The h Bar

Slereah

00:01

Noooo

Now I have to integrate $\int d\lambda \frac{\dot w(\theta)}{w(\theta)}[\frac{\dot \theta^2}{2} - \frac{K}{a^2 w^3(\theta)}]$

Oh buns

That $\dot\theta$ is quite bothersome

Hm

This might look like the ansatz kind of equation

0celo7

do it

yolololo

Slereah

That is secret code for "Take the basic solution and cram a function everywhere until it fits"

Slereah

00:24

I dunno man, how do mathematicians do it

Do they just ansatz it until something comes out

0celo7

there is probably a book on ansatzes

what do I plug in where

Slereah

Just add, multiply and compose functions until something comes out

0celo7

did you try $\cosh\Gamma(\int \mathrm{d}x \exp J_n(ax))$?

maybe find an equation for $a$

$J_n$ is a Bessel

Slereah

what

0celo7

I gave you an ansatz

Slereah

00:34

Sure, but I'd like one that works

0celo7

that one will work

Slereah

Making the equation spit out an extra $f$ function probably isn't too hard but then there's the $\dot \theta^3$ term

0celo7

@Slereah why does curve minimizes energy functional $\implies$ curve minimize length

I know $L[\gamma]^2\le 2(b-a)E[\gamma]$

@ACuriousMind maybe you know?

Slereah

Because the energy is given in terms of a length?

0celo7

no the energy and length are related as above

we know they share critical points

but how do we know that a minimum of the energy is a minimum of the length

maybe it's just a saddle of the length

Slereah

00:43

Hm, let's see

What's a similar ODE

To Eq World!

Hm

This might call for

THE BOOK

The book of ODE solutions

0celo7

huh

SE logged me out

thought I got permabanned for a sec

ACuriousMind

@0celo7 Because that inequality becomes an equality for curves parametrized by their arc-length.

Slereah

"Polyanin A.D., Zaitsev V.E. Handbook of exact solutions for ordinary differential equations"

God help me

0celo7

@ACuriousMind so?

Slereah

We make a lot of mathematica jokes, but in the end

0celo7

00:49

geodesics are parameterized by arc length, sure

Slereah

You can't beat the reference books

0celo7

@Slereah jesus

Slereah

700 pages of ODEs

0celo7

wow

Slereah

This isn't some namby pamby book on differential equations where you get chapters of explanations.

No.

0celo7

00:50

pic?

Slereah

Ten equations per page or so

Looks like that

I would recommend it, but it is the last refuge of the damned

If you have to use it, you have sunk quite low

0celo7

@ACuriousMind pls why does the geodesic parameterization matter

Slereah

Oh god

I have to go all the way p. 423

Bad sign

0celo7

why

Slereah

Well they are roughly arranged by simplicity order

Further in you go the worst it gets

Like the circles of hell

Hm

$y'' + f(y) (y')^2 + g(y) = 0$

Pretty close to what I want

Even without the exact form there's plenty of hints on how to do it

Gonna have to cook up some solution from this

0celo7

01:05

@ACuriousMind Ahhhhhhhhhhhh

Nevermind, I get it

So either you ignored me or wanted me to figure it out on my own

Ghost

very good

TanMath

01:39

I am bored, so I have come here!

Watcha doing?

Slereah

Uh

After a whole bunch of substitution, I'm ending on a much simpler looking equation

Not sure it's correct tho

Plus it is still second order with arbitrary functions

But at least it's linear

Oh wait, first order even

neat

0celo7

You can solve it then

Slereah

Well, technically

Not sure about closed form, though

Also it's almost 3 AM so it will wait for later

0celo7

Nasty integrating factor?

Slereah

It's a lot of sines and cosines

0celo7

01:47

Oh. That's too bad.

Slereah

I might require the OTHER BOOK

There should be a list of all the handbooks, really

All the books that are just the information you need without any frills

0celo7

03:41

@DanielSank homework can anyone help

Secret

05:32

Random 5
http://www.iflscience.com/editors-blog/kid-nailed-his-math-test-some-unorthodox-thinking

In the context of physics, however one has to be careful that unorthodox thinking can easily become crank theories if unsupported or unfalsifiable

DanielSank

06:53

@0celo7 Each day when I arrive home, I drop my things, wash my hands, and open my laptop to see if I have any interesting messages on this site. I really relish that moment every day because so often I would find an interesting new question, an insightful comment, or some new rep on one of the answers I'm so proud of writing. Then came the days of @0celo7. Having discovered my dislike of poor question titles, he now sends me chat messages with links to the worst of the worst.

That brief daily moment of joy has been replaced by a daily jolt in my blood pressure.

So thanks, @0celo7, for nothing.

