The h Bar

user218912

02:00

@0celo7 do I contract the metric in the expression with the deltas?

user218912

and simplify it?

0celo7

Yes, you are.

Bernard Meurer

Inductive set

Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty. In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ1n formula, for some natural number n, together with a real parameter. Inductive set can be defined as follows: A set J of real numbers is called an inductive set if it obeys the following : the number 1 belongs to J, if d is an element of J then d+1...

0celo7

Wiki says $1\in X$.

Sure, if $1\in X$ then I believe it.

@IceLord always

Bernard Meurer

Ah!

My prof. didn't say that!

0celo7

02:00

Shoot him

Bernard Meurer

Let's see his office hours and pester him

0celo7

No wait, this is set theory. No one cares about this

@BernardMeurer Protip: I have some experience with higher mathematics and have never seen "inductive."

Maybe because I don't know algebra, but algebra is boring anyway.

Bernard Meurer

I think this is cool :(

0celo7

Once you learn real mathematics, you won't ;)

user218912

@0celo7 does the metric contract on both deltas?

user218912

02:02

or only 1?

0celo7

@IceLord Sigh. What're you trying to compute?

I'll work it out and see

user218912

so is $\eta^{\omega\xi}\delta_{\omega\alpha}\delta_{\xi\alpha} = 1$

0celo7

is that $\alpha$ being summed?

what's going on there

user218912

@0celo7 thanks.

user218912

oh

user218912

02:04

no

user218912

it's not

0celo7

you have to tell me what you're doing first

user218912

$\frac{\partial}{\partial A_\alpha}\big[ \frac{m^2}{2}\eta^{\omega\xi} [A_\omega A_\xi ]\big] =m^2\eta^{\omega\xi}\delta_{\omega\alpha}\delta_{\xi\alpha}$

user218912

?

user218912

$ = m^2$

user218912

02:07

?

0celo7

no

user218912

what did i do wrong?

0celo7

the derivative

user218912

is it $m^2 A_\mu$

user218912

can you show me your steps so I can learn how to do it?

user218912

02:09

then i'll compute the other lagrangian derivative myself.

0celo7

@IceLord wrong index

user218912

is it $\alpha$?

0celo7

yes

user218912

okay

user218912

I don't get how I got that though.

user218912

02:14

not the $\alpha$ I understand that, but Idk how I got the $2$ and the $A_\alpha$

user218912

from my work

0celo7

product rule

user218912

I know what the product rule is

user218912

maybe I don't because this whole time I was doing the wrong product rule xD

user218912

okay it's all good

user218912

02:24

@0celo7 my issue was I forgot about the metric when I did product rule

user218912

so it made no sense

0celo7

02:39

are you convinced now

user218912

yes but I have 1 more issue that is similar

user218912

what is

user218912

$\frac{\partial A_\alpha}{\partial A^\beta}$

user218912

0?

0celo7

no

user218912

02:41

here we go again...

0celo7

raise the index on $A^\alpha$, pull the metric out, do the derivative, contract again

user218912

oh

0celo7

the metric is constant, remember

user218912

okay

user218912

right

user218912

02:41

in the lagrangian we had

user218912

is

user218912

$\partial_\mu = \frac{\partial }{\partial A^\mu}$?

user218912

or is it $x$ instead of $A$

user218912

I'm trying to show why the first 2 terms are $0$

0celo7

Sigh.

@IceLord I'm sorry, you're just very unprepared for this.

And this isn't stuff that learning QM would help with. It's general "maturity" stuff.

user218912

02:50

@0celo7 that's already been established

0celo7

@IceLord So I'm not sure how to help you.

If you didn't understand some QFT thing, ok. But you're struggling with calculus.

user218912

it's cause I haven't used it for a long time

0celo7

How do you forget calculus?

user218912

by not using it

user218912

but I did learn calc 1-4, 3 years ago, and I did a lot of problems too.

user218912

02:55

I just didn't use it for so long

user218912

I should probably have a refresher but

user218912

what part of my question is stupid?

0celo7

$\partial_\mu$ only ever means one thing.

user218912

I know.

user218912

it's $\frac{\partial}{\partial x^\mu}$

user218912

02:58

i was just making sure

user228700

03:33

Hello :-) Anybody here? I have a quick doubt; energy is defined in most textbooks as the "capacity to do work". I was wondering if this definition is precise and if you have come across other ways in which energy is defined.

DanielSank

Well @KaumudiHarikumar there could be many answers to your question.

"Ability to do work" is a fine definition.

user228700

@DanielSank It's perfectly fine?

DanielSank

I think so.

It is a very good definition.

user228700

Okay, if someone asked you to define energy, how would you go about doing it?

