The h Bar

John Rennie

10:18

That is kind of rubbish :-)

Even when you're listening for it that really doesn't sound like "Hail Satan"

Slereah

nac ew sey

GPhys

I think I recall my professor saying in class at one point that $\partial_\mu \epsilon^{\mu\nu\lambda\sigma}F_{\lambda\sigma}=0$ but I don't remember why. I know this is two of the Maxwell equations, but I'm writing this term down in the context of a modified Lagrangian that I'm deriving the equations of motion in. Was there some reason with the properties of the tensors alone this is zero? i.e. that F is antisymmetric and something with the levi civita and the partial?

Slereah

@GPhys Because that's $ddA$ I think?

GPhys

it's also possible I'm just misremembering what he said and you can't conclude this at all

Slereah

And for any differential form $dd\omega = 0$

GPhys

10:24

@Slereah how does it become ddA?

Slereah

$F = dA$

By definition

And $d\omega = \partial_{[\mu} \omega_{abc...]}$

And antisymmetrization can be expressed via the Levi Civitta tensor

I think?

Let's pick the 2D case

GPhys

I think he had just said something about the antisymmetric properties of it

Slereah

$$d\omega = \frac 16 (\partial_\sigma\omega_{\mu\nu} - \partial_\mu\omega_{\sigma\nu} - \partial_\sigma\omega_{\nu\mu} - \partial_\nu\omega_{\mu\sigma} + \partial_\mu\omega_{\nu\sigma} + \partial_\mu\omega_{\nu\sigma})$$

$$\partial_\sigma \epsilon^{\mu\nu\alpha\beta}\omega_{\alpha\beta} = ...$$

Hm

Might be a bit long to solve at work

but wait

antisymmetrization isn't via levi civita

It's via the generalized Kronecker delta

But...

$$\delta^{\mu_1 \dots \mu_p }_{\nu_1 \dots \nu_p} = \begin{cases}
+1 & \quad \text{if } \nu_1 \dots \nu_p \text{ are distinct integers and are an even permutation of } \mu_1 \dots \mu_p \\
-1 & \quad \text{if } \nu_1 \dots \nu_p \text{ are distinct integers and are an odd permutation of } \mu_1 \dots \mu_p \\
\;\;0 & \quad \text{in all other cases}.\end{cases}$$

could still be correct

The equality is $$T_{[abc]} = \frac{1}{3!} \, \delta_{abc}^{def} T_{def}$$

you can probably sort it out

GPhys

I found another source that says it follows because of antisymmetry of levi civita and "exchange properties of the derivatives"

Slereah

also you get $$\delta^{\mu_1 \dots \mu_n}_{\nu_1 \dots \nu_n} = \varepsilon^{\mu_1 \dots \mu_n}\varepsilon_{\nu_1 \dots \nu_n}$$

@GPhys yeah that is why you get $dd\omega = 0$

GPhys

10:40

I see that

$\epsilon^{\mu\nu\lambda\sigma}F_{\lambda\sigma}=2\epsilon^{\mu\nu\lambda\sigma}‌\partial_\lambda A_\sigma$

Slereah

not quite

$$F_{\lambda \sigma} = \partial_{[\lambda} A_{\sigma]}$$

Or does that cancel out with the epsilon?

i dunno

GPhys

$F_{\lambda\sigma}=\partial_\lambda A_\sigma-\partial_\sigma A_\lambda$

Slereah

Hm, is there a factor of 2 or not

GPhys

the levi civita applied to the second, you can switch the last two indexes in the levi civita on the second term only and add a negative sign to it

Slereah

I forget

GPhys

10:45

then you relabel the contracted indexes

and sum them

Slereah

aight

GPhys

is there a reason why $\partial_\mu\epsilon^{\mu\nu\lambda\sigma}‌\partial_\lambda A_\sigma$ is 0 then

oh!

