The h Bar

The Dark Side

14:00

The Laplace Runge Lenz vector is a constant of motion in the Kepler problem, right?

ACuriousMind

"Classical mechanics" is so broad as to convey no useful info - I can imagine many parts of it I'd like to discuss, and equally many I wouldn't like to discuss

The Dark Side

@ACuriousMind :P

ACuriousMind

@TheDarkSide Yes.

Emilio Pisanty

@rob mind your 's in 't Hooft

Avantgarde

@BalarkaSen Can't say that here. Greenleaf seems like a fairly known band. How come I didn't know about them..

Slereah

14:02

@ACuriousMind is there any work these days for non-Euclidian space path integrals

ACuriousMind

@JohnJack My point is that your "specific case" doesn't simplify anything. In mathematics, we generally only prove things for specific cases if the proof there is somehow different from the general case, which is not the case here. Whenever I read the proof of something and some hypothesis does not seem to be used, I wonder whether a) I did not understand the proof or b) the author did not understand the proof, since they thought it necessary to restrict to a specific case.

Slereah

Path integrals without Wick rotations

The Dark Side

@ACuriousMind OK, now in order to define the position vector, we need some origin of co-ordinates ...

ACuriousMind

@TheDarkSide No. :P

rob

@EmilioPisanty Delayed editing of comments is a nice superpower.

Cryolune

14:03

@Avantgarde so... is that basically edm?

Emilio Pisanty

@rob correct spelling on the first try is a nicer one

The Dark Side

so that we can define $\vec A = \vec p \times \vec L - mk \hat r$

ACuriousMind

I can view position as an element of an affine space without any choice of origin. However, in order to do useful things with that, I'll need to choose coordinates and therefore an origin.

John Jack

@ACuriousMind Yeah agreed.

Emilio Pisanty

@rob $\Large{😝}$

Avantgarde

14:04

@Cryolune Lol, I was just joking about that. Balarka likes progressive/psychedelic rock, at least.

Emilio Pisanty

@ACuriousMind @rob Moderator access to PII is logged, right?

ACuriousMind

@EmilioPisanty Yes

The Dark Side

@ACuriousMind Yes. So, that poor origin is at the center of the gravitating body?

Balarka Sen

@Avantgarde That's ok. I was more asking if you knew Bengali, because I know of a 70's band from Bengal that I'd recommend pretty much literally anyone. :P Yeah, Greenleaf is really good.

Avantgarde

@BalarkaSen Greenleaf seems alright. Mix of hard and stoner rock

ACuriousMind

14:06

@TheDarkSide Usually, yes.

rob

@EmilioPisanty Of all the languages where I'm a good speller, Dutch isn't one of them.

Avantgarde

@BalarkaSen Oh sure, I don't care about the music's language. Share away

The Dark Side

@ACuriousMind Alright. How about we shift the origin to some other more convenient spot?

ACuriousMind

Sure, you're allowed to do that.

Emilio Pisanty

@rob oh, for sure

but then that's what google is for

Cryolune

14:07

@Avantgarde Lmao because it wasn't making any sense. I was searching the artists/bands you referred to and also progressive dance pop and it did not really fit. xd

Balarka Sen

@Avantgarde Moheener Ghoraguli. I think they are the oldest rock bands of India or something?

ACuriousMind

Note, however, that then the formula for the conserved quantity that's the L-R vector of course changes.

Emilio Pisanty

(i.e. for googling the spelling before you post =P)

Avantgarde

@Cryolune hahahahahaha

Balarka Sen

@Cyolune I do like progressive dance pop though. As an example.

The Dark Side

14:08

@ACuriousMind Yes it does. OK. Now, suppose I pick a point on the orbit as the origin. The physics doesn't change, it is only a co-ordinate transformation...

Avantgarde

@BalarkaSen The vocals are very nice. Well, they're Bengali

Cryolune

@BalarkaSen I don't really have any specific genre of music I listen to because I like basically any song that's interesting to listen to, from any genre.

Avantgarde

Sometimes it feels like I'm he's talking physics lol, since there are many Bengalis in physics

Cryolune

but I think most of songs people link me or what I find ends up being some form of EDM for some reason.

Avantgarde

@Cryolune Wait, I'll show you something that's not EDM

Balarka Sen

14:13

@Avantgarde Here is my favorite album of them by the way. They use unreal guitar riffs at places.

