The h Bar

Semiclassical

14:00

I'm fond of ginger beer

John Rennie

@Semiclassical now you mention it, me too!

Secret

ah, that one has a nice sweet taste

John Rennie

Good ginger beer is really nice.

Semiclassical

I don't really know what the difference between ginger beer and ginger ale is, tbh, beyond the latter often being marketed as a soft drink

Secret

here's a mocktail I tried in the past:

Slereah

14:01

the alcohol, I guess

Semiclassical

I imagine more traditional ginger ale is closer to ginger beer

Secret

> Mocktail. Contanis 5/6 lime, orange, strawberries, ginger beer, honey.

It is sweet and taste nothing like any of the ingredients above (although the fizz o th ginger beer is detectable) and it does not taste like fruit punch either.

The drink is so cold that the orange is one of the best orange I have ate since many years ago. I have no idea how they can keep the ice so cold

Slereah

put some grain alcohol in there and you're in business

Sha Vuklia

Guys, I have a question on the following: "Note that idealized waves are of infinite extent. That is, for any fixed value of $t$, there is no mathematical limitation on $x$. Real ways are never monochromatic. Even a perfect sinusoisdal generator cannot have been operating forever." I don't understand why we would need the wave to exist 'forever', because can't we just say that - in a real world - the amplitude decreases anyways, so at some point the wave extinguished anyways?

Slereah

Riot Juice

►

appropriate drink

Binging with Babish: It's Always Sunny in Philadelphia Special

►

John Rennie

14:04

@ShaVuklia any real wave is an infinite plane wave multiplied by an envelope function.

Semiclassical

@ShaVuklia the point is that a waveform like $\sin(kx-\omega t)$ doesn't decrease in amplitude anywhere.

John Rennie

Envelope (waves)

In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. The envelope thus generalizes the concept of a constant amplitude. The figure illustrates a modulated sine wave varying between an upper and a lower envelope. The envelope function may be a function of time, space, angle, or indeed of any variable. == Example: beating waves == A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: F ( x ...

Semiclassical

so it's not going to have any chance of being truly realistic

Sha Vuklia

O right, I forgot it was the entire waveform

but still, a 'sinusoidal' waveform that descreases could still be monochromatic?

because it's really the frequency that matters for being monochromatic, not the amplitude

John Rennie

If you Fourier transform the product you'll find it no longer has a single frequency

Sha Vuklia

14:06

oh, of course

I completely forgot about Fourier

but that's indeed the answer

thanks

John Rennie

The frequency spectrum is now the Fourier transform of the plane wave (a delta) convolved with the FT of the envelope.

Slereah

it will be the convolution!

Semiclassical

there's also a bit of uncertainty principle logic here. if you want to have a monochromatic wave (infinitely narrow in frequency space) then it'll have to have infinite extent in real space

Sha Vuklia

so there's an uncertainty principle in classical physics too?

Semiclassical

in wave physics, sure

Sha Vuklia

14:08

right okay

Semiclassical

wave-particle duality and all that.

Slereah

After all position space and momentum space in QM are related by their Fourier transform

Semiclassical

right

Secret

The more general uncertainty principle, beyond quantum

►

excellant video on that

Sha Vuklia

also, @Slereah you wine-beer-vodka chart is fake. Bosnians don't drink wine!

Slereah

14:13

@ShaVuklia does Bosnia even still exist

Semiclassical

"Bosnia and Herzegovina", technically

which is a weird name for a single country

Sha Vuklia

single country is almost a stretch for Bosnia. like honestly, too many Serbs

Jim

@Semiclassical You'll often find that the real world is often far sillier than the internet could ever hope to be. For, while the internet has a great deal of fact in it, it also has a large component that is pure fiction. The real world, on the other hand, is pure fact. And we all know that fact is stranger than fiction, so I'll let you do the math from there

Slereah

Serbstorm - Fire and Flames

►

Sha Vuklia

I know that meme

Semiclassical

14:17

The Balkans seem very confusing to me out here in the US

Secret

@Jim for example:

14 hours ago, by Secret

Astronomers take note: here's a galaxy that is ultra diffuse and almost devoid of dark matter

Jim

Indeed

Secret

but I like strange, as long we knew how to work with them

John Rennie

@Secret I'm not sure I see why that's strange.