Slereah

Every term of constant sigma and nu will be of the form $\partial_\mu \partial_\lambda A_\sigma - \partial_\lambda \partial_\mu A_\sigma$

I think

GPhys

@Slereah the ($\partial_\mu \partial_\lambda$) is symmetric on these indices, because you can exchange them, and it's being contracted with levi civita, which is anti symmetric on those indices, so the result is 0

Slereah

yes

GPhys

10:56

weeee

now I can write the eq of motion for whatever this thing is he had us do

Slereah

is it a charge

GPhys

it was the usual F^2 term, plus a term that looks like what I was just showing you, but multiplied by a scalar field, and then plus a term for that scalar field

Slereah

Is it the whole scalar electrodynamic thing

Or is it the EM theory that's not parity invariant

GPhys

$\frac{2}{f}\mathbf{B}\cdot\mathbf{E}+\Box\phi=0$ and $\partial_\mu F^{\mu\nu}-\frac{1}{f}(\partial_\mu\phi)\epsilon^{\mu\nu\lambda\sigma}F_{\lambda‌\sigma}=0$ are the two EoM

where f was just a constant to fix the units for the extra term, and where I rewrote in terms of B and E just so I didn't have to write out that invariant

user929304

@EmilioPisanty Hi, it was about this post, physics.stackexchange.com/questions/371080/… we were discussing why the product states have measure 0

GPhys

11:03

the first EoM is just $\frac{1}{4f}\epsilon_{\mu\nu\lambda\sigma}F^{\mu\nu}F^{\lambda\sigma}+\Box\phi=‌0$

it says "extra axial electromagnetism"

Slereah

yeah I think that's the one that's not parity invariant

GPhys

$\slashed\partial$

QQ

Curio

12:19

What is the valence of scandium? 3?

John Rennie

Yes, apart from a few esoteric compounds Scandium always forms the Sc^3+ ion in its compounds.

The Dark Side

Hi @JohnRennie. Can I bother you with a freak question?

Curio

What, my professor said that it's 2 (going against the period table...)

John Rennie

@TheDarkSide you can certainly ask ...

Scandium

Scandium is a chemical element with symbol Sc and atomic number 21. A silvery-white metallic d-block element, it has historically been classified as a rare earth element, together with yttrium and the lanthanides. It was discovered in 1879 by spectral analysis of the minerals euxenite and gadolinite from Scandinavia. Scandium is present in most of the deposits of rare-earth and uranium compounds, but it is extracted from these ores in only a few mines worldwide. Because of the low availability and the difficulties in the preparation of metallic scandium, which was first done in 1937, applications...

Slereah

According to Wikipedia it's [Ar] 3d1 4s2

Curio

12:25

Because she said that I have to see the electrons in the last orbital, but I really disagreed with B groups

Slereah

So yes 3

The Dark Side

@JohnRennie There is some missing piece in this which I'm a little unclear about.

John Rennie

@TheDarkSide Yes?

The Dark Side

More specifically, with @ACuriousMind's answer

That argument is fine.

John Rennie

OK ... ?

@Curio the Wikipedia article says: Scandium chemistry is almost completely dominated by the trivalent ion, Sc3+

The Dark Side

12:27

@JohnRennie But that only guarantees $M_L = 0$ for a closed shell. How do we take it to mean $L = 0$? Since it is possible to have $M_L = 0$ while $L \ne 0$?

John Rennie

All the $p$ (for example) electrons have $L=1$.

But angular momentum is a vector so when you add up the angular momenta of the individual electrons you have to take the direction into account.

The Dark Side

Right. So, how do we get $L = 0$ for a closed shell?

John Rennie

The $m = 1,0,-1$ basically means the direction is up, horizontal and down respectively

The Dark Side

There seems to be some missing piece, no?

Curio

Fine

John Rennie

12:31

And if you have equal numbers of up and down angular momenta they obviously add up to zero.

The Dark Side

@JohnRennie Hmm... Right, what seems to be a silly confusion to me is the following: consider the total spin of two spin half particles. It can be either $S = 0$, or $S = 1$. For the first, $M_S = 0$ necessarily, but for the latter $M_S = 0$ is still a viable possibility.

So, that possibility has $S \ne 0$ but $M_S = 0$.

Now, how exactly is this case any different from that case?

