The h Bar - 2017-04-19 (page 1 of 4)

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12:07 AM

1

Q: Why was PhysicsStackExhange made?

I am curious to know "Why was PhysicsStackExhange made?"I mean certain objectives and did PSE fulfil them?

discussion support

12:21 AM

0

Q: Rigorous mathematical definition of Vector Operator?

In standard QM-textbooks, the concept of operators is often introduced as linear maps that map a hilbert-space $H$ onto itself: $$ \hat{O}: H \rightarrow H $$ However, directly after, we use the position operator $\hat{\vec{x}}$, which isn't of the said shape, but instead is somewhat a triple of...

quantum-mechanics vectors tensor-calculus mathematics

12:54 AM

0

Q: What type of questions receives maximum downvotes?

I was thinking on this and thought that it might interest you to answer the above query as opinion differs from person to person. I think mostly such questions are homework or show no research.But again we all think differently. I hope this gets maximum support and people read it so that they avo...

discussion questions insufficient-effort

1:07 AM

0

A: Are there any ways to alter frequency of wave?

That happens in phyics everyday. It is how we use any of our energy. It creates a change in physical makeup of matter through a chemical process, ei burning wood. All matter is EMR at different frequencies. When you burn wood, you are changing the emr frequency of the wood and harvesting a change...

:O

" Other: I'm voting to close this question as off-topic because it should be closed. "

lol

> Let us next consider normal modes of oscillation of an air column with one end and the other open. A glass tube partially filled with water illustrates this system.

How will it look like^ ? (@JohnRennie)

Or anyone

The water will act as a solid surface.

The length of the column excluding water is the effective length of the air column.

I still can't imagine it :(

user image

@Yashas then waves it mentioned is sound wave ?(in air)

1:21 AM

....

It is an air column.

The air inside it viberates.

Air vibrating = sound waves

K

1:47 AM

mornin

'My boobs exhibit steady growth over time': Woman emails her crush a very funny - and persuasive - PowerPoint presentation listing the reasons why he should date her / dailymail

I'd rather not open the daily mail

@Slereah lol too high class for you? :P

hi

hi

2:07 AM

is a Lorentz transform its own inverse transform?

Only if it's the identity

Or a reflection

if you mean a Lorentz boost, then definately no

The inverse, you change the signs of $\beta$

I'm reading off one of the courses suggested on relativity here
https://preposterousuniverse.com/wp-content/uploads/grnotes-one.pdf

On page 17 they talk about the lorentz transform and how an inverse of the lorentz transform is a lorentz transform itself.

yes

but not the same one

ah I see

so to arrive at the inverse we take a lorentz transform again, which may or may not be the same as what we took earlier.

It's not, except for the identity

2:18 AM

@Slereah nice exercise: the fundamental group of a connected topological group is abelian

Is it?

$F_2$ isn't abelian

What?

I don't think so anyway?

What group is that supposed to be a fundamental group of

Punctured torus

2:20 AM

...how is that a group?

Oh

You mean a lie manifold

nvm

No

I mean a topological group

alright

Yeah nevermind then

Thought you meant a generic topological space

oh no

those are horrible

However, a manifold always has a countable $\pi_1$

What would be a topology that has an uncountable fundamental group

2:26 AM

$$\varinjlim_{j\to\infty}\bigvee^j S^1$$

So... $\Bbb Z^\omega$?

It would be the free group with $\omega$ generators

Something like that

Ah yes

Maybe it's countable, actually

Wouldn't infinite dimensional torus have $\pi_1$ being $\Bbb Z^\omega$?

2:28 AM

Maybe

I don't think that's countable

probably depends on choice :P

user image

... wouldn't an infinite dimensional punctured torus also have $\pi_1$ being $F_\omega$?

2:50 AM

In the course of moderation activity one sometimes encounters the barely perceptible tracks of skilled cheater. These users approach their cheating with a sense of pride and craftsmanship and accordingly design elaborate campaigns to elude moderation and subvert site policies.

Can't say I like them, but at least you have to give them their due: they will think and worker harder for their rep than merely earning it honestly would require.

I know

Then there are the kinds of cheater to whom that description simple does not apply.

I was actualy John Duffield all along

Sad. No challenge. No mystery. No question. Not even any entertainment value. ::sigh::

You're no Sherlock Holmes, @dmckee

2:52 AM

user image

@Slereah the proof

@Slereah No. I'm not. Which means that cheating that doesn't even interest me is even more pathetic.

