The h Bar

1:47 AM

Yesterday (UTC) was my eighth day to get rep-capped on physics. That means that I am alomst a sixth of the way to being epic.

dmckee

2:16 AM

And that's only the silver badge in the category!

But it does mean that I now have more capped days on Physics than on Stack Overflow.

vzn

3:05 AM

@0celo7 why dont you ask it on the site? think its very worthwhile, as stated have been turning over in head/ vaguely pursuing a similar concept for many yrs. will upvote. am collecting some links on this subj to bang into a blog sometime but dont have much right now. :|

0celo7

Because I'd have to (a) dig up my old notes on it (b) do lots of work

vzn

> knowledge is power + a little knowledge is a dangerous thing

> if you think education is expensive, try ignorance —lederer

@Secret you know that expr get a room? how about get a blog

@JohnRennie sounds interesting, do you have any refs on that?

vzn

3:40 AM

@0celo7 found a pdf of HE "of shady origins". am looking over that section. it seems to be considering the lagrangian of a "perfect fluid" aka isentropic in warped spacetime, maybe not exactly what am looking for myself, but close, aka something like "relativistic fluid behavior". iiuc & leveraging some learned-long-ago fluid dynamics theory, the isentropic field could possibly be considered a limit case of a matter field with "very small" repulsive particles— very much like an "ideal gas"...

John Rennie

4:02 AM

@vzn I don't have a specific reference becauyse it's such a well known phenomenon. It just means the Navier-Stokes equations can have singular solutions, but then so can lots of PDEs.

The resolution is that the Navier-Stokes equations are emergent and don't apply when we get down to the molecular scale.

vzn

@JohnRennie ok. somewhat doubt this, but worth asking anyway ("for the record"): has anyone drawn the seemingly ripe analogy to QED singularities?

0celo7

I just bought food at midnight

I'm officially a slob

vzn

thx/ congrats for definitively removing all doubt :) :P

0celo7

@vzn I went on a walk to call my gf and talk to her with some privacy and before I knew it I was half way to Walmart

I bought some crunchy peanut butter and jam

vzn

@0celo7 fyi brand new scientific study links junk food consumption with sleep deprivation

hows the gf anyway? the music student?

0celo7

4:14 AM

this isn't junk food

@vzn yes, good

John Rennie

@vzn you doubt it? Admittedly this isn't my area but I thought everyone knew we get singularities in solutions of the NS equations. You're a mathematician aren't you? There must be loads of papers on this subject.

vzn

@0celo7 reminds me, just saw trailer for "theory of everything" after avoiding it for a few yrs, have you seen that movie?

0celo7

no

why would I watch a film about Hawking

He can't even write a decent book

vzn

@JohnRennie that is, doubt that anyone has drawn an analogy of fluid dynamics singularities to ("infamous/ notorious") QED singularities. conjecture there could/ would/ should be some eerie resemblance.

John Rennie

Ah, oops, sorry :-)

I don't think there is any analogy with QED singularities.

vzn

4:17 AM

@0celo7 zen question of the nanosecond, if you took away the sarcasm from your writing aka thinking, what would be left? :P

John Rennie

It's a general property of certain types of PDEs that they have singular solutions. I say certain types since I don't understand the details.

0celo7

@vzn The most intelligent writing you'll never experience

vzn

lol

yuggib

4:54 AM

@JohnRennie what do you mean by singular solutions?

solutions with a finite-time blowup or solutions that are not smooth/continuous?