DanielSank

Oh, I'd probably say "capacity to do work" or some such thing.

user228700

03:40

Okay, I see.

user228700

Thanks :-)

0celo7

@KaumudiHarikumar Do you mean you have a quick question :P

DanielSank

@0celo7 Har dee har.

user228700

@0celo7 Oh crap, yes. Need to work on that.

DanielSank

03:56

@KaumudiHarikumar I'm happy I finally know why so many posts on this site say "I have a doubt..."

It seemed so weird for a long time.

user228700

@DanielSank You could've just googled it :P

DanielSank

@KaumudiHarikumar Too easy.

0celo7

@DanielSank What's the explanation?

Something something India.

That's not satisfying.

DanielSank

Apparently.

@0celo7 Sure it is.

0celo7

Is "question" not a word in whatever language they speak?

Or do they use "question" differently?

user228700

03:58

First of all, I'd like to remove @Ocelo7's notion that the people of India speak just one language. Our country has 22 official languages but a total of 1652 languages.

0celo7

@KaumudiHarikumar I don't have that notion.

Which is why I said "whatever language they speak"

user228700

Okay, sorry.

0celo7

I had it the other night, sorry.

So, that makes the question more interesting!

DanielSank

@0celo7 What's "it"?

0celo7

Why do 1652 (wow!) language translate question as doubt?

@DanielSank The misconception that there was one major language in India.

DanielSank

04:00

@0celo7 Because people are silly about translations. Here's my favorite example:

In China, they have certain fermented beverages made from sorghum.

They translate this rotgut to "wine" in English.

It's not made from grapes or any other fruit.

Why do they call it "wine" instead of "liquor" or perhaps "engine degreaser"?

0celo7

Sorghum?

DanielSank

@0celo7 You thought India had one major language?

0celo7

@DanielSank Sure, why not.

DanielSank

Sorghum

Sorghum is a genus of plants in the grass family. Seventeen of the twenty-five species are native to Australia, with the range of some extending to Africa, Asia, Mesoamerica, and certain islands in the Indian and Pacific Oceans. One species is grown for grain, while many others are used as fodder plants, either intentionally cultivated or allowed to grow naturally, in pasture lands. The plants are cultivated in warm climates worldwide and naturalized in many places. Sorghum is in the subfamily Panicoideae and the tribe Andropogoneae (the tribe of big bluestem and sugarcane). == Cultivation and... ==

0celo7

@DanielSank ya I can google.

What's rotgut?

Googling...

DanielSank

04:03

@0celo7 I'm confused about something. Where are you from, anyway?

user228700

@DanielSank Well, the national language of India is Hindi and most people(Except some belonging to the Southern states) know how to speak it fluently.

DanielSank

@0celo7 Stuff that rots your gut.

0celo7

@DanielSank Germany

@KaumudiHarikumar Aha!

DanielSank

@0celo7 You grew up in Germany?

0celo7

@DanielSank yes

DanielSank

04:03

@0celo7 Until what age?

0celo7

@DanielSank Clever name.

@DanielSank Ages 7-14.

The major formative years.

DanielSank

@0celo7 You were in Germany from 7 to 14, and then?

0celo7

DC area.

DanielSank

@0celo7 No kidding. Where are your folks from?

0celo7

Indiana and Slovakia.

DanielSank

04:06

What were you doing in Germany? Military parents?

0celo7

Yes.

Why am I being quizzed?

DanielSank

Because I'm fascinated.

0celo7

Probably not in a good way.

DanielSank

And I want to see if you get the answers right.

user228700

The point that I'm trying so hard to make is that the explanation "Something something India" is definitely satisfactory. English is the language that the people of India use in offices and schools but having our own mother tongues, this is problematic since we do tend to mix up words and not really understand the whole meaning of words before we use them in the way we want to.

0celo7

04:07

What's fascinating you?

@KaumudiHarikumar I just want to know: do you have a word for "question" in your own language?

user228700

The fact that so many people speak English here, is the reason the term "Indian English" even exists.

DanielSank

@KaumudiHarikumar I love Indian English.

But I should admit, I like a lot of things about Indian people.

user228700

I'm not saying that the usage is correct or anything but as long we're sticking to India alone, 100% of the population(who understand English) have no problems with using the word "doubt" like that.

DanielSank

That's interesting.

Also, in my opinion, language is "correct" if it's understood. So in India, it is "correct" to use "doubt" in that way.

user228700

@DanielSank Exactly what I'm trying to say.

DanielSank

04:10

@KaumudiHarikumar Are there good tongue twisters in Hindi?

user228700

I didn't know that the usage was wrong in any way until @Ocelo7 pointed it out to me the other day!