Oh I found a topology with uncountable fundamental group

Apparently just

Uncountably many holes

in what

Like $\Bbb R^2 \setminus (\{ 0\}, \Bbb Q)$

in MSE

2

Q: Proving that a fundamental group is uncountable

Given the space $\mathbb{R}^2 - \bigl(\{0\}\times\mathbb{Q}\bigr)$, I need to show that the fundamental group of this space is uncountable. I thought of taking two points $A=(x_0,y_0)$ in the area where $x_0 < 0$ and $B (x_1,y_1)$ where $x_1>0$, now i can find a path between them since I removed...

algebraic-topology

Wait, couldn't a manifold have that?

Take the long line

Make it a long plane

Remove a point at every intersection

boom, $\mathfrak c$ holes

that's not a manifold.

2:58 AM

why not

or do you assume paracompactness

not locally euclidean

why not

I think paracompactness is key

@Slereah because $\Bbb Q$ is not closed nor open

I don't mean that one, I mean the long line example

still probably not one, but idk

I don't know the long line

3:00 AM

The long line is like

Unit interval x $\mathfrak c$

Just take an uncountable ordinal $\omega_1$, then put the lexicographic topology on $\omega_1 \times [0,1)$

it's v. long

yeah that's too large

I bet paracompactness is needed

If you can't cover by a countable number of charts, you're screwed

Hm

what to use for a section

$s$ or $\sigma$

s

let's go with $s$

Math people should really thing about using more alphabets

Put in some cyrillic letters

Some coptic

Ϣ

there's a good letter

it descends directly from hieroglyphs

Ϯ

3:59 AM

The existence of the 0 section is because vector bundles have structure group $GL$ and that preserves the 0, right?

what existence?

just write down the zero section

That every vector bundle admits a global zero section

what is there to prove?

that the local sections go together well

define $\zeta:M\to E$ by $\zeta(x)=(x,0)$.

That's it

Done

I don't know what you want to prove

4:01 AM

Well why would that work better than defining some section $(x, \vec e_1)$

are you asking why that's well defined

that it's what you said i guess

any VB chart transition is linear on fibers, hence preserves the 0 in (x,0)

So yes what I said :p

no you said some strange thing

@BalarkaSen are you up?

He's not on the chat, certainly

@ACuriousMind wtf does it mean to splice two sequences of sheaves?

@Slereah so are you learning cohomology?

user image

I am currently in cohomology hell

4:18 AM

I'm trying

But

even wikipedia is a bit shy about telling me what it's about

I have a big old chain of groups linked by homeomorphisms

But I do not know what they are for

do you mean homomorphism

maybe, I dunno

what what is for?

you first learn simplices and singular homology

What are those groups I'm supposed to align like ducklings, anyway

you don't start with chain complexes

4:20 AM

I guess I need to go back to Hatcher

maybe read lee

he explains everything very gently

I can't read a confederate general!

you're not black

Are you sure

I could be

I've seen your hand in pictures.

4:24 AM

Maybe I have vitiligo

Like Michael Jackson

Although I guess I posted that Finland photo

I don't look very black in it

user image

How does anyone actually come up with this stuff?

I guess when it's your job and you have to do it 8 hours a day

You find weird stuff

this is nuts

de Rham's theorem takes one paragraph with this formalism

it takes a chapter in Lee

also what's lee

I can't google "lee"

intro to topological manifolds

4:37 AM

in theory salon, 51 secs ago, by vzn

Physicists Attack Math’s $1,000,000 Question— Physicists are attempting to map the distribution of the prime numbers to the energy levels of a particular quantum system. / Wolchover, Quanta

thx

Hm, should I skip straight to cell complexes

4:50 AM

@0celouvsky I am now.

@BalarkaSen Hola. Consider $p:\tilde G\to G$ a covering map of topological groups that is also a homomorphism. Suppose $G$ is abelian. How does one show that $\tilde G$ is also abelian? Apparently one is supposed to use that $\tilde G$ is Abelian iff $\tilde \mu\tilde\tau=\tilde \mu$, where $\tilde \mu$ is multiplication and $\tilde\tau$ is the switch operator on $\tilde G\times \tilde G$

I have done this many moons ago. Give me a while to remember; you have to fiddle with the commutative square with maps $G \times G \to G$ and $\tilde{G} \times \tilde{G} \to \tilde{G}$.