John Rennie

@yuggib points where the equations of motion become singular

@yuggib don't know, probably both

yuggib

@JohnRennie well, in fact both situations may happen

but the first one is much more singular than the second

I mean, in many situations (e.g. the Schrödinger equation) there is no physical requirement of continuity/smoothness for the PDE solution

the finite-time blow up instead means that the "magnitude" (usually the norm) of the solution explodes at a finite time

the finite time blowup has very rarely some physical interpretation: I very vaguely recall that e.g. in water wave equations, the blowup means something like the wave breaking up/losing its "wave nature"

vzn

5:13 AM

½-lol "much more singular"...

my understanding is that QED singularities are "roughly" spacetime discontinuities, havent studied this at length, but found the informal descr/ discussion in feynmans QED book quite memorable (full disclosure, popsci! aieee!), its a deep mystery that has persisted for decades & continues, & seems to point to a glitch and maybe a tip of iceberg of new theory, not so unlike nonlocality in QM etc

...the QED singularities are typically centered around particles, arent they?

yuggib

QFT singularities are, mathematically, a problem of singular perturbation theory

DanielSank

5:30 AM

What the f--- do you call an energy divided by hbar?

I'm not talking about an energy difference divided by hbar, which is obviously a frequency.

Just an energy.

Ugh, forget it.

Grah!

Language is stupid.

yuggib

7:45 AM

so today is the day slereah will be put to the test... :P

our french guinea pig

"cochon de la Guinée (française)"

user116211

Next turn will be yours.... grins

yuggib

hehehe

nothing official for the moment :P

in all the ama pages, there is no mention of my possible session

user116211

Experiment with mice often reminds me:

user116211

yuggib

these rodents are fancy

user116211

7:52 AM

@yuggib Slereah has no hairs ;_;

yuggib

ah...that is a problem shared by at least two thirds of men

user116211

ah! Lumo has new works..... he is busy modifying his 5yr old answers.....

yuggib

and some very unlucky women

user116211

@yuggib errrr....

Physics Meta

9:21 AM

0

Q: duplicate questions

Who should the onus fall on to check if a question has already been asked, the person who asks the question (who may not have much background in the question they are asking) or the person answering the question (especially if they give a different answer to those previously presented)?

Physics Meta

9:32 AM

0

Q: URGENT MATTER - reopening of question

My question Spawning a VW Beetle was closed. I dont want to speculate on reasons, as none where given. I here give close-voters a chance to explain themselves. If no reason is given, then reopening must ensue. I find this an abuse of the system to close good questions for abusive reasons, can t...

discussion

Slereah

10:53 AM

hey

Slereah

11:07 AM

Hm

Thinking about it

The notion that the surgery spacetime thing would have a discrete spectrum sounds WRONG

Because a function of compact support not crossing the wormhole would be completely independant of those bits

And I'm pretty sure you can't make it with a discrete spectrum

dailycaller.com/2016/06/11/…

user116211

11:20 AM

I given you many chances to explain, prepare for ban — Loffen 40 mins ago

user116211

O.O

Slereah

PREPARE TO DIE

user116211

I really don't want to sully the mood before AMA ;((

Slereah

I should make some little diagrams before going in maybe

Slereah

11:54 AM

Oh no

Lumo made a reasonable answer

I had to upvote him

user116211

;D

0celo7

12:10 PM

@Slereah is the Euler characteristic a functor

Slereah

Probably

Isn't everything

user116211

Say again? I mean say again?

user116211

Algebric Topology after high school o.O

0celo7

Holy crap the exercises in Milnor are ridiculous

user116211

@Loffen The mods like him, he won't get banned. — 0celo7 6 mins ago

user116211

12:20 PM

Was it required ;P

Slereah

Did he ask you to solve the Riemann hypothesis

0celo7

He asked me to prove that you're a man

It's not possible

at least within ZFC

Slereah

Check my mooscles, though

B)

mooscles

►

0celo7

@Slereah You are insane.

It's quite sad.

ACuriousMind

@DanielSank I call it energy because $\hbar = 1$ :)

0celo7

12:33 PM

@ACuriousMind could you please provide a hint for problem 6 in Milnor?

ACuriousMind

no

0celo7

why not

FrancescoS

Why did i receive a bonus of 100 in the reputation?

:O

Slereah

Energy divided by hbar is angular frequency you butt

user116211

@FrancescoS because they trust you.

ACuriousMind

12:35 PM

134

Q: What is the association bonus?