The lyrics is good but of course unintelligible to non-natives :P

rob

@EmilioPisanty I would argue that particular apostrophe is especially tricky. I mean, I was just looking at the user page where it is spelled correctly. It's sort of like a a repeated article -- something ordinarily small that sometimes parses as correct even when it isn't.

The Dark Side

@ACuriousMind - What I'm trying to figure out is, what is we do this problem backwards? i.e. given a satellite in orbit, suppose I record the co-ordinates relative to some origin and the velocities, I must be able to determine the LRL vector and hence, this constant of motion, right?

ACuriousMind

@BalarkaSen unintellegible, not unintelligent ;P

Avantgarde

BLUT AUS NORD - Epitome X

►

rob

I mean, I had just looked at it.

Balarka Sen

14:14

@ACuriousMind That's what I said, man

ACuriousMind

@TheDarkSide Sure, just look at the formula for the LRL vector and see how it transforms under the coordinate change from the gravitating body as origin to the satellite as origin. There's your formula.

Of course, it would be very difficult to figure out there even is a LRL vector if you had never seen the standard derivation. That's why clever choice of coordinates matters.

Avantgarde

@BalarkaSen Yeah, I can't understand what they're saying. But it's nice

Cryolune

@Avantgarde What genre is that?

Balarka Sen

(Maybe @Blue would like them. I think he knows Bengali?)

The Dark Side

@ACuriousMind Just a small problem with that. If the origin is in the orbit itself, I'm unable to imagine what all happens to the three vector terms all along the orbit ...

Anonymous

14:20

@BalarkaSen Which one? (I do know Bengali :P)

Avantgarde

@Cryolune Industrial black metal

The Dark Side

e.g. look at $\hat r$

Balarka Sen

@Blue Scroll up a few messages, I linked Avantgarde an album of Moheener Ghoraguli.

I don't know if you know of them or how much you have heard of them.

Anonymous

@BalarkaSen Oh sure. Checking.

Anonymous

I haven't heard of them before just now though :P

Balarka Sen

14:21

They're relatively unknown, which is a shame.

The Dark Side

At half an orbit away, it points e.g. from what we call a perigee to the apogee

Cryolune

@Avantgarde I have a friend who loves this kind of music and he plays it too.

The Dark Side

Now, velocity is tangential to the trajectory at any instant.

Avantgarde

@Cryolune Yeah, I knew quite a few people. I'm not sure if you liked it though? :P

Cryolune

@Avantgarde It's alright. I'm used to being linked similar songs so I've learned to like it. xd

Anonymous

14:25

@BalarkaSen Just listened to this. Yeah, it's really nice! I like calm tunes like this one. Will surely listen to more of this band. :)

The Dark Side

So, for $\vec L = \vec r \times \vec p$, won't $\vec p$ point in the same direction as earlier @ACuriousMind?

only a change in $\vec r$, and hence in $\vec L$, and hence in LRL?

Balarka Sen

@Blue Yeah they are fantastic. They're from the 70's, and the members were part of the Hungry generation.

If you ever want to listen to them rigorously start with this.

The Dark Side

Basically, something similar has been dished out earlier : physics.stackexchange.com/questions/208863/…

Or am I mistaken with my $\vec p$ direction preservation guess?

^ I suspect so.

So, the reason why I throw this here is, is an explicit calculation the only way of finding out, or can we deduce?

Anonymous

@BalarkaSen Yep, I'm listening to that now! What's Hungry generation btw? :P

Anonymous

Hungry generation

The Hungry Generation (Bengali: হাংরি জেনারেশান) was a literary movement in the Bengali language launched by what is known today as the Hungryalist quartet, i.e. Shakti Chattopadhyay, Malay Roy Choudhury, Samir Roychoudhury and Debi Roy (alias Haradhon Dhara), during the 1960s in Kolkata, India. Due to their involvement in this avant garde cultural movement, the leaders lost their jobs and were jailed by the incumbent government. They challenged contemporary ideas about literature and contributed significantly to the evolution of the language and idiom used by contemporaneous artists to express...

Anonymous

14:33

Ow

Balarka Sen

70's counterculture in US influenced a massive stoner culture in Bengal

that's what it is

Anonymous

My knowledge of History is poor. Ah, interesting!

Balarka Sen

surely they're not taught in any history textbook you will see in school, one does not simply turn a kid into a Naxalite :P I got to know about them very recently.