Is it an exercise in Hatcher?

I looked but couldn't find it

No, but it's in Munkres.

Well I'll be

algebraic topology or topology?

4:55 AM

topology

part II

I have it on my desk

looking

Consider the commutator $[x, y]$, which is a map $\tilde{G} \times \tilde{G} \to \tilde{G}$.

Push it down to $G$; that sends everything to identity.

yes, and the image of the commutator is connected

that's fine

but what does that have to do with the switch map

I don't care about the switch map. Wait up.

I know what proof you're trying to do

4:59 AM

Ah, yes, so $\tilde{G} \times \tilde{G}$ gets sent to a specific element in $\tilde G$ because the fiber over the identity is discrete.

And that has to be identity.

So you want to do this with the switch map?

I guess?

idk

I need to sleep

gotta get through this page of Cech cohomology though

k fine. I think you need to do this by lifting tricks.

where on Earth is this in Munkres

I don't remember. It's in part II, maybe the miscellaneous problems in fundamental group? I think it's along with the exercise which says $\pi_1$ of topological groups are abelian

I already did that one

It's not with that one

5:05 AM

@0celouvsky Ah! I think I have it.

There are two maps $f, g : G \times G \to G$, by sending $f(a, b) = ab$ and $g(a, b) = ba$.

$f = g$ because abelian.

Sure

These lift to $\tilde{f}, \tilde{g} : \tilde{G} \times \tilde{G} \to \tilde{G}$, which are exactly the same maps above again.

Or rather, start with those map (left mult/right mult) on $\tilde{G}$ and push them to $f, g$.

What's latex for a big bar

It's not clear to me that you get a lift

Like $f |_{t=0}$

But big

5:07 AM

You can get it locally

But why globally?

@0celouvsky Map lifting lemma.

you need a condition on the fundamental group for that

ah, these are not universal covers right?

hmm.

@BalarkaSen don't think so

@0celouvsky What if I start with $\tilde{f}, \tilde{g}$ on $\tilde{G}$?

That is to say, those are the right/left multiplications.

Can I push it down to $f, g$ on $G$?

Basically I want to use uniqueness of map lifting.

5:11 AM

@BalarkaSen Yeah, cuz $p$ is a homomorphism.

I don't buy it. If you have $\tilde{G} \times \tilde{G} \to \tilde{G}$ postcomposing with $p$ gives $\tilde{G}\times\tilde{G} \to G$.

I don't get the right domain.

The p gets turned into p x p or something. I've got to go, talk tomorrow

Yeah g'night. Frustrating that I can't remember the proof I originally knew.

Oh no

The dreaded tangent space of a fiber bundle

The double whammy

cute isn't it?

5:16 AM

user image

"Consider the tangent space $T_u \mathcal P$ of a point $u \in \mathcal P$ and a separation of $T_u \mathcal P$ into a vertical $V_u \mathcal P$ and a horizontal $H_u \mathcal P$ subspace"

What are you reading?

uu.diva-portal.org/smash/get/diva2:531162/FULLTEXT02.pdf

For an explicit characterization of the tangent bundle of a vector bundle, see Kolar, Michor, and Slovak.

Chapter 2

$\mathcal P$ isn't necessarily a vector bundle, though

it's a principal bundle

@0celo I think if you carefully follow my previous argument you can show the fundamental group containment you were worried about.

By fiddling with $p_* \pi_1(\tilde{G}) \subset \pi_1(G)$

5:25 AM

@Slereah oh, well. They probably have that too but I'm less sure about that

Oh going for real now

*ok

night

Hm

What to call the set of smooth real valued functions on a manifold

O'neill calls 'em $\mathfrak F$

Dunno if I like it

Wald goes with $\mathscr F$

I guess everyone uses fancy f's

I use $C^\infty(M)$

Guess that works, too

I have so many books to read

help

why can't it be 2000 BCE and there are like 5 books to read

pick up one, read. pick up next, read. ad inf

5:43 AM

Maybe I should read all books in chronological order

First the epic of gilgamesh

Then the pyramid texts

and so on

not a bad plan actually

Though really bronze age stories are really awful to read

Odd style, lots of metaphores that are barely comprehensible, lacunas, also most of them are really supposed to be songs

Iron age is where it's at

that's where the famous stories are from

Homer is just after Bronze right

he's the real stuff

Kind of

Like

at the junction, probably?

