@Semiclassical impressive! now what about the Riemann hypothesis? or collatz? :P

I swear sometimes it feels like even the people writing these textbooks don't understand what's going on

Sometimes I am deeply annoyed when people said anything about the collatz conjecture

Yet I am deeply annoyed for seeing that $e^e$ is still an open question, which thus makes me as stubborn as those I am annoyed at

annoyingception, anyone

@Secret i'm fine with people talking about the collatz conjecture. what i find irritating is the suggestion that Collatz is somehow more interesting than other math questions

you want to be interested in that? great. go ahead

but the attitude of "Why work on X when you could be working on Y" gets rather tiresome

When working on something that I am obssessed with, unless when people ask (or when I am talking to a politician) I usually won't bother trying to advertise it

yeah

i may bring it up, but usually because i'm trying to think through it out loud

Despite that, as many chat users have noticed, I do often do my workings on the chat room because deep down I want to share about it and the process even though I never claim it is more interesting than other problems (because things that I am not as interested with is probably because it has not sync with my thinking yet)

but then that creates a series of monologues and that look like spam

which is why (combined with the fact I am now busier in my PhD) people rarely saw my monologues nowadays

my monologues tend to be smaller, but i do do them

Your monologues are often interesting enough to get some responses, thus it is often found to become a conversation

Mine has similar properties for the chat population who like weirdness, but most users in chat rooms lately are the "normies" so spontaneous participation is not high

We do have a few more set theory people nowadays. This had helped me to improve my skills on dealing with set theoretic proofs in general

it's not my cup of tea either, but i don't mind it since it's clear that you're talking about it because you find it interesting, not because you presume other people "should" to find it interesting

(i'm probably a bit hypocritical insofar as I talk about pilot wave stuff. but there I feel genuinely a bit defensive, on the grounds that people tend to not understand it and therefore misunderstand where the issues actually are.)

what is annoying about the collatz conjecture? oh yeah it has been called a mathematical disease although by RJLs standards so is Riemann! dont like the metaphor myself o_O rjlipton.wordpress.com/2009/11/04/on-mathematical-diseases

Tbh, I still find that surreal trajectory thing not as intuitive as I thought, I might have to reread about that later to understand how the charge get delocalised to choose a trajectory like that

there's nothing "bad" about the collatz conjecture per se, imo. what's bad is the insistence that it's more important than other mathematical problems, just because it's unsolved

Well, let me correct: Both collatz and Riemannian hypothesis are such a stubborn mathematical disease that every time the names were heard, you cannot think of anything other than the thousands of people who claimed to have a proof and then failed

@Secret are you talking about the paper linking surreal (photon) trajectories to bohmian trajectories?

Pretty sure most mathematicians will share that sentiment to me

@vzn there are at least 3 papers talking and explaining surreal trajectories

@Semiclassical [citation needed] very few people insist collatz is important at all.

@Secret yes have seen at least 1 in here, dont recall who cited it, maybe Sc, have it on my blog somewhere...

the tldr about surreal trajectories in my book: just because particles have well-defined trajectories, doesn't mean that position measurements aren't weird

Tbh collatz is actually an important problem as riemannian despite I am not very interested in number theory, because it can affect things related to encryption due to it concerns about the way numbers are decomposed

@Secret very few mathematicians consider collatz and Riemann of anywhere near importance, most consider the former something of a "mere" curiosity and the latter very deep/ crucial. and that is somewhat justified given how much Riemann has been linked to other deep areas. there is one neat paper that draws parallels between the two... also Riemann has a $1M prize on it and Collatz has maybe a $5K prize on it... money talks™

@Secret nonlocality makes things weird, yeah

hi chat :-)

For example, I still don't get how the red charge can be pushed at all if the particle have already took the blue trajectory, and then hop into the later half of the red trajectory

The issue is that bohmian trajectories cannot cross, so how does that switching be possible

...and bs walks @vzn

@user2236 walks where? :P

good question

lol

← now looking up phrase on urban dictionary o_O

and if I recall correctly, each particle is allowed to take one of the many bohmian trajectories so you cannot have the particle to go through both blue and red at the same time to kick the red charge and then hit the lower part of the screen

Money talks and bullshit walks @vzn

But then, if the particle starts at the blue trajectory, hence not having any chance to kick the red charge, then the only way that can explain how the red charge is being kicked is that when the particle hops from blue to red, the nonlocality is directed back to the red charge as if at that moment, the red trajectory is the particle have always been taken

2(forgot)=skullpatrol

i suspect the point is that it's not the particle pushing the particle per se but rather that it's the combined particle-charge wavefunction

and this is present even if the particle doesn't pass near the charge

but eh. i dunno if i'm right about that

@vzn it appears the the answer is "walks away" from where the money is...