Anonymous

naxalite...lol XD

Omar Khayyam

What are some unsolved problems in the areas of quantum mechanics and particle physics which once solved, will be revolutionary to our way of perceiving the world.

I am going to solve them.

Anonymous

14:40

List of unsolved problems in physics

Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail. There are still some deficiencies in the Standard Model of physics, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical...

Anonymous

Good luck :P

Cryolune

Good luck indeed.

Balarka Sen

don't forget us when you win the nobel prize

Cryolune

Are you going to solve ALL of them?

Anonymous

Please give me a share of the Nobel Prize too for giving you the list of the unsolved problems. XD

Emilio Pisanty

14:42

@rob I'm not sure who you'd be arguing that against

that apostrophe is possibly the trickiest one of all

The Dark Side

Down to a more fundamental (or crap) question:

What happens to the unit vector $\hat r$ when this $\vec r = \vec a - \vec b$, and $\vec a$ and $\vec b$ refer to the same points?

Of course, the magnitude vanishes.

But unit vector?

$\hat r = \vec r / r$ is a $0/0$ form in that sense?

Or have I completely lost my mind?

Where will the unit vector point?

Omar Khayyam

"and why observed spacetime has 3 spatial dimensions and 1 temporal dimension?"

isnt this wrong

its from the link you gave

just because nothing travels faster than light there is 4 dimensions in total

The Dark Side

Once this is settled, the LRL vector shall be settled too ...

Omar Khayyam

and we assume nothing travels faster than light

we dont consider the imaginary dimension

there would be 8 dimension if we accepted that there are things which can travel faster than the speed of light.

John Rennie

@OmarKhayyam if you're planning to revolutionise physics you aren't making a great start.

Omar Khayyam

14:57

noononononononononono

ACuriousMind

@TheDarkSide What do you mean "unable to imagine"? You should be able to tell how each of the three vectors transforms, you're just doing a shift $r\mapsto r + r_0$.

No imagination involved

Omar Khayyam

i am just asking

Cryolune

for a friend right?

ACuriousMind

@TheDarkSide There is no unit vector.

Omar Khayyam

and actually where is the best start point to revolutionize physics

John Rennie

14:58

@OmarKhayyam learn it first?

The Dark Side

6 mins ago, by The Dark Side

What happens to the unit vector $\hat r$ when this $\vec r = \vec a - \vec b$, and $\vec a$ and $\vec b$ refer to the same points?

ACuriousMind

The zero vector is the one vector that doesn't have an associated unit vector.

The Dark Side

@ACuriousMind exactly!!

So, what happens to the second term in LRL?

Omar Khayyam

do you know cern beamline

i want to run an experiment

The Dark Side

$-m k \hat r$

Omar Khayyam

15:00

i need to know what is unknown in physics

Anonymous

@OmarKhayyam Maybe you need to learn what is "known" in Physics, first.

Omar Khayyam

thats not a good argument

ACuriousMind

@TheDarkSide Ah

John Rennie

@OmarKhayyam I'm afraid it is a good argument.

0celouvskyopoulo7

@ACuriousMind do you mean spoon?

The Dark Side

15:01

spoon?

ACuriousMind

Heh

Omar Khayyam

how can you know what is unknown by learning what is known

ACuriousMind

@OmarKhayyam By observing the gaps in what is known. Learning what is known is the best possible way to understand what precisely we do not know.

The Dark Side

@OmarKhayyam because then you only have to 'UN'do all that is known.

Omar Khayyam

so why cant you tell just one gap

Anonymous

15:03

@TheDarkSide lol :P

The Dark Side

@Blue :)

John Rennie

@OmarKhayyam we don't why Yang-Mills theories with a compact gauge group exhibit confinement, or even if all Yang-Mills theories with a compact gauge group exhibit confinement. Solving that one will win you a million dollars.

Emilio Pisanty

@OmarKhayyam how can you possibly determine whether some bit of physics is unknown if you don't already have a solid grasp on the bits we do know?

@JohnRennie we don't why?

The Dark Side

So, have we broken Laplace-Runge-Lenz vector with this choice of origin? @ACuriousMind

Omar Khayyam

how can i learn the bits that you know

John Rennie

15:05

@EmilioPisanty that's the mass gap millenium problem.