I was just awarded +100 reputation on all of my Stack Exchange accounts. What is this bonus for? It simply says Association Bonus on my reputation overview.

support faq-proposed association bonus-reputation

FrancescoS

ook

0celo7

@ACuriousMind Can you at least tell me if I need to use the Hopf degree theorem?

John Rennie

@ACuriousMind: you might consider deleting your comment to Loffen's recent meta question. While I completely agree with the first two sentences of it, I'm not sure that Stop wasting our time and start asking better questions is helping to calm things down :-)

Slereah

Tell him that if he angers you you'll become more powerful than he ever could imagine

John Rennie

ACM is the hulk?

Slereah

12:39 PM

He is

0celo7

ACM is skinny

Slereah

He is, as long as he's not angry

John Rennie

He becomes a supermassive black hole when angry

ACuriousMind

@JohnRennie I see your point, but since this is the second such meta question by the same user with the same pointless complaints and empty threats, I really do believe they are wasting our time. I replied charitably the first time, and it bore no fruit at all.

@0celo7 No, because I haven't looked at the exercise.

John Rennie

I'd guess we've run into someone several sigmas from the mean on the physics nerd scale, and for someone that far out nothing we say or do is going to make any difference.

But if the comment isn't going to make any difference anyway why be mean?

user116211

12:49 PM

Yes, it is definitely possible to learn differential topology without any strengthening of your foundations in analysis. In particular the content of "baby Rudin" is essentially irrelevant: rearrangement of series and gamma functions won't help you to understand, say, De Rham cohomology or Morse theory, nor even to compute in the tangent bundle! As an aside, I don't understand the American infatuation for that book, which I find boring, needlessly difficult and concise and without any show of enthusiasm for calculus, one of the most exciting and glorious achievements of mankind. — Georges Elencwajg Dec 20 '13 at 10:49

user116211

@JohnRennie: If he is not fool, your answer would be sufficient.

0celo7

@ACuriousMind It asks you to prove that a maps $S^n\to S^n$ must have a fixed point if its degree is not $(-1)^{n+1}$. I know the regular Brouwer fixed point and I tried googling this one and looking it up in Bredon and GP, with no luck

user116211

But as ACM's answer didn't seem to work, I don't think yours would work ;(

David Z

@ACuriousMind FYI the moderators are investigating.

0celo7

> There is no onus on site members to justify their actions.

ACuriousMind

12:52 PM

@JohnRennie Some people only understand blunt replies - does it really come across as me being mean for the sake of meanness?

0celo7

@JohnRennie $o\mapsto a$ changes the meaning of that quite a lot.

ACuriousMind

@0celo7 "There is na anus an site members ta justify their actians"? :P

John Rennie

There is na onus ? I don't get it :-)

ACuriousMind

@DavidZ Uh...investigating what exactly? Do you have means to determine whether questions are asked in bad faith or not? oO

Secret

4

Q: Is it possible to learn differential topology before analysis?

Currently I'm self studying for my own enjoyment topology and algebra (munkres and herstein). Since I start at the university next year everything I'm learning now is for my own enjoyment and I will probably relearn it in the university anyway. I'm interested in differential topology yet I haven...

analysis soft-question differential-topology self-learning advice

0celo7

12:54 PM

@ACuriousMind Now you're just making fun of Bostonians

John Rennie

@ACuriousMind David doesn't think so as he left your comment there. I'm probably just being a bleeding heart (again).

Secret

@Secret That is good to know, perhaps it will get me armed up to deal with these things abstractly

0celo7

@Secret Are you going crazy

Secret

@ 0celo7 I don't want my previous post to be mistaken for responding someone else's

and to show they are actually linked but putting them together cause the banner to not show. As I mentioned previously, it is best to have things umambiguriously indexed so that there will be no confusion. If there's a better way to do that I 'd like to know

David Z

@ACuriousMind not definitively, of course, but sometimes there's suggestive evidence.

0celo7

12:56 PM

@ACuriousMind So, now that you know what the exercise is, can I please have a hint :3

David Z

Anyway, we're investigating a few issues related to that account. I figure I shouldn't give away much (better safe than sorry, y'know). Just saying, it may not be worth getting into an extended argument.

