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user218912
00:08
I asked it as a question so I can save the derivation
user218912
0
Q: Maxwell's equations in covariant form

3750Maxwell's equations of electrodynamics in vector calculus form are $$\nabla \times \mathbf{B} - \partial_t \mathbf{E} = \mathbf{J}$$ $$\nabla \cdot \mathbf{E} = \rho$$ $$\nabla \times \mathbf{E} + \partial_t \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{B} = 0$$ Where $\mathbf{E}$ and $\mathbf{B}$ a...

user218912
answer if you want :)
user54412
00:31
Quote of the day:
user54412
Textbooks are for trivial beings. To write a textbook is to admit one used to be a trivial being. — Insulin69 yesterday
01:42
@3750 no, indices do not match
user218912
01:55
@0celo7 answer my question please?
@3750 I should VTC as homework like...
It literally is an exercise...
user218912
oh man
user218912
but I showed my work.
well, take it up with @ACuriousMind @dmckee @DavidZ
unless it's a conceptual question, close
user218912
@0celo7 can I divide by $\epsilon^{ijk}$ and replace the indices by $(i, 0, j) = (\mu, \nu, \lambda)$ to get the bianchi identity?
user218912
02:04
or does that not make sense to do.
user218912
it doesn't really work nvm.
well
I'm going to look in the book for a certain equation
if I find it, I'm voting to close your question because that means you didn't read
user218912
at least also tell me the equation.
user218912
and I know how to derive it using the $A_\mu$ definition.
user218912
I'm trying to do it without using that.
02:09
It does not appear to be in there...
user218912
what is the formula?
user218912
D:
Hmm, not even in the exercises
oh, it's in the comments.
user218912
comments?
user218912
oh
user218912
02:11
but he's working backwards
no
there is a way to "divide off" a Levi Civita symbol
user218912
how
did you read the wiki article
user218912
yeah
user218912
do you mean to
user218912
02:15
multiply by the inverse?
user218912
what I don't understand is basically
user218912
I have 4 indices in my equation
user218912
but the final answer has 3
user218912
different ones
@3750 HI. Physics Stack Exchange is neither the same as either other physics related internet site you may be familiar with nor the same as other Stack Exchange site.
We're much stricter about homework-like questions that Mathematics, for instance.
That's because each stack negotiates it's own rules during the boot-up process.
And the users of Physics have consistently voted to not be a problem working site.
user218912
02:18
I don't use any other physics related website and I've been here for a year and the site is full of homework like questions like these, which have been answered.
Your question is more advanced than many, and no one seems to be voting to close it, but a lot of our users don't like to just work problems for people.
You're more likely to get a few hints and be left to your own devices at first. Maybe someone will be bored or will take pity on you later.
user218912
yeah.
@dmckee I like how you give him the beginner's speech
He's been around for a while
Sorry. Didn't notice.
Have I mentioned that I have so-so people skills?
savage
@dmckee Yes, unlike you I remember things :P
user218912
02:20
It's alright.
@3750 It's not possible to do without working backwards a bit.
user218912
really?
@3750 I did the work in your question once. In grad school. Haven't thought about it since and those notes are in a box in an attic in another state if they still exist at all.
user218912
well
user218912
I can't find a full derivation anywhere on the internet.
user218912
02:22
They all just say
Egads! We did E&M out of Jackson, except where the professor thought that L&L was 'better'(apparently meaning more mysterious).
Egads?
user218912
"obviously maxwell's equations can be written in terms of the field strength tensor as [...]"
Ah. They consulted Jackson, then.
That means it's obvious to Jackson and the rest of us can simply consider ourselves stupid. Or something like that.
@dmckee You people complaining about Jackson haven't read Sachs & Wu
Where the Geroch theorem is an EXERCISE
@3750 Ok, let's put it this way
In analysis, when proving that a function has a certain limit, you actually work backwards to find the proof
And then you write the proof down in one shot in the forward direction
Here it's similar, you need to work backwards to find all of the parts of the proof but you can write it down in the forward direction
Basically, you show that different combinations of $\mu,\nu,\lambda$ give zero
Then you write down all of the stuff that gives zero and claim it can be summed up in a fancy tensor equation
user218912
02:27
does 0 count as an extra index?
hmm?