Emilio Pisanty

@JohnRennie yes, but the sentence seems to be missing a verb ;-)

ACuriousMind

@TheDarkSide You just have that the $\hat{r}$ becomes a $\hat{r'}$ for $r' = r - r_0$, where $r$ is now your coordiante as measured from the new origin and $r_0$ to position of the gravitating body in that system. That won't ever be zero.

Anonymous

@JohnRennie He was pointing out the grammatical error in "we don't why" I guess. :)

ACuriousMind

@TheDarkSide No, you're just doing the coordinate transformation incorrectly :P

The Dark Side

@ACuriousMind Hold on a second :P

John Rennie

15:07

@EmilioPisanty oops yes :-) Dang, it's too late to edit now. Oh well :-)

Omar Khayyam

i have a copy of principles of qm by mr. dirac

is it outdated?

Emilio Pisanty

@OmarKhayyam what does 'outdated' mean?

it's a spectrum

Omar Khayyam

you would not read einstens first papers of relativity if you wanted to learn relativity

Anonymous

@OmarKhayyam I don't know if you are trolling. But I guess you should start with learning Physics from standard textbooks and University lectures.

Emilio Pisanty

@OmarKhayyam I would not recommend Dirac's Principles of QM as a starting point in QM

Omar Khayyam

15:09

i finished the serway the last summer

Emilio Pisanty

But it's still a valuable resource

Omar Khayyam

i am also training for ipo

i just dont know qm

ACuriousMind

Dirac's QM will probably teach you some nomenclature that we don't use anymore, and not teach you some that we do use, but there should be nothing wrong in it.

0celouvskyopoulo7

@ACuriousMind o.o

Omar Khayyam

so what is the best resource for qm

0celouvskyopoulo7

15:10

Are you really going to say that classical QM is not wrong?

Emilio Pisanty

@OmarKhayyam assuming that everybody in the world knows the meaning of every acronym of your local examinations board won't really help you communicate much

0celouvskyopoulo7

It's pretty much 100% wrong

Technically speaking

Omar Khayyam

international physics olympiad

= ipo

Emilio Pisanty

60

Q: What is a good introductory book on quantum mechanics?

I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a s...

Anonymous

@OmarKhayyam That's IPhO and not IPO.

Cryolune

15:11

IPhO*

0celouvskyopoulo7

@OmarKhayyam "Quantum Theory for Mathematicians" by B. Hall

ACuriousMind

@0celouvskyopoulo7 Yes, I am going to say in a physics chat in a physics context that there is nothing wrong with QM.

Omar Khayyam

yes i call it ipo

big deal

0celouvskyopoulo7

@ACuriousMind Oh. I thought this was a cooking, music, and math chat.

The Dark Side

@0celouvskyopoulo7 you want him to die?

ACuriousMind

15:12

That no one here shares your standard of rigor is your problem, not mine :P

Omar Khayyam

thanks @EmilioPisanty

0celouvskyopoulo7

@ACuriousMind I can play loose with rigor

look

ACuriousMind

That's...not playing loose with rigor :P

Emilio Pisanty

@0celouvskyopoulo7 can you, really?

0celouvskyopoulo7

@TheDarkSide depends

a little functional analysis has never killed anybody

@EmilioPisanty There's one proof where say that someting is a diffeomorphism, but tbh I didn't actually check that

Does that count?

Emilio Pisanty

15:15

@0celouvskyopoulo7 not much, no

Balarka Sen

what is time orientability

is this equivalent to having a 1 dimensional trivial line bundle in TM

Emilio Pisanty

I reckon it's relatively easy to come up with some delta-function manipulations that'll make you choke on your own tongue

0celouvskyopoulo7

@BalarkaSen No.

Emilio Pisanty

but I can't be bothered to think them up

0celouvskyopoulo7

Secret

15:16

$$\sum_{k=1}^na_i\delta^k(x)$$

Mathematicians will cry at horror to this

Balarka Sen

what is timelike

0celouvskyopoulo7

@BalarkaSen $v\in T_pM$ is timelike if $g(v,v)<0$

Balarka Sen

ahhh ok

0celouvskyopoulo7

time orientable means it is possible to continuously define a "future"

ACuriousMind

@EmilioPisanty We did have that paper that Taylor expanded delta functions once...

0celouvskyopoulo7

15:18

@EmilioPisanty wait, what?

