The h Bar

0celo7

12:00 AM

@IceLord I'm going to learn some QFT today

I take it back, it's too boring

where is @Slereah when you need him

Slereah

Who knows

0celo7

in QFT on CS, what is momentum space?

in regular QFT we just have $\Bbb R^4$ for momentum space

Slereah

Mostly the same

You can have restrictions on the momentum depending on the topology

if you have cyclical coordinates it's more of a $\Bbb Z$

0celo7

the same?

so it's $\Bbb R^4$?

I would imagine you need to look at $T^*\mathscr M$.

Sir Cumference

1:07 AM

I need an inspirational quote

0celo7

1:19 AM

@SirCumference Wishing for a burner, to kill everybody walking. - Desiigner.

Slereah

user218912

wow so inspirational.

user218912

lol.

Sir Cumference

@IceLord [citation-needed]

All that's said is that energy cannot be created nor destroyed in a closed system

The Universe may be an open system

user218912

1:31 AM

I said lol for a reason.

user218912

because that quote is dumb.

Slereah

Garbage is, too

user218912

@SirCumference regardless you're still damn old, at least a few billions years.

Sir Cumference

@IceLord Well then again, every 10 years or so all the atoms in our body are replaced

So I'm not very old

user218912

@SirCumference all of them?

Sir Cumference

1:42 AM

@IceLord Approximately

user218912

@SirCumference I don't think so, but even then they're being replaced by equally old atoms.

Slereah

"In the classical functional analysis (i.e. where the scalar field is R or C) Hilbert spaces play an especially important role. Unfortunately, their non-Archimedean infinite-dimensional counterparts do not exist, i.e. there is no infinite-dimensional Banach space with an inner product for which every closed linear subspace has an orthogonal complement"

I am mad

Sir Cumference

@IceLord Perhaps. But if you call me old, how do you define me?

@Slereah Why are you mad?

Slereah

Well I was hoping for one to exist

Apparently some do but with weaker properties

user218912

@SirCumference let's not get all philosophical.

Sir Cumference

1:44 AM

@IceLord At what point does science become philosophy?

Okay I'll stop

user218912

I can do philosophy. "what is real?".

Slereah

Man I'm gonna have to think hard to build that Hilbert space

0celo7

my avatar is legit

@IceLord gg

@SirCumference what

How are you defining the universe?

Sir Cumference

@0celo7 Everything that exists, will exist, and has existed, everywhere

Essentially all of space and time and its contents

0celo7

I definite it as the maximal direct limit of chained closed systems ordered by inclusion.

It is by definition closed

Sir Cumference

1:49 AM

Wait

Now that I'm thinking about it, it should be isolated...

user218912

@SirCumference you can't define it like that and yet still stay things like it could be open.

user218912

doesn't make sense.

Sir Cumference

Yeah I screwed up

All right, but then again, conservation of energy doesn't apply at relativistic scales, as far as I know

So the law is just an approximation

@0celo7 You say closed or isolated?

You know what I hate about the Universe? The fact we have no idea what the Big Bang was.

I'm sure if we figure that out, we would have answers to so much more about modern physics

user218912

@SirCumference pretty sure we have an idea what it is.

Sir Cumference

@IceLord Oh?

What's that?

user218912

1:59 AM

Idk

user218912

I'm not a cosmologist.

Sir Cumference

All we presume is that's when entropy was at its minimum. GR and QFT break down at those scales.

0celo7

@SirCumference what's the difference

@SirCumference Proof?

Sir Cumference

@0celo7 lmgtfy.com/…

@0celo7 Proof?

0celo7

Ah, you're being annoying

user218912

2:02 AM

@SirCumference I'm pretty sure there are a lot more technical details as to why they break down.

0celo7

Not worth my time

Sir Cumference

@0celo7 I sent you a link...

user218912

@SirCumference you're being a popsci boy.

