The h Bar

Slereah

12:00 AM

Oh I had it written in my master thesis

0celo7

for fuck's sake

:D

skull petrol

We need more :D's

Slereah

$R = \frac{1}{2} g_{ab,c} g_{de,f} g^{ac} g^{de} g^{bf} - \frac{1}{2} g_{ab,c} g_{de,f} g^{ab} g^{de} g^{cf} + g_{ab,c} g_{de,f} g^{dc} g^{be} g^{af} + g_{ab,c} g_{de,f} g^{df} g^{be} g^{ac} + g_{ab,cd} g^{ac} g^{bd} - g_{ab,cd} g^{ab} g^{cd}$

Hm

Might not have enough room to paste it here

Let's open a tex doc

0celo7

do it

Darth Sidious Do it!

►

this chat is pretty stupid

all we do is troll and laugh at with Slereah

ACuriousMind

@0celo7 Using the royal "we", eh? :P

0celo7

12:04 AM

@ACuriousMind I'm a ~~fucking~~ holy emperor, you peasant.

@ACuriousMind you're the second biggest troll in here!!!!!!!

after @HDE226868

HDE 226868

@0celo7 I feel like you write a lot of relevant chat messages, then quickly and randomly sub in my name whenever I drop in here.

0celo7

you...you think I write relevant things??

oh how sweet of you!

well you're the only one in here who's impersonating an American

@Slereah are you literally writing out the Ricci scalar with every component?

Slereah

I am

It is p. long

0celo7

lol

pic of progress?

Slereah

0celo7

12:11 AM

jesus

Slereah

Gonna need to do a lot of factoring

0celo7

haha the title of the image :D

do we know more about solving the Einstein equation than Navier-Stokes?

Slereah

Probably not

But Navier Stokes tends to be more used for real problems so we usually can't assume a bunch of symmetries

0celo7

woo

real problems are woo

Slereah

When we will do the flow of spacetime in a pipe we will probably study it more

0celo7

12:17 AM

so is energy really when you inject more spacetime into space?

or do you pour some gin into space

or is it spacetime?

eh, whatever, they're the same

I've been wondering something

How much math does JR really know? I haven't seen him using anything fancy.

Slereah

I have mostly seen him use $E=mc^2$ and $E = h\nu$

Multiplications are his forte

0celo7

JR

not JD -.-

you have a habit of mixing the two up

Slereah

oh

0celo7

12:35 AM

BARDOCK THE TALKING GOOSE - LUCIAN FREUD & I | Damien Slash

►

Slereah

1:16 AM

This is just one term :(

obe

1:41 AM

speaking of handwriting

want to see mine @0celo7

my handwriting

shankar behind it for reference.

@0celo7

user54412

2:18 AM

@DanielSank I've been meaning to ask you about your first comment under the question. Is it "just" a warning about propagation of errors in any real calculation, or is there something there more fundamental? In particular, are you referring to the loss of phase information in having just the power spectrum on hand?

user54412

@NeuroFuzzy That's basically right. What wikipedia calls the Gauss-Faraday law is the evolution equation I use for E&M on curved spacetimes.

user54412

Sometimes you see it written $\nabla_\mu {}^*F^{\mu\nu} = 0$ (that epsilon contraction is the Hodge star in index form), where because $F$ (and thus its Hodge dual) is antisymmetric and rank 2 you can convert covariant derivaives to partials and all the connection coefficients vanish identically.

user54412

btw, it works on all stationary ($\partial_t g_{\mu\nu} = 0$) spacetimes, not just static (stationary + $g_{ti} = 0$)

user54412

If you really want to do this in practice, though, there is an extremely important but subtle numerical issue with the evolution.

user54412

There is a constraint in maxwell's equations (call it $\nabla \cdot B = 0$, or $\nabla_\mu {}^*F^{0\mu} = 0$ or whatever). And naively evolving a system according to the evolution equations tends to lead to violations in this constraint that accumulate over time. This is separate from the numerical stability of the integrator per se, and there are many volumes of literature written on how to properly evolve the electromagnetic field.

user54412

2:33 AM

Basically, treating the 4-divergence of an antisymmetric tensor as the flux-conservative evolution of 3 (ideal MHD, perfect conductor case) or 6 independent scalars is... morally wrong. We do it anyway, but we have to be extremely careful.

user54412

I actually wonder if some mathematician has figured out the right way to evolve tensors numerically, yet no one in physics or engineering has read the poor person's neglected thesis.

