The h Bar

12:00 AM

@Maks Oh, you're asking about refractive indices

@SirCumference Yeah I was watching the video about how speed is slower depending on the medium, and that the RI are actually the speed change that the photon suffers

Sir Cumference

@ACuriousMind Meanwhile, "electron" solely comes from "electric + ion"

At least, that's what Oxford's dictionary says

rob

@ACuriousMind Isn't -os vs. -on (at least in Classical Greek) the between masculine and neuter?

Sir Cumference

@rob ::shrugs::

Maks

But on minute 10, he says it's actually possible and it happens that photons travel faster that the speed of light, you cant send information with it tho

Sir Cumference

12:02 AM

I'm just following my dictionary

ACuriousMind

@rob Yes, it is

rob

Or is there something fishy with nominative vs. dative case?

I had this all worked out twenty years ago.

ACuriousMind

No, -os and -on are both nominative suffixes for masc./neut. nouns, as you say

Sir Cumference

@Maks Photons traveling through a medium other than a vacuum will, in layman's terms, take a longer path to get from point A to point B

They do not actually slow down

ACuriousMind

@SirCumference Well, certainly don't know what the people who coined it thought, but I would be interested to know how the dictionary knows.

@SirCumference wat

Sir Cumference

12:04 AM

@ACuriousMind I'm tired

Fix whatever made no sense

I haven't slept in 3 days

Maks

@SirCumference how's that ? And why not faster ? As said on the video

rob

Oh, it's the accusative case that's -on regardless of gender.

Sir Cumference

@ACuriousMind Well, for electron it says "late 19th century: from electric + -on."

For "-on", it says "originally in electron, from ion"

DanielSank

@heather bought Millennium Falcon sheet metal puzzle.

Sir Cumference

For "electric", it says "mid 17th century: from modern Latin electricus, from Latin electrum ‘amber,’ from Greek ēlektron (because rubbing amber causes electrostatic phenomena)."

@Maks Light will never move faster in a medium than it will in a vacuum

rob

12:08 AM

OED gives: Etymology: < -on (in electron n.2, itself after earlier ion n.), reinforced in both senses by -ον as a termination of Greek neuter nouns and adjectives and their derivatives, and (especially in sense 2) perhaps by ancient Greek ὄν being (compare -ont comb. form).
Productive from the end of the 19th cent. Compare magneton n. (after French), osteon n. (after German).

Maks

@SirCumference I know, but the physicist on the video says that, in a vacuum, the PHASE SPEED of a wave, can travel faster than the speed of light

ACuriousMind

@SirCumference Of course the photons "slow down"! But a "photon" in a medium is simply a slightly different kind of object than a photon in vacuum, so that's okay. You can also think of the photon being continually absorbed and re-emitted in the medium, but it's not so clear either of these descriptions is actually useful.

rob

So: both

Sir Cumference

@ACuriousMind I actually would've gone with the "being continually absorbed and re-emitted", but I wasn't sure how much @Maks knew about photons

@Maks Anyways, a photon in a gas will constantly be absorbed by the molecules and re-emitted, so it will always take longer to get to its destination

Interestingly enough, this leads to things like

Cherenkov radiation

Cherenkov radiation, also known as Vavilov–Cherenkov radiation, is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The characteristic blue glow of an underwater nuclear reactor is due to Cherenkov radiation. It is named after Soviet scientist Pavel Alekseyevich Cherenkov, the 1958 Nobel Prize winner who was the first to detect it experimentally. A theory of this effect was later developed within the framework of Einstein's special relativity theory by Igor Tamm...

Sigh...

Thought it could be cool...

Maks

@SirCumference yeah, the atom absorbs the photon and then after a period of time it re-emits it

The thing is (I'm getting this from the video) it says that that's not the reason why the light changes speed

Sir Cumference

12:13 AM

@Maks Sigh, lemme watch it

Maks

Because that period of time in which the atom absorbs and reemit the photon is actually random, and when you observe it, the time is not random

ACuriousMind

@Maks For faster-than-light phase speed, see e.g. this question and its answers

Maks

Then it is actually possible to travel faster than the speed of light

What's not possible is to send information faster than the speed of light

ACuriousMind

@Maks No, the point is that the phase speed doesn't measure anything "travelling", which is why it is not subject to the speed limit.