Well also note that cylic permuations are equivalent
so the index combination $00\lambda$ is the same as $0\lambda0$
for instance
It's not enlightening at all
and it's not as trivial as the other one, I don't think.
user218912
ok I'll work backwards and write an answer.
user218912
though is my equation correct?
user218912
the indices and such.
user54412
@dmckee Not your fault really, since the only clue that the persona has been around for a while is noticing that there seems to always be exactly 1 very blue avatar hanging around this chat room ;)
user218912
02:30
$$\epsilon^{ijk}\partial_k F_{0i} + \epsilon^{ijk}\partial_0 F_{jk} + \epsilon^{ijk}\partial_i F_{jk} =0$$
user218912
@ChrisWhite xD
@3750 I'm assuming it because it is equivalent to part of the general equation
user218912
ok
user218912
I figured it out btw
In particular the case $0jk$
$00\mu$ is trivial
Do you see why?
user218912
02:34
no.
you're taking the antisymmetric part
so $00\mu=-00\mu$ in an obvious notation
which implies $00\mu=0$
so now just check the case $ijk$
which is the fourth Maxwell equation added to itself three times
I think...
02:48
@3750 No, your equation is incorrect.
The indices are messed up
In one term there's a free $i$ not present in the others
user218912
03:02
yeah
03:15
aha, there is a trick @3750
Hint: $\dim\Lambda^3(\Bbb R^3)=1$.
user218912
what does that mean
user218912
is that a lorentz transformation?
user218912
03:42
I just wrote a really long answer and deleted it.
 
2 hours later…
07:01
@vzn this is more on their idea that BMS modes on the horizon may contain all the information. The jury is still out.
 
3 hours later…
10:21
@dmckee didn't you ask that a while ago?
@0celo7 do Americans say egad? It's one of those traditional Britishisms that no-one has said since Victorian times, and probably no-one ever actually said outside of a period novel. It's a euphemism for by God and dates back to the times when you were not supposed to take the Lord's name in vain.
They only say "Egad!" when they want to sound quaint british
The same way they would say "Zounds!" or "Cor!"
"Zounds" :-) I bet no-one ever said "Zounds".
Also only Gumbies say COR BLIMEY
I have heard "cor" used, though these days it's mostly used in an ironic way.
Most religious minced oath are pretty archaic in a lot of languages
French has BOUDIOU
Which is one for bon dieu (good god)
So I'm trying to find facts about the geodesic equation for Krasnikov spacetime with two tubes
Just bounds
That shit is complicated
It has 0 Killing vector
10:37
While you're around, do you know anything about the mechanism of gravitational wave generation in a binary black hole merger?
as far as I know it's mostly done numerically, so I don't know too much about it
There's one exact solution for a system of two black holes, but it's static
For real black holes, i.e. with only apparent horizons, does the radiated energy come from the gravitational potential energy?
Mostly I would guess, yes
Although with real black holes, there's always a whole mess of matter to muddy the issue
The LIGO measurements recorded several solar masses being radiated away. If this was just PE being radiated away that makes sense. However if it was actual matter being converted to GW energy that's a bit less clear as I can't see what the mechanism would be.
I don't think there is such a mechanism, classically at least
It would probably violate continuity equations of the matter
Although, you know
Violation of the conservation of energy in non-static spacetimes and all
Not sure it could take energy from whatever mass, though
Is Komar mass conserved?
Oh wait Komar is stationary
What's the non-stationary one
ADM?
apparently not conserved
So I dunno
11:39
user image
3
The essence of programming
12:04
@JohnRennie maybe old ones do
Nah
When old americans want a minced oath they will say darn
I'LL LOOK LIKE A GEE DEE IDIOT
GOSH DANGIT
GADZOOKS
BY GUM
LANDS SAKES ALIVE
HOLY TOLEDO
JUMPING JEOSAPHAT
Stop smoking crack please.
