - Ea_2$
Doesn't this give answer in kJ?
because we take $R$in $kJ$
we took $T$in $K$
 
R is 8.31 joules per mol
 
OH! It's wiki's fault @JohnRennie they say it's in kJ/mol
The gas constant (also known as the molar, universal, or ideal gas constant, denoted by the symbol R or R) is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) per temperature increment per mole (rather than energy per temperature increment per particle). The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. Physically, the...
See the table on the right.
 
 
Yes there is an error in the tble on the right, but the above from the main text is clear.
 
10:27 AM
Yes, I was checking from the table directly. (PS: I didn't notice that they had given same values for J and kJ)
Anyway, thanks for the help.
 
10:53 AM
@Abcd I don't see the discrepancy
1 J/mol = 1 kJ/kmol
Cc @JohnRennie
 
@EmilioPisanty oh yes :-) I hadn't noticed the kmol :-)
 
Hi all
 
Giving units as kilojoules per kilomole seems a remarkably silly thing to do.
 
My question about Christoffel symbols
 
Shoot
 
11:06 AM
Taking an example of cylinder with constant "ro" or r then we calculate the gradients of basis vectors which are only e_z and e_theta and we find: d_theta e_theta= -ro e_ro why?
So the coefficients vanish for a cylinder
 
12:03 PM
Time to see if the government recognizes me as a human
@BernardoMeurer at the DMV in Virginia
Good news: I am still an American human.
 
Anonymous
@0celo7 Alive?
 
Aw man
I got a big enveloppe in the mail
I thought it was those articles I ordered
Turns out it's paperwork from my bank
 
@Blue I am legally alive!
@Slereah French banks still use paper?
 
12:19 PM
Well most of it is online, but they still send paper when there's something I need to sign
 
Anonymous
@0celo7 Congrats!
 
Anonymous
Lol
 
Anonymous
Why don't they make this license verification/update online....strange
 
@Blue I tried to renew after it expired. Didnt think it would be a big deal...
Apparently that's as good as dying
 
Anonymous
Here driving licenses are valid for 20 years from date of issuance
 
Anonymous
12:27 PM
So, not many people face that problem :P
 
Anonymous
I should get a driving license, but I'm too lazy to join driving school
 
 
2 hours later…
2:53 PM
@JohnRennie of course
 
3:04 PM
@Semiclassical the seminar schedule is still wrong. I don't even care now
Just want to get it over with
 
3:25 PM
:/
 
Anonymous
3:46 PM
 
Anonymous
I can't understand why the time taken to go from $0$ to $\pi$ infinite.
 
Anonymous
They say something like $T=\int_{0}^{\pi}d\theta/\dot{\theta}$
 
Anonymous
It is not integrable and blows up...something like that
 
Anonymous
However in reality that doesn't make any sense
 
@Blue i think it's a little easier to think about the path from $-\pi$ to $0$, with an eye towards what's happening near $-\pi$
and to make things concrete, take the particle to start from rest at $\theta\gtrsim -\pi$
there we go
 
Anonymous
3:57 PM
Umm, okay. So say initially it is as $-\pi$ angle (which implies directly above the hinging point of the rod of the pendulum assuming we are measuring angle from vertical)
 
Anonymous
 
Anonymous
When we release it from there, it will take infinite time to reach $\theta= 0$ ?
 
hang on. first, note that you just used the word 'rope'
that doesn't make a lot of sense in this case
you need it to be a rod so that it makes sense to put it at $\theta=\pi$ i.e. pointing straight up
 
Anonymous
Yeah, corrected :P
 
kk
now, what do you know about the system at $\theta=-\pi$?
 
3:59 PM
do balls on rods behave differently than strings?
@ACuriousMind My question was kinda important...
 
Anonymous
@Semiclassical I can take the potential energy to be $-mgl$ considering the hinging point as datum (and downward positive)
 
in this case, definitely. strings aren't rigid!
 
Anonymous
Kinetic energy is $0$ (initially)
 
right. and the fact that it's downward positive means it's an unstable equillibrium
so therefore if I put the rod directly at $\theta=-\pi$ then it'll just sit there for all time
 
Anonymous
Ooooo....lol
 
Anonymous
4:01 PM
Got it
 
to make this more precise, suppose we start the rod at $\theta=-\pi+\theta_0$
 
Anonymous
Okay?
 