@user2236 yeah was just gonna say that. looking it up on urban dictionary leads to lots of... colorful scenes. o_O

@Semiclassical hmm... that will suggest if we compute the charge density distribution, we should find it distributed between both the upper and lower half planes

Show me the money or walk away. @vzn

urbandictionary.com/define.php?term=skullpatrol

@user2236 lol ... Clay inst has the $1M and Erdos offered $5k for collatz iirc... what are you up to these days anyway? havent seen you around in ages it seems...

trying to stay incognito pal :-)

welp, definitely failed that coding test lol

:(

could not figure out why my strategy was not optimal

but the debugger said it's not optimal, only within 90% of optimal

fail

any probability questions?

I wrote some extra pseudo-code to show how I might find the optimal strategy by playing out the game many times

but I couldn't figure out why my strategy wasn't optimal from first principles lol

tbf, my strategy did seem quite naive

@user2236 lol as if your previous name wasnt anonymous enough :P

:P

can never be too anonymous ;-)

Well, hiding one's personality is perhaps the hardest thing to do

which is why the big tech companies are talking about shadow profiles and all that

← thinks you are too anonymous :P

I am clearly not anonymous, because my personality is too unique

sometimes, though, I wonder if that is an issue. It might be some time in the future

ah here it is about $2K for collatz with ¼ offered by Erdos and ¾ by Thwaites. thescienceexplorer.com/universe/…

frickkkk

but then it isn't easy to not being myself

... but what if Collatz is harder than Riemann? :P

I think collatz is an example of discrete time dynamics

because you have countable number of stages, two recursive relations ($\frac{n}{2}, 3n+1$) and an initial condition

some people call it the "hailstone" sequence

Thus the conjecture is basically whether at $t \to \infty$, all trajectories will converge to 1 regardless of initial condition

The problem however is that while the dynamics is deterministic, it is hard to work out when we choose the even function and when we choose the odd one

@ACuriousMind may I ask if you ever actually used this option?

:P

@ACuriousMind also, you may be interested in this blog post from a computer scientist about finding your passion :-)

(enjoy your week-off)

@Secret 646 ;-)

@JohnRennie omg, nobody knew pink floyd?

@user1414 none of those students were born when Dark Side of the Moon was released :-)

true dat

they are amazingly quick witted

Anyone here expert of QFT?

@apt45 we have lots of knowledgable QFT people, but the Americans are still in bed and it's Saturday morning in Europe so none of our experts are around.

@JohnRennie Physics should not go to sleep :P

Around 18:00 UTC seems to be the busiest time.

unrelated rambling: Still thinking of a good way to extend GR so as to make the topology of the spacetime manifold to be dependent on the observer's proper time (or coordinate time, I don't know)

well if you think about it, it kinda make sense since if one were to change history by making something that weren't there before, then logically some region in spacetime suddenly took a different topology

If the whole universe ever has only one time traveler, then such history change can be easily encoded as some generalisation of the trousers spacetime without any explicit introduction of changes in topology

because all that needs to happen is that for any given hyperplane slice, we are somewhere in one of the tubes of the generalised trousers

This simplification however breaks down once we have more than one time traveler interacting, or when there are more than one history changes that interacts with each other in a timelike fashion

This is because now the changes in topology of the manifold will be a function or even a relation of more than one coordinate frames

Currently one of my hypothesis is that perhaps when we have an ensemble of observers each in some frame of reference, as they try to reason about the events in the spacetime manifold, together than information might be able to provide some kind of effective internal clock of the universe, thus allowing the chronology of the changes in topology to be mapped and tracked

because even in such universe, if one were to avoid the grandfather paradox, some self consistency notions have to be obeyed and that will place a constraint on how frame dependent the dynamics of these topology changes are

Doing a rigorous proof that thin shell wormholes make sense is hard

arxiv.org/abs/1801.05516

hmm...

