The h Bar

John Rennie

15:00

But firstly it is far from obvious that the quantum foam idea is true, and secondly spacetime isn't really like a foam.

What actually happens is that it exists in a superposition of different topologies.

0celo7

@ACuriousMind what point?

John Rennie

At the scale the topology isn't well defined, so topology change isn't well defined either.

0celo7

@JohnRennie I don't think that's what we mean by topology change

John Rennie

Describing the quantum foam as tiny rips in spacetime is very misleading.

Danu

Hi @docscience, @JohnRennie

John Rennie

15:01

But at the pop sci level you hear it done quite a lot. Oh well.

docscience

Hello

Swapnil Das

I was calculating the equation of a light ray in a medium of variable refractive index. I spotted the following property:

John Rennie

Hi Danu. We're talking about rips in spacetime.

Danu

Ah, the age old truth... If it's easy to visualize in physics, it's probably wrong. If it's easy to visualize in math, it's definitely right :D

John Rennie

Anyhow, the bottom line is that i don't think rip in spacetime means anything.

And the fact you hear it said on pop sci programmes doesn't change my view!

If anyone disagrees please shout now ...

Swapnil Das

15:04

docscience

@JohnRennie what about near singularities where gravity turns in on itself?

0celo7

@ACuriousMind I've found the worst type of person

Swapnil Das

Could anyone provide a substantial reason for the same?

Danu

@JohnRennie Pretty much correct

I mean, AFAIK all current theories abandon a geometric point of view at the relevant scales

Aaron Abraham

Um @JohnRennie, I've got a little doubt......would you mind hearing me out? [If you're an Optics guy that is...]

Danu

15:05

Geometry is kind of viewed as emergent, so a notion of "rips" in a otherwise smooth spacetime doesn't really work

John Rennie

@docscience singularities are points where the geometry becomes undefined

they aren't rips

0celo7

What is a rip if not that?

Danu

I'll rip you one! :D

docscience

What about the collision of two singularities (realizing I'm reaching...)

user228700

@SwapnilDas You can prove this using Huygens's principle.

docscience

15:07

do singularites in GR have direction?

0celo7

@JohnRennie I should look up the topology change theorems in GR

Swapnil Das

@Kaumudi Was that obvious?

docscience

@Danu thanks

John Rennie

depends what you mean by direction

Danu

So @docscience I think a better way to think about stuff is as follows: Right now, nobody really knows, or claims to know, what exactly is going on super close to the singularity*. We know for a fact that GR is great at describing everything that's just a liiiittle bit away from where it predicts a singularity. So we work with the GR picture in practice, but do not regard its claims about singularities as "the final word".

user228700

15:08

@SwapnilDas What was?

Swapnil Das

@Kaumudi the proof

0celo7

The usual statement is that the topology of a spacelike hypersurface should not change

But that's (a) trivially true in the globally hyperbolic case

(b) probably false in the non globally hyperbolic case

so I don't know what the actual content is

docscience

I'm not a GR expert, but would think it's the metric tensor that leads to the singularity, and don't tensors have direction?

user228700

@SwapnilDas What do u mean was the proof obvious? If u mean to ask whether it's simple, then yes, it's ridiculously simple; very basic geometry.

Aaron Abraham

@Kaumudi Why use Huygen's Principle? The R.I and angle of incidence are already constants...

John Rennie

15:10

> don't tensors have direction?

no

0celo7

@docscience What does that mean?

Swapnil Das

@AaronAbraham That's correct. But why equal at all varying conditions?

user228700

@AaronAbraham To prove that Snell's law.

0celo7

@JohnRennie The metric tensor does have a direction in GR.

The time orientation.

user228700

Yes, this^ The proof is very simple. Look it up.

0celo7

15:10

probably not what's meant, but still

Aaron Abraham

@SwapnilDas What conditions? I don't see any in the picture ._.

Maybe I missed it?

