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12:04 AM
@BernardoMeurer hanging with Michelle
It gon be zoppity
12:40 AM
@BernardoMeurer I'm going for the free booze
Of course
@BernardoMeurer Princeton has expensive af booze
I had to buy red label
was as expensive as black in knoxville
That's fucked up
I wonder why
long time
1:08 AM
@SirCumference I have no idea!
@enumaris greetings
1 hour later…
2:26 AM
2 hours later…
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.
5:22 AM
hey all! I was hoping for some thoughts on a recent calculation I did ...
Q: Is this analysis contradictory with the $2$'nd measurment?

More AnonymousIntroduction 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)
2 hours later…
7:47 AM
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
3 hours later…
10:37 AM
@knzhou this should be an answer
Unless @Semiclassical wants to have a go
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?
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
11:34 AM
Please ignore my previous post, all 4 copies of that answer have been deleted.
12:15 PM
Happy second Father's Day @dmckee
12:29 PM
Is @dmckee a second father
Who was the first
12:42 PM
12:59 PM
@PM2Ring Sounds like it. 2 mSv is not a dose rate. Do they mean 2 mSv/h in 3 m distance?
@Slereah what are you trying to learn
Functional analysis
I need some reassurance wrt variational stuff
what exactly
I know lots of books
that's not one of them
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
uh are you studying functionals which are not just integrals
1:08 PM
I am not
then what is the issue
But I would like to know nonetheless
I don't think you'll find that in a linear FA book
you want something like Berger's "nonlinear functional analysis"
which is an all-around great resource for calculus of variations
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
How do you know it’s a differentiable function
Well assuming it is differentiable, yes
hopefully the case
@Slereah what GR quantities
Well the various possible GR quantities in some action
$R$, $\Lambda$, and possibly more general terms
You mean derive the Einstein field equations from an action?
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
Those are all fine as long as you do compactly supported variations
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
I think the only annoying step is justifying the Palatini identity
Also shouldn't I use the variation for functionals with up to second derivatives
Since the Riemann tensor has second derivatives of the metric
That's why you use the $\delta$ method and integration by parts to avoid that madness
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 $D^2u$
Ah yes, the Bad Term goes away bc it's a total derivative
it hopefully goes away
I think globally you're still in trouble
I guess I'll need to check out the full formula just in case
I guess the GHY drops out of that term
1:41 PM
I think this has it from skimming
There's something off about this
Like it was made with Words or something
oh wait it's on vixra
Words is entirely possible
The actual formal derivation is on vixra and everyone else lazily uses $\delta$ :p
Vixra has always been at the cutting edge
He quotes himself 12 times in the first page
a bit gauche
My guy was quoting Wald, Hawking etc not martians fyi
You'd think martians would know more GR than us
Pretty sure one of them was a professor at my uni
1:56 PM
@RyanUnger here's a convoluted version, your kind of thing
A: Geometric derivation of the Einstein’s field equation from the Hilbert action.

Bennett ChowComment: 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...

@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
@bolbteppa that’s the standard way to do it
@Slereah besse’s book definitely skips all of the details there
2:13 PM
Indeed ever since Einstein whipped out the Ricci-Hamilton-DeTurck flow
2:26 PM
Einstein was a punk
How many GR solutions did Einstein even do
I can think of like 2
Minkowski space
Couldn’t even find a rotating black hole
I mean he did Minkowski space
But certainly Minkowski did it before
I know he did approximations to Schwarzschild
2:42 PM
So did he find any solutions
Well he did the Einstein universe
And Einstein-Rosen bridge
Has anything even happened in GR in the past 30 years
Not even quantum
Nothing interesting to you
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
3:22 PM
That looks completely incomprehensible
Why can’t physicists state theorems and properly prove them like actual people
Math is hard
3:52 PM
We're talking about a place where $\infty$'s are often simply thrown away
hii @JohnRennie
@user8718165 hi
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?
@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.
@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?
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.
@bolbteppa you don't throw them away
You simply substract infinity from infinity
@JohnRennie yes...got it...thank you:-)
1 hour later…
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
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/…
@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
But at least he's beginning to occasionally put spaces after his commas. :)
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
@PM2Ring Huh, that's actually a fascinating reason
Sure as hell sounds more interesting than this
@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
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.
@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:
@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"
@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.
@PM2Ring Mike G's response to this one cracks me up:
@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
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 :/
@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.
Even Writing SE's 100+ upvoted speech is being ignored:
Q: Writing.SE clamours for graduation

GalastelWriting.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 ...

Staff responds with "stay tuned" and no update for half a year
@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.
@PM2Ring Oh wow. Were you a mathematician or just interested in it?
@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. :)
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/…
@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. ;)
welp, time to grab some TPUs...
@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
7:05 PM
The FLRW metric is a good approximation for reality right?
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.
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
@SirCumference It's the best we've currently got, and any improved theory has to mostly agree with it.
@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
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.
2 hours later…
9:57 PM
> Our results emphasize the role of the Bohmian momentum in giving an intuitive picture of wave-particle duality and complementarity.
10:35 PM
hey vzn!
by "Our results emphasize the role of the Bohmian momentum in giving an intuitive picture of wave-particle duality and complementarity."
is this ur stuff?
oh nevermind just saw that line in the article

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