Emilio Pisanty

@ACuriousMind ah, yeah, that's what it was

0celouvskyopoulo7

I'm confused as to what I'm being accused of

And why I would choke

ACuriousMind

Mar 16 at 18:29, by 0celo7

He's Taylor expanding a Dirac delta holy shit

0celouvskyopoulo7

that paper was satan. So?

Secret

I reckon a power series delta function is even worse

Emilio Pisanty

15:19

@0celouvskyopoulo7 $$\delta(x-x_0) = \sum_{n=0}^\infty \frac{(x_1-x_0)^n}{n!} \delta^{(n)}(x-x_1)$$

0celouvskyopoulo7

@Secret You can't multiply delta functions, so yeah.

Pretty awful.

Emilio Pisanty

let's see you use that in practice

0celouvskyopoulo7

@EmilioPisanty You know, that's not even that bad.

Emilio Pisanty

then you can say that you can play loose with rigour

0celouvskyopoulo7

The derivatives could be distributional and the series might converge in the $\mathscr D'$ topology

The Dark Side

15:20

@ACuriousMind - Remember that bad gravity analogy. Ball on a membrane.

Emilio Pisanty

@0celouvskyopoulo7 the fact that you're quibbling about that stuff instead of just rolling with it takes you out of the play-loose game

The Dark Side

distortion of spacetime ...

Secret

Nowadays I just think of a grid of cloth where the grid itself get distorted without the cloth become buckled

The Dark Side

So, the ball on the membrane is (a bad) example of a satellite ...

Secret

that eliminates the "need to embed in a higher dimension" problem

Emilio Pisanty

15:23

In other news, I just found out that Pasteur discovered molecular chirality when he was 24

0celouvskyopoulo7

I wonder how my knuckles smell like Canadian bacon

Emilio Pisanty

it's people like that that make you realize how little you've accomplished

0celouvskyopoulo7

They certainly never touched any

The Dark Side

@EmilioPisanty and I still can't fix coordinate transformations... (cf. above) :D

0celouvskyopoulo7

@EmilioPisanty Lebesgue discovered measure theory while trying to solve some PDE

Emilio Pisanty

15:23

for instance, it's well known that when Évariste Galois was my age, he'd been dead for nine years

0celouvskyopoulo7

he couldn't get the Riemann integrals to converge so he just YOLO'd it

he did that as a small part of his thesis

The Dark Side

So, back to the point, how do you choose the LRL for this problem, the origin: "center" of gravity is sitting where?

("warped" space)

ACuriousMind

@EmilioPisanty I'll bet your life has fewer duels than his, though

Emilio Pisanty

(with due apologies to Tom Lehrer)

ACuriousMind

@TheDarkSide I do not understand the question

0celouvskyopoulo7

15:27

@ACuriousMind If we were in 1800 would you accept my challenge to a duel?

The Dark Side

@ACuriousMind Of course, the paradigm itself is wrong. But just saying ...

ACuriousMind

Depends on how good I'd actually be with the weapon ;P

The Dark Side

@ACuriousMind Take a fabric, launch a marble on it.

As bad as the analogy is, it can simulate a satellite.

In this sense that it orbits.

ACuriousMind

no, there's no 1/r^2 force

Just "orbiting" is not enough for a LRL vector

Emilio Pisanty

0

Q: Other spaces like Fourier space

Are there any other spaces like Fourier space in which one can more physical information than configuration space? In a summer school about scattering amplitudes, someone told me that this relation between twister space and scattering amplitudes is like the correspondence between Fourier space an...

spacetime scattering fourier-transform twistor amplituhedron

too broad?

The Dark Side

15:29

@ACuriousMind OK. Just give me a minute.

0celouvskyopoulo7

@ACuriousMind isn't it amazing how math experience works?

A year ago I was unable to understand this proof, and asked a few professors for help and still didn't get it

The Dark Side

@ACuriousMind - can you access this?

0celouvskyopoulo7

Yesterday I did it without looking at the book

Quite strange how something goes from impossible to routine

Although maybe all of life is like that

Balarka Sen

life is nonexistent simplicity

0celouvskyopoulo7

@BalarkaSen here's a question...does the existence of a Lorenztian metric imply the existence of a Riemannian one?

that is, does a Lorentzian metric imply the manifold is paracompact

@Slereah ^

Balarka Sen

15:37

I was about to ask what that even means, but then I realized you have nonstandard definition of manifolds

The Dark Side

@0celouvskyopoulo7 That's clear from the proof of the theorem.