Hey hold on, an RPG mod in hbar !!

Hello @nitsua60! What brings you here? No flags I hope ...

Emilio Pisanty

13:08

@user929304 I imagine @ACuriousMind is referring to this answer

22

A: Are there more entangled states or non-entangled ones?

I'm assuming that you have a finite-dimensional base Hilbert space $\mathcal H_0$ and that you're building your full Hilbert space as $\mathcal H=\mathcal H_0\otimes \mathcal H_0$. In these conditions, the set of separable states has measure zero. (It gets a bit more complicated if you have $\ma...

ACuriousMind

@EmilioPisanty I think I was

Emilio Pisanty

@ACuriousMind ;-)

nitsua60

13:42

@TheDarkSide not flags--I've just got this room on my list of "favorites," so I suppose I appear to be popping in and out more often than I intentionally do so.

@TheDarkSide An RPG mod with a pair of physics degrees, mind you =)

Anonymous

@nitsua60 Heh. You should hang around here a bit more then. We don't have enough physicists around ;)

The Dark Side

@nitsua60 Ah! Alright! I was only wondering ...

:)

uhoh

6

Q: Have LAGEOS' germanium corner cube reflectors ever been used?

When I was writing this answer about the LAGEOS satellites, I notices that four of the over four hundred corner reflectors are made of optical germanium rather than fused silica. Fused silica (FS) is transparent to some wavelengths in the infrared, but it's limited. For a wider transparency win...

bounty expires in 3 days...

nitsua60

14:10

@Blue I think I'm here most of the time. I wouldn't call myself a physicist, though--that was a former life.

0celo7

14:31

@ACuriousMind we played Left 4 Dead 2 btw

Mithrandir24601

15:27

@Phase interesting addition: Aside from making more sense of the concept of CPT symmetry, Kaluza-Klein also explains the not-officially-discovered-but-definitely-strongly-hinted-at Z' boson, so is possibly actually worth looking into, at least for curiosity's sake

GPhys

this is a mess

what an awful calculation

Mithrandir24601

15:45

@GPhys supersymmetry on the other hand, is distinctly lacking in recent years of particle physics, I'm told ;)

BAYMAX

16:00

Hi guys just in case someone is interested in Complex Systems, I would like to mention the Area 51 version of this SE -

5

Complex Systems

Proposed Q&A site for scientists, students, and other aficionados of complex systems, including networks, nonlinear dynamics, chaos, pattern formation, and self-organizing systems.

Currently in definition.

Also Rationale for the Complex Systems proposal

Anonymous

@BAYMAX Isn't that a part of math/physics?

BAYMAX

Yes it is interdisciplinary

Please have a look the reason on why creating such a SE site in the last line!

Anonymous

Okay, makes some sense, but I guess you'll have a hard time finding experts for that site

Anonymous

Too narrow scope

Terry Bollinger

so... my email 3 hours ago said chat time now... is that correct though?

Anonymous

16:04

Yes, it's chat time now :P

Anonymous

But DavidZ isn't here yet it seems

Terry Bollinger

Drat, I've lost mathjax on my laptop again...

BAYMAX

Hmm... lets hope for the best though, at least the users who answer questions related to Dynamical Systems, Non-linear Dynamics, Chaos theory, Complex systems at least may take part there, let's hope for the best!

Terry Bollinger

Ah, the link worked that time, mathjax is back up...

Complex systems, very computer

science ish topic that.

Phase

@CooperCape rearrange the expression, but also you have the second derivative wrong

it's not $k^2 u$ it's $i^2 k^2 u = -k^2 u$

0celo7

16:11

I volunteer to take over

Phase

@0celo7 is that your cat?

Emilio Pisanty

@JohnRennie this was a surprise:

As a side note, none of the transitions you list are possible in the real world because none of the states you list are possible in the real world except for the ground state. The NIST ASD marks all the $2p^5 3\ell$ configurations (search for Ne I) as having term symbols $^2[1/2]_J$ and $^2[3/2]_J$, which means that they're not LS-coupled; they're primarily split via intermediate coupling as explained here. — Emilio Pisanty 39 secs ago

but it got even better

John Rennie

@EmilioPisanty that was a lot of effort to go to for a homework question :-)

@Phase that comment is on the rude side ...

