The h Bar

Ryan Unger

12:04 AM

@BernardoMeurer hanging with Michelle

Bernardo Meurer

It gon be zoppity

Ryan Unger

12:40 AM

@BernardoMeurer I'm going for the free booze

Bernardo Meurer

Of course

Ryan Unger

@BernardoMeurer Princeton has expensive af booze

I had to buy red label

was as expensive as black in knoxville

Bernardo Meurer

That's fucked up

I wonder why

enumaris

hello

long time

Avantgarde

1:08 AM

@SirCumference I have no idea!

danielunderwood

@enumaris greetings

enumaris

2:26 AM

greet

PM 2Ring

4:09 AM

@Slereah You get some pretty large numbers when you throw stuff like powersets and permutations into the mix. Eg, the number of subsets of the protons in the observable universe dwarfs your $2^{99999}$. Now count the number of permutations of that powerset. ;)

@SirCumference From the POV of continued fractions, phi is the most irrational number, that is, its continued fraction takes the longest to converge. So all rational approximations of phi are relatively bad, compared to the typical nice approximations that continued fraction convergents give. Conversely, that means it's easy to find rational approximations to phi with smallish denominators.

Ramanujan found some cute series etc using phi, but I don't know if you'd call them useful. I suppose if your doing stuff with pentagons, dodecahedra etc, phi comes up a bit.

The ratio of terms in any Fibonacci-like sequence $F_{i+1}=F_i+F_{i-1}$ converges to phi, no matter what the two initial terms are. So phi turns up in discrete approximations to exponential growth.

If you want a really useless irrational number, try the solution of $x^x=x+1$. It's transcendental, and it has a handful of cute properties, but it doesn't appear to lead anywhere interesting, and it hasn't been studied very much.

More Anonymous

5:22 AM

hey all! I was hoping for some thoughts on a recent calculation I did ...

0

Q: Is this analysis contradictory with the $2$'nd measurment?

Introduction There are $2$ systems $1$ and $2$. Let the Hamiltonian of system $1$ be $H_1$ and let it be in an energy eigenstate: $$ \hat H_1|E_m \rangle = E_m |E_m \rangle $$ Now, a measurement is done (forcing the system to a momentum eigenstate): $$ \hat p |p_j \rangle = p_j |p_j \rangle$$...

I hope it is somehow resolved by me making a silly mistake in the conclusion

and by that I mean a calculation mistake

(It's left me confused to say the least)

Slereah

7:47 AM

morning

Slereah

8:01 AM

One thing I need to do is that Project I had of just doing the variation of various quantities

I'm not sure I've ever done it by hand for any GR quantity

Emilio Pisanty

10:37 AM

@knzhou this should be an answer

Unless @Semiclassical wants to have a go

PM 2Ring

This new member is replicating this answer to a bunch of old dark energy questions. It's basically a plea for people to peer-review his new gravity theory. I realise it's not commercial spam, but I figured it's worth the mods taking a look at. I just tried to raise a custom flag, but I fumble-fingered my phone & I think I submitted the flag before I completed my explanation. Should I bother resending the flag?

Slereah

11:14 AM

Currently trying to read Rynne & Youngson's Linear functional analysis, but that book seems to have 0 proofs so far

A bit worrying

PM 2Ring

11:34 AM

Please ignore my previous post, all 4 copies of that answer have been deleted.

skullpatrol

12:15 PM

Happy second Father's Day @dmckee

Slereah

12:29 PM

Is @dmckee a second father

Who was the first

PM 2Ring

12:42 PM

I seriously hope this is BS physics.stackexchange.com/questions/486531/…

Loong

12:59 PM

@PM2Ring Sounds like it. 2 mSv is not a dose rate. Do they mean 2 mSv/h in 3 m distance?