0celo7

@obe you have issues

@ChrisWhite Hmm, interesting!

Sounds like a mission for thesis-topic searching me in a few years

obe

@0celo7 we already agreed on that...

user54412

@0celo7 If no one has done it (and certainly no one I've spoken too has heard of such a thing) it would be an extraordinary breakthrough. I'm not even exaggerating -- solving this problem would get you instant job offers from hundreds of research groups and industrial teams.

0celo7

@ChrisWhite Hmm

ACuriousMind

2:40 AM

Do you currently just reimpose the constraint after a few steps, or what do you do?

0celo7

German outta nowhere

user54412

@ACuriousMind You clearly didn't read my paper ;)

0celo7

Current goals in life:

Get some form of PhD

Tell Zee his QFT book is shit

Tell Weinberg his explanation of cluster decomp is shit

Learn analysis

That's pretty much my bucket list.

@ChrisWhite Link?

I'll save the pdf to my iPad and read it when time permits.

user54412

You can project onto a divergence-free solution after each timestep, which amounts to doing a global elliptic solve akin to poisson's equation. Or people figured how to achieve similar results with parabolic or even hyperbolic operators. Parabolic damps monopoles away, but kills your timesteps in the courant condition. Hyperbolic is best from a performance standpoint, but it introduces unphysical waves carrying monopoles off your grid.

user54412

Alternatively, you could evolve the vector potential itself, though this comes with all sorts of subtleties about gauge choice.

user54412

2:45 AM

Or you could do crazy prestidigitation with your discretization scheme.

user54412

@0celo7 its just this one; bottom of page 2 I (very briefly) summarize what people do, at least in relativistic codes

user54412

the references show that people have been worrying about this for 40+ years

0celo7

is that your PhD thesis?

or is that still in the wind

user54412

It's the numerical basis for my thesis. Certainly the most time-consuming part.

user54412

No amount of math or numerics without applications will get me a degree -- my thesis committee has made that abundantly clear.

0celo7

2:48 AM

Do they like you?

That might be a stupid question

But it would be something I'd worry about

user54412

Let's put it this way: my adviser (who's really nice) said I should have tough people on my committee to balance things out. And whenever I tell people in my department who they are, the response is "wow, they must ask really tough questions."

0celo7

Is Stone your adviser?

user54412

yes

DanielSank

@ChrisWhite It is not just an error propagation issue.

This is a very fundamental issue about the difference between noise and not noise.

Suppose I have a process such as the emission of radiation from a black body.

This process has certain statistical properties.

One way to describe these properties is through the power spectral density.

We typically denote this $S(\omega)$.

This function is related to the correlation function of the process.

Call the process $x(t)$.

user54412

But this is just the ... two?... point correlation, right?

user54412

3:00 AM

For any non-gaussian statistical properties there's more to be learned from higher-order correlations?

user54412

(I'm phrasing this in cosmology terms, not sure if it makes sense outside that field)

DanielSank

Then it turns out that $S(\omega) = \int (d\omega/2\pi) \langle x(0) x(\tau) \rangle \exp[-i \omega \tau]$

where the average is over realizations of the process.

@ChrisWhite Yes, more or less.