Sir Cumference

@IceLord What?

user218912

it means you're into popular science descriptions of things, but don't bother to learn them for real.

user218912

2:03 AM

and as 0celo7 said it's annoying.

0celo7

If $(X,d)$ is a compact metric space, any family $\mathcal F\subset C_E^b(X)$ which is equicontinuous at each $x\in X$, is uniformly equicontinuous on $X$.

*Proof.*
Let $\epsilon>0$.

I think I've got a good start there.

Sir Cumference

Find me one paper describing what the Big Bang is.

user218912

you wouldn't be able to understand it.

user218912

even if there was such a paper.

Sir Cumference

@IceLord I read papers all the time

0celo7

2:04 AM

DAMN

Sir Cumference

General relativity can't accurately explain the conditions of a compressed universe

0celo7

how compressed?

user218912

@SirCumference technical papers?

Sir Cumference

@0celo7 Hmm...let's get on the same page. What do you say happened 13.8 billion years ago, at $t_0 = 0$?

@IceLord 'Course. You've gotta read papers if you're gonna cite them on astronomy SE.

user218912

right...

Sir Cumference

2:07 AM

@IceLord Er, believe what you want.

Check my answers if you care enough.

user218912

Did you learn GR?

0celo7

@SirCumference I'm not a physicist.

user218912

from a real book?

Sir Cumference

@0celo7 Find one

Find any.

Ask them if they know what the Big Bang is.

user218912

I'm certain they know what the big bang is, just not all the details and how it works exactly.

Sir Cumference

2:09 AM

@IceLord No one will tell you they know what it is.

It's a major unsolved problem in cosmology.

user218912

I know that.

Sir Cumference

GR suggests that 13.8 billion years ago, the Universe was compressed into a singularity. But GR wouldn't be able to explain such hot and tiny conditions.

user228700

Hello, good morning :-) @JohnRennie: Sir, dyou mind discussing a very small mechanics situation with me..?

Sir Cumference

No currently available physics model can explain the Big Bang.

0celo7

GR can't explain your tiny condition either.

user218912

2:11 AM

dude you know nothing about cosmology so stop talking about it.

user218912

everything you say is superficial.

Sir Cumference

@IceLord Sigh...you don't even need to know cosmology to understand that.

Plenty of cosmologists admit it.

0celo7

@Kaumudi I can probably help with mechanics.

Sir Cumference

@IceLord But I encourage you. Find me a cosmologist here or elsewhere who claims to understand the Big Bang.

user218912

they are fucking working on it.

Sir Cumference

2:13 AM

@IceLord Our modern theories break down at those scales!

We're not near discovering it!

user218912

who is we?

user218912

you're working on discovering it?

Sir Cumference

Humanity

user218912

well you're clearly being a dead weight.

0celo7

oh my gosh this conversation is booooring

Sir Cumference

2:14 AM

@IceLord Ad hominem, my friend.

At least have a civil discussion...

user218912

@SirCumference what?

Sir Cumference

@IceLord You're attacking me instead of proving your point.

I'm asking you to prove me otherwise. I'd love if you proved me otherwise.

user218912

I know what ad hominem means.

Sir Cumference

It'd make me a lot happier knowing that cosmologists understand the Big Bang.

But as it stands, no modern theories can explain it.

user218912

5 mins ago, by IceLord

everything you say is superficial.

Sir Cumference

2:17 AM

@IceLord Ad hominem...

user218912

you don't know enough to talk about these big ideas.

Sir Cumference

@IceLord It's not my knowledge. It's the knowledge of cosmologists.

Plenty admit that no available theories can explain the early conditions of the Universe.

user218912

you don't know what they mean by that though.

user218912

it's like the rest of the facts you keep collecting.

Sir Cumference

@IceLord Sigh, I'll just google something to get my point across

Here's an article from a professor at Penn State

einstein-online.info/spotlights/avoiding_the_big_bang

Read it thoroughly.

user218912

2:19 AM

@SirCumference lol are you JD?

