The h Bar

Balarka Sen

19:01

vOv

ACuriousMind

If you're asking for what kind of manifold, I think you usually should just think of $\mathbb{R}^n$, with $n$ being the number of variables you use to describe your macrostates

Actually, it's probably a hypersurface in $\mathbb{R}^n$, the one on which the equations of state are fulfilled.

That is, for the standard setting where we use temperature, pressure and volume $T,p,V$, it's the zero locus of some function $f(T,p,V) = 0$ that depends on the system we are considering.

0celóñe7

Is is possible to have a degenerate level set?

Balarka Sen

@0celóñe7 are you a big fan of the internet's busiest music nerd?

0celóñe7

Yes

Balarka Sen

Look at the first comment here.

You'll enjoy it.

Anonymous

19:12

@BalarkaSen I need some good reference with quite a few solved examples on "epsilon-delta formulation of limits". I'm still struggling with it.

Balarka Sen

@Blue I don't really have a lot of reference other than the textbooks I suggested, honestly.

Anonymous

I need to see Piskunov

Anonymous

hmmm

Balarka Sen

Piskunov has lots of examples

and exercises

Anonymous

docs.google.com/file/d/0B0uVd31B7zGEOHZiWWVUclRHYm8/edit

0celóñe7

19:15

Why do you ask him

Anonymous

Looking for epsilon delta in there

Anonymous

@0celóñe7 Why not?

0celóñe7

The correct answer is to learn epsilon n proofs first

They are much easier and the skills carry over

Anonymous

@0celóñe7 What type of proofs?

Balarka Sen

@blue I'm pretty sure it's on the continuity chapter

0celóñe7

19:17

@Blue convergence of sequences

Anonymous

We'll start with convergence of sequence next week I think at uni

Anonymous

Okay

dmckee

@Blue That comment is basically predicated on the idea that the historical order in which ideas were discovered is the important thing in determining what we're going to consider 'fundamental'.

Most pros use a internal decision procedure based on generality and elegance.

Anonymous

@BalarkaSen Can't find the page in the continuity chapter. Could you tell me the page number if you have the book?

Anonymous

Wait.....41

Anonymous

19:21

Oops 35...found it :)

Anonymous

@dmckee agreed

0celóñe7

19:39

@BalarkaSen Jesus Christ I can't read a porno in public

Might poke a hole in my chain mail

@ACuriousMind don't read that it's a GoT spoiler

CooperCape

okay so how does $(\epsilon_{ijk}a_jb_k\hat e_i)\cdot (\epsilon_{nlm}c_ld_m\hat e_n)$ equal $\epsilon_{ijk}\epsilon_{nlm}a_jb_kc_ld_m\hat e_i\cdot \hat e_n$

or should I ask it as a proper q?

I feel like there's a simple rule though so no point.

ACuriousMind

@CooperCape These two things are not equal - where did the $c$ and $d$ come from?

CooperCape

good point

lemme edit

tada?

ACuriousMind

Aside from that, you're just shuffling numbers around - aside from the $\hat{e}$ which are presumably vectors, the dot product doesn't care how you order the factors.

CooperCape

oh really?

that... would be why

yeah the e's are a unit vector

in directions i & j.

ACuriousMind

19:42

I.e. you're just using $(a\vec v) \cdot (b\vec w) = ab (\vec v \cdot \vec w)$, and all the indices are just distraction ;P

Anonymous

@CooperCape In $i$ and $n$ it seems.

CooperCape

that one

Anonymous

You wrote $\hat{e^n}$

CooperCape

yeah I just realised :p

thanks @ACuriousMind all the greek and indexes overwhelmed me a tad...

Anonymous

@CooperCape I've not seen you around here much. Are you an undergrad? What subject? :)

CooperCape

19:45

Currently doing physics A-level applying to uni this year for physics.

Just like physics I guess

Anonymous

Oh. So you're a high school student!

CooperCape

uk version but yah

Anonymous

Well, you have loads of good unis in uk unlike here. :P Good luck though

CooperCape

thanks

ACuriousMind

Dammit, I'm stuck in algebraic geometry hell again

CooperCape

19:47

got AS results thursday for maths so...

eek

AHB

hi

I got a short question about statistical mechanics(?)