Jim

I prefer charm

Secret

14:19

@JohnRennie well, ultra diffuse galaxies are already quite rare to begin with, and I think before that report, we never had a galaxy that is devoid of dark matter (i.e. tat all baryonic matter can account for its mass)

John Rennie

@Secret I would expect some form of distribution for the dark matter content, so there would be a few galaxies with much less than normal and a few with much more than normal.

We happen to have found one of the low dark matter end of the distribution.

Secret

well I guess that is not very strange then. Still, having these low dark matter galaxies will give us a better idea on how dark matter shapes the evolution of galaxies

0celo7

@Slereah yo

does one always get a time function for a GH spacetime

or is that just a stably causal one

Slereah

Stably causal spacetimes all have a time function, yes

Though unlike GH spacetimes, it may not be a temporal function

In particular it may not be smooth

0celo7

what

so a GH one has a smooth one?

Slereah

14:28

Yes

Sanchez has a proof of it

Although temporal functions aren't just smooth

They also have a timelike derivative

0celo7

a time function is C^1 or what

Slereah

I think it's only required to be $C^0$

Lemme check

0celo7

then what does a gradient of that mean

this work seems to be quite mew, 2005-2006

it seems Christo was assuming it in 1990

Slereah

Time function is a continuous function strictly increasing on every future-directed timelike curve

Temporal function has past-directed $df$

0celo7

page 198 of HE though

Slereah

14:32

Hm

I guess only a specific set of time functions hold for stably causal spacetimes

although...

Sanchez only assumes continuity and still says a time function

which he only defines as continuous

0celo7

is this the big Sanchez paper

Slereah

Oh wait

He says that it has to admit a time function and a temporal function

yes

0celo7

wtf is the difference

isn't a temporal function stronger

Slereah

Hm, I guess from the definition, technically a temporal function may not be a time function?

The definition doesn't specify that it has to be strictly increasing on future-oriented timelike curves

"Notice that a temporal function is always a time function, but even a smooth time function may be non-temporal."

Oh I guess not

0celo7

is this in the usual Sanchez paper

Slereah

14:37

yes

He also wrote a bunch of papers specifically on the topic of time functions

0celo7

yeah it's in one of Ringstrom's books too

good book

but it's confusing because people in the 90s used this stuff implicitly I think

Semiclassical

I think I knew the following at one point but I'm not remembering it now

Slereah

Oh apparently

time functions and temporal functions are equivalent

under a big theorem

Semiclassical

In 2D, the Laplacian in Cartesian coordinates is $\nabla^2 = \partial_x^2+\partial_y^2$ (duh)

Slereah

arxiv.org/abs/gr-qc/0411143

As seen here

John Duffield

14:39

@Abcd : Sleareah doesn't like it when I point out that he's talking about abstract things which remain hypothetical even after 45 years, and talking about them as if they're real things.

Slereah

so yeah stably causal is enough for a temporal function

Theorem 4.15 If a spacetime admits a time function $t$ then it admits a temporal function $\mathcal T$ .

Semiclassical

whereas the Laplacian in polar coordinates $(r,\theta)$ is $\nabla^2 f =\frac{1}{r}\partial_r (r \partial_r f)+\frac{1}{r^2}\partial_\theta^2 f$

Slereah

@Semiclassical true

Secret

deriving that is index hell, however...

Semiclassical

now, one that doesn't come up much: the Laplacian in bipolar coordinates $(\sigma,\tau)$ (with their weird definitions) is $$\nabla^2 f = \frac{1}{a^2}(\cosh \tau-\cos\sigma)^2 (\partial_\tau^2+\partial_\sigma^2)f$$

What do you call it when the Laplacian of $f$ in a given coordinate system is some scalar multiple of what you'd get if they were just cartesian coordinates?

