The h Bar

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

15:01

over 10,000 hours later...

Secret

https://en.wikipedia.org/wiki/Pop_(physics)
A Jerk snapped with a loud crackle after watching pop momentarily

0celo7

15:19

@DanielSank well according to @Danu you shouldn't learn GR from anything less than Carroll, and he has topology I think

Learn GR without any math

David Z

@Slereah is that a serious recommendation?

Slereah

Care to take a guess?

0celo7

@DavidZ Sigh...why did you remove that?

Secret

the answer is obvious... (both questions)

0celo7

It's not obvious to me

All moderation decisions are nonobvious to me :(

Secret

15:36

0celo7

@Secret huh?

Secret

Cannot find a better sign that say "any attempt to discuss further on the issue will be met with severe consequences" as an answer your "it is not obvious to me"

you know what I mean given the long history of everyone being documented in h bar

(This message is intentionally cryptic, yet direct at the same time)

Secret

Anyway...

how do we know which term is which?

0celo7

@Secret Huh?

ACuriousMind

@Secret What do you mean? What terms are you talking about?

Secret

15:52

Tracing all the way back to the first equation

$$\frac{d^2 u_j}{dt^2}=\frac{d\Omega}{dt}\times u_j+\Omega \times (\Omega \times u_j)$$

why is the centrifugal force depend on the jerk of the unit vector of the rotating frame?

$$\Omega \times (\Omega \times u_j)$$

Centrifugal force

In Newtonian mechanics, the term centrifugal force is used to refer to an inertial force (also called a 'fictitious' force) directed away from the axis of rotation that appears to act on all objects when viewed in a rotating reference frame. The concept of centrifugal force can be applied in rotating devices such as centrifuges, centrifugal pumps, centrifugal governors, centrifugal clutches, etc., as well as in centrifugal railways, planetary orbits, banked curves, etc. when they are analyzed in a rotating coordinate system. The name has historically sometimes also been used to refer to the reaction...

@ACuriousMind I am talking about the 3 fictitious force terms, how do we know which term is which as all we have is just a couple of angular velocities, velocities and positions being related by cross products?

ACuriousMind

@Secret I don't understand the question. When you compute the fictitious force, you get those three summands. what is there to know?

@Secret That's not a jerk. It's the centrifugal acceleration

Slereah

Jerk appears pretty rarely in physics

Since all basic equations are second order

Secret

I don't understand why is $$\Omega \times (\Omega \times x_B)$$ is the centrifugal force but not any of the other two fictitious force

How does one deduce which force is which by just staring at the 3 terms?

Slereah

You don't.

You do it by performing coordinate transforms

ACuriousMind

@Secret You define that term to be called "centrifugal force".

Slereah

15:57

You take the equation

$\frac{d\vec p}{dt} = 0$

You switch the coordinates to a rotating frame

You will see those terms appear

ACuriousMind

"which is which" would only make sense if you had defined "centrifugal force", "Euler force" or "Coriolis force" prior to getting those three summands. But you can't. You compute the total fictitious force, get three terms, and decide to call each by its own name

Slereah

Although beware

It's not too trivial

Because the basis vector themselves depend on time

(if you use polar coordinates)

Rotating reference frame

A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.) == Fictitious forces == All non-inertial reference frames exhibit fictitious forces. Rotating reference frames are characterized by three fictitious forces: the centrifugal force, the Coriolis force, and, for non-uniformly rotating reference frames, the Euler for...

^useful

ACuriousMind

If you're asking why one should conceive of those forces as three distinct forces, just look at their dependence on derivatives - the centrifugal force is always there, the Coriolis force only acts on things moving with respect to the rotating reference frame, and the Euler force only acts when the rate of rotation is changing.