Anything that "travels" in a meaningful sense can be used to transmit information, so that's not possible.

Maks

Oh, now that's messing with my brain, so, how could you move without travelling ?

Sir Cumference

12:17 AM

@Maks Hubble flow :D

Maks

Because, if you have speed, that means you are moving right ?

Because of the space expands you can move faster than the speed of light ? That's what you mean ?

Sir Cumference

Well Hubble flow is pretty interesting. You see, we'll first have to discuss what it means for the universe to expand.

Maks

Like how everything outside the observable universe is moving away from us faster than the speed of light because of the expansion of the universe ?

Sir Cumference

@Maks Uh, everything outside of the Hubble sphere is receding faster than light.

Things within the observable universe can still recede faster than light.

ACuriousMind

Yeah, that's the point - the phase velocity doesn't actually measure the motion of anything. For more on what "phase" and "group" velocities actually mean, see e.g. Wikipedia.

@SirCumference I'm rather certain that cosmological expansion is pretty unrelated to Maks' issue

Sir Cumference

12:21 AM

@ACuriousMind I know, that's why I had ":D"

Though he seems pretty interested

Maks

@SirCumference Mmmm then how can we see it ?

I presume because the hubble sphere is also expanding ?

Sir Cumference

@Maks Yes

Maks

And so as it expands it can capture the light that has been traveling and now it can actually move and reach us ?

Sir Cumference

@Maks To my understanding, yes

Maks

But then again, can things travel faster than the speed of light or not ?

Ignoring the expansion of the universe

Sir Cumference

12:23 AM

@Maks No

Maks

And what did the guy on the video mean ?

Sir Cumference

I didn't watch the video

Maks

oh

Sir Cumference

It's 16 mins long

Maks

Nono

look at minute 10

from minute 10 to 11

its the only part when he mentions going faster than the speed of light

the rest of the video is about refraction

heather

12:26 AM

@DanielSank nice! Is it Metal Earth? I have a few of those

Sir Cumference

@Maks Gimme a minute. My extensions are screwing with the video

DanielSank

12:57 AM

@heather uhhh, not sure.

heather

anyway, those models are cool.

user228700

Hi, everyone :-)

heather

hello @Kaumudi.H

new profile photo, I see.

user228700

@heather :-) Yeah. It's synced to my Google profile photo and I changed that so.

Sir Cumference

@Kaumudi.H Huh, you got smaller

heather

1:10 AM

lol

user228700

x'D That's me...when I was about 4/5.

Sir Cumference

Uh, I looked on Wikipedia to study for a spectroscopy test and I got my way to something weird...

heather

@Kaumudi.H, if you don't want to that's absolutely fine, but would you mind looking at this pdf and perhaps sharing your thoughts? (Note the rough derivation section is not completed.)

@SirCumference what?

Sir Cumference

Well, I kid you not. Maybe it's my own immaturity but that acronym seems a bit off.

heather

@Kaumudi.H you're very grown up for only four-fifths of a year in age =)

Sir Cumference

1:16 AM

Ironically I need to learn about that kind of stuff.

heather

@SirCumference ::tries to not laugh::

Sir Cumference

It's not a problem until I write on my test that spectroscopists use that to measure the metal content in gases

user228700

@heather That's a long document. I'm so sorry but I haven't got the time to complete a lot of my own chapters .__.

heather

hmm...you could just spell it out @SirCumference

@Kaumudi.H, okay, not a problem =) It's pretty bad anyway.

Sir Cumference

@heather That seems even worse, somehow

@heather Who's writing that?

user228700

1:18 AM

@heather :-P 4 or 5 yo is what I meant.

heather

@Kaumudi.H I know, I was just giving you a hard time

@SirCumference How so? I see no problems there...

user228700

:-P I know.

heather

@SirCumference I wrote it

Sir Cumference

@heather All that? Jesus

heather

@SirCumference you've got that right

Maks

1:19 AM

@SirCumference so ?

heather

half of it isn't even general relativity notes, lol

Sir Cumference

@Maks I need to find my extension that's giving me the problem and fix it

heather

@Kaumudi.H, random comment - have you learned/need to learn linear algebra yet?