Slereah

14:44

Also true, or at least it doesn't look wrong, from what I remember

Secret

wolfram confirms

Semiclassical

I guess it should amount to the off-diagonal scale factors being zero and the diagonal scale factors being the same

I'm grabbing that from Wikipedia, so I'd hope it's correct :P

Slereah

Laplace equation is separable in bipolar coordinates, btw

But

not the Helmoltz equation

It makes the bipolar wave equation very ugly

You have to use toroidal wavefunctions

Semiclassical

Yeah. I have in mind the magnetic field of a toroid

so Laplace should be fine, used appropriately

Slereah

oh by the way

there's a nice book for all these things

it's... what's it called again

Semiclassical

14:47

lol

Slereah

It's a big book with nothing but various coordinates of Euclidian space

it's written by a guy and his wife

0celo7

@Semiclassical Please use $\Delta$ for the Laplacian

$\nabla^2$ is the Hessian

Semiclassical

I guess what I"m looking for is a name for a coordinate system in which Laplace's equation is separable

Hell no

I hate $\Delta$

0celo7

were you dropped as a baby

what kind of opinion is that

Slereah

@Semiclassical springer.com/gp/book/9783540184300

Semiclassical

14:49

if you want to argue against $\nabla^2$ for the Laplacian, fine

Slereah

It's a very nice book if you have coordinate troubles

Semiclassical

but $\Delta$ is awful.

Slereah

amazon.com/Field-Theory-Handbook-Coordinate-Differential/dp/…

Semiclassical

nice

Slereah

If you have coordinate troubles I feel bad for you son

0celo7

14:50

every PDE book since Hadamard uses $\Delta$

Slereah

It has the Laplace equation solved for a whole bunch of crazy coordinates

Semiclassical

Good for them.

Slereah

"The book is limited to orthogonal coordinate systems in Euclidian 3-space. Skew coordinates do not allow separation of variables and will not be considered."

Is that the word you were looking for perhaps

Semiclassical

Hmm

Slereah

Aaaaaaaah

Semiclassical

14:52

lololol

0celo7

Wonder if the author is Jewish

Slereah

I think it's just supposed to be $\Delta \nabla$

0celo7

but that is exactly the Hodge laplacian on 1-forms

Semiclassical

main thing I don't like about $\Delta$ is that it's not self-evidently a second derivative

0celo7

@Semiclassical this confuses first semester freshmen

do you always write with them in mind

Semiclassical

14:53

whereas $\nabla^2$ is. (Plus, $\nabla^2=\nabla\cdot \nabla$ fight meeee)

0celo7

clearly $\nabla^2=\nabla\circ\nabla$

Slereah

$\nabla \!\!\!\!\!\!\! \Delta$

Damn

It's hard to do

Semiclassical

lol

Slereah

Also not the appropriate size to form $\Huge ✡$

Semiclassical

$\davidstar$

nuts.

Slereah

14:57

I don't think it's in basic mathjax

Semiclassical

yeah, I don't think so either

that's what it would be in the wasysym package

Slereah

3

Q: Is there a religious symbols font collection?

I can find collections for chess, cards, etc. But could not locate a religious fonts collection.

@0celo7 all of this wouldn't happen if you just used indexes

like civilized people

$\nabla_\mu \nabla^\mu$ vs $\nabla_\mu \nabla_\nu$

0celo7

That becomes unmanageable when working with forms

Slereah

that is when you use the superior notation

Penrose notation

Semiclassical

I'd suggest diagrammatic notation, but even I can't take that seriously

sniiiiped

Slereah

15:03

Semiclassical

is that the birdtracks book?

Slereah

yes

Semiclassical

I've tried to read it a few times and I just fail

Slereah

aka the only book actually in Penrose notation

I had to read part of it at some point

Due to my master thesis

it wasn't fun

Semiclassical

whistle

Slereah

15:05

Since then, wikipedia actually has an article in sensible notation on the topic I was looking into

Would have made things a bit easier!

Semiclassical

lol

Slereah

Clebsch–Gordan coefficients for SU(3)

In mathematical physics, Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations, where the type and the multiplicities of these irreducible representations are known abstractly. The name derives from the German mathematicians Alfred Clebsch (1833–1872) and Paul Gordan (1837–1912), who encountered an equivalent problem in invariant theory. Generalization to SU(3) of...