Danu

Also PSA

0celo7

well, it's not uniquely defined

Danu

in Mathematics, 2 hours ago, by Danu

Whoa, Bob Dylan winning the Nobel for literature

user228700

@AaronAbraham He means to ask about Snell's law.

0celo7

15:11

but one can give it a direction @JohnRennie

Aaron Abraham

@Kaumudi Now why do you want to prove that ?

Danu

@0celo7 shaddap and stop confusing people.

user228700

@AaronAbraham I don't? @SwapnilDas does.

John Rennie

there is a direction in GR in the sense that time always flows forward

user228700

Anyway, I have to get back to Chemistry. @SwapnilDas: Seriously, look it up.

Aaron Abraham

15:12

@SwapnilDas You're trying to prove Snell's law?

Swapnil Das

@Kaumudi I got it , thx!

0celo7

@Danu I thought you had ignored me?

user228700

@SwapnilDas No problem :-)

0celo7

This constant ignoring and unignoring is confusing :(

Swapnil Das

@AaronAbraham Thanks u too.

Aaron Abraham

15:13

Whaaaa?

John Rennie

There are singularities that can only exist in the future and not in the past - these are called spacelike singularities. e.g. the static black hole has a spacelike singularity.

Swapnil Das

I combined both your ideas and created a nice image.

John Rennie

But there are other singularities that can exist in the past as well as in the future e.g. in rotating black holes.

docscience

@JohnRennie hey thanks for the intro to the h bar. Interesting discussions. But I have to run now ..

Aaron Abraham

Elaborate @SwapnilDas

John Rennie

15:14

@docscience OK bye :-)

0celo7

@JohnRennie what does "past" mean here

Danu

@0celo7 ?

0celo7

such things always confuse me

Swapnil Das

@AaronAbraham Just can't. It is kind of thought expt.

0celo7

@Danu You said the other day that you were ignoring me

after the complex geometry thing

Aaron Abraham

15:15

Alright....

Swapnil Das

@JohnRennie Why do black holes tend to rotate?

Thanks anyways.@AaronAbraham

0celo7

@SwapnilDas most astronomical objects rotate

Aaron Abraham

Why?

Danu

@0celo7 Read it again

0celo7

angular momentum

Swapnil Das

15:15

Why?

0celo7

@Danu Ted got the same impression.

Aaron Abraham

As a result of?

0celo7

I have proof.

Danu

@0celo7 Hmm?

0celo7

he said "you can block me too"

Aaron Abraham

15:16

Lets see it ;)

Swapnil Das

Everything at the micro and macro level seems to rotate? Why? @JohnRennie

0celo7

Implying you had blocked someone earlier

(me)

Danu

@0celo7 To whom?

0celo7

@Danu you

I will find it, hold on.

in Mathematics, 2 days ago, by Ted Shifrin

You can put me on ignore, too. :D

Danu

Oh well

He got the wrong impression, then

Aaron Abraham

15:19

Does anyone happen to know what exactly causes the scattering here?

0

Q: what causes water to be white in a river?

I know it is because of turbulance, causing air to enter the water. But neither air nor water are White, why does the combination of the two make White.

0celo7

@JohnRennie In the standard terminology, a static black hole has a past and future singularity

so I'm confused by what you're saiyng

ACuriousMind

@AaronAbraham scienceblogs.com/builtonfacts/2013/04/01/why-are-clouds-white

John Rennie

@0celo7 you're thinking of the white hole singularity in the maximally extended Schwarzschild metric?

0celo7

Yes.

Aaron Abraham

@ACuriousMind You're alive! I'll read up on it, thank you!

Danu

15:22

eyyo ACM

John Rennie

@0celo7 well, yes, but the other singularity cannot be in the past of timelike worldline.

That's what makes it spacelike. I'm actually not sure what the term is for the white hole singularity ...

0celo7

> In 2+1-dimensional GR, curvature vanishes identically

...what

John Rennie

because that cannot be in the future of any timelike worldline.

@0celo7 that's true isn't it?