Slereah

Since you've done some GR

Those are basically terms that the connection gets from coordinate change

Secret

I think this wikipedia article have worked through this
https://en.wikipedia.org/wiki/Fictitious_force
which is what I have jotted down the paper and convince myself by redoing the derivation

and yes I got those 3 terms. In particular

$$\frac{d^2 u_j}{dt^2}=\frac{d\Omega}{dt}\times u_j+\Omega \times \frac{du_j}{dt}$$

and

$$\Omega \times \frac{du_j}{dt}=\Omega \times (\Omega \times x_B)$$

I recognise the $\frac{d^2u_j}{dt^2}$ as the jerk of x_j

====
OK I mistaken, because I misread the $\frac{du_j}{dt}$ in $\Omega \times \frac{du_j}{dt}$ as jerk, it is clear now

0celo7

16:09

@Slereah Apparently fourth derivatives appear in civil engineering problems.

Slereah

yeah

also it's used in like

rollercoaster mechanics

0celo7

uh, @Slereah how do you actually calculate the acceleration in Schwarzschild spacetime felt by a stationary observer

Slereah

Isn't that just from the geodesic deviation?

FenderLesPaul

@user507974 I mean you don't need anything beyond the techniques in GR and QFT

0celo7

probably not

FenderLesPaul

16:12

which I certainly wouldn't call advanced math

since it's basically physicists' level complex analysis and tensor calculus

0celo7

@FenderLesPaul hahaha

You've never taken a look at the Cauchy problem?

FenderLesPaul

Who cares about the cauchy problem?

0celo7

Math people

It's the interesting part of GR

FenderLesPaul

Who cares about math people?

0celo7

@FenderLesPaul </3

FenderLesPaul

16:13

@0celo7 I love you for who you are not what you do!

0celo7

well good because I do fucked up shit

I had way too much fun doing this in AssCreed

@FenderLesPaul what about twistor GR

that uses sheaf cohomology

FenderLesPaul

Do people use twistor GR?

0celo7

@FenderLesPaul maybe one or two

also I'd hardly call the proof of the pos energy theorem easy math

FenderLesPaul

Literally none of that has to do with AdS/CFT related research

0celo7

do you not need Kähler geometry for that?

Slereah

16:21

Did that ER = EPR business go anywhere, by the way

0celo7

@ACuriousMind what's the space called that's like the set of $k$-planes through a vector space

ACuriousMind

@0celo7 Grassmannian

FenderLesPaul

@Slereah it's still being advocated by Susskind and Maldacena as a solution to the firewall paradox

0celo7

@ACuriousMind nice to see you're not consistent :)

Mr. Gauß

FenderLesPaul

@Slereah although I think a lot of people don't buy it just yet

because it relies on very special situations: eternal (double-sided) black holes and thermofield double states

0celo7

16:23

(that was a trick question to see if you'd spell it correctly with ß)

ACuriousMind

@0celo7 I actually just didn't know that Graßmann has properly an ß in there

Slereah

Also wasn't it extremely vague

Like "They both have the same entropy"

ACuriousMind

Only ever saw Grassmann, even in German contexts

0celo7

Hermann Grassmann

Hermann Günther Grassmann (German: Graßmann; April 15, 1809 – September 26, 1877) was a German polymath, known in his day as a linguist and now also as a mathematician. He was also a physicist, neohumanist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. == Biography == Grassmann was the third of 12 children of Justus Günter Grassmann, an ordained minister who taught mathematics and physics at the Stettin Gymnasium, where Hermann was educated. Grassmann was an undistinguished student until he obtained a high mark on the examinations for admission...

ACuriousMind

@0celo7 I can look it up, too :P

0celo7

16:24

@ACuriousMind :(

it took me a while

FenderLesPaul

@Slereah I don't think it was vague

0celo7

@ACuriousMind So I saw Hansel & Gretel, was very disappointed that it wasn't in German.

Slereah

Couldn't say

I don't know AdS/CFT theory

FenderLesPaul

it basically said that you can regularize the entanglement entropy at the horizon if particles are entangled through ER wormholes

would be cool if it was true though

because it would provide a very cool conceptual picture for how space and time emerge from entanglement

0celo7

but QM is wrong

Slereah

16:27

Would be neat

Does it provide an alternative interpretation of QM by the way?