Semiclassical

I do like penrose notation when doing multiple cross products

Slereah

^the topic, btw

Semiclassical

e.g. $(a\times b)\times (c\times d)$

Slereah

15:06

one of my topics was to do the sigma model for mesons with $SU(N)$ symmetry

First $SU(2)$, which was alright

Then $SU(3)$, which wasn't

Semiclassical

in conjunction with the diagrammatic notation for $\epsilon_{jkl}\epsilon_{jmn}=\delta_{km}\delta_{ln}-\delta_{kn}\delta_{lm}$

I like doing it that way because keeping track of so many dummy indices just gets tedious

Slereah

yeah there was a lot of that

lots of symmetrization and antisymmetrization stuff

Semiclassical

Right.

Slereah

Which sounds alright in theory, but

If you have 4 indices, that's a lot of legs

and there's a shitload of terms

Semiclassical

I always wanted that sym/antisym stuff to work out nicely in diagrammatic form, but it seemingly never did

Slereah

15:08

I mean, it's doable

but I dunno if it really makes things easier

Semiclassical

Yeah

With cross products it's nice because it turns it into combinatoric stuff

But ehh

I always liked the idea of diagrammatic notation better than the practical reality of it

Slereah

Young tableaux are alright, I suppose

but then again the calculations are never that long for any typical case

you get like 5 or 6 terms tops

Semiclassical

it's also a pain in the butt to find a good source for Penrose notation

b/c it is just not that fashionable

Slereah

birdtrack book is probably the only one to do it extensively, I think

Even Penrose isn't dumb enough to use it

Semiclassical

yeah

It shows up in his popular RtR book, as well as in an appendix to one of his academic texts

0celo7

15:12

I have two weeks to make my GR presentation

Semiclassical

but beyond that it's just not much

0celo7

For physics people

Slereah

just remove all the math

Semiclassical

which is too bad, b/c I do like pictures like this:

but I could never convince myself that it actually works

Slereah

also what physics thing are you showing

from the yamabe theorem

Semiclassical

15:19

(also, i had a hard time keeping track of whether the bar was for symm or antisymm, and whether or not antisymm had a factor of 1/n! in it)

Slereah

Oh apparently you only need causal continuity for a time function

John Duffield

@0celo7 : easy peasy, just tell them how gravity works.

Secret

Hey guys, do you know of any dance moves that involve lifting the person by holding their thighs, cause I vaguely recall seeing something like that in some music MV advertisement in youtube?

John Duffield

Not me. Look up dance lifts.

0celo7

@Slereah stability for stars

Secret

15:30

specifically, two person facing the front, the person at the front lean backward, and the person at the back caught them and then lift the front person up by holding both thighs

0celo7

@JohnDuffield I don’t know how it works

John Duffield

@0celo7 : I do. But I suspect if I told you, and you presented it, you would feel their wrath and get drummed out of the brownies. I found myself at a function a few weeks back, sitting next to a physicist. I told him that "a curvature of rays of light can only occur where the speed of light is spatially variable", and he went ape. Sheesh, some people think they know it all, when actually they know **** all.

2

0celo7

what do you mean by spatially variable

Slereah

15:51

As far as I can tell JD seems to go on early ideas for GR where they look at the speed from the coordinates of null curves or somesuch

Semiclassical

Within classical electromagnetism, that's definitely true: curvature in light rays tells you that there's a gradient in the local index of refraction.

Slereah

Which isn't a great idea because it's not a diffeomorphism invariant concept

But that was fairly common back then

Although I think he misunderstands even that because even by 1914 they used spacetime curvature as the fundamental idea

Semiclassical

I think there are some definite differences between how Einstein understood GR and how modern relativists do

But that’s a historical claim, not a philosophical one

He can have been right about a lot of it and still wrong about some of it

Slereah

The whole invariance thing took a while to get down

John Rennie

"Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have a an immediate metrical meaning."

From the man himself. In Living Philosophers, vol 7, p67.

