The h Bar

skullpatrol

02:45

He's probably dancing with Michael Jackson...

skullpatrol

02:56

John Rennie

04:48

@JMac I started Unsouled last night and I'm about halfway through. So far I am enjoying it :-)

JMac

@JohnRennie Nice. The book definitely starts to pick up when it finds it's direction in the middle. I plowed through book 8 today and it was my favourite in the series so far; though it was pretty intense since it was like no filler.

Physics Meta

06:41

0

Q: html tag rendering

An old answer of mine just got an upvote, which caused me to look at it again, and I was surprised to discover that my html tags for italics (that is the letter $i$ between two pointy brackets) were not rendering. This made the answer almost impossible to read, because I had used italics instead...

bug

FakeMod

07:15

Yo! Long see no time...

Anyways, I want to do the following thing and I don't know how to do it. I would be glad if someone helped.

Let's say we graph the phase space of a certain one-body dynamical system. In case of 1D motion, the phase space can be represented by the coordinates $(x,v)$, and the trajectory of the system will be represented by a 1D line on a 2D plane.

Extending this to $n$ dimensions, we can obtain a $2n$ dimensional phase space with a $(2n-1)$ dimensional trajectory.

For simplicity, let's stick to only one dimension as of now. Also, for simplicity, let me choose a specific example of a dynamical system, say, a particle moving according to the linear and homogeneous DE: $\ddot x=ax$, where $a>0$.

It is easy to see that the following relation also holds true $$\dot x^2-ax^2=\rm constant$$ (The above relation can be derived either from energy conservation or from integrating the original DE once).

This corresponds to a family of hyperbolas in the phase space.

The above is finely discussed in the following video (from 1:17 to 16:00)

Mod-01 Lec-03 Dynamics in phase space

►

Now the phase trajectory (with direction) as drawn in the above video, to me, looks awfully similar to a vector field. I suppose it is termed as velocity field.

Now all I want to do is to analytically find the divergence and the curl of the above velocity field. Or, even better, obtain the velocity field. But I don't know how exactly to do it. Also, although the above example is one dimensional, I am looking for a general way to find the velocity field for any $n$ dimensional system.

Also, here I am not exactly talking about finding the velocity field, rather I am trying to find a vector field which resembles the phase trajectories drawn in the above video.

BTW, JEE's over (seeing the starboard, I guess you already know that). And I have gotten a two-digit rank (which is a fancy way of saying that my rank < 100), and thus I am extremely happy. Moreover, now I am unrestrained to study stuff which I previously didn't study because of lack of time.

YouKnowMe

07:41

@FakeMod Congrats

FakeMod

@YouKnowMe Thanks!

@YouKnowMe Did you also appear for the JEE?

John Rennie

@FakeMod wow, congratulations! :-)

Do you know which IIT you'll be going to? With that rank I guess you can go anywhere you want.

YouKnowMe

@FakeMod LOL I am in 10th.

FakeMod

08:07

@JohnRennie Thank you :-)

Superfast Jellyfish

@FakeMod hey congrats! That’s an amazing achievement!! :D

FakeMod

@JohnRennie So I got a rank in the 90 to 100 range, which means that I have chances to get any IIT (or for that matter any other college) except one, IIT Bombay. The reason being that the cutoff of IIT Bombay Computer Science lies around rank 60. IIT Delhi Computer Science cutoff lies around 95. So yeah, around 50% chance for IIT Delhi. All other IIT Computer science is available to me.

If I were not so choosy about my branch (i.e. computer science) I could go to whichever IIT I want to. But I would rather compromise IITs than to compromise my interest.

John Rennie

:-)

FakeMod

@SuperfastJellyfish Thank you! Indeed it is a memorable achievement :-)

BTW, the AIR 1 guy is a true genius. His track record is astounding :o

Emilio Pisanty

09:48

experiment: `` <i> ``

huh

this renders differently on answers and on comments

(i.e.: backtick backtick space backtick <i> backtick space backtick backtick)

Jack Rod

11:24

@FakeMod all ready two three guys within top 100 missing iit so you will get easily

Shing

14:16

my electrodynamics professor (whose field is applied physics) said the size of electron cannot be possibly be zero. I am not so sure if there is a solid reason?