Phase

@JohnRennie that's satire right?

John Rennie

I agree with the sentiment but not the way you have expressed it.

I think you should delete the comment

Phase

16:26

I doubt 0celo7 would mind

Emilio Pisanty

@JohnRennie it wasn't effort for a homework question

John Rennie

@Phase this comment

Emilio Pisanty

it was to show up an OP who hadn't put in any effort

there's a difference

Phase

@JohnRennie that makes a lot more sense

I was legitimately confused

John Rennie

@EmilioPisanty in principle yes there's a difference. Whether the OP gives a damn is of course another matter :-)

@Phase incidentally, you didn't vote to close. Or at least that post has only one close vote, which is mine.

Phase

16:28

@JohnRennie I retracted the close vote after I deleted my comment

Figure I'll just leave that sort of stuff to high rep users

0celo7

@Phase maybe, why?

Phase

@0celo7 it's just a pretty cute cat

Mine are jet black and go from rubbing against you purring to scratching like hell, yours looks chill

Emilio Pisanty

@JohnRennie frankly, I'm quite pleased with the episode

that's the smallest and cleanest example I've seen yet with intermediate coupling

0celo7

Ok so first you think I’m gonna sound like a 300 stone fatso and now you think it’s strange I have a nice looking cat

Not very nice, wtf

Phase

@0celo7 *sound like a man firing guns on mic

Emilio Pisanty

16:30

the ones in the linked Q&A are in ytterbium

way off on the other side of the periodic table

and with wonky excited states, too

0celo7

@Phase only 300 stone people do that

Emilio Pisanty

much easier to forgive those states for not having $L$

but the first excited state of neon?

Phase

@0celo7 I dont think 300 stone people do anything

I think they just die from hyper obesity

The heaviest ever human was 1/3rd that

0celo7

Idk how much a stone is

Emilio Pisanty

@0celo7 "stone people" is a demeaning term to talk about cavemen. Plus, why do you need 300 of them?

@0celo7 never learn

the stone as a measurement unit is an aberration and it needs to be erradicated

0celo7

16:33

If Emilio hates it, it might have merit.

:p

Phase

Here in the UK we have atrocious conventions

Emilio Pisanty

Rest of the world: "How much do you weigh?" "About 90kg" "oh, ok."

Phase

We use miles, stones and kilograms, celsius

It's a mix of all of them

Emilio Pisanty

UK: "How much do you weigh?" "About 90kg" "Wait. How much is that in stones?"

...

.....

.......

Phase

@EmilioPisanty at least we use Celsius

Emilio Pisanty

16:34

depends on the size of the stone, dunnit

@Phase the UK's alleged "metric-system-ization" is a sham

Phase

@EmilioPisanty proposal: reform the units systems of all countries to give measurements of mass in $\frac{E}{c^2}$

Emilio Pisanty

though to be fair, you did get rid of the ridiculous Old Money

Phase

What... What's Old Money..?

John Rennie

To be fair the stone is banned from commercial use. You can't go into a shop and buy anything in stones.

Emilio Pisanty

Decimal Day

On 15 February 1971, known as Decimal Day, the United Kingdom and the Republic of Ireland decimalised their currencies. Under the old currency of pounds, shillings and pence, the pound was made up of 240 pence (denoted by the letter d for Latin denarius and now referred to as "old pence"), with 12 pence in a shilling and 20 shillings (denoted by s for Latin solidus) in a pound. The loss of value of the currency meant that the "old" penny, with the same diameter as the US half-dollar, was of relatively slight value, while the farthing, which was worth one-quarter of an old penny, had been demonetised...

John Rennie

16:37

It's only use is in measuring weight, and it's popular there because most peoples weight is of order ten stones so it's an easy number for the non-nerds to manage.

0celo7

@JohnRennie What a totalitarian thing to do.