Anonymous

hi

Anonymous

just ask

Anonymous

someone might answer

AHB

I was typing... They define temperature as $\frac1{k_BT}=\frac{d \ln \Omega}{dE}$

Anonymous

19:50

lol....we were discussing this just sometime back. :P

AHB

So it means that if the number of microstates associated with a certain energy, doesn't change locally, we have infinite ttemprature?!

any idea?

Anonymous

You're basically asking if $E$ changes but the microstates remain constant, then the temperature is infinite? I guess: yes.

Anonymous

8

A: What's the most fundamental definition of temperature?

It's the differential relationship between internal energy and entropy: \begin{align} dU &= T\,dS + \cdots \\ \frac{\partial S}{\partial U} &= \frac 1T \end{align} As energy is added to a system, its internal entropy changes. Remember that the (total) entropy is $$ S = k \ln\Omega, $$ where $\Ome...

Anonymous

Read this once ^

AHB

hmmm. let me read it...

That was useful. Thank you.

Anonymous

19:57

No problem. :)

Anonymous

I think we have spoken before

Anonymous

You're preparing for IPhO iirc ?

CooperCape

I'm assuming you don't mean me...

Anonymous

@CooperCape I meant @AHB.

Anonymous

BTW are you too? @CooperCape

AccidentalFourierTransform

20:06

"Aximos" !!! i only believe in mathematical proofs , — El Mouden 2 mins ago

0celóñe7

@ACuriousMind See, that's an example of the stupid liberal

AccidentalFourierTransform

obvious troll is obvious

0celóñe7

I don't think algebraic geometry is anything other than a hell

Ender Look

Which of this 3 calculations are used to calculate the "fake" frequency of light using the Relativistic Doppler Effect when the observer is moving?
$$ \beta_v' = \frac{\beta_v + \beta_u}{1 + \beta_v \beta_u} \;.$$
$${\displaystyle f_{o}=f_{s}{\sqrt {\frac {1-v/c}{1+v/c}}}}$$
$$ v' = \frac{u + v}{1 + \frac{uv}{c^2}} \;, $$

Latex doesn't work?

AccidentalFourierTransform

AXIMOS

ACuriousMind

20:07

@AccidentalFourierTransform Chill

AccidentalFourierTransform

top right corner

ACuriousMind

@EnderLook upper right corner

Anonymous

@EnderLook What is $\beta$ ?

0celóñe7

@ACuriousMind make him

Ender Look

@Blue That is the greek beta letter.

AccidentalFourierTransform

20:08

$v/c$

Anonymous

@EnderLook What does it stand for?

AccidentalFourierTransform

aka, $v$

Anonymous

I couldn't have typed $\beta$ without knowing its name obviously :P

ACuriousMind

@EnderLook What do you mean by "which of this"? The first seems to be for added velocities as a proportion of $c$, the second for the Doppler-shifted frequency, the third for added velocities. What is the question?

Anonymous

@AccidentalFourierTransform Oh

AccidentalFourierTransform

20:09

lol

Ender Look

ß

In German orthography, the grapheme ß, called Eszett (IPA: [ɛsˈtsɛt]) or scharfes S (IPA: [ˈʃaɐ̯fəs ˈʔɛs], [ˈʃaːfəs ˈʔɛs]), in English "sharp S", represents the [s] phoneme in Standard German, specifically when following long vowels and diphthongs, while ss is used after short vowels. The name Eszett represents the German pronunciation of the two letters S and Z. It originates as the sz digraph as used in Old High German and Middle High German orthography, represented as a ligature of long s and tailed z in blackletter typography (ſʒ), which became conflated with the ligature for long s and round...

ACuriousMind

wat

Anonymous

Oh, my goodness.