Sir Cumference

@IceLord Dude. I'd love if you could prove me wrong.

user218912

I'm not trying to prove you wrong though.

user218912

why do you keep saying that?

Sir Cumference

What are you trying to say then?

user218912

I'm just saying you're being dumb by wasting time on popular science.

Sir Cumference

2:20 AM

This is popular science?

This is actual goddamn science

user218912

@SirCumference for you it is.

Sir Cumference

NO physical theories can currently explain the Big Bang. This is commonly known among astronomers and cosmologists.

This is a major unsolved problem in physics.

user218912

why do you care?

user218912

you're not bothering to learn real physics with all the math and formalism.

Sir Cumference

24 mins ago, by Sir Cumference

You know what I hate about the Universe? The fact we have no idea what the Big Bang was.

22 mins ago, by Sir Cumference

I'm sure if we figure that out, we would have answers to so much more about modern physics

@IceLord 'Course I am. I'm studying to be an astronomer.

0celo7

2:22 AM

oh my god you two

just stop

Sir Cumference

What did you think I'm majoring in? Business?

0celo7

yes

user218912

@SirCumference book keeping.

Sir Cumference

Oh boy.

I'm dealing with someone who relies on his opinions.

user218912

what?

Sir Cumference

2:23 AM

Tell me what the hell a fact is.

It's a true statement.

Of course I'm relying on facts. They're by definition the truth.

user218912

okay but you don't understand them.

Sir Cumference

Do you know what you're talking about anymore?

user218912

do you?

Sir Cumference

GODDAMMIT

This is going nowhere!

I can't talk to someone who repeatedly says "no. no. you don't understand it."

user218912

because you're missing the point.

Sir Cumference

2:25 AM

What point?

We were talking about the Big Bang.

You're clearly talking about something else.

user218912

you shouldn't talk about cosmology like you're a cosmologist when you know nothing about the physics of cosmology.

user218912

14 mins ago, by IceLord

everything you say is superficial.

Sir Cumference

@IceLord I'M NOT.

My word means nothing! But when I link you to a cosmologist's word, you reject it.

It's ridiculous!

user218912

wtf?

user218912

I didn't reject anything.

user228700

2:27 AM

@0celo7 OK. We're applying a force on a block attached to a spring (hinged at its other end) so that it starts going around in a circle with angular velocity $\omega$.

user228700

If we were to examine the motion of this body at any point, it becomes clear that for the body to be moving with constant angular velocity $\omega$ in a circle, a centripetal force must be acting on it. The only force that is capable of applying a force on the block in the radial direction is tension arising from the extension of the spring. Everything correct, so far?

user218912

I'm saying I don't like it coming from you.

Sir Cumference

8 mins ago, by IceLord

@SirCumference lol are you JD?

user218912

@SirCumference that's a joke.

Sir Cumference

Seriously? I give you a link and you shrug it off?

user218912

2:27 AM

you linked an einstein website.

Sir Cumference

Oh...

Nevermind, didn't realize that...

Regardless, this conversation isn't going anywhere.

user218912

k bye.

user218912

@0celo7 I saw the jet black iphone 7 at best buy today and it looks better irl than in the photos.

user218912

are you considering getting that one?

0celo7

3:05 AM

@IceLord maybe

I'll get a case anyway

user218912

okay so following what slereah said for problem 1

user218912

I expanded the time ordered product using step functions

user218912

then I apply the differential operator?

user218912

and that's it?

user218912

how long is the calculation?

0celo7

3:07 AM

I already said I don't know how to do it.

user218912

but that is how you do it.

0celo7

I don't know that.

user218912

@0celo7 what does $(\partial_\mu \partial^\mu)_x$ really mean? does it mean that you are taking the derivative only wrt. to $x$?

user218912

so how does it look like?

user218912

are there still 4 terms?

0celo7

3:16 AM

$x$ is a spacetime point

user218912

oh so you're taking the derivative at $x$?

user218912

I don't get this notation, can you show it explicitly please?

user218912

like does it mean there is no more components for the derivative anymore?