Semiclassical

16:04

Here’s a recent Physics Today article by an Einstein scholar who I know myself : physicstoday.scitation.org/doi/full/10.1063/PT.3.2979

2

Slereah

Worst part about GR really is the experimental aspect

It's hard to define measurable quantities that do not have assumptions about the metric

Proper time is okay, but distances

Semiclassical

Which references the relevant papers/letters written by Einstein at the time

Slereah

You kinda have to assume that the metroc doesn't vary too much

Semiclassical

And (apparently) gives a bit different picture of how Einstein got to the field equations than Einstein himself would present/recollect it later in life

John Rennie

@Semiclassical that's standard practice. We all conceal the hideous hacks and dubious shortcuts that got us our new insight, and pretend it was pure intellectual genius :-)

Secret

16:11

tbh, I still trying to get used to how the metric behaves near a black hole event horizon

John Rennie

@Secret Really?

Secret

As I mentioned upteen many times already, it screws up the intuition of (configuration) space so much that I have trouble building a GR memory palace

Semiclassical

@JohnRennie lol

John Rennie

@Semiclassical true though!

Secret

this is why I think quantum mechanics is more striaghtforward, since you still have the wavefunction as some kind of anchor to know where concepts are located, no matter how weird the outcome is

John Rennie

16:13

@Semiclassical when you build a cathedral you use lots of scaffolding. But before you show it to anyone you take all the scaffolding away leaving every to wonder HTF did he build that!

Secret

whereas in GR, the entries of the metric will change depends on the coordinates and the reference frames

so you don't really have some invariant "anchor" that you can orient yourself in the space of GR knowledge so to speak

Slereah

QM is much worse than GR wrt observers

Different observers won't have the same sample space in QM

Semiclassical

@JohnRennie lolyes

Slereah

@JohnRennie aliens

Secret

@Slereah but won't they all share the same wavefunction?

Slereah

16:16

Sure, but who cares for the wavefunction

We can't measure it

Secret

ah right, experimentally, that is a problem

Slereah

also saying they all share the same wavefunction is a bit tricky

Since the real wavefunction to consider after measurement is the system plus the observer itself

Semiclassical

Hence the whole “Wigner’s friend”weirdness

Slereah

The trick in GR is to just remember that the measurable quantities are gonna be scalars evaluated along timelike curves

different curves for different observers

It's not too complex

Semiclassical

One sample idiosyncrasy of Einstein vs modern relativists

For modern relativists, what tells you about the presence of a gravitational field is the non-vanishing of the curvature tensor

But Einstein consistently used the non-vanishing of the Christoffel symbols for that purpose instead

Slereah

16:24

Hey, equivalence principle!

Depends if you like to consider the centrifugal force as gravity, I suppose!

Secret

in other news: O great, I reach my knowledge base limit on conformal maps, might need some help here to convince that resident philosopher...

in Mathematics, 2 mins ago, by Ropstah

@Secret :43694890 in what way is the preservation of angles not a linear part of the transformation?

John Duffield

@0celo7 : the speed of light varies in the room you're in. If it didn't, your pencil wouldn't fall down.

Secret

@Semiclassical chrisoffel symbols = ewwwwww

Semiclassical

Source for that claim: first paragraph on page 20 of physics.umd.edu/grt/taj/675e/QuestforGR.pdf

0celo7

I dunno @JohnDuffield

Semiclassical

16:27

(Same author I know from the other article)

0celo7

Who cares about that

Seems like semantics

John Duffield

@Semiclassical : Einstein spoke of "the refraction of light rays by the gravitational field".

@Semiclassical : the difference is that Einstein understood GR.

Sha Vuklia

Guys, we know that we can manipulate Maxwell's equations for free space into two wave equations for $E$ and $B$. My question is: is the main conclusion we can draw from this that any electromagnetic femonemom is automatically a wave? And does that also mean that any electromagnetic wave (which by definition should satisfy the wave equation) satisfies Maxwell's equation?

That seems untrue to me, because Maxwell's equation surely aren't equivalent to the electromagnetic wave equation, but I wanna check

Slereah

No.

Plenty of solutions to Maxwell's equations aren't waves

ie

Coulomb field

John Duffield

@Semiclassical : I've read some good stuff by Michael Jannsen, but IMHO in this article he misses the trick.

Slereah

16:31

perfectly valid solution

John Duffield

@Secret : it doesn't behave at all.