Yeah something like that

5:46 AM

The Trojan War happened during the bronze age collapse

where does ancient Hindu literature fit in? Iron age?

Well it's always a bit hard to apply ages to the whole planet

but most of it is roughly from that era, yeah

I think some bits of the Veda are maybe from the bronze age

But overall it's the iron age

Ya I'm thinking of Europe, so can't quite match up the history

gotcha

Well there is an era that applies to all of Eurasia

Called the axial age

Which is roughly the iron age

Fun

5:51 AM

Did u know

ancient indian math used colors for variable names

no. how does that even work out

Just the name of the variables

they liked to assign numbers to colors i suppose

I mean it's no weirder than using $xyz$

The scheme was from Brahmagupta

Although colors didn't come up until the second variable

strange

5:55 AM

First variable was ya for yavat-tavat

Second was ca (calaca), black

Third was ni (nilaca), blue

etc

they were on the deep end of numerology

Apparently a formula looked like

ya v 1 ru 2

v for varga, the square

So $x^2 + 2$

except in Sanskrit, course

Writing out explicitely what's a variable and what's an "absolute number" was a common thing back then

Diophantes did the same

They didn't like using a symbol for +

user228700

6:28 AM

@JohnR: Morning :-)

Morning :-)

user228700

How's it going?

mornin

@Kaumudi.H sorry for the high latency, just answering a really simple question but one I remember being puzzled by as a beginner.

user228700

What is it?

6:43 AM

1

Q: Can we add attraction forces?

From Newton's Law of gravitation we know that: $$F=G\frac{m_1m_2}{d^2}$$ For simplicity, let's say that both $m$ are $1 kg$ and that the distance apart was $1 m$. Yielding $G$ as the attraction force in Newtons. Hence $F= 6.67\times 10^{-11}$. Now what if you had two $0.5kg$ glued to each othe...

homework-and-exercises gravity newtonian-gravity coulombs-law

user228700

Ah, nice.

really like that perspective

7:00 AM

Can anyone here review Griffith's electrodynamics? I would like to hear the perspective of experts.

Review book: Introduction to electrodynamics by Griffiths.

Well when I hear about any EM book, it's always Griffiths or Jackson

So I'm guessing it's alright

Aha, thanks! @Slereah

Btw, from where did you study?

France

Or do you mean EM

I didn't have an EM book

Oh yeah :P

Oh, Ic.

I still don't really have one

The closest i have to an EM book is a 60's French book that has an EM section

7:10 AM

Oh, that doesn't make a difference. Important thing is to learn the material properly :)

@EmilioPisanty Sorry I think I had to put that comment below the main question, and not below your answer. I did not have any negative intent doing that, it was simply mistake.

7:58 AM

The backup on one of my servers failed last night with the error message "irgendwas grausames ist passiert".

:-D

Google Translate tells me this means "something cruel happened". Not the most helpful error message, but it raised a smile on a dreary Wednesday morning.

user228700

@JohnRennie Haha x'D

8:27 AM

0

Q: If I can receive information from the future, would it violate the second law of thermodynamics?

Details: Here, the laws of time travel assumes not a deterministic universe, so while it is not possible to alter the past (when one wants to send information to the past, it is already received in the present moment), there are plenty of possible futures, receiving information from one of those ...

thermodynamics entropy information time-travel landauers-principle

Any time travel researchers wanna have a take on this?

time travel researchers include whoever that wants to build a time machine

8:47 AM

@ACuriousMind : A.k.a. bullcit! :)

From a Facebook friend:

user image

user228700

Remus Lupin would've loved this infographic )-':'-)

user228700

Speaking of Remus, @JohnR: Who is ur fav. character in the H.P series?

According to the PLANCK data the fundamental domain of the universe's topology is very likely to be larger than the surface of last scattering

Very sad

@Kaumudi.H Apart from the obvious nerd choice, Hermione, and the obvious lad choice, Hagrid, my favourite is Mad Eye Moody.

I've always been partial to the mad savant stereotype. It's a shame we didn't see more of Moody.

user228700

8:54 AM

Is Hagrid really the "obvious lad choice"? How come?

user228700

@JohnRennie Ah, I see...