0celo7

@KaumudiHarikumar btw that's a 0 in my name

@DanielSank So what are you fascinated about

You can't leave me hanging now

user228700

Now that I do know, I can try my best to use the word correctly but like I said the other day, I will come across as being extremely pedantic if I go about correcting the people who use the word like that here. "Screw off, we understand it so what's the problem?" And yeah, there IS no problem here.

DanielSank

@0celo7 Just, where does this mathematics fanatic, nuclear engineer grew up in Germany but likes Trump, often socially awkward guy come from!?

user228700

That's why I'm saying that it's a satisfactory explanation.

DanielSank

04:13

@KaumudiHarikumar Definitely do not go about "correcting" other Indians!

0celo7

@DanielSank Often socially awkward?

user228700

@DanielSank And no, I don't speak Hindi at home. But I know some GREAT tongue twisters in Tamil, if you're interested. (Tamil is the language of the state Tamil Nadu, where I presently live)

0celo7

Wait. 1652 languages?

user228700

@0celo7 That's correct.

DanielSank

@0celo7 Not quite what I meant. I was trying to say "awkward in written expression" or some such thing.

@KaumudiHarikumar Please tell me. I like tongue twisters.

0celo7

04:15

@DanielSank Awkward in written expression?

I don't know what that means, I of course do not think I am awkward in written expression.

DanielSank

@0celo7 Yeah, every now and then you really let someone have it in chat, and I think not really on purpose.

user228700

@DanielSank The problem is that I can't type it here because I need to speak it so that you understand what I'm saying.

DanielSank

@KaumudiHarikumar hmmmm, youtube?

user228700

Pronunciation is KEY.

0celo7

@DanielSank Oh. I'm in a bad mood in chat more often than not.

DanielSank

04:16

I wonder if someone has posted videos of these phrases.

@0celo7 Well there you go.

0celo7

I come here to procrastinate I guess. Or when I'm stuck on a math problem. (Like right now.)

DanielSank

My favorite Russian tongue twister is also a tongue twister in English:

user228700

Hm, maybe.

DanielSank

Carl stole Clara's corals, and Clara stole Carl's clarinet.

In Russian it is beautiful.

0celo7

Not bad in English.

@DanielSank I used to be a socialist. Don't know when I flipped.

user228700

04:18

I see :-) Anyway, I need to get back to physics. @JohnRennie: Whenever you're up and about here, would you mind having a small discussion with me about work, energy and all? I'm a little confused.

0celo7

My language tutor in Germany was a hardcore socialist. "Americans are taking over the world" and all that. (Didn't mind taking our money of course.)

DanielSank

Work is just force times displacement.

If you push with force F over distance d, the word done is Fd.

This is an energy, of course.

user228700

@DanielSank Yes. I was thinking I'd maybe take up the specific case of a block attached to a spring, resting on a friction-less surface. The classic example, you know.

user228700

I wanted to talk about that case.

user116211

@0celo7 Sounding like a real commie.

user228700

04:20

But I'm not ready now. I need to finish reading up on some things before I can have a proper discussion.

DanielSank

@KaumudiHarikumar very good

@KaumudiHarikumar Ok. Enjoy your reading.

user116211

@DanielSank What a coincidence! I'm also studying virtual work in generalised coordinates!

DanielSank

@MAFIA36790 Do you understand Lagrange multipliers?

user228700

@DanielSank Okay :-) And google "Tamil tongue twisters". They'll drive you mad, I swear.

user116211

@DanielSank Kinda; but it will come in Calculus of Variations Chapter 2 of Lanczos.

DanielSank

04:22

@KaumudiHarikumar Ummm.... youtube.com/watch?v=IDbo4eUlcKg

Why is he holding his nose?

user116211

@0celo7 okay. So you are from the then East Germany? I guess so.

0celo7

@MAFIA36790 No.

user116211

@0celo7 ohh.

user228700

@DanielSank I don't have the time to look into it right now but sometimes, people do that here :P

user228700

05:14

It turned out that Google Chrome had just failed to update for my system (Since erm, mine is Windows Vista and I can't do anything about it, I'm afraid), and so, I wasn't able to enable Latex here. But now, I'm using Mozilla and still, it hasn't been enabled despite having added the bookmark. Any advice?

user116211

06:08

@KaumudiHarikumar Could you provide a snapshot of the screen?

user228700

Okay.

user228700

user116211

@KaumudiHarikumar Where is the bookmark?

user228700

Inside the bookmarks tab.

user228700

Here:

user228700

06:15

user116211

@KaumudiHarikumar looks good.

user116211

Here it's mine, the first from the left in the bookmark bar:

user116211

Now, press this and see what happens @KaumudiHarikumar.

user228700

Oh, I didn't know that I had to actually click on it. It's working now. FINALLY! Thank you!

user116211

06:20

@KaumudiHarikumar good.