:P

Balarka Sen

Slereah would probably be able to answer that better than me, certainly

0celouvskyopoulo7

@BalarkaSen Yeah, assuming "manifold" does not mean paracompact, for the moment.

It should be noted that Kobayashi and Nomizu do not assume manifolds are paracompact.

Balarka Sen

how vulgar

0celouvskyopoulo7

So in half the book they have to write "if M is paracompact"

For a Riemannian metric, you can show that it induces a distance function, hence $M$ is metrizable. Stone's theorem implies it is paracompact.

But if $g$ is Lorentzian...there's no distance function.

Slereah

15:42

@0celouvskyopoulo7 If you have a Lorentz metric just do the reverse construction of the usual thing

Balarka Sen

lol

Slereah

$$h = g + 2\frac{\xi \otimes \xi}{g(\xi, \xi)}$$

Or something

Balarka Sen

What's that supposed to do

Slereah

Define a Riemannian metric tensor

Balarka Sen

huh

Slereah

15:43

also from the Steenrod theorem you can see that a section of Lorentz metrics means you always have a Riemannian metric

It relies on some matrix theorem showing that a matrix of that signature is the product of a Riemannian one and some other matrix

Wait how do integral curves work

Why does $X(\gamma)$ make sense

$\gamma$ isn't $C^\infty(M)$

Apparently there's a Ruse

You define $\gamma$ as the equivalency class of functions $f \circ \gamma$ for all $f \in C^\infty (M)$

or something

Balarka Sen

I don't understand the question. Integral curve of $X$ is a smooth curve $\gamma(t)$ such that $\gamma'(t) = X(\gamma(t))$

Slereah

I'm guessing it's covered in the isomorphisms between vectors as tangents and vectors as derivations

Well yes, but $X$ doesn't act on curves, it acts on smooth functions

(of M)

$M \to \Bbb R$ not $I \to M$

Balarka Sen

$X(\gamma(t))$ is the vector on the vector field $X$ at $T_{\gamma(t)} M$

It's not acting on anything

$X(p)$ means the vector at $T_p M$

Slereah

Ah alright

Balarka Sen

I also dislike this notation, btw :)

Slereah

15:55

I thought it was the action of the vector on a function

Balarka Sen

@0celouvskyopoulo7 You know J Peter May right

Slereah

This isn't my stupidest confusion, really

One time I was stuck for days on some expression that involved $\sigma^2$

Turns out it was the second Pauli matrix, not a square

Balarka Sen

Notations, notations

Let us make some math which does not use any notation whatsoever

Cryolune

Or it could be some kind of telepathic thing.

Also that sounds weird.

yuggib

@0celouvskyopoulo7 there are paracompact spaces that are not metrizable

Slereah

16:08

Paracompact and hausdorff he means, I assume

Although you can certainly define metrics on a non-hausdorff manifold

yuggib

still there are paracompact and Hausdorff that are not metrizable

Slereah

Much better than a non-paracompact one, anyway

@yuggib and second countable :p

(and connected)

although I'm guessing that if it's all that, it admits a Riemann metric anyway

yuggib

if it is second countable and paracompact and Hausdorff, then it is metrizable

Slereah

yeah

but anyway, I think my point remains

0celouvskyopoulo7

@yuggib I never claimed that was the case?

Slereah

16:11

Even if it's not metrizable, if it admits a Lorentz metric tensor, it admits a Riemann metric tensor

It's just that the Riemann metric tensor may not define a distance function

0celouvskyopoulo7

I claimed a metric space is paracompact.

@BalarkaSen the algebraic topologist?

yuggib

@0celouvskyopoulo7 I know. But you complained they had to write it explicitly, even if it is necessary to do it if you deal with non-metrizable spaces

0celouvskyopoulo7

@yuggib Most people take paracompact to be a part of the definition of manifold

they didn't, so for stuff where they need a metric, they had to specify paracompactness

Emilio Pisanty

question merges are weird

10

Q: Why is the speed of light defined as 299792458 m/s?