ACuriousMind

The ß and the $\beta$ have nothing to do with each other

AccidentalFourierTransform

Apr 20 at 17:14, by AccidentalFourierTransform

no, its a fancy beta and I dont want it anywhere near Gauss

ACuriousMind

20:10

@AccidentalFourierTransform ßuck it up :P

AccidentalFourierTransform

D:

H=T+V =E_toatal ; H=P²/2m+V ; E=i h d/dt and when E=H we get Schrodinger equation My Problem is where E expression came from — El Mouden 4 mins ago

the troll is strong with this one

Ender Look

mmm... I... I want to make an little "experiment" and I need that.
I want to calculate the change of frequency of light when the observer is moving at 99% light speed

Anonymous

Your second equation is the correct one for Doppler effect (for light).

Ender Look

@Blue Thanks!

ACuriousMind

@AccidentalFourierTransform Be nice, please.

Anonymous

20:13

@AccidentalFourierTransform wow

AccidentalFourierTransform

> Troll troll troll lalalala — AccidentalFourierTransform 1 mins ago

Ender Look

Using $${\displaystyle f_{o}=f_{s}{\sqrt {\frac {1-v/c}{1+v/c}}}}$$.
If the light is travelling `--->` at 100% c (like always) and the observer is travelling `<---` at 99% c (they would collide), is `v = (100% + 99%) * light speed`

Anonymous

rick rolled -_-

ACuriousMind

@EnderLook No, $v$ is the velocity of the receiver with respect to the light source

Ender Look

So?

v = (100% - 99%) * light speed?

ACuriousMind

20:16

So what?

@EnderLook No.

Ender Look

What is $v$???

AccidentalFourierTransform

youre missing a Thomas rotation

ACuriousMind

@EnderLook The velocity of the receiver with respect to the light source. Since you haven't specified where the light source is or with respect to whom the receiver is moving with 0.99c, this is currently underspecified in your scenario.

macco

Any good non-fiction book suggestions?

ACuriousMind

Weinberg's QFT. Next!

Anonymous

20:19

@macco This

macco

I read feynmanns QED which was great, dont know if i'd enjoy a pure textbook curiousmind?

AccidentalFourierTransform

pure textbooks are the worst

I only like partial textbooks

ACuriousMind

@macco It was sort-of a joke. If you are not interested in learning actual technical QFT, don't read it.

Ender Look

AccidentalFourierTransform

arxiv.org/abs/1708.03872

these are great

Ender Look

20:21

That could be a possible escenario?

I just made it with the paint

Anonymous

Ah, now you're getting into special relativity :)

Anonymous

Speed of light is independent of reference frame

AccidentalFourierTransform

@EnderLook that looks like the omniscient olive sandwich from Cow and Chicken

in that episode where they go relativistic

Ender Look

I don't know what is that

0celóñe7

@macco "An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps, and Minimal Graphs"

AccidentalFourierTransform

20:25

actually I think it was from I Am Weasel

Anonymous

@EnderLook Watch professor Ramamurti Shankar's lectures on SR at Yale. I think it is a series of 4 lectures

Anonymous

You'll get it

ACuriousMind

@EnderLook In that case the $v$ you want to plug into the equation is simply -0.99c. The minus is because the observer is moving towards the source.

Ender Look

Thanks!

AccidentalFourierTransform

tonic water is the best thing ever

why some people dont like it Ill never know

ACuriousMind

20:31

@AccidentalFourierTransform You forgot a "with gin" there ;P

AccidentalFourierTransform

edit: tonic water is the second best thing ever

0celóñe7

Best thing ever?

@macco the prose is pretty mediocre but it's one of the best physics books I've read in a long time

In terms of technical stuff

AccidentalFourierTransform

Anonymous

Is this your first +--- meme ? @AccidentalFourierTransform :P

Anonymous

All the previous ones were -+++

ACuriousMind

20:35

@AccidentalFourierTransform $\mathrm{d}^{-2}k$?

Is this from the "Taylor expand the $\delta$" people? :P

AccidentalFourierTransform

+--- is the good one, -卐卐卐 is the bad one

@ACuriousMind yes.

Anonymous

Don't get banned XD

AccidentalFourierTransform

@ACuriousMind no, it is from the best physicist ever

my good friend Bryce

0celóñe7

Bryce?