@JohnRennie : Chocolate perpetuum mobile: i.stack.imgur.com/d2OKd.gif (Source: math.stackexchange.com/a/348298/11127)

@Kaumudi.H He's a big strong chap, basically well meaning and nice but firm when he needs to be. I mean, if you spilled his beer you'd buy him another :-)

user228700

:-) Yes, I've always been fond of Hagrid.

@Qmechanic :-)

user228700

8:57 AM

However, Remus Lupin would be my favorite character if forced to choose. He's not a nerd or anything but examples can be cited to prove that he was an excellent wizard and an even more excellent teacher/mentor.

user228700

What with his lycanthropy and all, he has gone through much suffering in his life. Jeez, can you imagine waking up one morning to the news of the loss of all four of your best friends?

user228700

His character development was done so well by J.K.R.

$$\Huge{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}$$

The Eyes

@peterh No idea what you're talking about there.

$$\Huge{}^{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}_{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0} \overset{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}{\underset{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}{0}}{}_{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}^{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}$$

Going to expand it one more level

9:19 AM

Warning: May cause lag, hence post in smaller size

.
$${{}^{{}^{{}^{{}^{{}^{0}_0 \overset{0}{\underset{0}{0}}{}_{0}^0}_{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0} \overset{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}{\underset{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}{0}}{}_{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}^{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}}_{{}^{{}^{0}_0 \overset{0}{\underset{0}{0}}{}_{0}^0}_{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0} \overset{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}{\underset{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}{0}}{}_{{}^0_0 \overset{0}{\underset{0}{0}}{}_{0}^0}^{{}^0_0 \overset…

I am NOT going to do the 4th iteration as it will most surely crash mathjax

9:37 AM

@0celouvsky Yes, a "fine sheaf" is a "sheaf with partitions of unity". Although I recall there are some subtleties in the definition, but on manifolds all the versions of "fine" should agree

@Qmechanic Hehe, I didn't even think of that!

Simply Beautiful Art

9:48 AM

@Secret lol, please don't flood

@JohnRennie ...why are you using some German software with a sense of humor to backup your servers? :D

@0celouvsky Beautiful, isn't it? deRham is just the statement that the differential forms resolve the constant $\mathbb{R}$-sheaf, none of these laborious proof that it agrees with singular cohomology by hand necessary.

bleh

10:12 AM

@0celouvsky You can split a longer exact sequence into short exact sequences by adding (co)kernels, that is you can split $\to A_{i-1} \to A_i \to A_{i+1}\to$ into $0\to \mathrm{ker}(d_i)\to A_i \to \mathrm{im}(d_i)\to 0$ for every $i$. Splicing is "reversing" this process, i.e. if you have two sequences $\to A\to B\to C\to 0$ and $0\to C\to D \to E\to$, you get a map $B\to D$ and $\to A \to B \to D \to E \to $ is exact.

@BalarkaSen blub

@ACuriousMind zang tumb tumb

yeah, that escalated quickly

@ACuriousMind I use an app called DriveSnapshot. It is a real server nerd's tool - very basic but awesomely good at what it does. I've used it in anger, i.e. to restore dead servers, many times and it always works :-)

It's the sort of app I wish I had written myself - there is no higher praise :-)

10:31 AM

What are those SQL servers use for: commercial, financials, research databases,etc.?

@Secret SQL Servers?

Uh if I recall, the servers you took care of day and night in your job are SQL servers...?

so that means they are for managing and storing some large volume of data

But what type of data? Intuition suggest it might be financial transactions, but I might be wrong

I look after many types of server. Some of them run SQL but the majority don't.

The company I work for provides support to businesses that can't afford to (or don't want to) employ their own IT guy.

@JohnRennie I see

Hmm I see

10:40 AM

the ideal database is comma separated values in a text file

@Slereah It has the advantage of simplicity, though the performance suffers once you have a few million records in the database.

0

Q: I need help reverse engineering standard firefighting hydrant static and residual pressures

I'm trying to program a virtual fire pump panel; I have all the friction loss and gpm equations working. One of the last steps is to figure out the static/residual pressure. All off my fellow firefighters are stumped as this type of calculation is done by "reality" (we don't have to figure htis ...

fluid-dynamics pressure flow

^on-topic or off-topic as engineering?

11:15 AM

Please help me here ;- sound pressure of a sound wave is 14 Pascal and the pressure of air is 10^5 Pascal find the difference between max and min pressure

Guys I want to know how to get max and min pressure of sound in different medium which the above question related to.

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Apr '1719

The h Bar

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