0celo7

what's the context

is there a $y$ floating around

user218912

the context is the question only.

user218912

3:24 AM

want me to link it again?

0celo7

$(\partial_\mu\partial^\mu)_x$ just means $\eta^{\mu\nu}\frac{\partial}{\partial x^\mu}\frac{\partial }{\partial x^\nu}$

user218912

okay.

user218912

so you're summing over all the indices?

user218912

how does that look when applied to a term

user218912

like the step function

0celo7

3:30 AM

ok now that you can write out yourself.

I estimate this problem will take a page at least

user218912

can you give a hint please?

user218912

like the first term please

0celo7

what is $\eta^{\mu\nu}a_\mu b_\nu$ in general

user228700

@0celo7: What about my mechanics problem..?

0celo7

I said I can probably help.

user228700

3:31 AM

@0celo7 It turns out that u can't..?

0celo7

I haven't seen it.

user228700

I typed it out, above...

user116211

@Kaumudi Give him the permalink.

user228700

1 hour ago, by Kaumudi

@0celo7 OK. We're applying a force on a block attached to a spring (hinged at its other end) so that it starts going around in a circle with angular velocity $\omega$.

0celo7

Ok what about it?

user228700

3:33 AM

1 hour ago, by Kaumudi

If we were to examine the motion of this body at any point, it becomes clear that for the body to be moving with constant angular velocity $\omega$ in a circle, a centripetal force must be acting on it. The only force that is capable of applying a force on the block in the radial direction is tension arising from the extension of the spring. Everything correct, so far?

user116211

Anyways,

user116211

The easiest Theorem of the Day: Unit of a ring is not zero divisor.

user218912

@0celo7 you just sum over all the indices and the terms that are not matched become 0 because of the metric tensor.

0celo7

@Kaumudi Well if you have anything going around in a circle like that you'll have tension on whatever is connecting it, no?

user218912

so it's like

0celo7

3:36 AM

@IceLord ok so what's the issue?

user218912

oh

user218912

no issue.

user218912

sorry.

user218912

thought it worked differently

user218912

oh my god

user218912

3:39 AM

this calculation will take forever

user218912

so many terms

user218912

and... if I make a mistake somewhere in the middle i'm doomed

user116211

@IceLord How dare he to link EINSTEIN's website? Must be JD's conspiracy ;(

user228700

@0celo7 That's exactly the problem that I am facing in my reasoning; see, I have examined the situation and then concluded that there must be some extension in the spring, so that it exerts the force of tension on the block. What is the correct way to think about this, in which it becomes clear that the spring gets stretched?

0celo7

@Kaumudi draw a free body diagram!

user228700

3:46 AM

@0celo7 I did do that and it didn't help me in my reasoning very much, but it's becoming more clear to me now; the tension starts acting because the block is accelerating..?

user218912

well I give up for today, will continue this tomorrow.

user228700

Basically, why does the tension start acting? That is my question.

0celo7

Interesting.

If the spring is not in tension when you start it, it will certainly be pulled outwards

(I think)

so then it will be in tension

but how much tension?

user228700

@0celo7 Well, the magnitude can be calculated by equating the formula for the centripetal force acting on the block, $mv^2/r$ to the tension caused by the extension in the spring, $kx$.

0celo7

@Kaumudi What is $r$?

user228700

3:53 AM

Here, $r=l+x$ where $l$ is the natural length of the spring and $x$ is the elongation in the spring.

user228700

@0celo7 Yes, this is the point that I missed. When I exert some force on the block to get it moving in a circle, the spring will be pulled outwards..? How is this so..?

user218912

phd level mechanics?

user228700

And since the only force acting on the spring is this radial tension, the radius of the circle doesn't change, due to the absence of tangential acceleration, to change the speed of the circle. (A change in speed will result in a change in the radius of the circle)

user228700

@IceLord Lol, no.

user218912

@0celo7 how does the ETCR come into this calculation?