;P

Secret

Phase space and Parameter space[edit]
"In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space" I think this phrase is misleading. There is a difference between phase space as defined here and parameter space. The phase space is all the possible states of a given system (usually over time for different initial conditions). Changing the parameters of a system (for example the stiffness of a spring) can give a different phase space. If we allow the parameters to be changed then we obtain a family of phase spaces. Usually, if t…

Slereah

09:49

Parameter space and phase space are basically the same

Paramerer space is $(x(t), \dot x(t)$, phase space is $(x(t), p(t))$

Secret

So a plot of a thermodynamic system U=U(S(t),V(t),n(t)) with time dependent state variables is an example of a phase space?

Slereah

No.

Because a phase space is a symplectic manifold while a thermodynamic system has a contac manifold!!!

Secret

what do we call the abstract space obtained by plotting out all the possible states of the time dependent thermodynamic system as?

I recall the time independent version is a state space, which is a type of configuration space

Also is there some umbrella term that refers to an abstract space where phase space etc. are a subset of it

such as what is the name of that space that "a family of phase space" is living in called?

Slereah

They are all bundles

Secret

I see

Slereah

10:09

A bundle basically lets you define a couple of coordinates

$(x,y)$

Where $x$ is a point on the manifold and $y$ is a point on the fiber at $x$

Stephani makes me laugh because it doesn't even talk about causality issues for the Gödel metric

It's just "maximally symmetric fluid spacetime? Yowza!"

Slereah

12:26

I should get a specific avatar for Stack Exchange

Hm, what to take

skill patrol

13:37

@Slereah Come and join raider nation ;)

Slereah

I am only vaguely aware of what the Raiders are because I am somewhat steeped into US culture

But otherwise people outside the US have no clue what that is

skill patrol

:D

Ghost

hello

skill patrol

hi pal

Slereah

Hi

Ghost

13:50

just been checking over my A51 stuff

Slereah

14:01

How are the greys

Ghost

they are fine and send their regards (and anal probes)

Slereah

The whole mythology of alien anal probing really sounds like the people pretending to be abducted have some unresolved issues

3

Ghost

quite plausibly

John Duffield

@Slereah "He would show him he is wrong with his own book." Damn cheek. I'm forever telling you and 0celo7what Einstein said, and you're forever dismissing it because you think you know better.

Ghost

@JohnDuffield give it a rest - we're talking about the greys

skill patrol

14:12

::popcorn::

Ghost

pretty much

skill patrol

Ghost

lol

skill patrol

:D

John Duffield

Anybody want to talk physics?

Ghost

14:20

depends

crickets chirping

skill patrol

For every natural phenomenon there are different levels of explanation. I like to call these "why" values. For the first value of why, the question "Why is the sky blue?" can be answered with some simple hand-waving about light from the sun passing through our planet's atmosphere. For a value of why + 2 (also known to parents as, "But whyyyyy?") you have to start talking about the fact that light comes in different colors. I believe @JohnDuffield is stuck at the value of + 1.5.

John Duffield

Only light doesn't come in different colours. Colour is a quale. Light comes in different frequencies. And as to why the sky is blue, everybody knows that.

Ghost

oooh boy

skill patrol

But whyyyyy?

Ghost

+2

Physics Meta

14:55

0

Q: Why is PSE so restrictive in the Q&A it is willing to accept?

There is already a Physics Overflow. Why then not being more lenient in the Q&A to be accepted in PSE? Mathematics SE has 10 times as many questions. SO leads with +10M questions. Those other sites are thriving yet feel way more welcoming. In contrast, here there are way too many questions put on...

John Duffield

15:41

@dmckee : I've just finished answering the above meta question, to find that I've got two anonymous downvotes to a PSE question I've just answered. I want to make a complaint about "naysayer trolls" hanging around sniping and close-voting and downvoting.

It's like you've got a gang of vagrants camped on your fornt lawn frightening people away from the party. I think you should try to do something about it.

obe

15:55

Because your answer is kind of bad.

3

dmckee

16:06

@JohnDuffield John, with very limited exceptions votes are plenary. Users may deploy them how they wish. That's how crowd-sourced evaluation works.

You don't get to tell other users how to vote any more than they get to tell you how to vote. And its time you stopped bothering the mods directly about this stuff.

5

Don't like it, make a question on meta. Otherwise, suck it up. It happens to us all.

Slereah

Please do make a question on meta.

skull petrol

Meta Evidence!

Danu

@skullpetrol ?

skull petrol

It just sounds cool @Danu :P

Einstein and The Meta Evidence.

0celo7

Oh no I missed a JD convo!

Slereah

16:17

@0celo7 : Here's a tip : It's the same as always

skull petrol

But Whyyyy?