These are the fine words of your country, @0celo7
Do not be ashamed of them
13:10
@Slereah I've heard one of those
@ACuriousMind Please explain
This seems to be some sort of maths
user116211
Did PSE ever apply the blackboard theme?
user116211
user116211
Also, the witty @dmckee ;)
user116211
@Jonathan: At ::random land grant university:: the answer is the physics building was put up shortly after Sputnik and the boards haven't been replaced since then. Besides, half the inhabitants were hired shortly after Sputnik and they're a little set in their ways. (Though actually we're losing the real post-sputnik generation pretty fast, now.) — dmckee ♦ Feb 20 '11 at 17:00
13:17
@MAFIA36790 well not quite like that, but the very first design the site had was blackboard-based. It didn't work out very well.
@Slereah well yes
but why does skew/(skew skew) equal that thing
user116211
ohh.
According to Some Site, this is how you do a krasnikov tube
I'm 90% sure that the spaceship to go there looks like this
@Slereah wtf
@0celo7 The skew/(skew skew) thing is supposed to be a very brief illustration of what you do when you divide out that subalgebra from $\mathfrak{so}(n)$.
@ACuriousMind yes, clearly
but how does the result follow?
13:31
By, uh, carrying out the quotient?
hmm?
You do know how a quotient space is defined, right?
You ask me this every time a quotient pops up
Because you act every time as if you haven't seen a quotient before! :P
@ACuriousMind ok I clearly do not understand it in this case
13:36
You can write a general $\mathfrak{so}(n)$ matrix as $\begin{pmatrix} A & B \\ -B^T & C\end{pmatrix}$ where $A\in\mathfrak{so}(k),B\in\mathrm{Mat}(k,n-k),C\in\mathfrak{so}(n-k)$, agreed?
No, else the result would be trivial and I would not have asked you.
Well, but it is just applying that $\mathfrak{so}$ are the antisymmetric matrices
I don't know what I could explain about that.
Hm
Thinking about it
Krasnikov with one tube is causal
But it's not stably causal
You can have arbitrarily close points in a causal curve
@ACuriousMind what is an antisymmetric matrix?
@0celo7 ???
13:40
I clearly do not understand the concept.
It's one where $A^T = -A$
What is $T$?
@ACuriousMind yes
what then
@0celo7 Taking the transpose
@ACuriousMind clearly
I'm asking what it is, not what it is.
...what?
13:43
I know what a transpose is
But I cannot feel what it is
@ACuriousMind Ok, let's say I accept your result
what then
I do not know what a quotient is, clearly.
@0celo7 You should take either more or less drugs, I'm not sure which :P
2
@0celo7 I thought:
9 mins ago, by 0celo7
No, else the result would be trivial and I would not have asked you.
i changed my mind
14:01
@0celo7 Well, you just quotient out the matrices of the form with $B=0$ (that's what $\mathfrak{so}(n-k)\times\mathfrak{so}(k)$ is.
@ACuriousMind what does that mean
user147690
14:21
He just wants to know what it isss.
I want to know
What's the intuition @ACuriousMind
Hi @Slereah
Hello
@ACuriousMind I really am confused
@ACuriousMind Hi, any chance we can talk about that question? (the one I posted as a comment earlier) if you have some time.
14:43
@0celo7 That's apparent, but I don't really know what is confusing here
@user929304 Yes (you might want to ask here directly instead of using comments on unrelated posts, btw): The "propagation" of the wave is determined by the Hamiltonian/time evolution operator and will, for a free particle, be given by the momentum, not the speed of light. QM is non-relativistic, there is no reason for the speed of light to enter anywhere
@ACuriousMind Did you earlier meant photon experience time or not?
@AnubhavGoel What?
A photon does not "experience" anything.