Secret

@ <insert user> (note the space) allow me to refer to someone in a way just noticeable enough but not annoying them with a ping bomb

David Z

@JohnRennie I consider the comment blunt but not mean.

ACuriousMind

@0celo7 The proof of that statement that I know uses the Lefschetz fixed point theorem.

Loffen

hahaha investigating me

I am flawless

John Rennie

1:10 PM

Well I guess that's all the proof we needed that whoever is using the Loffen account is not posting in good faith.

Loffen

Why?

Do you say that?

Secret

Prepare your logs, agents! We have a target to secure

David Z

OK, to be more direct: if there's anything to be taken care of, the moderators will take care of it. Everyone else, we'd rather you leave it alone. Just keep dealing with low-quality posts and such as normal.

Secret

@ David Z don't worry , I am always as random as I usually am

ACuriousMind

@neoDev Uh, we're physicists. Are you sure there aren't people more qualified to help you with whatever the issue is?

0celo7

1:15 PM

@ACuriousMind I'm not.

Speak for yourself, buster

ACuriousMind

@0celo7 Yeah, I dunno what you're doing here, either ;P

0celo7

@ACuriousMind Ok, I checked the section on GP on Lefschetz fixed point theory and it's not there either

John Rennie

@neoDev OK, but what does this have to do with physics?

0celo7

I shall ask my professor when I meet him today

John Rennie

I suggest you ask on the Stack Overflow chat

Well that was random ...

0celo7

1:17 PM

you're random

ACuriousMind

@0celo7 What's not there? IF you know the Lefschetz theorem, you can just compute the Lefschetz number of the self-map of a sphere and observe it's not zero unless the degree is $(-1)^{n+1}$.

user116211

@JohnRennie but nice.

John Rennie

@MAFIA36790 for a limited subset of meanings of the word nice

0celo7

@ACuriousMind I wouldn't know how to calculate that though

Bernard Meurer

@0celo7 Have you talked to Michelle recently?

user116211

1:22 PM

Hey @BernardMeurer!

0celo7

@BernardMeurer not for weeks

Slereah

hey

Bernard Meurer

@MAFIA36790 Heya

@Slereah Hey

@0celo7 She isn't answering my texts

ACuriousMind

@0celo7 You do know the homologies of a sphere, right?

0celo7

@ACuriousMind Ok I'm getting a little annoyed that you keep telling me to do algebraic topology when I'm taking a course on differential topology and you know I don't know algebraic topology.

ACuriousMind

1:24 PM

...how did you define the Lefschetz number if not by homologies?

John Rennie

Try chat.stackoverflow.com

Bernard Meurer

@neoDev Try the stackoverflow chat

John Rennie

Just ask on the main StackOverflow site

0celo7

@ACuriousMind the intersection number of the diagonal of the manifold with the graph

I have literally no clue how to actually calculate that

Bernard Meurer

@neoDev Then wait

ACuriousMind

1:26 PM

@0celo7 Then I can't help you, because I've never seen that version. You know that I know algebraic topology but not differential topology :P

user116211

@neoDev O.O

Bernard Meurer

@neoDev Dude, this is a physics chat, wait for someone to answer your question on SO and chill meanwhile

John Rennie

@neoDev You can go away and stop interrupting our discussion about physics

Bernard Meurer

@JohnRennie S A V A G E

John Rennie

Now it's me being mean :-)

user116211

1:27 PM

niice ;\

Bernard Meurer

And on that note, hey John :p

ACuriousMind

@JohnRennie ...what discussion about physics, to be fair? :P

John Rennie

→ 28 messages moved to Trash

user116211

Would not name him, but actually I'm missing his quote ... let's talk physics

Slereah

I hear there's an AMA here today!

Bernard Meurer

1:29 PM

@MAFIA36790 He never explained me what the Kuiper cliff is :(

John Rennie

@MAFIA36790 :-) Don't remind me, we only have a few days of peace left!

Slereah

Can't wait to see who's gonna be doing it

user116211

@JohnRennie ;) would he come?