Phase

@JohnRennie could you delete that please

"most people" is discriminative to @0celo7 and his 300 stone physique

0celo7

That’s the kind of government overreach that really boils my blood.

Emilio Pisanty

downthelane.net/extras/2012/08/23/whats-that-in-old-money

John Rennie

@0celo7 it's done for consumer protection. To stop unscrupulous traders using obscure units and getting away with overcharging because most people aren't good at converting units.

In the UK the only legal weighing system is metric. That means consumers only need to get used to one price per unit weight.

In the UK we like our governments to do this sort of thing on our behalf, or at least we keep re-electing them when they do it.

0celo7

16:44

If people can’t convert units maybe they deserve to be cheated

Emilio Pisanty

@JohnRennie if I understand things correctly, that's the kind of government overreach that really boils 0celo7's blood. It's the Land of the Free, dammit, and if unscrupulous traders want to cheat people out of their money then they should be Free to do so.

0celo7

Exactly, but with less sarcasm.

John Rennie

@0celo7 I'm afraid I think that's a very insular viewpoint.

Perhaps we should stop people being allowed to reproduce unless they show competancy in mental calculation. Can't have them polluting the human germ line now can we?

Phase

@EmilioPisanty do we really 'know' dark matter exists?

What if GR just needs a revision?

John Rennie

@Phase it's hard to revise GR

0celo7

16:46

Many people are thinking about that

Phase

@JohnRennie There's no need for that

0celo7

@JohnRennie Nah, because that forces people to not have consensual relations which is Evil.

Phase

@JohnRennie Cornwall will inbreed themselves out of fertility

John Rennie

Or at least its hard to revise it and keep the theory sensible

Emilio Pisanty

@JohnRennie along those lines

John Rennie

16:48

@Phase There are many suggestions for revisions to GR e.g. f(r) gravity, but none of them have managed to explain away dark matter while staying consistent with observations.

Phase

@JohnRennie but there's no need to necessarily rule one out this early in the stage right? Provided my head isn't too deep in the sand, we haven't directly detected any evidence for other models like WIMPs yet have we?

John Rennie

@EmilioPisanty Evolution in action :-)

enumaris

my prof used to say...if it looks like dog shit and it smells like dog shit, it's probably dog shit

Emilio Pisanty

@JohnRennie well, they got away, didn't they?

John Rennie

This time ...

Emilio Pisanty

16:50

@JohnRennie exactly

that story is much funnier if you add ozzy accents to the quotes, too

John Rennie

@Phase no, and indeed there's a lot of soul searching among the WIMP fans because it's beginning to look as if either they don't exist or they interact so weakly we'll never see them above the cosmic neutrino background.

Emilio Pisanty

does this one-box with a picture?

Srsly? The meat we put in these traps is bait. For crocodiles. Don’t swim in them! It’s stupid, and illegal. @qldpol @7NewsCairns

Tweeted by StevenJMiles on October 23, 2017 at 5:02 AM

boom

John Rennie

@Phase in fact the whole dark matter area is looking like it might be headed for a paradigm shift. Neither GR modifications nor WIMPs seem to be doing the trick.

0celo7

Paradigm shift gives many points on the crackpot index

Phase

@JohnRennie maybe the fault lies with the filthy astrophysicists

not wiping smudges off their lenses

John Rennie

16:54

My own personal favourite is something along the lines of Verlinde's entropic gravity idea.

That is, GR is an emergent theory. It's the large scale limit of some physics we don't currently understand.

0celo7

String theory

Say anything else and Lubos the Tank will destroy you

John Rennie

Well no. String theory predicts gravity in the sense that the low energy limit is a spin 2 quantum field. But at low energies that is the same as GR so it would have the same problems with describing dark matter and dark energy.

0celo7

@JohnRennie get left for dead two

Phase

@0celo7 you recruiting more merry members?

John Rennie

Interesting times though. It's fun to think that there might be a radical overhaul of the way we describe gravity and it might yet happen before my own personal universe ends.

user929304

16:59

@EmilioPisanty Thank you Emilio!

Emilio Pisanty

@user929304 no worries

Transcript for