Similar to whatever vague shit Penrose did

QM interpretation through topology

FenderLesPaul

Not that I know of

but I don't really understand the details of ER=EPR very well

Slereah

I should look it up but then again I'd have to learn CFT

The horror

FenderLesPaul

There are a bunch of KITP lectures on firewalls and ER=EPR and fuzzballs

you should watch them they're pretty instructive

let me find the link with the videos

Slereah

I should probably learn AdS/CF first

0celo7

@Slereah CFT is even worse than quadratic equation theory

FenderLesPaul

16:30

@Slereah online.kitp.ucsb.edu/online/fuzzorfire-m13

they aren't all super technical talks

The ones by Marolf and Susskind are very intuitive

0celo7

Susskind is crazy

FenderLesPaul

"The Case for Firewalls" (Marolf) and "ER = EPR" (Susskind)

0celo7

he always eats during talks

FenderLesPaul

Maldacena's talk is more technical

Slereah

So does Richard Stallman

FenderLesPaul

16:31

Also just for kicks you should watch the talks under "The view from GR"

Slereah

FenderLesPaul

The ones by Jacobson, Wald, and Hawking are fine

but Bill Unruh's talk is hilarious

that guy is legitimately a nutcase

Slereah

Plenty of crazy dudes in the field

0celo7

link?

FenderLesPaul

Unruh is just freaking crackpotty haha

Slereah

16:32

Penrose, Tipler, Mallett

FenderLesPaul

@0celo7 online.kitp.ucsb.edu/online/fuzzorfire-m13/unruh

0celo7

Hawking is crazy too

not physics crazy, just crazy in general

Bernard Meurer

Stallman is a legend

0celo7

16:53

@BernardMeurer never heard of him

Bernard Meurer

stallman.org

0celo7

huh

never heard of him

Bernard Meurer

Are you stuck in repeat now?

0celo7

no

@BernardMeurer never heard of him

Jacobadtr

17:14

"Compute the entropy increase of the ice/water system due to the melting of the ice cubes
and that due to the warming of the resulting water, within the assumption that the resulting
water does not exchange an appreciable amount of heat with the remaining ice."

Does this assumption mean that the water continues to rise in temperature before all the ice has melted?

Jacobadtr

17:31

It certainly sounds like that, but that's wrong isn't it?

Danu

18:20

@DavidZ oh I know that, don't worry!

@Qmechanic I'm in principle up for doing more. But no pressure ;)

sharaf zaman

@ACuriousMind physics.stackexchange.com/questions/126512/…

the stronger will the repulsion due to the Pauli principle be, since it can never happen that two electrons possess exactly the same spin and the same probability to be found in an extent of space. in his answer he has written about pauli's principle but o don't understand what this principle will do here

DanielSank

18:45

@0celo7 Are you teasing or do I actually have to explain why that's an absurd statement?

ACuriousMind

18:56

@sharafzaman I can't explain it any different from what I have written there. The "first" reason why you can't push matter into other matter is electromagnetic repulsion of the electrons. But when you try to overcome that by just applying more force, you'll hit the point where the matter turns into degenerate matter, and then the Pauli principle becomes the main obstacle to further compression.

0celo7

@DanielSank dunno, is Danu wrong?

sharaf zaman

19:18

@ACuriousMind hey i it true that if i press something by my hands too much its atomic size decreases so electrons come close to each other

DanielSank

@0celo7 It makes an absurdly general statement. Some people need GR for applications and don't need to understand it in the way Danu wants to understand it.

0celo7

Sep 12 '15 at 10:29, by Danu

I, as a self-learning conservative, don't think it's a good idea to learn GR at all until you're ready for something like Carroll's book.

@DanielSank you should fight him about it

@ACuriousMind How come in calculus we learn $\lim_{x\to c}f(x)$ first and then $\lim_{n\to\infty}a_n$, but in analysis we do it the other way around?

ACuriousMind

19:38

@0celo7 How would you propose to define $\lim_{x\to c}f(x)$ if not by $\lim_{n\to\infty}f(x_n)$ for every sequence $x_n\to n$?

0celo7

@ACuriousMind Uh, $0<|x-c|<\delta\implies |f(x)-L|<\epsilon$?

The standard way?

ACuriousMind

Hm, yes.