0celo7

what the hell

I've never heard that

why would it be true?

John Rennie

@0celo7 there are too few degrees of freedom in 1+2G GR for spacetime to curve

0celo7

15:24

oh, the EFE are overdetermined?

John Rennie

I don't know about overdetermined but there is too little fredom for curvature.

The singularities in 1+2D GR are just angular deficits.

ACuriousMind

Relevant article about 2+1 GR being locally flat

0celo7

I've never heard of that

John Rennie

@0celo7 I know something you don't know :-)

Aaron Abraham

@ACuriousMind Thanks, the link helped !

0celo7

15:26

where would one even hear about such a thing

John Rennie

@0celo7 have you not read Witten's paper on quantum gravity in 1+2D?

0celo7

No

I think they're cheating

They're applying Lovelock's theorem in 2+1D

i.e. trying to do physics

bah

hmm, no

they're still using the EFE

Interesting!

In 3D one can write the Riemann tensor in terms of the Ricci tensor!

I must have known that

@JohnRennie Ok I knew that :)

Just had to think

It comes from the sectional curvature decomposition of the Riemann tensor

@JohnRennie But still, @ACuriousMind 's paper (thanks) treats the case $T=0$.

^that's why it's true

John Rennie

@SwapnilDas there's a question that deals with this. Let me look ...

43

Q: Why does everything spin?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons. Where has all the angular momentum come from? Why is it so natural? I was also thinking do photons spin? we always think of the wave as a standard 2d sin wave but could this rotate ...

angular-momentum rotational-dynamics quantum-spin conservation-laws

7

Q: What is the origin of spin of celestial objects?

In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is asking about the origin of the rotation of celestial bodies. The accepted answer (with 17 votes) states the following: When things collapse under their own g...

astrophysics angular-momentum rotational-dynamics conservation-laws celestial-mechanics

0celo7

15:42

@JohnRennie so no reaction to what I just said :(

that was the first GR rant I've had in a while

John Rennie

@0celo7 to be honest I don't know enough math to understand the detail. I just knew that was the case.

user228700

@JohnRennie: Sir, are u busy? I've got a really quick chemistry question.

John Rennie

@Kaumudi ask away ...

0celo7

@JohnRennie Basically, you can write the Riemann tensor as a linear combination of metrics and Ricci tensors in 3D

because of that above matrix equation

in 4D I think it becomes undetermined

So $T=0$ implies Ricci flat implies Riemann flat.

But the case $T\ne 0$ is unsolved

John Rennie

I knew it because I attempted to understand Witten's exact solution for 1+2D quantum gravity, and it's the restricted freedom that allows gravity to be quantised in 3D.

user228700

15:46

@JohnRennie I keep hearing about how the reason that water is polar is because the molecule is bent in shape. I just thought it was largely due to the difference in electronegativity b/w the H and O atom..?

ACuriousMind

@Kaumudi How would it be polar if it was H-O-H in a straight line? Where would the negative/positive pole lie?

John Rennie

It is largely due to the difference in electronegativity b/w the H and O atom. However if the molecule were straight there would be no net dipole.

But close up to the molecule you'd still have a measurable dipole moment.

user228700

Sigh. Yeah, I'm super dumb. Thanks guys.

0celo7

@ACuriousMind How the hell do you remember chemistry

ACuriousMind

By not having a sieve for a memory? :P

0celo7

15:50

@JohnRennie aha, I think I knew that too

@ACuriousMind :(

I don't know what to do

I can't remember anything

I need help

I can't remember months, left/right, I have trouble with the alphabet...

ACuriousMind

Alas, my parents are both chemists by training, and I think I learned most things I know about it from my father and not in school

John Rennie

@ACuriousMind Cool :-) My mother was a bacteriologist, but I've always hated biology.

0celo7

My mother is a writer, I hate writing

John Rennie

My father was a company director and i know bugger all about directing companies!