Ryan Unger

@Slereah what are you trying to learn

Slereah

Functional analysis

I need some reassurance wrt variational stuff

Ryan Unger

what exactly

I know lots of books

that's not one of them

Slereah

Well currently

I'd like the certainty that you can indeed do a Taylor expansion to $F[\phi + \varepsilon f]$

For instance

Sounds reasonable certainly

and it is certainly the case if it can be expressed as an integral of a function

Ryan Unger

uh are you studying functionals which are not just integrals

Slereah

1:08 PM

I am not

Ryan Unger

then what is the issue

Slereah

But I would like to know nonetheless

Ryan Unger

I don't think you'll find that in a linear FA book

Slereah

Strange

Ryan Unger

you want something like Berger's "nonlinear functional analysis"

which is an all-around great resource for calculus of variations

Slereah

1:13 PM

Oh wait

Some page indicates that "The functional $F[f + \varepsilon \eta]$ is an ordinary function of $\varepsilon$. This implies that the expansion in terms of powers of $\varepsilon$ is a standard Taylor expansion."

Quite a reasonable argument indeed

Also more importantly what the hell is going on with mathjax lately

Mathjax is fucking up the formatting lately

Way too tall

look at how tall these are

Ryan Unger

How do you know it’s a differentiable function

Slereah

Well assuming it is differentiable, yes

hopefully the case

bolbteppa

@Slereah what GR quantities

Slereah

Well the various possible GR quantities in some action

$R$, $\Lambda$, and possibly more general terms

bolbteppa

You mean derive the Einstein field equations from an action?

Slereah

1:23 PM

Also terms of the form $\int T^{\mu\nu} g_{\mu\nu} dx$ for some tensor $T$, $\int T^{\mu\nu} R_{\mu\nu}$, etc etc

And weird $R^2$ terms and so forth bc they can be of use

Ryan Unger

Those are all fine as long as you do compactly supported variations

Slereah

yeah that is part of the issue

Gotta beware of thems boundary terms

Since I can't assume that the fields vanish on the boundary

bolbteppa

I think the only annoying step is justifying the Palatini identity

Slereah

Also shouldn't I use the variation for functionals with up to second derivatives

Since the Riemann tensor has second derivatives of the metric

bolbteppa

That's why you use the $\delta$ method and integration by parts to avoid that madness

Ryan Unger

1:36 PM

The Riemann tensor is indeed shitty for that very reason

in some sense that makes studying Einstein metrics very hard

most functionals are in the form $$\int F(x,u,Du)\,dx$$

the bad ones are linear in $Du$

but having a $D^2u$

oof

Slereah

Ah yes, the Bad Term goes away bc it's a total derivative

Well

Ryan Unger

locally

Slereah

it hopefully goes away

Ryan Unger

I think globally you're still in trouble

Slereah

Yeah

I guess I'll need to check out the full formula just in case

I guess the GHY drops out of that term

bolbteppa

1:41 PM

I think this has it from skimming

Slereah

There's something off about this

Like it was made with Words or something

oh wait it's on vixra

Words is entirely possible

bolbteppa

The actual formal derivation is on vixra and everyone else lazily uses $\delta$ :p

Slereah

Vixra has always been at the cutting edge

vixra.org/pdf/1906.0227v1.pdf

He quotes himself 12 times in the first page

a bit gauche

vixra.org/pdf/1812.0481v1.pdf

Martians!

bolbteppa

My guy was quoting Wald, Hawking etc not martians fyi

Slereah

You'd think martians would know more GR than us

Pretty sure one of them was a professor at my uni

bolbteppa

1:56 PM

@RyanUnger here's a convoluted version, your kind of thing

2

A: Geometric derivation of the Einstein’s field equation from the Hilbert action.

Comment: the following is a somewhat convoluted way of deriving the Euler-Lagrange equation using Clairaut's theorem for the volume functional and some standard, albeit not simpler, variation formulas (all is $C^{\infty}$ in the following). Let $g_{0}$ be a Riemannian metric and let $v$ be a symm...

Slereah

@bolbteppa This is the greatest crime ever commited

I'm getting a headache just reading it

Apparently Besse is a fine book for terrible math on the Hilbert action

$$S(g) = \int_M s_g \mu_g$$

The horror

Ryan Unger

@bolbteppa that’s the standard way to do it

@Slereah besse’s book definitely skips all of the details there

bolbteppa

2:13 PM

Indeed ever since Einstein whipped out the Ricci-Hamilton-DeTurck flow

Ryan Unger

2:26 PM

Einstein was a punk

Slereah

How many GR solutions did Einstein even do

I can think of like 2

bolbteppa

Minkowski space

Ryan Unger

Couldn’t even find a rotating black hole

Slereah

I mean he did Minkowski space

But certainly Minkowski did it before

I know he did approximations to Schwarzschild

Ryan Unger

2:42 PM

So did he find any solutions

Slereah

Well he did the Einstein universe

And Einstein-Rosen bridge

bolbteppa

Has anything even happened in GR in the past 30 years

Not even quantum

Ryan Unger

Yes

Nothing interesting to you

bolbteppa

3:09 PM

"The new story part I: Gravity=(YM)^2 Over the last 20, and increasingly so 10 years" seems like a big deal