I guess you can do it both ways, but a sequence is a "simpler" object than a general function, so it seems somewhat natural to start with sequences

0celo7

I guess, but in calculus one always does it the other way around.

In fact most first calculus courses do not cover sequences.

ACuriousMind

Since I'm still not exactly clear on the difference between calculus and analysis, that statement doesn't mean much to me

0celo7

@ACuriousMind You should read a calculus book to educate yourself.

ACuriousMind

19:45

But I'd guess it is because calculus is about computing stuff about functions, so it would be somewhat strange to start talking about sequences instead.

0celo7

@ACuriousMind Maybe.

But the way I was taught sequences in calculus was this

We learned about limits of functions at infinity, so stuff like $\lim_{x\to\infty}f(x)$

then we defined $\lim a_n$ like this

let $f(x)$ be the function so that $f(n)=a_n$

then $\lim a_n=\lim_{x\to\infty}f(x)$

@ACuriousMind now I'm pretty sure that's wrong in general

but when we had stuff like $a_n=\frac{n}{\mathrm{e}^n}$ it worked.

ACuriousMind

@0celo7 Well, the $\lvert x-c\rvert < \delta$ doesn't make sense for $c=\infty$.

0celo7

@ACuriousMind >implying we did $\epsilon-\delta$ in high school

oh boy you are German

we calculated limits by looking at graphs

ACuriousMind

@0celo7 Uh, no, you told me you wanted to define $\lim_{x\to c}$ by that.

0celo7

@ACuriousMind how I define things and how the class defines things are not the same

the class never defined limit

we just used them

ACuriousMind

19:56

then your answer is that analysis is rigorous and calculus isn't :P

0celo7

yes, calculus is to analysis what physics is to math

the smelly nonrigorous cousin

ACuriousMind

Yeah, so...what was your question again?

0celo7

@ACuriousMind hmm

I don't have one, just stuck on a PDE proof

and if I ask you or @yuggib, you'll demand to know the function space and topology

@ACuriousMind Sigh, I was staring at $-x\phi\phi'|_1^b$ for 15 minutes, trying to figure out why it's $\ge0$. $\phi$ has Dirichlet BCs -.-

sharaf zaman

20:11

@ACuriousMind hey is it true that if i press something by my hands too much its atomic size decreases so electrons come close to each other

0celo7

53 mins ago, by sharaf zaman

@ACuriousMind hey i it true that if i press something by my hands too much its atomic size decreases so electrons come close to each other

sharaf zaman

correct

but this is quite annoying this SE site has so many restrictions

ACuriousMind

@sharafzaman "Atomic size" is an ill-defined concept. On the scales where it is well-defined, it doesn't change, and on the scales where you might like to say it changes, it doesn't make sense to speak about it. Atoms are not little billard balls with definite diameters.

@sharafzaman All of the "restrictions" are in place to facilitate good, focused questions that can receive useful, clear answers.

sharaf zaman

then on physics overflow no restrictions but still good question even better answer

0celo7

^

ACuriousMind

20:18

@sharafzaman "no restrictions"? "Only grad-level and above" sure sounds like a quite heavy restriction to me.

0celo7

@ACuriousMind according to this chat, anything from analysis to sheaf cohomology is the starting point for "grad level"

sharaf zaman

that is just for namesake but even highschool students ask question @ACuriousMind

ACuriousMind

@sharafzaman The restriction is not on the type of asker, but on the type of question. If you like PhysicsOverflow better, why are you here?

sharaf zaman

because i want to make some score on this site

ACuriousMind

Why?

sharaf zaman

20:22

and chat room here is the best

0celo7

@ACuriousMind Internet points.

sharaf zaman

no reputation @0celo7

i mean i want to make some reputation

0celo7

@sharafzaman Yes. Internet points.

ACuriousMind

@0celo7 The only reason to want to get rep that I can see is that you like this site and want more reputation to help shape it.

0celo7

@ACuriousMind bwahahaha

so naive

some people just want swag internet points

sharaf zaman

20:25

don't indirectly point at me lol

ACuriousMind

@sharafzaman But why do you want reputation if you think the site is "annoying"?

sharaf zaman

because i love physics!