0celo7

My father is a pilot and I can't drive a car without people fearing for their lives

Secret

15:54

Both my parents are not scientists or did anything science related

ACuriousMind

@JohnRennie Heh, well, I like chemistry well enough but it doesn't really excite me

John Rennie

Yessssssssss! I just got this for £84!

Secret

In fact: None of my friends except those in uni have something to do with science, thus most of the time, I am kinda a loner

0celo7

@ACuriousMind Rebecca wants to learn topos theory

John Rennie

My niece has been hinting she wanted a laptop with a bigger screen for watching films at sleepovers. Now I shall be favourite uncle again!

0celo7

15:58

should I just send her the link to nLab or is there a good way of doing it

@JohnRennie How many does she have?

John Rennie

@0celo7 Dozens of the frakking things. Teenagers!!

0celo7

I mean uncles

ACuriousMind

@0celo7 I don't know any actual topos theory. If you look through the references on the nLab there should be a reasonably nice introductory article among them, though

John Rennie

@0celo7 only two. So being favourite uncle isn't that great an achievement especially when the other uncle is a complete twa ... er ... twit.

0celo7

@ACuriousMind Well she should presumably learn commutative algebra and algebraic geometry first, right?

ACuriousMind

16:01

I don't think either is required for topos theory

0celo7

Hmm, ok

ACuriousMind

A basis in category theory would be probably assumed, though

0celo7

Oh, that's what I meant.

not algebraic geometry

ACuriousMind

And one should probably take care to pick something that doesn't use alg.geo. examples

0celo7

Right...well she decided to read a book on mathematical music theory

one of those books written by musical Urs Schreiber

ACuriousMind

16:03

I think @Danu talked about some of those a while ago

0celo7

Yes

I showed her that one

Danu

@ACuriousMind Yeah, I did

0celo7

it's not something that anyone at our school can help her understand

I don't think we have any category theorists

Danu

I think the consensus is that it's (I mean topos theory is) kinda useless to learn music theory :P

0celo7

@Danu She's a flute performance major

oh

yeah but it seems neat

user218912

16:06

idk what area of physics to specialize in!!!

user218912

so lost

0celo7

you're a freshman

you don't specialize in anything

user218912

I want to get a head start.

user218912

specialize now

0celo7

not sure what the point is

user218912

16:07

point is I like obsessing over things so I want to specialize on a topic.

John Rennie

@ACuriousMind I ended up doing physical chemistry, which I found enormous fun. It has a lot of physics in it and you get to play with some cool kit. Up to and including neutron scattering measurements at Grenoble.

ACuriousMind

@bl00 You should obsess about getting a broad basis so you can make an informed decision what to specialize in

user218912

true

0celo7

this might be the best wallpaper ever

user218912

but I have a good idea of what different areas of physics are like by observing you guys talking in chat and also looking at random questions on the site. @ACuriousMind

user218912

16:09

@0celo7 why?

John Rennie

@0celo7 I don't use wallpaper on my PCs or laptops. I think being in the business I just regard them as tools.

Though I do use wallpaper on my phone and tablets, but then they're basically toys.

0celo7

@bl00 it's so pretty

I can flick over to

ACuriousMind

@bl00 I'm not sure one can get a good impression about physics from this chat.

The distribution of specalizations and opinions about subfields here are highly unusual

user218912

@ACuriousMind well before you guys used to talk about physics.

user218912

good times btw.

Danu

16:13

@0celo7 God that'd be terrible as a wallpaper! So busy!!!

The super high quality version of this from here is awesome.

John Rennie

@bl00: there will be areas of physics you've never even heard of. You need to have a much fun as you can learning as much cool physics as you can. Then make a decision as you approach your graduation.

0celo7

@Danu that's not my wallpaper

I have two desktops

when I need it, I can perform a special trackpad gesture

it brings it up

my wallpaper is the one above it

user218912

@0celo7 I prefer this wallpaper

user218912

Danu

lel

Bernard Meurer

16:18

That's ugly af dude

user218912

no, it's impossible for anything blue to be ugly.