I was thinking about the uncertainty principle, but I don't think position of a particle has much to do with its size?

ACuriousMind

define "size of the electron"

Shing

@ACuriousMind does it have to do something to do with scattering cross section?

ACuriousMind

See physics.stackexchange.com/q/264676/50583, physics.stackexchange.com/q/119732/50583, physics.stackexchange.com/q/24001/50583 for discussions of notions of "size" and "shape" for elementary particles like the electron

@Shing Well, the definition that leads us to say that the electron is "point-like" does, see the links above. But it's not clear whether that's what your teacher meant when they said that (you need to ask them if you really want to know).

Shing

@ACuriousMind thanks. That was a mistake of mine when I did not ask him.

Sir Cumference

14:50

i know i haven't woken up when i search "facebook.com" in youtube's search bar

@Shing "size" is something we take for granted in the macroscopic world, but defining it is tricky in QM where the location of the electron is wavelike

ACuriousMind

Not awake enough to navigate to a website, but awake enough to do QM? QM is dream logic, checks out.

Sir Cumference

at this point all my dreams are of physics :P

i remember that dream i had where my friend was a vector

2

ACuriousMind

How did that work? Just a talking arrow with googly eyes? :D

JMac

So it's like the tetris effect but you don't even get to clear lines?

Sir Cumference

i think this was during my linalg class so i dreamed my friend group was a vector space

prob a side effect of constantly thinking of math lol

ACuriousMind

15:02

I still don't really have an idea of how that looked but maybe I'm on too few drugs

2

Slereah

@ACuriousMind do you need some more

ACuriousMind

yes please

Slereah

15:21

Speaking of drugs

Tried reading Burkhard Heim's field theory

oh boy

The math seems coherent enough, but the interpretation is kind of weird

Superfast Jellyfish

15:50

@SirCumference thankfully they weren’t a vector of the bio kind :P

FakeMod

@JackRod Well, my fingers are crossed ;-)

Hey @ACuriousMind could you please clarify my confusion, which I started describing from this message?

ACuriousMind

@FakeMod The phase space trajectories of a system are the integral curves of the Hamiltonian vector field associated with its Hamiltonian.

note also that using $v$ for the non-positional phase space coordinate is rather usually, most people use the momentum $p$.

Jack Rod

16:38

@FakeMod why you didn't go for iisc?

You are indeed eligible for it

ZeroTheHero

17:11

Ryan Unger

18:53

@JohnRennie And in his honor we spent quite a bit of time on Penrose diagrams and his incompleteness theorem on my qualifying exam.

Physics Meta

0

Q: What can I do to improve this question which I posted?

Recently I posted this question about Stefan-Boltzmann law which ended up getting three downvotes over the days. So, I'm wondering what exactly I did wrong. I had asked for help from a friend and found a paper that described the situation and after a discussion with some friends, I came to a conc...

discussion specific-question down-votes

vzn

19:08

congrats penrose! penrose was enamored of Turings undecidability and argued it was a case against A(G)I. also, how about his wild ideas about QM interference in microtubules being a basis for consciousness? ah, but its a bit of a shame how long Nobel prizes are awarded after the actual accomplishments. decades... penrose is 89

Penrose, Roger (1965), "Gravitational collapse and space-time singularities", Phys. Rev. Lett., 14 (3): 57

↑ o_O over ½ century ago! yeah we can all rest assured physics (community) will spot the next paradigm shift, right? lol!

Slereah

It was well spotted by the physics community back then.

vzn

doubtful it was fully understood/ recognized quickly. thats my point.

Slereah

It was.

There was a lot of work in the field.

vzn

lots of work is not the same as quick recognition. the work comes years afterward.

Slereah

The singularity theorem was one of the biggest topic in the 60's

I would say that is recognition

vzn

19:16

it takes time for paradigm shifts. they dont happen instantaneously. they travel at the speed of (human) thought which has limitations even in the information age. btw Kuhn was trained as a physicist, but physicists rarely study or cite him. would be delighted if you can cite early widespread recognition of Penrose, but think its likely wishful thinking.