Sir Cumference

@heather Yeah, some of it is just calc

But damn

heather

@SirCumference and linear algebra, yeah

I find it a bit of a bad sign that it's so long actually

it means i can't explain anything succinctly

and, seeing as most of it isn't even good, well...

Sir Cumference

1:21 AM

@heather Er, I'm almost entirely sure the Big Bang is not a solution to the field equations

heather

my excuse is that I started writing it Friday =)

@SirCumference I read somewhere that it was

user228700

@heather No, not that much.

heather

but I will take the word of someone in college studying it.

Sir Cumference

Either that or I'm crazy

heather

@Kaumudi.H oh, well if you do, watch 3Blue1Brown's videos on it, they're amazing.

@SirCumference let me see if i can find a reference to my ignorance

General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations...

Sir Cumference

1:24 AM

@heather Also, a little more formally and clearly, would be to say that the Big Bang refers to the time when the cosmic scale factor was 0, and as such, all (physical) distances were 0.

user228700

@heather Oh, nice. Thanks! :-)

heather

" solutions of these enhanced equations, the Friedmann–Lemaître–Robertson–Walker solutions,[123] allow physicists to model a universe that has evolved over the past 14 billion years from a hot, early Big Bang phase."

@SirCumference okay, that makes sense.

Sir Cumference

@heather Yeah, the FLRW metric

heather

@SirCumference so...a solution allows physicists to find a solution that represents the Big Bang?

(sort of)

Sir Cumference

The Big Bang is merely an event in the Universe. It can be derived by Hubble's law.

Maks

1:26 AM

@SirCumference seems like you are very fond of hubble

heather

hmm, so i really messed up there...let me rewrite and see if the rewrite makes sense to you.

Maks

You are like churchill

Sir Cumference

@heather Er, the FLRW solution describes a universe, which we can derive began a Big Bang approximately 14 billion years ago.

heather

@Maks well, hubble is an important guy in cosmology

Sir Cumference

@Maks Cosmology is fond of him :)

heather

1:26 AM

@SirCumference ::facepalms::

Sir Cumference

But yeah, he's a pretty cool guy, up there with Newton and Cyrus the Great

heather

where'd cyrus the great come from?

Sir Cumference

@heather Eh idk, cool guy I learned about in history class

heather

@SirCumference ah, okay then. i think i have heard of him.

Sir Cumference

He was a ruler of Persia two thousand years ago or so who was supposedly super nice and accepting and all that

Helped the Jews rebuild their temple too, and even prayed in it

heather

1:28 AM

oh, i've definitely heard of him

Maks

What about john michell ?

Sir Cumference

People wanted to get conquered by him because he made their lives better

@Maks Who?

@heather Anyway, I'd be happy to give you an introduction to the Friedmann models

Some basic cosmology

Maks

The guy who discovered and first named black holes, although he named them "dark starts"

user228700

@heather: You wrote all of it? I...wow, I don't even know what to say.

Sir Cumference

@SirCumference Sigh, *began with a Big Bang

@Kaumudi.H Freaky, right? o_O

Like, jeez, that's some serious dedication

@heather Also, different metrics describe different types of black holes

user228700

1:31 AM

Not only do I respect her (@heather) dedication toward writing it, but her passion toward the subject is also greatly commendable.

Bernardo Meurer

Only beer chugging competitions are commendable

the rest is child's play

user228700

@SirCumference It's not freaky...I dunno what it is but it does make me question what in the world I was doing when I was 13/14.

Sir Cumference

@Kaumudi.H I was differentiating between facts and opinions, not differentiating f(x) with respect to x.

user228700

^ Exactly.

Sir Cumference

Oct 27 '16 at 21:53, by 0celo7

in middle school, I picked my nose

I'm pretty sure no one was doing what @heather is doing

@Kaumudi.H Except some of those 11 year olds in Math SE who know ridiculous maths

user228700

1:35 AM

Yeah, them as well .__.