Bernard Meurer

This is mine

google "blue waffle"

ACuriousMind

0celo7

I love blue waffles

2

so...tasty

John Rennie

Boring, boring, boring, oh well ...

Danu

16:22

lol

OLD COMPUTER MAN

You're living up to the image :D

ACuriousMind

That'd be like starting at a blank cell wall for me!

Secret

Genuine Royal Air Force R... ?

John Rennie

Ooh, looking at that I've just noticed my diary says the new Wormrot album is out tomorrow!

0celo7

what the hell @JohnRennie

user228700

Yeah, omg.

user218912

16:24

@JohnRennie mine is similar

John Rennie

@Secret Something I've bought on eBay

user218912

Secret

@JohnRennie nice

0celo7

@ACuriousMind Crap! I have to buy a symphony ticket after QM today. I was planning on playing FNV :(

John Rennie

@Kaumudi you're a Wormrot fan????

0celo7

16:24

It's impossible to say Wormrot without a German accent

ACuriousMind

It is?

John Rennie

Vurmroat

0celo7

@ACuriousMind Yes

You wouldn't know because you have a German accent

user228700

@JohnRennie Nooo, sorry to disappoint you lol. That comment was me agreeing with @0celo7 when he said "What the hell", as a reaction to your wallpaper.

0celo7

But even for us who can speak English correctly it's impossible

@Kaumudi I was reacting to the Wormrot comment

ACuriousMind

16:26

I mean, it lends itself very well to the typical German accent, but I don't see it's impossible to pronounce it "properly".

user228700

@0celo7 OK. In any case, I was, to the boring wallpaper :-P

John Rennie

Odd, seeing as the band are from Singapore

@Kaumudi I work with computers all the time. They're just tools. You don't see mechanics painting their spanners to make them look cute.

I almost said you don't see mechanics painting their tools but that is open to misinterpretation.

0celo7

The R needs to be rolled heavily

John Rennie

amazon.co.uk/Voices-Wormrot/dp/B01I0MUL26

0celo7

jesus

@ACuriousMind I have a doubt

ACuriousMind

16:32

@0celo7 Fine. Come back when you have distilled it into a question.

0celo7

suppose I have the potential $V(x)=g[\delta(x-a)+\delta(x+a)]-u\delta(x)$

I need to find the conditions on $g$, $u$ and $a$ for there to be bound states

how the HELL do I do that

I don't even know where to begin

ACuriousMind

You...try to solve the Schrödinger equation and see what happens?

I can't get any more specific without actually attempting the exercise, either

0celo7

@ACuriousMind But how do the boundary conditions work?

Do I need to evaluate the discontinuity in the derivative at each delta?

ACuriousMind

You know how it works fora single $\delta$, right? Is there anything that doesn't straightforwardly generalize?

0celo7

No, I don't know how it works for a single delta.

user218912

16:38

@0celo7 does amazon refund you if your prime order doesn't arrive in time?

0celo7

If you complain, yes

I think

user218912

did you ever try it?

0celo7

Do you want my address?

ACuriousMind

I don't believe that they demand that you solve that exercise before you know how to do it for a single $\delta$.

user218912

@0celo7 I ordered a field theory book and it arrived 3 days late with prime.

0celo7

16:38

@bl00 yes that's why I have two copies of Weinberg

they sent me a second copy that arrived the same day

user218912

@0celo7 in a few days, I can't buy it right now.

0celo7

@ACuriousMind This is supposed to be review

oh wait

we did a single delta on this week's homework

so what you get is an overdetermined system of equations for $g,u,a$, right?

in terms of the energy?

I'll work on it later

user228700

17:00

@JohnRennie True :-P

user228700

Goodnight!

Secret

Trivial looking division by zero that is not the trivial ring:

1

Q: Type or classification of a distributive algebraic structure made from a subsemigroup and a subgroup?