@ChrisWhite I believe that is correct.

user54412

---
Apparently I'm missing Einstein-related festivities in Princeton right now (100th anniversary of GR). Not just talks, but independent films, a theatrical play by Brian Greene, a performance by Joshua Bell, ... Wouldn't surprise me if there's a look-like-Einstein contest.
---

DanielSank

@ChrisWhite: Now here's the thing everyone forgets: If you actually record a realization $x(t)$ and compute it's power spectrum, it will not be exactly $S(\omega)$.

$S(\omega)$ is an average, and there are fluctuations about this average for any one realization.

user54412

That makes sense. I think.

DanielSank

3:10 AM

You can actually compute things explicitly! Check this out:

user54412

@DanielSank Is the integral over $\omega$, or should it be $\tau$?

DanielSank

2

Q: What is the statistics of the discrete Fourier transform of white Gaussian noise?

Consider a white Gaussian noise signal $x(t)$. If we sample this signal and compute the discrete Fourier transform, what are the statistics of the resulting Fourier amplitudes?

@ChrisWhite Oops, definitely over $\tau$ and without the $2 \pi$.

@ChrisWhite: the Fourier transform $\tilde{x}(\omega)$ of a white noise signal is a Gaussian distributed complex number.

It turns out that this means that the mod square of the Fourier transform is exponentially distributed.

So now suppose you want to generate a realization of so-called black noise (black body radiation noise).

You have to generate your frequency domain data according to the Planck law, but with the fluctuations built-in. In other words, the mod square of each frequency component should be drawn from an exponential distribution with the mean determined from the Plank law!

And, if I remember all this correctly, the phases should be uniformly random.

user54412

For the phases, that sounds ok. Though in the end the simple theory of human hearing is that we don't distinguish relative phases between frequencies anyway. (There was a really good post here that linked to a claim that that's not quite true -- can't locate it now.)

user54412

@DanielSank But what happens if we don't do this?

DanielSank

@ChrisWhite I don't know, but surely the statistics of the resulting noise realization won't be right.

@ChrisWhite if you use enough samples in frequency space it may be that the noise in the Fourier amplitudes doesn't matter much, now that I think about it.

I'm just not sure.

@ChrisWhite We should do an experiment.

user54412

3:34 AM

I like the sound of that.

user54412

I also like the taste of food, so I might bow out for a bit.

0celo7

signals is strange

skull petrol

3:56 AM

things can only be as strange as The Evidence suggests :P

::looks around for The Evidence::

user685252

5:26 AM

Advisor or adviser?

user685252

5:47 AM

books.google.com/ngrams/…

Shing

7:33 AM

@JohnDuffield When I was reading Purcell's Classical EM book, I was under such an impression that fields are more fundamental than charges (and what we exactly measuring really), and really left me wondering if it is all about fields changes obeying some kind of laws (such that makes us think there are charges)

JokelaTurbine

@HDE226868 .. My logic. I f you look the old horse power definition you will find my logic; en.wikipedia.org/wiki/Horsepower#Definitions_of_term if something happens in certain time, it just need a certain power. And this power need certain amount of energy. And energy just don't come "somewhere". I am challenging the LOD change be searching this source

JokelaTurbine

7:53 AM

; If 25.4 TW change is happening with 47 TW (x0.3 through mass) source or with 200 TW source, which would you accept? physics.stackexchange.com/questions/214042/… with variable energy source must be prepared to instabilities; which makes this question very interesting; physics.stackexchange.com/questions/216411/… I hope you find it worth re-opening.

John Duffield

8:15 AM

@Shing : IMHO you should be a little wary of Purcell, there are some issues with it. But yes, I would agree that the electromagnetic wave is more fundamental than electromagnetic charge. We make electrons and positrons from photons in gamma-gamma pair production. We can diffract electrons. And in atomic orbitals "electrons exist as standing waves". Standing wave, standing field. The wave nature of matter is not in doubt.

@0celo7 : now it's -6, even though I refer to Einstein and WMAP and more. It's a demonstration of the downvote problem we have here at stack exchange. Do not take comfort from it.