@user2236 No, I never failed a course (though I didn't take the exams in a few I attended because I didn't need the credit)

@user2236 Why would you think I particularly might be interested in that? I'm not driven by an all-consuming passion, and I've been fine with that for a long time.

just trying to relate to your switch :-)

I didn't start working as a programmer because I suddenly realized I hate physics and like programming. I've always liked programming, and I didn't stop liking physics.

:P

i gotta stay incognito, pal

...one could argue that you're not really incognito if everyone knows it's you :P

true dat, but my raider persona got busted

@ACuriousMind i didn't mean it at all like that; i just found it kinda interesting...

> it might give some people a more realistic way to approach finding their life's work.

@ACuriousMind I've always hated programming

And yet

Here I am

I tried my best to avoid programming

Part of the reason I went more into theory

bc programming's lame

Making algorithms can be fun, but programming itself is p. fucking lame

The prophecy came true!

I say destroy all computers

before they destroy us

(but, the bills will always be there)

@Slereah Ah, I very much enjoy writing code and then seeing it working. It's an entirely different kind of satisfaction than that from understanding theory, but it is satisfaction none the less

Experimental thermodynamics (heating the chocolate fudge cake in the microwave)

I also did some phase equilibria studies to determine the miscibility with cream

(Chocolate sauce and cream are miscible)

The cake is currently being converted into carbon dioxide and water :-)

Lunch was sausage in a bacon, tomato and cream sauce with pasta:

@Blue yes. I cooked them then pulled them to bits with a couple of forks. I prefer that to cutting them into chunks because the ragged edges you get when you tear them absorb the sauce well.

Chef Rennie

Now I want JR to yell at people about GR the way Gordan Ramsay yells at people about food

Is representing a vector with an underline like $\underline{x}$ a British thing?

Well I thought it was just a one time thing, but now I'm watching David Tong's lectures and it looks like he may do that as well

Though his looks more like a hat under the vector

I think I've only seen it in writing and not text though

I think that's because you are working with $\underline{x} = (t,\mathbf{x}) = (t,\vec{x})$ and want to distinguish

Ahh that would make sense

This question showed up in my review queue and I'm not sure, uh, what to do... :physics.stackexchange.com/questions/437193/…

I think I remember hearing about a similar question a couple weeks ago. No idea what happened to it though

@Blue That's what I thought as well. But he clearly looked up a YouTube video, which is possibly enough research effort, lol

Oh looks like the one I was thinking about was closed for homework physics.meta.stackexchange.com/questions/10842/…

Also looks like it was edited to remove the poopiness

I voted to close as "opinion-based"

Chaos theorists would spend hours arguing over whether it's flush or toilet water

hey, quick check: if our Lagrangian doesn't depend on time ($\partial\mathcal L/\partial t=0$) and we're working with natural coordinates (the coordinates don't have a specific time-dependence), is it then guaranteed that $\mathcal H=T+U$, in other words, that the Hamiltonian equals the total energy? And is it also true that we haven't made the assumption that the lagrangian $\mathcal L$ is given by $T-U$? It might as well have a different form?

Well, it's a matter of definition when it's toilet water or flush water. When the flush activates and the water enters the toilet bowl, does it become toilet water? If so, then the answer is not both

@ShaVuklia No, see physics.stackexchange.com/a/194925/50583

I'm having a weird night. It's 0200 here and I should be focusing on my research

Hong Kong

Well, I'm not going to sleep just yet

@ACuriousMind so Taylor is leaving out some assumptions here?

@ShaVuklia If you mean that Taylor is assuming certain restrictions on the assignment of phase space variables of the Hamiltonian for his claims, then yes

Well, there are already unapparent massive restrictions when you're performing functional analysis on physical systems

@ShaVuklia Yes

One assumption is for sure that $L$ was $T-U$ to begin with, the other is that the mapping between generalized velocities and generalized momenta is invertible, i.e. that the system is free of gauge symmetries/constraints.

oops

i can't read

right, I see that he assumed indeed that $L=T-U$

Note that your text seems to be assuming that there is a map from the "Cartesian" coordinates to the generalized ones; this is not, in general, true. This assumption is the assumption that the system is free of gauge d.o.f. in another guise, basically.

(removed)

right, so if we're assuming $L=T-U$ and we're working with natural coordinates (i.e., invertible map between Cartesian and generalised), and $\partial L/\partial t=0$, then the hamiltonian is the total energy?