Bernard Meurer

@Slereah word on the street say's it'll be bomb ass

ACuriousMind

I hear it's some crazy Frenchman

One of these time travel crackpots

user116211

1:30 PM

French Guinea pig experiment .....

Slereah

Really a poor idea for a first AMA

Bernard Meurer

Dude my toenail just got buried on my flesh and it hurts

halp

user116211

urrrggggg

Slereah

Hangnail?

Oh more ingrown I guess

Bernard Meurer

Yeah, ingrown

Slereah

1:31 PM

Well dig it out and suck it up, because I'm afraid there isn't much pleasant solution

It's gonna suck for a bit

Bernard Meurer

Yeah I did that but it hurtses

And I have to walk to get lunch today

Hello darkness my old friend

Slereah

Put a lil band aid

Also take some opium

Bernard Meurer

Lel, this is Brazil, not the middle east

Slereah

What is the popular drug in Brazil

0celo7

the people are the same color in both places

user116211

1:33 PM

Speaking of Brazil, they are out of COPA!!

0celo7

therefore they're the same

Bernard Meurer

@Slereah Cocaine, weed and recently synthetics have been growing

@MAFIA36790 Hum?

Slereah

Well you know what to do

Bernard Meurer

@Slereah I'll just drink a lot as usual

user116211

Damn, I mean to say EURO cup ;/

Slereah

1:44 PM

0

Q: What values of jerks are considered acceptable in vehicular-automobile travel?

Are these values of jerks different while accelerating or decelerating? Links to any references would be appreciated

jerk

I want 0 jerks in the car plz

bolbteppa

This looks so different to what's in Milnor, from Schwarz 'Top for Phys':
"A heuristic justification for Sard's theorem is the following: if $f$ is a smooth one-to-one map on $S \subset E$, the volume of $S' = f(S)$ equals $\int_S |J(f)(x)|dx$. If $f$ is smooth, but not necessarily one-to-one, the volume of $S'$ is at most this integral. Applying this to the case where $S$ is the set of singular points of $f$, we conclude that the volume of $S'$ cannot be greater than zero, since $J(f)(x) = 0$ for all $x \in S$. This is not a complete proof because, strictly speaking, the formula $\mathrm{v…

Bernard Meurer

physics.stackexchange.com/questions/tagged/jerk

Best tag

user116211

@BernardMeurer it's actually $\dddot{\mathbf r}~.$

Slereah

$\ddddot r, \dddddot r$

One d too many

$$^{\ddddot r}_{\ddddot r}\ddddot r^{\ddddot r}_\ddddot r$$

0celo7

Oh lord

Loffen

1:55 PM

its good to not be banned, mods like me

0celo7

@ACuriousMind I'm fully convinced one cannot do the exercises in the back of Milnor without extra material

@Loffen Hey!

I'm a fan

I have some suggestions though

Slereah

Proving Geroch's theorem?

Yeah sounds a bit challenging

0celo7

@Slereah no that's Sachs-Wu

Slereah

I think Milnor might be a crazy man

Oh

What is Milnor asking

0celo7

To prove a bunch of stuff for which the reader is not prepared

You need to invent freaking slice charts for one of them

that's pretty nontrivial

Slereah

1:57 PM

Well

Do what I do

Google milnor+solution+pdf

0celo7

then the tubular neighborhood one requires either a heap of bundle theory

Slereah

See if anything comes up

Bernard Meurer

@0celo7 Revive your sister plox

0celo7

@BernardMeurer she's on vacation

Bernard Meurer

@0celo7 ged demmit

ACuriousMind

1:59 PM

@0celo7 So?

0celo7

@Slereah hey should I read Steenrod for this course

John Rennie

This was surprisingly entertainingto calculate:

Slereah

I am not giving you my Steenrod

0celo7

The plan was little Milnor + GP and then big milnor if we have time

John Rennie

0

A: How cold air is less dense in one case and more dense in another case when compared with warm air?