AccidentalFourierTransform

yes, the best physicist ever

0celóñe7

20:37

That doesn't sound like Bahoran Jewliger

macco

@0celóñe7 thanks. It doesn't have to be physics related. Just looking to extend my booklist. For example I have read "three stones make a wall" (Archeology), QED feynmann, The planet remade (Geoengineering), I contain multitudes (microbiology), life on the edge (quantum biology) recently and enjoyed them.

0celóñe7

@macco it isn't physics beyond the fact that a physical being wrote it (allegedly)

You should still read it

AccidentalFourierTransform

@0celóñe7 dr. Bryce DeWitt

@macco read The Plague and thank me later

ACuriousMind

@AccidentalFourierTransform macco said non-fiction

AccidentalFourierTransform

macco doesnt know what s/he wants

0celóñe7

20:41

Not sure you'll be able to thank me afterwards

Read "The Analysis of Linear Partial Differential Operators" Volumes 1-4

AccidentalFourierTransform

s/he wants to read The Plague

0celóñe7

@ACuriousMind Can we please have a gender neutral pronoun policy in chat?

Anonymous

Use (s)he

ACuriousMind

@0celóñe7 What do you mean?

ιllιlılMostafaıllııllıl

@EmilioPisanty Have you ever seen this journal?

Is it a respectable journal?

AccidentalFourierTransform

20:43

can we omit pronouns as we do in most languages

Anonymous

I think in English the gender neutral pronoun is "they"

Anonymous

It sounds awkward though

ACuriousMind

@AccidentalFourierTransform Hm? what do you mean by "omit pronouns"?

0celóñe7

@ACuriousMind I think it is preferable to call people "ze" or something similar before they state what zeir preferred pronouns are.

Anonymous

I prefer using "he" unless someone clarifies they are female. "he" is widely accepted as gender neutral. (afaik)

ACuriousMind

20:45

Are you thinking of languages where all relevant information is in the flection of the verb?

0celóñe7

@Blue That is horribly offensive, you are suggesting a male-female gender dichotomy.

AccidentalFourierTransform

yeah

Ender Look

I found in [this link](https://en.wikipedia.org/wiki/Radiation_pressure#Radiation_pressure_by_absorption_.28using_classical_electromagnetism:_waves.29) this:
$${\displaystyle P_{\text{absorb}}={\frac {\langle S\rangle }{c}}={\frac {E_{f}}{c}}}$$
But I want to calculate the pressure of a single photon, so I don't have **W/m2**, I have **eV**. Is there something that I can do?

Anonymous

Third-person pronoun

A third-person pronoun is a pronoun that refers to an entity other than the speaker or listener. The English pronouns he and she are gender-specific third-person personal pronouns. The English pronoun they is an epicene (gender-neutral) third-person pronoun that can refer to plural antecedents of any gender and, under certain circumstances, to a singular antecedent that refers to a male or female (but not inanimate) entity. Many of the world's languages do not have gender-specific pronouns. Others, however – particularly those that have a system of grammatical gender (or have historically had such...

0celóñe7

@Blue There are gender neutral pronouns, (s)he is not one of them.

Anonymous

20:46

(s)he was just a joke

Anonymous

:P

Anonymous

I just use "he"

macco

the problem Im having with my books recently is that a lot of the popular science books explain some concepts again and again with tedious analogies, however textbooks are usually far to dry for me to enjoy reading. There should be more middleground.

AccidentalFourierTransform

I propose we use $\nu$e as a gender neutral pronoun.

Anonymous

-+++e

ACuriousMind

20:48

@0celóñe7 You're welcome to ask people to use that. I personally much prefer the singular they, possibly because German has no comparable option.

Ender Look

It's me or Latex doesn't work on chat?

0celóñe7

It's you.

Ender Look

oh...

0celóñe7

Damn, trying to pirate books on hotel internet isn't working

Anonymous

18

A: Is using "he" for a gender-neutral third-person correct?

It's still considered acceptable. If you really want to cover your bases, include a definition at the front that reference to one gender imports all other genders, unless the context requires otherwise, and explain that you'll be using "he" for the sake of simplicity. Edit: As per below discussi...