Bernardo Meurer

In middle school I couldn't even write I think

I learned that first year of high school

Sir Cumference

In middle school I could write pretty well, but not at the level of @heather

Eh actually, maybe

user228700

In middle school, I read quite a lot of books, wrote in my blog, watched T.V and studied for school.

Sir Cumference

But still, that's determination on her part

@Kaumudi.H I always liked astronomy, though I didn't know I wanted to be an astronomer

user228700

I wasn't actively choosing what to do with my time in middle school.

user228700

1:37 AM

@SirCumference I see.

Sir Cumference

I didn't even know how to program till I was 14

user228700

Oh, hang on. I was 12 when I graduated middle school.

Sir Cumference

@Kaumudi.H I was 14...

Jeez, I started middle school when I was 11

user228700

When I was 13, well, I still wasn't doing anything of much value but I was reading more books (fiction) and starting to learn physics...

heather

okay, i'm back

Sir Cumference

1:39 AM

@Kaumudi.H Huh, the basics or the particles?

I was doing something kind of like @heather when I was 15, trying to learn QM qualitatively

user228700

@SirCumference Sort of...both.

heather

@SirCumference, I'd be honored to learn about the FLRW metric

Sir Cumference

@heather Well, I could go over the three types of Friedmann universes

user228700

In any case, I don't believe that I was doing much with my time.

user228700

@heather: Dude. You. What. Wow.

heather

1:41 AM

@Kaumudi.H what?

did i do something?

::looks around embarrassedly::

user228700

@heather: Did u not read all the comments above about us commending your passion and determination and all? :-P

Sir Cumference

@heather All right, so how much have you looked into cosmology?

user228700

(Followed by a brief existential crisis about what we chose to do with out time when we were your age)

heather

@Kaumudi.H ::scrolls up::

oh…thanks guys!

::blushes::

user228700

@heather: Keep at it! :-)

heather

1:42 AM

@SirCumference a bit (read: a few brian green's books, a bit of gaping at string theory, and my recent reading about general relativity)

Sir Cumference

@heather Er, I don't know much about those first two...

Ok, first, have you heard people say "the universe is expanding"?

heather

@SirCumference the first two are like the most unrigorous things possible =)

Sir Cumference

We can start by explaining what that means

heather

@SirCumference sure, yeah, inflation theory, alan guth, etc.

Sir Cumference

@heather Um, ok

heather

1:43 AM

inflaton field, perhaps

Sir Cumference

So yes, space itself is expanding. It's not like a ball growing in size. Rather, you can imagine everything on a grid, and that grid is growing

heather

and then there's the cosmological constant, and dark energy, and the value's just above the threshold where it would collapse in a big crunch scenario, so the universe is going to expand forever.

Sir Cumference

heather

@SirCumference yeah, like the space between things, not the things themselves

Sir Cumference

@heather Yep

heather

1:44 AM

@SirCumference that's a cool diagram

Sir Cumference

@heather Thanks, made it

Anyways, let's start with some history.

As Einstein developed his general theory of relativity, he wondered how a universe with his gravity could possibly exist

heather

hmm, because galaxies hadn't collapsed on themselves, right?

Sir Cumference

@heather Yep, exactly

heather

so $\Lambda$

Sir Cumference

Well, actually, it was because everything in the universe hadn't collapsed

@heather Yep

heather

1:47 AM

@SirCumference oh =)

Sir Cumference

The cosmological constant was, in a sense, an anti-gravity. It countered the contraction with an expansion

heather

@SirCumference it's supposed to be represented by dark energy, I think

right? or no

Sir Cumference

@heather Nowadays, yes

heather

@SirCumference that makes sense.

Sir Cumference

Thus, the cosmological constant would counter gravitation, thereby keeping the universe from either expanding or contracting. We call such a universe a "static" universe

In particular, we call Einstein's idea of a static universe an "Einstein universe"

heather

1:48 AM

huh, okay

but the cosmological constant is greater than that necessary to merely balance, right?

that's where inflation comes in.

Sir Cumference

@heather The cosmological constant is stronger, but we'll get to that

Anyways, an Einstein universe isn't stable. Even the tiniest change in the universe, such as thermal fluctuations, could cause either the cosmological constant or gravity to gain the upper hand.