@ACuriousMind oh I see, let me take an example to clarify my confusion: in a michelson interference scheme, for a single photon, the photon itself is not split (after BS), rather its wavefunction is split and propagates down the possible paths (of reflection and transmission), then it is known that even for one photon we observe interfenrece between the returning (off of the mirrors) probability waves. Question is, what is the propagation speed of this wave? can it be infinite in principle?
If our frame moves with speed of light, can we say it photons rest frame, where photon seems to be at rest?
14:52
@ACuriousMind Check your mass priviledge
@AnubhavGoel there's no rest frame for photons
Rejecting the experience of massless particles
@ACuriousMind I do not see why that matrix is a representant of the equivalence class of the quotient
0
Q: Why are boundary terms important in Chern-Simons theory?

Anarchist Birds Worship FungusI am learning about Chern-Simons theory. I work in Euclidean space. The action is given by $$ I=\int_{\mathbb{R}^4}d\omega=\int_{\partial\mathbb{R}^4}\omega $$ where $\omega$ is the usual Chern-Simons form, and I have used stokes' theorem. My first question is, what is the boundary of for dimensi...

@ACuriousMind Am I insane or isn't $\partial\Bbb R^4=\emptyset$
@AnubhavGoel There are no frames moving at the speed of light. There is no Lorentz transformation into such a frame.
@user929304 Why is it so please?
14:56
@0celo7 It's probably the good ol' "sphere at infinity". Or the user doesn't know what they're doing :P
@user929304 That would be the speed of light since it is, well, light that is moving there.
But non-relativistic QM indeed doesn't impose any restriction on that speed.
@ACuriousMind That's absurd, I thought we could choose any frame of reference.
You need relativistic QM or better yet QFT to discuss causality issues.
@AnubhavGoel Yes, you can choose any frame that exists.
But there simply is no frame associated to "moving with the speed of light".
You can't choose what does not exist.
Why no such frame exists? GW move at that speed too
@ACuriousMind Q3. p.223-226 Susskind seemed to run through a proof akin to the no communication theorem. While from that proof due to how the evolution operator of bob's $U_{bb'}$ is unitary, the density matrix of Alice is unaffected as $\sum_{b,b',b"} \psi^*(a'b")U_{b"b}U_{bb'} \psi(ab')=\sum_{b',b"} \psi^*(a'b")\delta_{b"b'} \psi(ab')=\sum_{b'} \psi^*(a'b')\psi(ab')$.

I am wondering then how can one show that the density matrix of Alice's be changed when Bob's subsystems evolve and the two subsystems are |spatially close enough that they can interact under the confines of the speed of li
@ACuriousMind Can you please explain this thing I'm helplessly confused
15:02
@dmckee Much perplexed (if only temporarily) by this comment
(10k+)
@0celo7 Hmm...maybe what's confusing you is that the quotient is taken as a quotient of vector spaces?
@ACuriousMind ...wrt addition?
@Secret I'm sorry, I don't really understand what you just said.
@0celo7 Yes
@ACuriousMind sigh...thank you
If you were trying to take it as a quotient of rings or something then I finally know what was confusing you! :D
15:06
@ACuriousMind oh that would simplify many things for me. So it means the speed of propagation of a quantum system's wavefunction (which is not a physical wave), depends on the physical system itself, (e.g. if a photon, then bounded by speed of light). right?
@ACuriousMind I was.
@user929304 Yes
I know that algebras are vector spaces with multiplication, and I was trying to quotient wrt. multiplication
What is the difference between the path integration of the action $\int d^4x \partial \varphi \partial \varphi$ and \int d\lambda \dot x^2$
@0celo7 Ah, that is the horrible thing about Lie terminology: Lie algebras are not algebras!
15:07
With $\dot x$ a 4bector
@ACuriousMind ...huh
They do not have a multiplication, they just have the Lie bracket
is the Lie bracket not multiplication tho
They embed into their universal enveloping algebra where they get a multiplication, but the Lie algebra itself doesn't have multiplication.