0celóñe7

20:49

wonder if libgen is blocked

ACuriousMind

@EnderLook Sure, you need to compute the energy flux - for which you need to know how many of your photons are hitting your target per unit area per unit time.

Anonymous

@0celóñe7 nope

Anonymous

It's working here

Anonymous

Maybe in US....

0celóñe7

@Blue I mean on the hotel internet

Anonymous

20:49

hmm...use proxy :P

0celóñe7

oh no, the download is just so slow that OSX won't estimate how long it's taking

ACuriousMind

@EnderLook Did you activate ChatJax with one of the methods linked in the upper right corner?

@0celóñe7 Would you prefer it displayed "ETA: After the heat death of the universe"?

AccidentalFourierTransform

TIL OSX is Java

0celóñe7

@AccidentalFourierTransform For the last time, I deleted my Java.

Ender Look

@ACuriousMind It worked, great! Thanks!

AccidentalFourierTransform

20:52

$\phantom{you cant see me now}$

Anonymous

now i c u

AccidentalFourierTransform

I.C. Weiner

0celóñe7

@ACuriousMind I want a new keyboard

ιllιlılMostafaıllııllıl

@EmilioPisanty Hmm, according to this, looks like it is; as its editorial board are all well-known researchers in the field.

Never had seen any paper from it before :/

0celóñe7

;'(

why is this taking so long

...

Anonymous

20:59

@0celóñe7 ........ that sucks...

AccidentalFourierTransform

try again in an incognito window

0celóñe7

@AccidentalFourierTransform Download again?

Maybe I should try a diff mirror

AccidentalFourierTransform

no

load it again

on incognito mode

Anonymous

Internet Explorer comes in handy in such situations

0celóñe7

Nah, the Mac PDF reader won't open it

Nor Chrome

Anonymous

21:01

Opera mini too

0celóñe7

Gonna download from a different source

CooperCape

@Blue Apologies I never got back to you an hour ago. No, I'm not preparing for IPhO... that's why I assumed it wasn't me :p

Anonymous

@CooperCape oh, no probs

0celóñe7

hmm

this is very suspicious

Anonymous

start praying

CooperCape

21:05

hate it when the document loses 200 KB between downloads...

0celóñe7

that download failed too

screw it

AccidentalFourierTransform

well I hate world hunger, poverty, child deaths and capitalism

shallow much?

0celóñe7

stop using a computer you commie

AccidentalFourierTransform

I hate commies too

I just hate people.

0celóñe7

figures

all commies hate people

CooperCape

21:16

o wow

what's wrong with a lil' bit of communism guys...

0celóñe7

@CooperCape people die

CooperCape

okay okay so there's a fewwww flaws

0celóñe7

It inherently violates human rights

CooperCape

major

0celóñe7

No one has fun

CooperCape

21:17

yeah but ignoring that...

AccidentalFourierTransform

lol

ACuriousMind

Great, it only took me four hours to find a comparatively simple formula these authors were using implicitly!

0celóñe7

@ACuriousMind boohoo

It once took me a week to find a formula

AccidentalFourierTransform

"$(a+b)^2=a^2+2ab+b^2$"

ACuriousMind

@0celóñe7 I'm pretty mad they didn't write it down since without knowing it what they were doing just looked like black magic :P

CooperCape

21:21

@AccidentalFourierTransform can you show me the proof for that... I'm a bit confuzzled.

AccidentalFourierTransform

first, assume $1+1\neq 0$...

Anonymous

What are $1$ and $0$ and $\neq$ ?

Anonymous

=P

0celóñe7

@ACuriousMind the author did not mention the formula from do carmo here math.stackexchange.com/questions/1887646/…

AccidentalFourierTransform

Peano is inconsistent.

0celóñe7

21:23

"from this, we deduce that" required at least two formulae not mentioned anywhere

Phase

21:58

Hey

Could one argue that there are some phenomena in the universe where causality doesn't apply / is a lot messier than cause ---> effect

AccidentalFourierTransform

Rarita-Schwinger coupled to an electromagnetic field

but no, causality (in its technical manifestation) always holds, as far as we know

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