0celo7

@ACuriousMind Hey, please calculate $$\int_1^b\sin\left(\frac{n\pi}{\log b}\log x\right)\sin\left(\frac{m\pi}{\log b}\log x\right)\frac{\mathrm{d}x}{x}$$

$m,n\in\mathbb{N}$

ACuriousMind

@sharafzaman That doesn't make sense. What has a love for physics to do with gaining reputation on some internet site?

@0celo7 Ew. What's the $\frac{1}{x}$ doing in my Fourier orthogonality relation?

sharaf zaman

okay! i agree i like this site but here are lot of restrictions

ACuriousMind

20:27

@sharafzaman Such as?

0celo7

@ACuriousMind also note the $\log x$s

oh, can one substitute $u=\log x$

sharaf zaman

when i see a great post and i want to clarify my some question i can't comment unless i get 50 reputations

ACuriousMind

@0celo7 Oh! I somehow parsed that as $\log(a)$

@sharafzaman Comments are not for asking follow-up questions. The 50 rep condition is there precisely so new users don't do that.

0celo7

@ACuriousMind u sub works!

ACuriousMind

If you have a question, ask a question.

0celo7

20:29

see, @ing my questions to you answers them half the time

ACuriousMind

@0celo7 Yes, it does

sharaf zaman

@ACuriousMind yes even if i ask a question i gets duplicated

0celo7

@ACuriousMind doing eigenfunction analysis of the operator $x^2D^2+xD$.

ACuriousMind

@sharafzaman You mean, it is closed as duplicate? Then you need to make clearer what about your question is different from the one already asked.

sharaf zaman

1

Q: my question is about gibbs energy, entropy and all that

I learnt that Gibbs energy is a free energy to do work! Tell me, what is this free energy and what is the work done (I mean what kind of work). Please also provide me an example of Gibbs free energy, like which energy and what work it is doing. Entropy is said to be a measure of randomness in a ...

ACuriousMind

20:31

That's not closed because it is a duplicate.

It's closed because "Those three questions are rather unrelated, please ask them seperately.", as I say in a comment there

sharaf zaman

see this question there is no answer for the first 1, if i ask for another question it will get duplicate as tag

ACuriousMind

@sharafzaman I don't know what that's supposed to mean.

0celo7

@ACuriousMind My PDE prof is so sad. I've seen him erase $\in\mathbb{R}$ and $\propto\delta_{mn}$ after writing it on the board because the engineers in the class aren't used to that notation

sharaf zaman

@ACuriousMind i mean if i ask again i will get a duplicate tag so i will get -2 points and i don't want that to happen

ACuriousMind

@sharafzaman That's...not at all how it works.

You get "-2" for downvotes, which have nothing to do with close votes or duplicates.

A tag is something like quantum-mechanics, and has nothing to do with duplicates.

And you're not supposed to "ask it again". You're supposed to choose one question in there, remove the other two and ask them as new, separate questions.

0celo7

20:35

@ACuriousMind How does one show, easily, that $\sin(\frac{n\pi}{\log b}\log x)=0$ $(n-1)$-times in $(1,b)$?

sharaf zaman

@ACuriousMind i see.

0celo7

@ACuriousMind $\log =\ln$

ACuriousMind

@0celo7 Well, you know when the $\sin$ is zero, right?

yuggib

That doesn't mean it's not a math question. Trust me. You will get the "full download" over there. There are entire mathematical fields like functional analysis which live and die by this very question. Flag this to be moved to the math folks and you will get much better answers. — CuriousOne 1 hour ago

::referred to the triangle inequality ::

0celo7

@ACuriousMind Last time I checked, $\sin n\pi=0$

ACuriousMind

20:38

@yuggib lol

yuggib

T__T this explains a lot about his level of mathematical knowledge

0celo7

but I haven't been to PDE class in ... 2 days

jeez fingers

yuggib

@0celo7 do you know the triangle inequality?

ACuriousMind

@0celo7 Exactly. So solve $n\pi \frac{\ln(x)}{\ln(b)} = m\pi$ for free $m\in\mathbb{Z}$.