Anonymous
$\theta=-\pi+\theta_0$..then?
 
then the potential energy behaves as $U(\theta)-U(-\pi) \sim -\theta_0^2$
that's just a restatement of what you said, of course.
but it means that the force near the peak goes as $-U'(\theta) = \theta_0$, so the smaller the initial angle the weaker the acceleration
 
Anonymous
In practice it is almost impossible to keep it at $\theta=-\pi$....however I'm surprised that the integral deals with that situation. If I integrated from $-\pi+\epsilon$ ($\epsilon$ being an arbitrary small positive number), then I'd surely get a finite time.
 
Anonymous
4:04 PM
@Semiclassical Right, gotcha
 
right. the key is that the period diverges as $\epsilon\to 0^+$
 
Anonymous
Yup, thanks :)
 
this kind of thinking actually shows up if you talk about tunneling in quantum mechanics, incidentally.
in that case you need to think about not only the classically allowed trajectories but the tunneling trajectories
and for the tunneling trajectories, it takes an infinite amount of time to go from one classical minimum ($\theta=0$) to another ($\theta=\pi$)
so there's stuff blah blah blah
 
@0celo7 Which one?
 
on that note, here's a horrible integral which I really wish I knew a closed-form for:
$$\sqrt{a}{2} \int_{-\infty}^\infty \frac{\left( \cos \left(\frac{a k}{2}\right)\right) \exp \left(-i k^2 t/2+i k x\right)}{\sqrt{2 \pi } \left(\pi ^2-a^2 k^2\right)}\,dk$$ (that's c/p'd from mathematica, will edit that for clarity momentarily)
blah, ran out of time
 
4:11 PM
@ACuriousMind I only asked you one recently
14 hours ago, by 0celo7
@ACuriousMind "Es möge $\vartheta(x,y,z)=\vartheta(\tau)$ eine in $T$ und auf dem Rande $S$ von $T$, kürzer in dem Bereiche $T+S$, erklärte beschränkte, integrierbarge Funktion bezeichnen"
 
$$\Psi(x,t)=\sqrt{\frac{a}{2}} \int_{-\infty}^\infty \frac{\cos (ka/2)}{\pi ^2-k^2 a^2}e^{-i k^2 t/2+i k x}\,dk$$
okay, that's better
(for a certain definition of better)
 
"Let $\vartheta(x,y,z) = \vartheta(\tau)$ be a bounded integrable function defined on $T$ and the boundary $S$ of $T$ - shorter "on $T+S$".
 
I don't know what "shorter on T+S" means, that's the point
 
@0celo7 He's just saying that instead of saying "on $T$ and the boundary $S$ of $T$" it's shorter to say "on $T+S$".
 
i think the word 'briefly' rather than 'shorter' captures that a bit better in english
 
4:18 PM
oh
 
it's a little funny to me that, in physics, we use the word translation to denote something that's (usually) quite simple: changing coordinates by a constant shift.
whereas 'translation' in the literary sense is a far more complicated transformation
no reason for the words to mean the same thing in both contexts, of course, but the comparison amuses me
 
@Semiclassical The Latin word it derived from means to displace or to carry something over to somewhere - the physicists take it literally, the translators figuratively: You carry the meaning of a text into another language.
 
right
one point being, i suppose, that the 'languages' of two different coordinate systems are not basically different
(different in the sense of $x'=x+a$, I mean)
the way we use the word 'transformation' is perhaps closer to the literary meaning
but meh. language
 
4:42 PM
what do you physicsts mean by translation?
it's always ever the usual $x'=x+a$ thing in math
of various shades
 
Yeah
I'm not sure there's really a difference, tbh
but for instance the Wiki page on 'translations' does contain a section on how it's used in physics: en.wikipedia.org/wiki/…
 
Anonymous
We mean "moving in a straight line" :P
 
I mean you said "whereas 'translation' in the literary sense is a far more complicated transformation".
I am just asking what that is
 
well, suppose you took a random Russian sentence from Tolstoy and fed it into Google translate.
 
Anonymous
Lol
 
4:45 PM
...
 
you'd certainly get some output, but there's a pretty good chance of that output not actually capturing the meaning of it in the original language
hence why translators get paid money to do what they do: it takes work to take a sentence in one language and present it in another in such a way that the meaning is preserved
 
yeah i didn't realize you were talking about actual translation :P
 
misread literary as literal
 
4:47 PM
lol
 
that's a pretty good way to compare what Google translate does vs. what a professional translator does, though
literal vs. literary translation
 
i'd rather feed Dostoyevsky in than Tolstoy though
much better
 
up to you :P
 
Dostoyevsky >>> Tolstoy universally
 
where it gets tricky, i suppose, is when it's already hard to understand something in its original language
e.g. imagine someone trying to translate Joyce's Ulysses into another language
it'd be basically impossible.
 