Ryan Unger

3:22 PM

That looks completely incomprehensible

Why can’t physicists state theorems and properly prove them like actual people

Slereah

Math is hard

4

bolbteppa

3:52 PM

We're talking about a place where $\infty$'s are often simply thrown away

user8718165

hii @JohnRennie

John Rennie

@user8718165 hi

user8718165

4:07 PM

@JohnRennie under influence of a strong magnetic field...why doesn't the ferromagnetic material have multiple smaller N-S poles since almost all the dipoles point in the direction of applied field?

John Rennie

@user8718165 It does, but from a distance it appears to be a single dipole.

If you measure the field very close to the magnet you would detect that it is from a collection of dipoles not a single dipole.

user8718165

@JohnRennie the region near the marked S pole of the material also has aligned domains which have their north poles but no north pole is indicated at that point...why?

John Rennie

4:23 PM

@user8718165 the individual dipoles align themselves head to tail so the field lines end up looking the above i.e. they look like they've come froma single big dipole.

Slereah

@bolbteppa you don't throw them away

You simply substract infinity from infinity

user8718165

@JohnRennie yes...got it...thank you:-)

JMac

5:36 PM

physics.stackexchange.com/a/486202/127931 -_- this is aggravating. "I know I'm right because no one has told me I'm wrong" is not a good defense when people are telling you that you are wrong. Like holy heck there is absolutely no logic to it

PM 2Ring

6:02 PM

@JMac He had me at his second question on Astronomy, when I asked him to clarify a statement he replied with the classic "I mean what I say". astronomy.stackexchange.com/questions/32120/…

JMac

@PM2Ring Look at the comments on the answer I'm talking about too. Blondie responded with "I asked an astronomer and they confirmed it". Since I can't see deleted things, I don't remember what specifically Blondie was involved with; but I remember something of his that got deleted due to him ignoring concerns in comments as well

PM 2Ring

But at least he's beginning to occasionally put spaces after his commas. :)

JMac

So I'm a bit concerned that it's looking like legitimate support from someone else who has a hard time actually backing things up

Sir Cumference

@PM2Ring Huh, that's actually a fascinating reason

Sure as hell sounds more interesting than this

PM 2Ring

@JMac Looks like he's got some supporters... or maybe a sock or 2. I'm almost certain that this answer had a score of -10 last time I looked. And I think I mentioned it here.

Jun 12 at 17:17, by PM 2Ring

Eg, -10 & he won't back down, or delete his crap answer: https://physics.stackexchange.com/a/482821/123208

Sir Cumference

6:17 PM

It's a shame astro's consistently getting nonsense posts by newbies. Although I guess it's better than the constant "do my homework" questions on Physics.

PM 2Ring

@SirCumference Yeah, well that's just the definition. Another thing about phi is that it's one of the few irrationals that are interesting to use as a number base:

See en.wikipedia.org/wiki/Golden_ratio_base

@SirCumference Did you see this one? chat.stackexchange.com/transcript/71?m=50692597#50692597

Sir Cumference

@PM2Ring Huh, I see. Gonna look into it more. I remember in high school our math teacher just showed us crap like this

"If you squint really hard, Africa becomes the golden spiral. WHOA"

JMac

@PM2Ring Right, I forgot he had that gem too. Ugh. It's super frustrating when he will insistently stick to his guns with no supporting evidence.

Sir Cumference

@PM2Ring Mike G's response to this one cracks me up:

PM 2Ring

@SirCumference That last link I posted has been cleaned up. He made 2 necro answers about calculating astronomical distances using nonsense algebra involving the fine-structure constant, and the mass of the electron, and stuff like that.