The equations for the density of air are available on the engineering toolbox site. The density of dry air is approximately given by: $$ \rho_{dry} = \frac{0.0035\,P_0}{T} $$ where $P_0$ is the pressure and $T$ is the temperature. The density of moist air is approaximately given by: $$ \rho_{w...

0celo7

1:59 PM

@JohnRennie Btw I'm going to write an answer on your canonical time dilation thing

can I please have the link?

I'll do everything in the geometric optics appriximation

John Rennie

41

Q: What is time dilation really?

Please will someone explain what time dilation really is and how it occurs. There are lots of questions and answers going into how to calculate time dilation, but none that give an intuitive feel for how it happens.

relativity time-dilation

bolbteppa

I didn't even know there were exercises in that little book :\

John Rennie

Be gentle with me

0celo7

@bolbteppa they are devilish

I've solved two of them

I know the solution for one more

But it's LONG

Beyond that, no clue

Actually I might solve the graph one

I recall doing it in Lee once

@JohnRennie that's what she said

@ACuriousMind You probably think I skimmed the book because I can't do any of the exercises

ACuriousMind

@0celo7 What? No, I simply think that the exercises might not be intended to be easily solvable with the material in the book, but some more as "stuff to think about".

0celo7

2:03 PM

@ACuriousMind He uses at least two explicitly in the text

Obliv

@acuriousmind is optics still a heavily researched topic in physics?

0celo7

(I proved one of them)

(the other is in GP and requires a lot of technology not in Milnor)

ACuriousMind

@0celo7 Again, so what? Not everything can or should be self-contained.

Slereah

What about Bourbaki

Also @ACuriousMind, the problem is that those are exercises

I don't think he indicates the sources to solve them

0celo7

^

Slereah

2:05 PM

It would be nice to have a reference book

0celo7

@ACuriousMind He wants the reader to prove that sphere thing but doesn't even mention the Lefschtz theorem

Slereah

No exercize, no putting proofs to other books

user116211

Differential Topology | Lecture 1 by John W. Milnor

►

user116211

@Slereah Bourbaki has exercise, oh.

Slereah

What about Russell Whitehead then :p

bolbteppa

2:07 PM

I assume he expects you to know algebraic topology inside out and to just re-prove theorems from there modifying those proofs with tools from this book tbh

0celo7

@bolbteppa He never calls upon algebraic topology in the main text

Although he does randomly use Riemannian geometry, which I thought was strange

ACuriousMind

Well, possibility 1 is that there are slick proofs of these assertions that Milnor knew but you don't. Possibility 2 is that he simply didn't bother to indicate where to find the proofs because they were in the "standard" literature (not the best attitude, but one that happens). Possiblity 3 is that the exercises are the stuff that you should think about and go find out if you want to know how it's done.

bolbteppa

From the preface:
"These lectures ... present some topics from the beginnings of topology, centering about L. E. J. Brouwer's definition, in 1912, of the degree of a mapping. The methods used, however, are those of differential topology, rather than the combinatorial methods of Brouwer."

Secret

1

Q: Free Particle: Time dependence of expectation value of position Paradox

It would be really appreciated if somebody could clarify something for me: I know that stationary states are states of definite energy. But are all states of definite energy also stationary state? This question occurred to me when I considered the free particle(plane wave, not a Gaussian pack...

quantum-mechanics

0celo7

@ACuriousMind Well I'm not even sure how to go find out

You make it seem so obvious

Secret

2:12 PM

Well the expectation value of energy of the plane wave is just one single value, right?

Obliv

is this question asking how long it would take to 'spawn' a volkswagen beetle? what physics.stackexchange.com/questions/262427/spawning-a-vw-beetle

Secret

I wonder, if there actually exists time dependent states that has expectation value of energy being time independent, that would help address the OP's question

or better, time dependent states with single value energy states

(need to dig the maths)

I am guessing if it is heat death, we do't expect things to go back together and make another big bang (or at least some activity) for like eternity, right?