Slereah

Why are you saying these things when I am quite literally telling you that this isn't how it happened

vzn

@Slereah oh you are the authority on physics history now? you were alive in 1965? ok.

Slereah

Also Kuhn was certainly cited, in particular with respect to the study of singularities

I was and I am.

I am Roger Penrose.

vzn

lol so how are you gonna spend the cash? let me guess booze and hookers? :P

ACuriousMind

@vzn 71 citations of Penrose's paper up to 1970 on Google Scholar

pretty early recognition I'd say

vzn

19:20

@ACuriousMind ok, its something definite, but note a citation is not the same as an endorsement. how many of those were skeptical? not easy to untangle.

Slereah

it's a theorem

ACuriousMind

@vzn You're welcome to present me a single "skeptical" one from them.

Slereah

You can question whether or not it applies to real world situation, but the math was pretty firmly there

vzn

@Slereah right. there are zillions of theorems. some of them are more important than others.

Slereah

not my point

vzn

19:23

theres plenty of skepticism of penroses other ideas. have never said he doesnt deserve a nobel prize, to the contrary just congratulated him. think you guys will argue no matter what is said by me.

Slereah

You certainly make it easy

ACuriousMind

well, of course we're going to disagree if you don't even try to argue your point, whatever it is

Slereah

I've had to peruse a lot of those articles so I'm not gonna agree certainly :p

vzn

am sure some prominent physicists argued against penrosian physics ideas. dont really feel like making a big effort to prove you wrong, because you guys dont really seem to care one way or the other.

Slereah

Good.

ACuriousMind

19:24

You. "would be delighted if you can cite early widespread recognition of Penrose" Me: Gives citations You: not delighted

:(

Slereah

Hell there's a whole chapter of Hawking-Ellis dedicated to it

vzn

the point is that "recognition" is not as simple as people think it is. ½ century to win a nobel prize is an abundant demonstration of that.

Slereah

The nobel prize is about the whole career, not a single act

It isn't common to get a nobel prize at a young age

vzn

@Slereah it cites his work on the singularity thm. etc

Slereah

Yes, because that's his most significant contribution

But if that was all he ever wrote, he wouldn't have gotten a nobel prize

Your view of physics is a bit too religious

You seem to be going about people with the Truth against Doubters

vzn

19:27

← actually somewhat delighted somebody posted something tangible

Slereah

People did have doubts about the singularity theorem (its applicability to the real world, anyway), and they should have

vzn

@Slereah physics is about ideas. memes. its a belief system at heart.

Slereah

All theories need to be checked

Many things are about ideas, but not all are religions

vzn

all human belief systems have a resemblance to religion.

Slereah

Sure, and all mammals resemble dogs

That's because they are all mammals

You've got your causality backward

vzn

19:30

anyway, think it likely there is prominent argument against the singularity thm somewhere... think a very erudite physicist might be able to cite it.

Slereah

Sure, plenty of people did

cf. above

Einstein was fairly opposed to singularities in general

Doesn't mean he wasn't quickly recognized by the community

vzn

there are lots of arguments about black hole physics among experts, its an area of strong contention, esp given that it evades experimental analysis.

Slereah

I know because I actually read those articles

Hence why I argue about it

I'm not even sure that Penrose himself particularly wanted to prove the Ultimate Truth that Singularities are Real

He just proved a math theorem showing that they can occur in general relativity

vzn

← thinks arguing is often a waste of time...

Slereah

feel free to stop

vzn

19:33

← sometimes just think out loud on chat lines

Slereah

Penrose was enough put off by singularities himself to champion the cosmic censorship hypothesis for a long time

vzn

ok. (the plot thickens.) that is along the lines am talking about. isnt cosmic censorship inconsistent with singularities? sigh, this stuff is subtle. did look up cosmic censorship idea a few yrs ago, maybe after you mentioned it

Slereah

Cosmic censorship is compatible with singularities

just not naked singularities

hence the censorship part

It cannot suffer nakedness

ACuriousMind

the universe is a prude

vzn

it would seem physicists are the prudes who would like to censor kuhnian ideas/ povs. maybe a bit too "promiscuous" lol

ACuriousMind

19:39

given that physicists don't usually control philosophy journals censoring Kuhn seems a bit hard :P

vzn

dictionary.com/browse/promiscuous?s=t

1. characterized by or involving indiscriminate mingling or association, ...