:D

0celo7

@Slereah don't you secretly love JD

Slereah

No, I am a naysayer

(nay)

skull petrol

Scroll up, I left some popcorn to eat while you read his links.

~~read~~ skim

dmckee

@Slereah Well ... they have similar information content, but they obey different conservation rules. The Liouville Theorem only works in $(\vec{x},\vec{p})$ phase-space.

Slereah

16:23

Isn't there a Liouville equivalent for Lagrangian mechanics?

0celo7

@Slereah not that I know of

0celo7

16:35

@DanielSank <3

obe

16:53

can someone explain this to me? en.wikipedia.org/wiki/…

how is that equivalent to the definition as a semigroup blah blah blah?

Secret

@Slereah Right now my friend and I had a discussion about the tachyon antitelephone

Slereah

I think the math for the tachyonic antitelephone is basically the same as any causality violating spacetime.

Either you have no solution that works, or one solution, or multiple solutions

also if you talk about tachyons don't use the term "closed timelike curve"

They are not timelike

Secret

o crap...

I didn't know that

Slereah

it is kind of their thing

Secret

I must make the correction now

Slereah

17:01

I think you're gonna have problems with the initial value problem for tachyons, but I dunno

Classical tachyons are not very studied anymore

Secret

so to remind my memory, the reason the tachyon in the tachyon antitelephone can travel back in time is because their worldines are spacelike, hence to some observers they are going backwards in the time coordinate?

ok, I will investigate the quanutm case later along with the rest of my project

Slereah

When you move in a spacelike fashion, it is not overly difficult to go wherever you want, anyway

There are no hard limits like the light cone

Secret

makes sense

OMG those last few mins before you reminded me that they are spacelike, I have caused a disaster in misknowledge

(Page 3 is comming, because it is still not the present pontof the conversation yet)

page 3

and that's the present
now to inform him my mistake

0celo7

@obe what?

before @ACuriousMind comes by and rants

not "unstable quantum field/false vaccum" or whatever

Slereah

"tachyon" just means it is part of the tachyonic little group :p

(representation)

Secret

17:11

tachyons cannot be null, because they are not lightlike, right?

0celo7

@Secret what

oh

lol

tachyons are spacelike

Slereah

It must means $P^2 < 0$

0celo7

do they violate causality or not!?

Slereah

You know I wonder what fields that are tachyonic but of non-zero spin are like

@0celo7 : Depends!

Point particle tachyons obviously do

Free tachyon fields do not, apparently

Anything else I don't fucking know

According to what's his name they don't because the principal part of any tachyonic field will still be the same as a massive field

But I have yet to see the proof

For point particles the tachyonic part directly modifies the principal part since the Lagrangian is $\frac{m}{2} \dot x^2$

But not for fields

Also I wonder what that means for phantom fields, too

How do free phantom fields propagate

Hm, maybe not

Secret

I think I once asked a question on the main site about whether tachyonic (insert name for fields with a wrong signed lagrangian (ghost or phantom, i don't remeber)), and they said it is possible

Slereah

17:17

Point particles the factor is $m$, not $m^2$

Phantom.

Secret

but we have not investigate any time related things about it

Slereah

Ghost field is another thing

Secret

I hope I am not saying anything crank

@slereah I see

0celo7

@dmckee I prefer the formulation: "The symplectic form and its exterior powers are integral invariants of the phase flow." But I'm weird :P

Slereah

Is that the theorem about the volume form being preserved

Volume of phase space being invariant by hamiltonian flow

Or whatever

John Duffield

17:20

@dmckee : that's maybe how crowd-sourced evaluation works, but science is not a democracy, and it isn't working for PSE. I'll think about starting something on Meta.

0celo7

@Slereah Yes.

Slereah

And what does that mean, concretely

I forget

0celo7

That + Poincare recurrence means gas will eventually cluster in the corner of the container

Slereah

Well yes but not for long :p

0celo7

Also it might take a while for that to happen

Slereah

17:23

True, but it could happen RIGHT NOW too

0celo7

yup

Slereah

Help I can't breathe

All the air is on the other side of the room

Secret

0celo7

Ok, according to Arnold Liouville's theorem is important in stat mech.

Secret

as far we know, there are almost nothing done on the fermion case.

0celo7

17:24

And it allows one to apply ergodic theory to mechanics.

Slereah

Apparently it's just a theorem about conservation of probability?

Basically the classical version of unitarity

0celo7

In stat mech? Yes.

Slereah

Hey it's Angus Potgurney!

DanielSank

@0celo7 <3

0celo7

@Slereah ...huh?