Why is the speed of light defined as $299792458$ $m/s$? Why did they choose that number and no other number? Or phrased differently: Why is a metre $1/299792458$ of the distance light travels in a sec in a vacuum?

speed-of-light

0celouvskyopoulo7

I'm not sure what you're talking about

Emilio Pisanty

16:15

click on the "Active 1 year and 4 months" link on the right

CC @rob

bolbteppa

Spivak's DG appendix proves paracompact = metrizable = etc if that is what you are trying to prove

0celouvskyopoulo7

16:32

I am not trying to fucking prove that

God dammit people

John Rennie

Ha! Suck it up Oxford! :-)

Anonymous

@JohnRennie lol, I suppose you had several quarrels with the Oxford guys during your grad days XD

John Rennie

@Blue no, there was never any real rivalry, or at least none that I was aware of. There was the boat race of course, and various other sporting fixtures like rugby, but the science students seemed generally not very interested in these.

Balarka Sen

@0celouvskyopoulo7 Correct. Now watch this

yuggib

16:48

@JohnRennie In my experience (mostly confined to the world of academic research), only the graduate programs of these "high-ranked" universities stand out (and not always) compared to the others. And of course, they are able to hire very good people. But I cannot see such a difference in effectiveness/quality when it comes to undergraduate programs.

Physics Guy

BOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Hey guys

How are y'all doing?

DID YOU HAVE A NICE

DAY?

Slereah

@0celouvskyopoulo7

What symbol for vector flow

$\Phi_X$?

Jaime Gallego

Meh day overall. Trying to finish up some last work.

Physics Guy

Meh day overall. Trying to finish up some last work.

Haha.

Jaime Gallego

?

Physics Guy

16:53

I'm having fun by acting in a stupid manner.

Naveen Balaji

0

Q: Energy density of dust in f(R) gravity

Usually during the calculation of the Einstein-Hilbert action, we consider the integral of the variation of the Ricci tensor to be zero as the variation of it, at the boundary was assumed to be zero, as: $$-\frac{1}{16\kappa{\pi}}\int{d^{4}x[\delta\sqrt{|g|}(R+\Lambda)+\sqrt{|g|}(\delta{g^{\m...

general-relativity cosmological-constant

Anyone? please

0celouvskyopoulo7

17:28

@Slereah that or $\mathrm{Fl}^X$

Slereah

fairly ugly

let's go with Phi

Mostafa

@EmilioPisanty Have you seen this?: physics.stackexchange.com/questions/340190

I'd like to know the answer for the orbital angular momentum

Abcd

17:44

Can someone please help me understand atomic structure? I am tired of reading contradicting stuff every where :'(

0celouvskyopoulo7

@Slereah if you say so

@Slereah What's a good TeX editor for PC?

Slereah

I use texstudio

I have also used texwork in the past

Both are fine

Anonymous

@Abcd What type of help?

Balarka Sen

I use sharelatex :3

Abcd

@Blue I can't understand the difference between Principal Quantum Number, Energy Levels, Orbits and Shells. They all seem to mean the same.

0celouvskyopoulo7

17:55

@BalarkaSen Hippie

@BalarkaSen I will watch your video after work

Balarka Sen

principle quantum number is a number, and orbit(als) are regions (where the electron lies with high probability density) in the 3-space, so there's that :P

Anonymous

@Abcd They are essentially the same thing. The Principal Quantum Number is defined in a slightly different way. n=1 holds for electrons in first shell, n=2 holds for electrons in second shell and so on...

Balarka Sen

a number can't be the same as a region. it's just associated to the regions in some way

#pedant

Abcd

@Blue :( . Circular orbits and energy levels are same!?

Balarka Sen

@0celo Sure, sure

Anonymous

17:57

@Abcd "Energy level" is a very vague term. But at your level, yes.

Abcd

@BalarkaSen orbit(als)? WHy complicate things more :(

ACuriousMind

@Abcd The orbitals (not orbits!) are just the energy levels. Every orbital/energy level has a specific value of the principal quantum number, and a "shell" is the set of all levels with the same principal quantum number.

Abcd

@Blue I am in Grade 11.

0celouvskyopoulo7

@Blue is it vague?

Balarka Sen

@Abcd Nobody is complicating anything. I am just saying a number cannot be the same as a region.

0celouvskyopoulo7

17:58

it's just the eigenvalue of the Hamiltonian

energy level is exactly what one calls it

Anonymous

@0celouvskyopoulo7 Yeah. Depends heavily on the context.

0celouvskyopoulo7

@Slereah Can you please read my Section 1.2?

I am actually quite proud of it

I managed to avoid the argument in Wald with the auxiliary metric

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