2. consisting of parts, elements, or individuals of different kinds brought together without order.

3. indiscriminate; without discrimination.

4. casual; irregular; haphazard.

Ryan Unger

vzn insane rambling

this chat really is a snapshot of the past

Slereah

and you complaining about it

vzn

~~0cel07~~ RU you inspired me to revisit with your revisit :P

Slereah

Things truly never change

Ryan Unger

19:43

you're not wrong

Slereah

On the freenet physics chat we used to just ban cranks outright

it made for smoother proceedings

vzn

"history doesnt repeat itself, but it does rhyme" --anonymous

@RyanUnger "promiscuous" is an interesting word. one might argue kuhnian shifts are about what might be called the promiscuity of ideas... :)

JMac

"you miss 100% of the shots you don't take" --Wayne Gretsky --Michael Scott

ACuriousMind

@Slereah any thoughts on BG3 going early access?

Slereah

I haven't even finished BG1

ACuriousMind

19:47

:O

Slereah

not my favorite RPG

it's alright, but

kind of bland

it's your basic RPG

ACuriousMind

I can see that for BG1. BG2 is better in every way (and you can see almost all the later Bioware staples with NPC interaction and player bases starting there)

Slereah

Maybe

In my opinion, just stop making medieval RPGs altogether

I'm so sick of it

vzn

heres a long detailed historical analysis of the 1965 thm arxiv.org/abs/1410.5226 p.14 Penrose’s singularity theorem shook the GR community. Its impact was ample, profound and straightaway, see [105, 305].

Ryan Unger

@Slereah what about KCD

Slereah

20:02

KCD?

Ryan Unger

kingdom come deliverance

Slereah

haven't played it

Ryan Unger

it's quite jank

Slereah

Ironically I'm currently replaying Land of Lore : Throne of Chaos

A fairly bog standard RPG

Ryan Unger

the only game I've played recently is halo

ACuriousMind

20:05

the coop is fun, never played that solo

Ryan Unger

halo or the other game?

Slereah

Land of Lore was from the early 90's

unlikely to have coop

ACuriousMind

yeah, halo. I think I know what Land of Lore looks like but I don't think I've played it

Slereah

I did play it

in 95

It took me about 20 years to find it again because I only remembered one thing about it

At some point, you have a hand in your inventory, and you must use it on some wall to open a secret passage

user6759997

20:21

New here, does anybody know much about surface tension and hydrogen bonds, not a homework question just truly want to know

Charlie

Might be a Chemistry question @user6759997

we do not practice the forbidden arts here

but if you go ahead and ask your question someone here might be able to help still :P

ACuriousMind

@Charlie aren't you a ~~fallen~~ redeemed chemist?

Slereah

or @JohnRennie

close enough anyway

ACuriousMind

sure, surface tension and hydrogen bonds sound toothpaste-related

Slereah

help my toothpaste is full of hydrogen

Charlie

20:40

@ACuriousMind Some would say reformed, some would say disgraced :P

bolbteppa

21:05

Why are the singularity theorems so important/magnificent that they deserved a Nobel

Slereah

It was to show that black holes weren't a pathological solution

and did potentially represent real objects

bolbteppa

How is Schwarzschild or Kerr etc potentially pathological

Slereah

neither are realistic solutions

Since they are static

Also specific collapse solutions like Snyder-Oppenheimer are unrealistically symmetric and have unrealistic matter

so it could have been that singularities are an artefact of those weird solutions

bolbteppa

21:33

2

A: Interpretation of the interior Schwarzschild solution

The Schwarzschild interior solution is a non-physical model that that gives the correct qualitative prediction for the interior metric of astrophysical bodies only within a certain parameter range. It is constructed by assuming that the density of the material of the "Schwarzschild star" is const...

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