4:50 PM
or Finnegans Wake
the words are all made up
it wouldn't translate to anything
 
arguably, the issue there is that a work like Ulysses is a bit of a language unto itself
 
it's hard to translate multi-level multi-lingual pun words to different languages
 
yeah
if it requires knowledge of the language to make sense, it's hard to translate
...i guess that's a bit too broadly stated
 
but even if there's no made up words, i can still imagine the translation work to be seriously hard if there's experimentation with sentence structures, grammatical breakdowns etc going on
which is standard in modernism
 
right
that's what i have in mind
Writing which depends on playing with grammar is hard to translate
 
4:55 PM
in fact it's kind of why dostoyevsky should be generally harder to translate than tolstoy actually
there's not much serious experimentation there, but there's a lot of long winded conversations which implicitly depict angst and agitation using length and literary contradictions
 
@JohnRennie Reheating in butter worked, although feels like cheating.
 
that kind of stuff i imagine can be pretty complicated to translate
 
Anonymous
Is $p_i=\frac{\delta L}{\delta q_i}$ by definition or is there some derivation for that ?
 
Anonymous
$L$ is the lagrangian
 
Anonymous
5:00 PM
$q_i$ is the $i$ th generalized coordinate
 
defn
 
Anonymous
I think that should be $\frac{\delta L}{\delta \dot{q}_i}$
 
Anonymous
@0celo7 I am still unclear about what the real definition of lagrangian is :P
 
there is none
it is god-given
 
Anonymous
Classical mechanics is more confusing than QM...phew
 
Anonymous
5:05 PM
I should read wikipedia perhaps
 
Anonymous
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either the Lagrange equations of the first kind, which treat constraints explicitly as extra equations, often using Lagrange multipliers; or the Lagrange equations of the second kind, which incorporate the constraints directly by judicious choice of generalized coordinates. In each case, a mathematical function...
 
tfw lagrangian mechanics is the god church
 
@Blue 1. Why the $\delta$s? That should be an ordinary partial derivative w.r.t. $\dot{q}$, not $q$. 2. That's the definition of the Hamiltonian canonical momentum - take care not to confuse it with the ordinary linear momentum, since the two need not be equal.
 
you've never tried to put a classical system in a quantum form
it's the most confusing of both
@ACuriousMind I don't see a $\delta s$, sir
 
@0celo7 Uh, what? There are two $\delta$s in what Blue wrote instead of $\partial$s
 
5:07 PM
@ACuriousMind When making something that's not a word plural, you can use a ' to make it less confusing
$\delta$s and $\delta s$ look essentially the same
@ACuriousMind Don't most physicists write $\delta$'s for $\partial$'s in classical mechanics to emphasize that you're differentiating wrt. a function?
 
Anonymous
Right. I used bad notation. It should be $$\frac{\partial L}{\partial \dot{q}}$$. Now, I don't know what Hamiltonian canonical momentum is, I should look that up
 
Where did you get $p= \frac{\partial L}{\partial \dot{q}}$ from if you're not doing Hamiltonian mechanics?
 
@ACuriousMind Lagrangian mechanics?
 
@0celo7 Of what use is that definition of $p$ in Lagrangian mechanics if you don't intend to Legendre transform to the Hamiltonian?
 
@ACuriousMind To make the Euler-Lagrange equations look like Newton's.
 
5:12 PM
I don't see how that's useful given that that $p$ need not be linear momentum :P
 
Anonymous
Yeah, it was stated in the Lagrangian lectures. Now the lecturer is using it while introducing Hamiltonian mechanics (after Legendre Transforms). I'm following this series of lectures
 
@ACuriousMind I don't see how most of physics is useful. SO THERE!
 
@0celo7 Gee, got up on the wrong side of the bed today? :P
 
I got up at 5 to drive to another state to prove I'm still alive. It was actually not that bad, so no.
Why do you think I got up on the wrong side?
Random italics. They don't convene the intended message.
Drive illegally, I might add. I can't have a government job now because I committed a crime.
I'll never pass a polygraph.
 