0celo7

3:58 AM

uhhh what

user228700

@0celo7 Hm?

0celo7

I don't know what the problem is

@Kaumudi that's @IceLord

user228700

@0celo7 And this is about my question?

0celo7

@Kaumudi no

user218912

@0celo7 it says using the ETCR and the field equations

user218912

3:59 AM

all we did was write everything out explicitly and then take the derivative

user228700

@IceLord I thought u were going to bed.

user218912

i am in bed.

user228700

@0celo7 OK, can you help me to understand how the tension starts acting?

user228700

@IceLord (Y)

user218912

@Kaumudi ask @MAFIA36790 he knows mechanics.

user228700

4:03 AM

@MAFIA36790@JohnRennie: Can you please help?

0celo7

@Kaumudi Sorry, I'm too tired for PhD level physics

user228700

@0celo7 Dude, this isn't PhD level! I'm 17 -_- In any case, thanks for trying. I'll wait for MAF/JR.

0celo7

Harder than anything we do in the West

user218912

@Kaumudi basically as you learn more you will find low level stuff more difficult.

user228700

@IceLord That doesn't make sense but OK.

0celo7

4:05 AM

@Kaumudi I thought I understood it, then you convinced me I didn't, then I thought you agreed with me, but looking back I can't find that message.

So I'm just confused in general right now.

user228700

@0celo7 Sorry :-P

DanielSank

4:18 AM

@Kaumudi Does DS qualify? ;)

DanielSank

4:34 AM

@0celo7 I've seen that somewhere...

user228700

@DanielSank Hello :-) Definitely! Can u help me out?

user228700

Aw man, did u leave?

user228700

Shucks.

DanielSank

4:50 AM

I'm here @Kaumudi.

I think I understand your confusion :)

Can we start with a slightly simpler problem?

John Rennie

Morning

DanielSank

hi

user228700

Hello, morning, aloha :-)

user228700

@DanielSank Um, will the simpler problem take very long to explain..?

DanielSank

Not at all

(Although I guess you've already learned I take too long to explains stuff)

user228700

5:02 AM

@DanielSank OK, then please go on...

user228700

@DanielSank Oh, crap. I haven't got a lot of time :-(

DanielSank

Anyway, to make sure: you're wondering how to think about why the spring extension is related to the centripetal acceleration, right?

You understand the answer, but you don't like how you reasoned to that answer, rigth?

user228700

@DanielSank Yes, well, my only question is this; how is it that the spring force starts acting?

DanielSank

@Kaumudi Right, good question.

Ok, forget the simpler problem, let's just get into it...

Suppose you have a mass and a spring.

user228700

OK...

DanielSank

5:04 AM

You pick up the spring by its end and start whirling it around you like a lasso.

user228700

@DanielSank Yes, OK.

DanielSank

The mass starts moving away from you --> the spring starts to extend --> the spring exerts a force on the mass because the spring is extended.

At some point, the spring extends enough that its restoring force matches the force needed to keep the mass going in a circle at the rotational speed at which you are twirling.

There is an approach to equilibrium. The system doesn't start already in equilibrium.

user228700

@DanielSank Riight...

DanielSank

That's it.

(When you have time, I'd like to hear why you turned into a red pizza man. I bet it's a funny story.)

user228700

@DanielSank Yes, I understand. I missed the "The mass starts moving away from you".

user228700

5:08 AM

@DanielSank Oh, that!

user228700

JOHN GREEN IS FAT.

►

DanielSank

@Kaumudi Well, just imagine actually doing this. You grab the spring, and somehow you have to get the mass moving. Either you pull hard enough on the spring to move the mass, or you start everything by throwing the mass away from you.

user228700

@DanielSank Yeah, OK...