If gravity were to get stronger, then the universe would keep contracting back to a single point. If the cosmological constant were to get stronger, then the universe would keep expanding faster and faster.

Einstein threw away his cosmological constant, calling it the "greatest mistake [he] ever made". However, we figured out he wasn't actually wrong. The cosmological constant is necessary, and our universe isn't actually static.

heather

@SirCumference huh, that's interesting.

Sir Cumference

@heather So now I'll get into some basic math. You know what a scale factor is?

heather

um…maybe like a scalar?

not sure.

Sir Cumference

Good guess. It's actually just the ratio between a galaxy's distance from us at time $t$, and its distance from us now.

Cosmologists usually denote it as $a$, but sometimes they'll use $R$.

heather

1:51 AM

so…basically the rate of change of distance between the galaxy and us over the time $t$?

Sir Cumference

@heather It's not a derivative, but merely a ratio.

heather

@SirCumference now that's confusing…isn't $R$ also the, uh, curvature scalar?

@SirCumference oh, okay

Sir Cumference

@heather That's another story

heather

okay.

Sir Cumference

@heather For example, if a galaxy is three times farther from us at a time $t$ compared to its distance from us now, then its scale factor is 3 at time $t$.

Mathematically we say: $a(t) = \frac{d(t)}{d_0}$, where $d(t)$ is the distance of the galaxy at time $t$, and $d_0$ is its distance from us now.

@heather Make sense so far?

heather

1:56 AM

@SirCumference are these derivatives now or no?

Sir Cumference

Hmm, I got a good example. If a galaxy is 1 billion light years away from us now, and 1000 years in the future it is 3 billion light years away from us, then its scale factor is $\frac{3 \rm{billion}}{1 \rm{billion}} = 3$ in a thousand years

@heather Just a ratio

@heather All right, lemme try with another example :)

heather

sorry, $d$'s will forever be my curse

::glares at calculus::

Sir Cumference

@heather Yeah, I realize how that'd be confusing. Ignore derivatives, $d$ here simply means distance.

Not actually related to derivatives.

heather

okay.

i think i understand then

Sir Cumference

Right, so I'm a galaxy. $d_0$ is my distance from you. Let's say I'm 2 lightyears from you, so $d_0 = 2 \rm{lightyears}$.

heather

2:00 AM

okay

and if 100 years in the future it's 6 lightyears away, the scale factor would be 3?

Sir Cumference

@heather Yep, $a(100 \ \rm{years})$ will be 3

user228700

I just read a little bit of the transcript. @heather: Oh, a social studies teacher wants you to write all of that? That sucks :-/ So much for being creative.

Sir Cumference

So our scale factor in 100 years will be 3

@heather Make sense?

Remember that the scale factor $a$ is merely the ratio between an object's distance from us at time $t$ versus its distance from us now.

heather

@Kaumudi.H I chose to write it in a notes format, and I chose the project. My social studies teacher made it nuts. =)

@SirCumference that makes sense, I think

user228700

@heather Oh, u did? What did the teacher do, then?

heather

2:04 AM

@Kaumudi.H she said it had to be written at an 8th grade level, in-depth descriptions, and she said that it had to come with videos (!?) all done 5 days later.

Sir Cumference

@heather OK, so now let's take a look at some calculus. If the ratio between an object's distance in the future versus its distance now increases at a faster and faster rate, then the universe is expanding.

user228700

@heather I read about it. Gosh. Where were u gonna go with it?

Sir Cumference

For example, if an object's scale factor is $3$ in 100 years, then $50$ in 150 years, then $200$ in 200 years, then our universe is expanding very fast

heather

okay, so the rate of change in the scale factor increasing swiftly?

@Kaumudi.H i was going to just type up my notes and be done =P

Sir Cumference

@heather Well, if the rate of change is increasing at all, then our universe is expanding

heather

2:05 AM

@SirCumference oh, true.

Sir Cumference

Likewise, if the rate of change is decreasing, our universe is contracting

user228700

:-/ I see. Well, at least you're doing something!

Sir Cumference

@heather So if $\frac{\mathrm{d}a}{\mathrm{d}t} > 0$, our universe is expanding, right?