@SirCumference Yeah, that's the one. :D

Sir Cumference

6:26 PM

@PM2Ring Yeah, I have enough rep to see it (Astro's in beta so the privilege is given at a lower rep)

Speaking of which, at this rate I'm pretty skeptical it'll ever graduate :/

PM 2Ring

@SirCumference Well, it's pretty. :) But there's enough maths related to phi & the Fibonacci number that The Fibonacci Quarterly is a thing, although they don't restrict themselves just to those topics.

Sir Cumference

Even Writing SE's 100+ upvoted speech is being ignored:

139

Q: Writing.SE clamours for graduation

Writing.SE has raised the issue of our desire to graduate a year ago Here it is: we're tired of being a beta site. We believe we have been a consistently successful site, we've been around for more than eight years, we have over 1,000 avid users, we have 100% answered questions, and we get over ...

discussion feature-request graduating-sites

Staff responds with "stay tuned" and no update for half a year

PM 2Ring

@SirCumference It's pretty slow. It'd be nice if it were a little more active, but the relaxed atmosphere is a nice change from Physics, or the sheer insanity of SO.

I've messed around a bit with phi & Fibonacci stuff off & on over the years. About 15 years ago I discovered a way to accelerate the convergence of the sum of the reciprocals of the Fibonacci sequence.

And I was the first person to create a Game of Life pattern that computes Fibonacci numbers, representing them in binary as streams of gliders. Unfortunately, it uses fixed length bit strings, but it's very easy to extend the pattern to handle any bit string length you want.

Sir Cumference

@PM2Ring Oh wow. Were you a mathematician or just interested in it?

PM 2Ring

@SirCumference Just an amateur.

I was playing around with the Binet formula for Fibonacci numbers, and realised that you can rearrange things to get some useful geometric progressions. I posted my results to a forum, but it no longer exists. I still have that stuff on my computer, but it's in HTML. I guess I should translate it to Latex. :)

JMac

6:45 PM

Calls Asimov an astronomer, then ignores everything about my response to say I'm "not very bright" for pointing out that it was an incorrect statement, even though it was irrelevant to the entire substance of my response... just wow. physics.stackexchange.com/questions/486197/…

PM 2Ring

@JMac Asimov wrote over 500 science articles for the Fantasy & Science Fiction magazine, many of which were collected into book form, with revisions. He was pretty fastidious about checking his facts. He was a chemist by training but self-educated in a very broad range of topics. I actually have one of his astronomy books, mostly about the solar system. It's quite good, but rather dated. We've learned a lot of stuff since he wrote those articles.

"which could not truthfully be said about Feynman,who has,alas,recently passed away" What the ... Feynman died 31 years ago!

Also, Walsby persists in posting answers & comments about relativistic mass, even though he's been told several times that the concept is deprecated, and been linked to relevant canonical answers. But I guess you've noticed that yourself. ;)

enumaris

welp, time to grab some TPUs...

JMac

@PM2Ring Oh absolutely. I wouldn't even have necessarily argued that he read it in Asimov's works; but trying to portray Asimov specifically as an astronomer seems a bit disingenuous. That's especially true considering that any information on astronomy he had could easily have been outdated by now, given when he was most active

2

Sir Cumference

7:05 PM

The FLRW metric is a good approximation for reality right?

PM 2Ring

7:18 PM

@SirCumference Sort of. We hope. :D But it works on a very big scale, where you treat the galaxies as particles of dust. And we really don't know how to handle dark energy properly, yet.

Sir Cumference

welp I was thinking of using it in my answer for the observable universe's radius, but I wasn't sure if it was viable

PM 2Ring

@SirCumference It's the best we've currently got, and any improved theory has to mostly agree with it.

Sir Cumference

@PM2Ring Welp I'm not too knowledgeable about how the Lambda CDM model differs from the FLRW model, but I've heard the former is more accurate

PM 2Ring

I mean, outside the observable universe, it could be full of giant space dragons, and invisible pink unicorns, and we'll never know. :D But it's very reasonable to assume homogeneity, isotropy, etc. And if there are insane density anomalies outside the observable universe, they're a long way away, otherwise they'd screw up the curvature in the patch we can see.

@SirCumference Yeah, ok. ΛCDM is an advancement on vanilla FLRW. You'll have to ask a real astronomer / cosmologist for details.