I don't see how the bracket is not multiplication.
what even is multiplication
15:09
@0celo7 It's neither commutative nor associative
@ACuriousMind awesome! thanks so much for your patience with me (as always)
@ACuriousMind I don't require multiplication to be commutative
or associative, really
all I really want from my multiplication is that $x\star(cy)=c(x\star y)$, etc.
Well, then you can call it "multiplication" of course - but to me, a "multiplication" is the second operation of a ring, and therefore at least associative.
@ACuriousMind well according to wiki its an algebra
@Acuriousmind Ok let me try again. p. 223-226 of susskind showed how entangled states cannot be used to transmit information by showing how because the time evolution operator of e.g. bob $U_{bb"}$ is unitary, Alice's density matrix $\rho_{aa'}=\sum_{b,b',b"} \psi^*(a'b")U^{\dagger}_{b"b}U_{bb'}\psi(ab')$ will be unchanged by $U_{bb"}$.

I am wondering how will $U$ be like if Alice's and bob's subsystem are placed next to each other such that they can interact directly, since if the two subsystems are placed next to each other, then intuitively, in principle they can interact and Alice's de
15:13
Can someone check my answer here physics.stackexchange.com/questions/230440/… It's on potential at centre of sphere due to external charge.
@0celo7 I guess my notion of algebra is narrower than that of Wiki
@ACuriousMind clearly.
let us check the Standard References
To me, an algebra over a ring $R$ is just another ring $S$ with a map $R\to S$ that allows for "scalar multiplication".
I hate crying children
@ACuriousMind No, the bracket is clearly mutiplication
Because this is consistent with the "abelian" terminology
@0celo7 But then what do you call the operation in the enveloping algebra that you need to define e.g. the Casimirs?
15:17
@ACuriousMind I don't need that stuff as a geometer.
What you algebrists do in your spare time is your business
@0celo7 The "Abelian" terminology comes from thinking of the bracket as a commutator.
And, in fact, it does become the commutator in the enveloping algebra
What is crying even supposed to do
BTW, the German Skyrim mod is out
@ACuriousMind random
link?
@0celo7 Get attention, I guess?
15:19
@ACuriousMind well this child is crying for his mother who cannot hear him
so really it's doing nothing
@ACuriousMind you getting it?
yo it says end of July
you liar
@0celo7 I have started it just now.
@ACuriousMind Will it wipe my Skyrim clean?
@0celo7 It will save your current Skyrim installation to a backup folder.
@ACuriousMind
Correction (and hopefully simplified enough version): p.223-226 of susskind showed a no communication theorem like proof on why Bob cannot transmit information to Alice by an entangled state by showing that $\rho_{aa'}=\sum_{b,b',b"} \psi^*(a'b")U^{\dagger}_{b"b}U_{bb'}\psi(ab')=\sum_{b',b"} \psi^*(a'b")\psi(ab')$

But what form will U take if the two subsystems are placed close enough such that they can directly interact as in such a scenario we expect both Alice and Bob's density matrix be affected by the state evolved by U?
@ACuriousMind Well it won't let me dl the thing
it's racist against Americans
@ACuriousMind When I moved to Germany I was scared about going to German school because I thought the kids would be salty over the whole WW2 thing
user147690
15:31
^Lie algebras are the standard thing one thinks of when they think of a non-associative algebra
user147690
(else the octonions)
user147690
But I guess one could say it is an anticommuative algebra with the Jacobi identity
¯\_(ツ)_/¯
@0celo7 Wait, are you seeing a German or an English site?
It might autodetect your location - and the English version is indeed only due at the end of July
@Secret I still don't understand the question.
@ACuriousMind English.
Why would you play the game in German?
@0celo7 Because it's made by Germans? Why would I choose the translated version when I can play the original?
