The h Bar

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…

9:49 AM

Parameter space and phase space are basically the same

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

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?

No.

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

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?

They are all bundles

I see

10:09 AM

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!"

12:26 PM

I should get a specific avatar for Stack Exchange

Hm, what to take

skill patrol

1:37 PM

@Slereah Come and join raider nation ;)

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

:D

hello

hi pal

Hi

1:50 PM

just been checking over my A51 stuff

2:01 PM

How are the greys

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

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

3

quite plausibly

@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.

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

skill patrol

2:12 PM

::popcorn::

pretty much

lol

:D

Anybody want to talk physics?

2:20 PM

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.

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

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.

oooh boy

But whyyyyy?

+2

2:55 PM

0

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...

3:41 PM

@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

3:55 PM

Because your answer is kind of bad.

3

dmckee

4:06 PM

@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.

Please do make a question on meta.

Meta Evidence!

Danu

@skullpetrol ?

It just sounds cool @Danu :P

Einstein and The Meta Evidence.

Oh no I missed a JD convo!

4:17 PM

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

But Whyyyy?

:D

@Slereah don't you secretly love JD

No, I am a naysayer

(nay)

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.

4:23 PM

Isn't there a Liouville equivalent for Lagrangian mechanics?

@Slereah not that I know of

4:35 PM

@DanielSank <3

obe

4:53 PM

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

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

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

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

o crap...

I didn't know that

it is kind of their thing

I must make the correction now

5:01 PM

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

Classical tachyons are not very studied anymore

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

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

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

@obe what?

before @ACuriousMind comes by and rants

not "unstable quantum field/false vaccum" or whatever

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

(representation)

5:11 PM

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

@Secret what

oh

lol

tachyons are spacelike

It must means $P^2 < 0$

do they violate causality or not!?

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

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

5:17 PM

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

Phantom.

but we have not investigate any time related things about it

Ghost field is another thing

I hope I am not saying anything crank

@slereah I see

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

Is that the theorem about the volume form being preserved

Volume of phase space being invariant by hamiltonian flow

Or whatever

5:20 PM

@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.

@Slereah Yes.

And what does that mean, concretely

I forget

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

Well yes but not for long :p

Also it might take a while for that to happen

5:23 PM

True, but it could happen RIGHT NOW too

yup

Help I can't breathe

All the air is on the other side of the room

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

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

5:24 PM

And it allows one to apply ergodic theory to mechanics.

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

Basically the classical version of unitarity

In stat mech? Yes.

Hey it's Angus Potgurney!

DanielSank

@0celo7 <3

@Slereah ...huh?

5:26 PM

@0celo7 Angustheman

Oh wait

Podgorny

ok... didn't expected that

lol

(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

It is best to avoid discussing consciousness in such scenarios

:) evening

5:30 PM

Arrest? SE mods shoot first, never arrest.

@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

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

@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

Headhunterz & Wildstylez - Down With the Hardstyle

►

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?

5:34 PM

Did you give up on the torus

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

jesus

what's the metric?

Yeah differential equations are the least fub part

did you calculate the Christoffel symbols by hand?

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

Nah I have a program to do that

5:37 PM

what is $f$

A function to deform the spacetime

@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.

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 $1 + \frac{1}{2}\sin(\theta)$

>:| 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.

5:40 PM

Like vixra

lel

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

haha always the best move ;)

>not solving ODEs by hand

what kind of theoretician are you

(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

5:46 PM

I was doing something...

Damn

OH!

Time to do the worst exercise in Arnold.

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

Oh boy

My equation is the Lienard equation apparently

Golly gee willicker

pik?

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!

@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.

Uh, I could have solved that. I think.

5:54 PM

Oh wait no

Wrong equation

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

that's the one

Hm, no typo

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