Sha Vuklia

but my book showed that we can derive the wave equation from Maxwell's equation. so that doesn't mean that if we have a solution of maxwell's equations, it's also a solution of the wave equation?

John Rennie

@ShaVuklia are you asking about solutions where there is no charge present at all?

Secret

Slereah, Sha, Semi, Johnrennie: actually that raises an interesting question: Must all solutions that involve both magnetic and electric fields somehow stuck together solves the wave equations?

Semiclassical

@JohnDuffield I think there’s substance in that remark as to how Einstein understood GR. But 1911 is awfully early given that he didn’t come up with the Einstein field equations until 1916

John Rennie

16:34

Slereah's example is a field propagating in a vacuum, but obviously there is a charge somewhere to generate it.

Slereah

Sure, but plenty will only do so trivially

All static solutions, for a start

Sha Vuklia

@John yea, we assume free space, so $\rho=\sigma=0$

Slereah

Oh well

John Rennie

@ShaVuklia That's ... a good question.

Semiclassical

So I’m a bit leery of how to read that remark in context

John Duffield

16:35

@Semiclassical : he was still talking about the speed of light varying in 1920.

John Rennie

@ShaVuklia Apparently plane waves are not the only vacuum solutions

Semiclassical

Source?

Secret

@JohnRennie While I knew there are vacuum solutions of EFE that are not gravitational waves, I don't know if something analogous holds true for free space in electromagnetism

Sha Vuklia

@JohnRennie o right, that's a good point

my book only really treats the solution form of plane waves

Slereah

in free (flat) space you either have empty space or EM waves

John Rennie

16:37

@ShaVuklia that's because the author was sane when they wrote the book :-)

John Duffield

@ShaVuklia : re "is the main conclusion we can draw from this that any electromagnetic phenomenon is automatically a wave?" It's incorrect to split the electromagnetic wave into E and B waves, but it is correct to say electromagnetic phenomena have a wave origin. The wave nature of matter tells you that a charged particle has a wave nature.

Slereah

They may not be flat, yes

Sha Vuklia

@JohnRennie hahaha:p

Slereah

You can have a bunch of shapes of waves

Based on characteristic surfaces in Minkowski space

Semiclassical

My main problem, though, is that GR, both in terms of equations and interpretation, didn’t just spring out of Einstein’s head in their final form

Secret

16:38

I think many math players such as poncaire is involved in GR history

Semiclassical

Einstein made mistakes along the way, and he acknowledges that in his correspondence

@Secret poincare is more SR

Hilbert, though, was very interested in what Einstein was doing, and got the field equations independently iirc

John Duffield

@Semiclassical : take your pick : 1914, 1915, 1916, 1920.

@Semiclassical : yes he made mistakes, but not about this.

Semiclassical

Hmmm. At the very least, those sources show that he was not committed to the speed of light being constant while GR was being born and raised

So I’ll agree on that point.

Slereah

well you know, it's the whole thing about measuring speed in GR

it's a tricky thing

vzn

16:54

@JohnDuffield your language is probably equivalent to known/ accepted GR properties but phrased in a different way than what is accepted. again the problem with languages/ word meanings/ vocabulary/ translation etc... GR requires careful description of frames of reference. GR states that local observers cannot ever measure variations in c its basically an axiom of the theory... were you at a talk or something?

Slereah

tho I think you get back the speed of light by considering Fermi coordinates along the curve

John Duffield

@vzn : it isn't. Sabine Hossenfelder calls that language idiotic. Then she censored my reply. I won't forget that.

John Rennie

@Semiclassical the speed of light is always locally $c$. The coordinate speed of light away from your location is just a function of the coordinate system you choose and is not an invariant and neither does it have any physical meaning.

Semiclassical

The long paper of Janssen I linked earlier actually mentions (bottom of page 40) that Einstein was willing to cede the light postulate in his 1912 version of the theory

John Duffield

@Slereah : it isn't tricky at all. If your clockwork alarm clock was going slow, and I told you it was because time was going slow inside it, you'd laugh in my face. You'd know it was because the clockwork was going slow, for some reason. You know that there's no time flowing through that clock. You know it isn't some cosmic gas meter gizmo. You also know that an optical clock goes slower when it's lower.

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