NB: $a,b,c \in S$ The following nontrivial (but trivial looking) algebraic structure $S$ is constructed. It was found that that $(S,+)$ is isomorphic to the left zero semigroup of 3 elements, while the $(S,\times)$ is isomorphic to $(\mathbb{Z}/3\mathbb{Z},+)$ Therefore $(S,\times)$ forms a s...

abstract-algebra group-theory semigroups

John Rennie

WiFi hotspots seen on a train in the UK:

6

0celo7

Did you take a picture of a computer screen

Bernard Meurer

17:18

@JohnRennie Lol

John Rennie

It was posted by a friend of mine on Facebook. Fun and games with SSIDs :-)

0celo7

@ACuriousMind I worked everything out

But I have 7 variables with 6 equations

How do I make such a system soluble?

Aaron Abraham

Electromagnetism anyone? I've a question I'm not able to clear elsewhere ...

In a capacitor that's discharging, current ought flow from the positive plate to the negative one via the external circuit right?

But then there's this diagram that confuses me.

The direction of current's from the negative to the positive plate, i.e- the other way 'round.

ACuriousMind

17:35

@0celo7 That should be solvable - just not uniquely

0celo7

I'll take a 0 on the homework if I have to solve a 6 or 7 dimensional system @ACuriousMind

It's just not happening

David Z

17:55

@AaronAbraham note the last phrase of the description

0celo7

@ACuriousMind So in that problem

the wave function will be $A_1e^{kx}$ on the left

but $A_4'e^{-kx}$ on the right

can I argue by symmetry that $A_1=A_4'$?

"left" and "right" means $x\to\pm\infty$

ACuriousMind

Well, do you know for sure that symmetric potentials will have symmetric eigenstates?

0celo7

@ACuriousMind Nope

Harmonic oscillator for one

ACuriousMind

Then how would you argue here?

0celo7

I don't know

these homeworks are insane

Aaron Abraham

18:05

@DavidZ Ah yeah...saw that, but what's the point in assigning the opposite direction to current?

David Z

@AaronAbraham Educational value I guess? There are plenty of situations where you can't avoid working with negative currents (i.e. where the actual flow of current is opposite the direction in which you choose to draw the arrow), so I guess you might as well get used to it from the beginning.

Aaron Abraham

@DavidZ Thanks! ^_^

(but that sorta sucks though...putting up with a weird situation like that :/ )

Alfred Centauri

@AaronAbraham Choosing a reference direction for a current variable is physically equivalent to choosing which direction to place your ammeter in the circuit - you have to choose a direction. If you solve for the current and find that it is negative, it is physically equivalent to inserting your ammeter into the circuit and recording a negative current. It's not wrong and it gives you the same information as if you had inserted it the other way.

Aaron Abraham

Sorta like how it doesn't matter when you assign an arbitrary current direction while using Kirchhoff's Junction rule right? @AlfredCentauri

[P.S- I voted for you ;) You're questionnaire was hilarious XD , though it's a pity you weren't elected :/ ]

Keshav Srinivasan

18:23

Can someone take a look at my question here?

2

Q: How do we prove that the angular velocity vector is equal to a limit?

The angular velocity vector of a rigid body is defined as $\vec{\omega}=\frac{\vec{r}\times\vec{v}}{|\vec{r}|^2}$. But that's not how most people intuitively think about angular velocity. Euler's theorem of rotation states that any rigid body motion with one point fixed is equivalent to a rotat...

newtonian-mechanics classical-mechanics rotation rigid-body-dynamics angular-velocity

ACuriousMind

Infinitesimal rotations are commutative — John Rennie yesterday

@JohnRennie ^what?

The algebra of infinitesimal rotations is the algebra of angular momentum, which is not commutative in 3D. What is that comment supposed to mean?

0celo7

Lol

@ACuriousMind I talked to the prof, he was very helpful

The problem isn't that hard

Bernard Meurer

@ACuriousMind Am I commutative in 3D?

ACuriousMind

@BernardMeurer You're lucky if you're associative

Bernard Meurer

@ACuriousMind Ha, smart

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