Since our rate of change is positive, we know that the scale factor will be growing at a faster and faster rate with time

heather

right, yes.

user228700

@heather: I've had a similar experience. We were studying "The Invisible Man" by H.G. Wells in English in 12th grade. My teacher wanted some of us to put up a skit. She had intended for each member to write their own dialogues but ours was a lousy class so I ended up staying awake for 48 hours, reading the book and writing the whole script. It was supposed to be held in front of a commissioner (a.k.a V.I.P) of some sort but nobody came and we held it inside our tiny class :-(

Sir Cumference

2:09 AM

@heather All right, so let me tell you about a time-saving (no pun intended) notation. If we ever want to say "the derivative of $x$ with respect to time", we can just say $\dot{x}$ instead of $\frac{\mathrm{d}x}{\mathrm{d}t}$.

We give this a fancy name, a "time derivative". It's merely a nice notation that you'll see often in physics.

heather

@SirCumference oh, i think i have seen that before

@Kaumudi.H ick, that's terrible

much worse than my scenario

at least i had the weekend

Sir Cumference

Likewise, $\ddot{x}$ means the second derivative with respect to time, and $\dddot{x}$ means the third time derivative, etc.

heather

huh, cool.

Sir Cumference

In LaTeX, you'd write \dot{x} for the first time derivative, \ddot{x} for the second, \dddot{x} for the third, etc.

user228700

@heather I wouldn't argue that it was much worse but in terms of the time limit, yes. Also, group projects almost always suck.

heather

2:12 AM

@Kaumudi.H they do. you always get stuck with all the work.

@SirCumference okay.

@mochacat hello.

Sir Cumference

@heather Okay, so we know that in an expanding universe, $\dot{a} > 0$, and in a contracting one, $\dot{a} < 0$. In a static one, $\dot{a} = 0$, since the scale factor's rate of change won't increase nor decrease over time.

OK, so after Einstein published GR, Friedmann solved Einstein's field equations and came up with the Friedmann equations

We can gloss over those for now, but basically they helped Friedmann come up with three possible universes

Universe 1: The Big Crunch

heather

ooh, heard of that one

user228700

@heather Heck, even that is OK. You see, when it's a skit and all, you absolutely cannot do everything on your own! Nobody really understood the spirit of the story. Besides, the audience was crap--hollering and making fun of us through and through. You'd think they'd shut up in the presence of a teacher but the teacher wasn't any better--she constantly complained and scolded.

Sir Cumference

In this universe, the matter in the universe is so dense, gravity's influence will keep slowing down the expansion and eventually reverse it

heather

the universe ends up collapsing into a nice tiny singularity =D if you extend this theory, you get the big bounce cyclic universe theory, where it big bangs agin

Sir Cumference

2:15 AM

@heather Yep :D

heather

@Kaumudi.H rude audience =/

i'm so sorry.

user228700

:-) Thanks for ur sympathy.

Sir Cumference

@heather So in that universe, $\dot{a}$ starts out positive, but becomes negative after a certain point. That tells us that $\ddot{a} < 0$ — thus, the scale factor's rate of change is decreasing over time.

Make sense?

user228700

@heather: I did end up complaining to the teacher that I'd had to write everything on my own. She, on the other hand, laughed and promised to buy me a present! Sigh.

user228700

I'm sorry for interrupting the discussion with useless anecdotes :-P

heather

2:17 AM

@SirCumference yes, I think so

@Kaumudi.H well, did you get a gift?

@Kaumudi.H no, your stories are always interesting

Sir Cumference

@heather Cool. So the second universe says that gravity will keep slowing down the expansion of the universe, but it will never overpower the expansion. As a result, the universe will keep expanding at a slower and slower rate.

Thus, $\ddot{a} < 0$, since the expansion rate is decreasing, but $\dot{a}$ will never become negative.

user228700

@heather No, I didn't :-( I bet she forgot about it the minute I walked outside the staff room.

user228700

@heather I bet you say that to everybody ;-)

Sir Cumference

@heather So contraction and a Big Crunch will never take place. Make sense?

heather

brb

heather

2:41 AM

sorry i have to go for the night