Yeah, I can't poke a hole in that off the top of my head.

I mean, obviously there are always many technical assumptions, but these are the (relevant) physical ones

cool okay:)

@ShaVuklia For a satisfactorily rigorous approach, I suggest you read Structure and Interpretation of Classical Mechanics by Sussman and Wisdom: mitpress.mit.edu/books/…

You also need that the map between the coordinates is time-independent, but your text already says that

@ACuriousMind yea, that's how Taylor defines natural

@GodotMisogi thanks! I might look at it later, for now this is "rigorous enough" for me 0:)

@ACuriousMind The Euler-Lagrange equations are invariant under a transformation of the Lagrangian L → L + df/dt. Perhaps that might lead to one?

@GodotMisogi To one what? It certainly gives you a Lagrangian that is no longer T - U.

@ACuriousMind To a hole in the implication of the question, but then the premise is no longer valid as you said

Derive an expression for speed as a function of the distance r from the planet's center A projectile is launched vertically upward from a planet of mass M and radius R; its initial speed is √2 times the escape speed. So I was equating kinetic energy and potential energy but it did not work then I tried v = √(4GM/R) but i don't know what to do next. Thanks for help.

oh sorry maybe I am at the wrong place

@EzioAltair Depends on what place you're looking for ;) You can ask questions here but usually you won't find much interest in homework exercises. There is another room dedicated to discussing solving exercises.

\o @dmckee

Help I am drunk

What kind of help does that call for?

Another drink perhaps

We drink and drink and drink

To Lily the pink, the pink

The saviour of the human race!

For she invented

a medicinal compound

Most efficacious

in any case

@Slereah Can't help you with that. I've been sick and my bottle is languishing unused and unloved on top of the refrigerator.

What part of most efficacious in any case do you not understand

it is panacea

@Slereah It's not even 9pm yet!

it's not

I seem to recall a "I'd after five in Iceland" meme floating around the early web for a while

Apropos of nothing, today's threepanelsoul:

threepanelsoul.com/comic/they-don39t

@ACuriousMind turns out there already are papers for the geodesic equation for thin-shell spacetiems

which is nice but also terrible apparently

It's one of those exceedingly analysis thing

are you drinking and deriving :P

Heyyyy

That paper is written by Podolsky!

I wonder if it's the EPR Podolsky

Also I guess I need to prove that thin-shell wormholes are $C^{0,1}$ metrics

gonna be hard if it's not Lipschitz

I also need to learn about Filippov solutions

which seems very bad

@Slereah Ew. that's not very smooth

@ACuriousMind It's not

But apparently it's doable to prove uniqueness of geodesics in some cases

It is true for gravitational shockwaves

I see, so you need to be drunk for GR to make sense

It's so obvious

It is the secret

Unfortunately it seems there's only like one book on the topic of discontinuous PDEs

So I'll have to read that one and none others

there's a few stuff on the topic of differential equations discontinuous in the parameter, but not discontinuous in the function itself

Except that book

@SirCumference xkcd 323

@Loong The Hawking peak?

\o @SirCumference

> OOF last GRE Math test of the year. I knew almost everything this time around, but I'm convinced that acing it takes a few months of just drilling speed

@user2646 Erm, are you someone I've met before?

from twitter^^

(removed)

Oh hey

What happened to your name? :P

gotta stay incognito for awhile, pal ;-)

That sounds...sketchy

It's the weekend!

Ah let's cut him some slack :P

@Blue The bees won't be dreaming much longer if they keep dying like flies :/

@Blue Well, many birds feed off insects, so that's to be expected

Yo guys so when i read griffiths or goldstein i get so excited by learning new stuff so i can't just sit there i get restless any advice???? i get super excited when i learn new things i just cant help my self how can i focus on reading tho

@Yellow do both, get excited then read

haha

Learning is for nerds

Says the Spivak cover

That paper has an example of a metric that has non-unique geodesics

Neat

$$ds^2 = (1 + y^{4/3}) (dx^2 + dy^2)$$

Ugh if I have to hear about Spivak again I'm gonna cry

Anyone interested in matlab? Please support:

area51.stackexchange.com/proposals/120523/…

$L^\infty_{loc}$ is the set of locally bounded functions right?

Spivak has brought a tear to many eyes

yup, a real classic