15:36
@ACuriousMind I could play the original too, but I won't
You forget that I speakth your tongue too
Wait, will the translated one be in the King's English
Suppose alice and bob's subsystems are placed next to each other (thus allowing them to interact with each other, how will the time evolution operator U that evolve the composite system look like. We knew it cannot be $U_{aa'}$ nor $U_{b'b"}$ as p.223-226 of susskind showed that these possibilities will not change Alice (and respectively, bob's) density matrices

Will U that describe the evolution of the composite system due to the subsystems interacting with each other (as they will be placed right next to each other, thus allowing them to physically interact) be $U_{aa'b'b"}$ and we will
Because German is preferable to that slop
@0celo7 I don't know
@ACuriousMind let me know if it's good
@Secret How the two systems interact depends on how they interact. "Putting them ext to each other" doesn't actually induce any kind of interaction, unless you stipulate they're charged particles and attract each other or something like that. I still don't understand the question.
15:44
> How the two systems interact depends on how they interact.
Wise words by Fut. Dr. Bajoran.
Can someone follow thread of comments in physics.stackexchange.com/questions/259287/… this question between me and Sanya
Ok, in that case, since in susskind's book the entangled states he explores are qubits, suppose there are two entangled qubits (one from alice and one from bob) that are placed next to each other such that they can feel each other's magnetic moment caused by the spin. Will the time evolution operator that describes such interaction be $U_{aa'b'b"}$ when wrote in index form as intuitively we will expect the density matrices of alice and bob be changed by such interaction?
16:12
@JohnRennie hello
Afternoon / morning
it is 12
so...noon
what is noon anyway
that sounds like a made up word
Hello
@0celo7 IIRC it's from an old English word
Presumably that would have come from the German since they invaded us in 500 AD or whatever. What's the German for "noon"?
Oh hang on, it's mittag isn't it?
Yes
16:15
Which is midday. Is there another word for "noon" in Grerman?
BTW NASA has a press conference about the Juno spacecraft's approach to Jupiter
From Old English nōn, from a Germanic borrowing of classical Latin nōna ‎(“ninth hour”) (short for nōna hōra), feminine of nōnus ‎(“ninth”).
@JohnRennie beats me how $tag\mapsto day$.
$mit\mapsto mid$ makes sense.
From Middle English day, from Old English dæġ ‎(“day”)
16:17
English is such a strange language.
@ACuriousMind Maybe German is better.
I'm willing to hear arguments for either side.
@DavidZ Cool :-) No, cooooooooooooooooooool! :-)
That's a brave move, livestreaming the insertion maneuver. If it goes wrong there'll be egg on faces ...
heheheh
"Insertion maneuver"
@JohnRennie Are they really? I thought this was just a pre-approach press conference
then again I haven't been paying that much attention to it
@DavidZ yes, on closer examination the insertion maneuver isn't for some hours yet
@0celo7 the great thing about English is that it's a bastard mongrel of a language so there are usually several different ways to say the same thing but they all have slightly different meanings.
For someone like me who got English beaten into them courtesy of the English public school system you can have endless fun playing with the language.
@JohnRennie can you give an example
maybe British English is a bastard mongrel...but not Glorious Murrican English
16:26
You misspelled 'MURICAN
@DavidZ ...says the expat.
Well, midday and noon for example. Both are used in UK English.
One came from Latin and one from German.
Americans casually invent words as needed. That's not a criticism, after all, that's exactly what Shakespeare did, but the results aren't always edifying.
example?
"deplane"
is that not a word?
16:30
We native speakers would say disembark, which is a much nicer word.
I would say both
"Deplane" sounds normal enough to me
Then again I'm used to hearing "alight" which seems to be popular in several non-English-speaking foreign countries
@DavidZ Deplane is strange because plane is not a verb.
Yeah, just saying, it's common enough not to sound weird
I'm not criticising - I think people who get precious about language really need to get out more, and a language that never changes is a dead language.
16:37
@JohnRennie Can you give another word?
*example.
Amazing
user image
2
The Hubble telescope caught bright auroras on Jupiter
@MAFIA36790 I seem to recall that the black background chalk-board theme was active for about a week. Certainly for long enough that someone wrote a greesemonkey script to override it (and I developed the habit of putting the site in its own window so I wouldn't run across it while flipping between tabs).
16:57
@SirCumference not really.
What are the applications?
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