Anonymous
Well, you said the US is 100% logical :P
 
5:17 PM
@Blue Classical mechanics is god-given. The Lagrangian is god-given, the action is god-given and the action principle is god-given.
@Blue I should turn myself in.
@Blue loooooooooooooooooooooooooooooool what are those intros
 
Anonymous
@0celo7 What intros? What's wrong?
 
the chanting
 
Anonymous
Oh, yeah. Apparently some melody/tune/song related to IIT Madras (it's in Sanskrit).
 
Anonymous
It's at the start of every NPTEL video made by them.
 
I like/admire/want to emulate vzn's way of writing/chatting too
 
5:26 PM
@Blue it's a schlock (geddit?)
 
Anonymous
I don't understand Sanskrit...so don't ask me the meaning
 
Anonymous
Some words are in Hindi though (they overlap with Sanskrit)
 
#toodamncringy
 
@ACuriousMind Ok
should I bake a cake?
 
No idea, I'm awful at baking
 
5:31 PM
@ACuriousMind I'm gonna go for it. Will post results.
 
What kind of cake is it gonna be?
 
@ACuriousMind Norwegian brownies
So basically brownies
Gotta start simple
But made from scratch!
 
5:43 PM
@ACuriousMind I'm gonna make souffle instead. Start hard and give up when it fails :P
2
 
Anonymous
6:18 PM
Does L=K.E-P.E only for non-dissipative systems?
 
@Blue It's not even necessarily true for those system - different Lagrangians can have the same equations of motion and hence describe the same system
 
I think you'd need to specify what's intended a little bit more, yeah
at the very least, though, i wouldn't expect that you can represent a non-conservative force in either the kinetic energy or the potential energy
 
Dissipative systems in the Lagrangian formalism are a pain anyway :P
 
yeah
one version that's not so bad is velocity-proportional friction
 
Anonymous
I'm confused now. On Wikipedia they say that the non-relativistic Lagrangian is defined by T-V. Then the lecturer says it is true only for non-dissipative systems. Then ACM says that may not be necessarily true. I'm so confused now. :P Is there any general equation for non-relativistic L ?
 
Anonymous
6:24 PM
@ACuriousMind Could you give an example?
 
Anonymous
I mean of different lagrangians which describe the same system
 
if you're doing non-relativistic systems with conservative forces then I think you should be able to write it as $L=T-V$ for some choice of canonical coordinates
 
@Blue As 0celo7 already said, the Lagrangian is god-given. It is guessed. You cannot derive it. If you want to describe a system where you know $T$ and $V$, then $T-V$ is a very good guess that will usually yield the correct equations of motion
 
@Blue a simple but important example: If $L'=L+\frac{d}{dt}f(\mathbf{q},t)$, then $L$ and $L'$ will yield the same equations of motion
(full disclosure, i stole that from wikipedia)
 
Anonymous
Alright. I think I get it a bit. By the way, does canonical coordinates mean generalized coordinates or something else ?
 
6:32 PM
yeah, I should have said 'generalized' since we're doing Lagrangian mechanics
 
Anonymous
Gotcha
 
7:04 PM
@JohnRennie making butternut squash curry tomorrow
 
7:17 PM
What does this guy's research areas mean?!
 
Anonymous
Looks like a theoretical chemist
 
@DanielSank I'm not sure if that's the same thing as its PSD... :/
@Blue But his profile says theoretical chemistry, theoretical physics, mathematics, computer science.
 
Anonymous
Those are overlapping areas
 
yeah, and you'd need a mixture of those to do high-level DFT simulations
 
7:24 PM
Yeah. He could have just written science.
 
Anonymous
"Professor, Heretical Physical and Computational Chemistry, Chemistry
School of Physical Sciences

Professor, Physics & Astronomy


Ph.D., UC Santa Barbara, 1989, physics
"
 
Anonymous
Okay, I'm impressed
 
Anonymous
wow
 
7:26 PM
@Semiclassical You do need things from CS, math and theoretical physics for DFT calculations but that's not usually the same thing as doing research in those areas.
 
Anonymous
computational physics seems to be a hot topic these days
 
@Semiclassical lol :)
Never saw anything like this :)
 
8:04 PM
@ACuriousMind Wow thanks for giving credit :P
 
8:22 PM
@DanielSank The correlation of each coefficient with itself should give the PSD.
 
@ACuriousMind Could you explain reversible and irreversible processes? What do they mean? The language of my book is not clear to me. (Context: thermodynamics in chemistry/)
 
 
2 hours later…
10:35 PM
@Abcd You'll have to be a bit more specific what you don't understand because my first instinct is to repeat the usual textbook definitions :P Have you looked at the corresponding Wikipedia pages?
 

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