DanielSank

That's all there is to it.

user228700

Also, I changed my Avatar because a creep kept inviting me into a room for no particular reason; I decided that it's better not to have my face on this website. And why the pizza John? 'Cause I'm a Nerdfighter (It's different than what it sounds) B-)

user228700

5:11 AM

@DanielSank OK, thank you! :-D

DanielSank

@Kaumudi Sure.

@Kaumudi Yeah, good idea.

user228700

Also, I just realized that you may not understand close to half the sentences that John says in that video. Sorry :-P If you feel so inclined, just google "Vlogbrothers". They are doing a heck of a lot more world-suck reducing than me.

user228700

5:33 AM

@JohnRennie: Are u there?

John Rennie

Yes

user228700

I have another small question. (Truly, it's small :-P) Do u have the time?

John Rennie

Yes, right now I'm just drinking coffe and postponing doing any work :-)

user228700

@JohnRennie I wonder if u're just copying and pasting that over and over again :-P

John Rennie

No, I just drink a lot of coffee and procrastinate a lot :-)

user228700

5:36 AM

@JohnRennie Haha, OK :-) So I'm trying to understand the motion of a body going around in a vertical circle.

John Rennie

OK, that should be easy ...

user228700

And from my textbook, I have learned that the minimum velocity of the body at the lower most point must be greater than or equal to $\sqrt{5gl}$ for it to complete the circle/"loop the loop".

John Rennie

If you say so. I'd have to do a few sums to check that's correct.

user228700

@JohnRennie No, that's correct :-) That fact is not even relevant to my question so never mind. Now we're handling the cases in which this velocity is smaller than required, so the body doesn't complete a full circle.

John Rennie

OK

user228700

5:41 AM

There seem to be two cases for this to happen: either the tension becomes zero first, while the speed remains non-zero or the speed vanishes while the tension is still present. This is correct, yes?

John Rennie

Yes, that's correct, though I'm not sure that's the best way to describe the two cases.

user228700

@JohnRennie OK...how would u describe these two cases then?

John Rennie

Suppose we take the angle of rotation to be zero when the object is at the bottom of the circle.

user228700

@JohnRennie OK.

John Rennie

So the angle is $\pi/2$ when the string (assuming it's a mass on a string) is horizontal

and $\pi$ when the object is at the top of the circle.

user228700

5:44 AM

OK.

John Rennie

Yes, I've just corrected it:-)

For angles between $-\pi/2$ and $\pi/2$ the component of $mg$ along the string (the radial component) points outwards i.e. stretches the string.

So between these angles (the bottom half of the circle) the string tension can never be zero.

If the velocity is small we just have a pendulum type motion.

user228700

@JohnRennie It points outwards?

John Rennie

Shall I draw a diagram?

user228700

@JohnRennie Hang on, I'll draw it and u tell me where I'm wrong...

John Rennie

user228700

5:52 AM

John Rennie

You've drawn the diagram for $|\theta| \gt \pi/2$

user228700

Oh, crap, yes. I misunderstood.

DanielSank

@JohnRennie Standard sysadmin operating procedure.

user228700

Okay, I understand your point. This only was my doubt in the first place; where $T$ tends to become zero and where $v$ does and I understand it now.

user228700

Thank you! :-D

John Rennie

5:55 AM

The point is that the string can't become slack for $|\theta| \le \pi/2$

user228700

@JohnRennie Yessir, understood.

John Rennie

So for the bottom half small $v$ just means we have a pendulum type motion.

user228700

But there is still one thing I don't quite understand...

John Rennie

The string can only go slack for the top half if $v$ is small enough. Specifically if $v^2/r$ is smaller than the radial component of the acceleration due to gravity.

I have to do a quick job for five minutes. Back in a moment ...

DanielSank

Mwaha hahahaha, I have gotten mathjax to work on my public journal!

user228700

5:58 AM

@DanielSank Congratulations! :-D

DanielSank

@Kaumudi Thank you. It was surprisingly easy.

@0celo7 Got mathjax working on my website. I think you had asked about how to do that...

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