Shing

um... I was trying to install numpy on python with Anaconda (in windows)

but I couldn't figure it out how exactly to do so...

would anyone be kind enough to teach me?

user116211

@Shing Maybe @Bernard could help when he returns, but I have no idea on this.

Shing

@MAFIA36790 okay, thanks man ;)

John Rennie

Morning

user228700

@JohnRennie Morning sir :-)

user228700

06:32

Do let me know when you're up for having that discussion I was talking about...

user116211

Hey @John, how much more to reach the mark?

user116211

I'm eagerly waiting ;)

John Rennie

@MAFIA36790 170

user116211

@JohnRennie ah!!

John Rennie

Touch and go if I'll make it today :-)

I had high hoped for that gauge symmetry answer, but the voting has petered out on it.

@KaumudiHarikumar Slightly bad timing - I have a scheduled task to do at 7:30 (UK time) and I have to start now. Back in around 20 minutes ...

user228700

06:35

@JohnRennie We're all waiting :-) Okay, no problem. Just ping me when you're free.

Secret

1

Q: Uncertainty principle in macroscopic world

Disclaimer: I am not an expert in quantum mechanics. Uncertainty principle says $\Delta x\Delta p\geq \frac{\hbar}{2}$. I recall having read somewhere that Heisenberg arrived at this result considering interaction of photon with an electron, which implied an in-principle limitation on our measur...

Actually, I think this is not very trivial, as otherwise we will be seeing cannonballs moving erractically in random velocities

DanielSank

08:08

@Secret explain

John Rennie

08:32

@KaumudiHarikumar: I'm back! It was a long 20 minutes, but work has a habit of throwing unexpected surprises at you - rarely good ones :-)

user228700

@JohnRennie That's great! :-)

user228700

I'm not troubling you too much, am I?

John Rennie

No, I need a bit of destressing after sorting out things at work and a chat about physics will do that nicely :-)

user228700

Discussions about physics are destressing for you? Wow.

John Rennie

That's "de-stressing" as in reducing stress.

Not distressing as in upsetting me :-)

user228700

08:42

Yes, I know. That's exactly what I meant. Discussions are DE-stressers?

John Rennie

> Discussions are DE-stressers?

Definitely!

user228700

I would've figured that going over the basics with beginners like me prove to cause headaches :P

user228700

In any case, I'm only glad that they're destressing :-)

user228700

I was hoping to discuss about work, force, energy etc.

user228700

See? Basics.

John Rennie

08:45

Yes, I saw you'd chatted to Daniel about it earlier ...

user228700

Yeah, a little bit...

John Rennie

If you're going to ask how to define energy my advice would be don't try to define energy

user228700

Why not..? Is it counter-productive to try and do so?

John Rennie

Because the word energy is used very vaguely and means different things to different people. Unless you have a specific context in mind trying to give it a precise definition is a difficult task.

user228700

Oh, yes, okay.

user228700

08:48

Nevertheless, in this context of physics, if someone were to ask you to define it, what would you say to them?

John Rennie

The conventional definition is the ability to do work

And that's OK if you stick to mechanics

user228700

Oh, so when will I run into trouble while using that def.?

John Rennie

In quantum mechanics or relativity the concept of energy is a bit different. Even in thermodynamics I'm not sure the ability to do work is all that useful a definition.

I'm not sure you'll run into trouble, it's just that the definition isn't all that useful.

user228700

Oh, I see. That's okay, because I don't need to learn QM/Relativity right now.

John Rennie

What brought this up? Did you have a specific situation where the definition of energy mattered?

user228700

08:54

This wasn't so much a confusion than just curiosity. A lot of the things in my textbook are written very vaguely and then, while doing problems, I'll land in trouble when I try to work with the basic concepts in mind. So I try and learn the best definition first so I don't have to struggle with having learned misconceptions later on.

user228700

So, okay. I'm not sure I fully understand what "negative work" means...

user228700

Let's take an example.

user228700

We'll look at that mass attached to a spring kept at rest on a smooth table.

user228700

When we pull this box away from the equilibrium position of the spring, the restorative spring force come into picture, yes?

John Rennie

Yes

user228700

08:58

If the force applied by us is say, $F$, then the work done by us to displace that box by a distance, say $d$ would be $F.d$

John Rennie

The force varies with distance so it's $\int F(x)dx$, but yes you're basically right

user228700

Yeah, yeah, sorry.

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