0celo7

@yuggib maybe

why

I used it about 5 times on the analysis homework I just completed

ACuriousMind

20:40

@yuggib Experimentalist ;)

yuggib

because apparently then you know all functional analysis

^^^^^^

0celo7

@yuggib oh shit, really?

yuggib

see the above technical explanation

0celo7

@yuggib huh?

yuggib

"There are entire mathematical fields like functional analysis which live and die by this very question"

--- referring to the triangle inequality

0celo7

20:42

@yuggib isn't it just $d(x,y)\le d(x,z)+d(z,y)$ with $d$ the distance function of a metric space?

ACuriousMind

@0celo7 It is

0celo7

that inequality might be the wrong way around.

@ACuriousMind ok, that was like day one in analysis

ACuriousMind

Hint: yuggib does not agree with CuriousOne's statement :P

0celo7

@ACuriousMind I'm countering sarcasm with sarcasm

hint ^

@ACuriousMind uhhh

ACuriousMind

How a single vowel can make the difference between enlightenment and being stumped... :D

0celo7

20:44

$x=\exp \frac{m}{n}\log b$

hmm

ACuriousMind

(I'm referring to your edit of "ohhh" to "uhhh")

0celo7

I feel like one should be able to simplify that

@ACuriousMind I know

ACuriousMind

@0celo7 Good :)

0celo7

@ACuriousMind why would you think otherwise?

@ACuriousMind ok so why is $\exp\frac{m}{n}\log b$ in $(1,b)$ $(n-1)$ times

user507974

Hey guys, if you had only 3 lessons (aka relatively small self contained subjects) you could give to a student to kind of summarize kind of the essential idea behind being a physicist what would you teach them? They dont have to be strictly physics, though they should kind of be focused on ideas to help orient a person to think as a physicist

0celo7

20:48

@ACuriousMind Oh, that's equal to $b^{m/n}$

ah, now it's clear because $m/n<1$.

danks

@user507974 Lesson 1: Don't bother proving equations have solutions, just solve them.

Lesson 2: Bathroom conversations are legitimate citations.

Lesson 3: Always trust Einstein and The Evidence.

user507974

lol mathematicians vs physicists is always a great one
you can have more time, I meant something on the order of 5-25 minutes per "lesson"

user54412

Time for my weekly rant about academia:

user54412

17

Q: Interviews for academic teaching positions and "diversity"

I am a Masters student in math, who loves teaching, and rather than go on for a PhD would rather teach at a community college. I've noticed in many of the schools to which I am applying the they emphasize the need to understand diversity and teaching to diverse ethnic, economic, and ability popul...

interview diversity

ACuriousMind

@user507974 Depends. How much do they know already? Do you want to make them to become interested in theoretical or experimental physics? Or do you perhaps only want to make them interested in science?

user54412

Everyone's basically like "oh yes, you do need to be understanding of diversity, cause black people learn differently from white people"

0celo7

20:55

@ChrisWhite Hmm, does learning vary by IQ?

If so, in general, that would be true.

user507974

@ACuriousMind if you need them to they can have a qualititive understanding of calculus and math in general

for scientific topics maybe 2-3 minutes of an intro to prereqs

0celo7

Math in general?

user507974

lower than calc,

they know well

ACuriousMind

@ChrisWhite That's not what DanRomnik's answer seems to be saying to me. He's actually saying it's not about their mode of learning facts, but about teaching and it not being a pure and rational transfer of knowledge, but also about human interaction, inspiration and such things.

user507974

so like a us high school student, maybe taken a first level calc class

user54412

20:58

I've taught Caltech geniuses, Princeton privileged rich people, and convicted felons who aren't up to high school standards by age 30. Asian, White, Black -- I teach them all the same, and I can't imagine how I could alter my lessons based on their skin color.

user507974

maybe they like science but theyre just curious what physics kind of is

0celo7

> convicted felons who aren't up to high school standards by age 30

user116211

@ACuriousMind: Can a post from here be migrated to Chem SE?

0celo7

Tell us more...

ACuriousMind

@user36790 Only by mods

user116211

20:59

@ACuriousMind O.O

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