Thus whatever that VW is, it gonna take a VERY LONG TIME to assemble spontaneously

Slereah

The only way for having time dependant hamiltonian eigenvalue is to break the time translation symmetry

Obliv

@Secret I don't know. I've heard of a poincare recurrence time. If the universe is 'closed' it might restart eternally? o_o

ACuriousMind

@0celo7 Well, one way would be to either learn the algebraic variant of Lefschetz or to learn how to compute that smooth definition of the Lefschetz number for the sphere.

Secret

2:17 PM

@Obliv Except our universe is not going to close anytime soon ,given that the accelerated expansion is much faster than we expected

Slereah

Poincaré recurrence time doesn't apply for spacetimes with singularities

0celo7

@ACuriousMind Well, obviously

But I'm not taking algebraic topology until the semester after next

So if I learn one it will be the smooth definiton

Maybe GP has some details

Obliv

@slereah what is different about singularities? Don't singularities eventually decay anyway?

Slereah

Don't know the details

It's an old paper from Tipler

Where he studied Poincaré recurrence for the FRW universe

Secret

@Slereah en.wikipedia.org/wiki/Space-time_crystal well our best bet are these guys, but their existence seemed to be ruled out (sadly...)

0celo7

2:20 PM

@ACuriousMind I have to say, proving things like "the projection is smooth" is very tiring :P

or "if $f,g$ are smooth then $f\times g$ is smooth"

Slereah

A smooth criminal

Hardcore string theory

0celo7

phil is like

"kill us"

Secret

@slereah Is cosmic time a way to define the coordinate system in describing the evolution of the universe, thus coordinate dependent like proper time of observers, or is cosmic time a coordinate independent concept?

Also does cosmic time sort of implying there is some kind of preferred frame in describing the evolution of the universe itself.

How to compare and contrast between cosmic time and proper time?

Slereah

I have no idea what you're talking about

0celo7

ok problem 9 in milnor is reasonable.

Slereah

2:30 PM

Is it ridiculously easy

0celo7

@ACuriousMind Would you happen to know about framed cobordisms/Pontryagin construction

ACuriousMind

nope

Secret

@slereah Ok nvm I think this article explains my question
https://en.wikipedia.org/wiki/Comoving_distance#Comoving_coordinates

I thought when the universe expands, *both* space and time are expanding, but (as shown in the FLRW metric, it seems only space is varying with time

Slereah

Yes

That's the FRW metric

Obliv

@secret how would time expand? I'm curious

Secret

2:36 PM

@obliv @Slereah So we generally believe based on our most accurate cosmology models that as the universe evolves from the big bang, the topology of spacetime along the time direction remains unchanged and only the space part (hence the spatial hypersurface) does?

Slereah

what

Topology doesn't change

Only the geometry does

Obliv

I think that's what he meant

Secret

umm, sorry, geometry then

0celo7

^allegedly the same data set plotted three times

Secret

@Slereah
Because by staring at the FLRW metric, since there is no complicated t or r dependent terms before the dt term, I am guessing the geometry of spacetime along the time direction does not change as the universe expands? (obliv do I managed to said what I am trying to say?)

Slereah

2:40 PM

They don't even cover the same range

Oh you can write FLRW with a component for $dt$

It's conformal to Minkowski space

$ds^2 = a(t) (dt^2 - dx^2)$

It's the conformal time coordinate

Secret

ah I see, so that equation said both space and time expand with the scale factor as the universe evolves

John Rennie

@Secret the time coordinate in the (non-conformal version of) the FLRW metric is comoving time, which is the same as the time coordinate for an observer at rest.

Secret

>A comoving observer is the only observer that will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame. The velocity of an observer relative to the local comoving frame is called the peculiar velocity of the observer.

I see, the observer is basically at rest with the cosmic microwave background (and by extension the universe (not sure if I deduce this statement correctly though))

@vzn On that, my mind is still way too incoherent to organise it into blog form. Besides, I got their help on figuring out what we missed

This inform us one thing, he displayed signs of fed up with the randomness. We previosuly detected that back with Danu and Slereah which caused me to drastically reduce the number of pics posted

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