Secret

17:26

@0celo7 Angustheman

Slereah

Oh wait

Angus Podgorny

►

Podgorny

Secret

ok... didn't expected that

lol

Secret

(After this one I am not going to post anymore of the above conversation, else Danu will arrest me for diary flooding)
(Friend)
Maybe our detectors and electronics had smeared them out as if temporal paradox is forbidden

Slereah

It is best to avoid discussing consciousness in such scenarios

AngusTheMan

:) evening

0celo7

17:30

Arrest? SE mods shoot first, never arrest.

Secret

@Slereah that's why I said to him to use something simpler, and he suggest a rasberry pi as a detector

which helps avoiding that murky consciousness stuff

Slereah

The simplest method to do that kind of thing is "billiard balls"

Point particles with a point interaction

In flat space it's pretty easy to do

Basically just geometry

Secret

@Slereah I might arrange him to meet with you on chat one day, he might be good to add into the conversation about time travel (and it gets tiring to relay conversations from both sides to each other)

His academic background is similar to mine, but he is 100% physics major and has studied complex analysis and lasers which I have not

0celo7

Headhunterz & Wildstylez - Down With the Hardstyle

►

Slereah

Hm, I wonder what the Lagrangian is for such particles

IIRC it is used for like statistical mech

What's the potential for point interactions?

0celo7

17:34

Did you give up on the torus

Slereah

Not yet

Still doing the geodesics for the deformed torus

I have solved the equation kind of

Currently it's not in closed form and it's two substitutions away from the original

0celo7

jesus

what's the metric?

Slereah

Yeah differential equations are the least fub part

0celo7

did you calculate the Christoffel symbols by hand?

Slereah

$ds^2 = -dt^2 + (c + a \sin(\theta))^2 d\varphi^2 + a^2f(\theta)d\theta$

Nah I have a program to do that

0celo7

17:37

what is $f$

Slereah

A function to deform the spacetime

AngusTheMan

@JohnDuffield I was one of the down voters on your answer to the Noether theorem question. It is not because I have anything personally against you or any other contributions you have made to the site, or that I wanted my answer to "look better". It is simply that I thought your comments were unfocused towards the answer that, (in my opinion), the question should of had. I hope you are not offended, this is not my intention. Best regards.

Slereah

Such that the distance for $\theta < 0$ is larger than the rest

It can be a variety of things but the simplest function for this is probably $1 + \frac{1}{2}\sin(\theta)$

0celo7

>:| One Man Army is not out yet >:|

>:|

dmckee

@JohnDuffield This site doesn't claim to be doing "science". In fact many of the ways if might, in principle, be put to use as a tool for doing science are disallowed by the rules. And that is fine because this is a site about collection good answers to good question.

If you want to "do science", submit your ideas to a peer reviewed platform of some kind.

Slereah

17:40

Like vixra

0celo7

lel

Slereah

Hm

I wonder if it's worth it to solve the full geodesic equation, actually

Currently I only really need the meridian geodesics

Those are the interesting ones

The equation gets a lot simpler then

Fuck it, let's do the meridians

much better

Let's go check the book of the damned for the solution

AngusTheMan

haha always the best move ;)

0celo7

>not solving ODEs by hand

what kind of theoretician are you

Slereah

(It is my little name for the Handbook of exact solutions for ordinary differential equations)

@0celo7 : All of them?

Hell I don't use Wolfram Alpha because I don't think it would work here

0celo7

17:46

I was doing something...

Damn

OH!

Time to do the worst exercise in Arnold.

$$\int_{\epsilon\partial \Pi}\omega=\epsilon^{k+1}\mathrm{d}\omega(\xi_1,...,\xi_{k+1})+\mathcal{O}( \epsilon^{k+1})$$

Slereah

Oh boy

My equation is the Lienard equation apparently

Golly gee willicker

0celo7

pik?

Slereah

eqworld.ipmnet.ru/en/solutions/ode/ode0317.pdf

I had to go to eqworld because I suspected the book of the damned had a typo

And lo, it had!

John Duffield

@AngusTheMan : no problem Angus. I don't think downvoting is an issue when people say something about why. IMHO the problem is when people don't say anything, and don't answer the questions either, and vote to close them, even when they're good interesting questions.

0celo7

Uh, I could have solved that. I think.

Slereah

17:54

Oh wait no

Wrong equation

eqworld.ipmnet.ru/en/solutions/ode/ode0344.pdf

that's the one

Hm, no typo

AngusTheMan

@JohnDuffield cheers John :) yeah it can be annoying when that happens, especially when you have started writing an answer :/

Slereah

I don't get why $y_{xx} = w_y$

For $w(y) = (y')^2$

AngusTheMan

typo for x?

Slereah

Why typo

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