The h Bar

9:00 PM

You know what I've noticed? The percentage of smokers (tobacco) is extraordinarily low among my physicist friends. Is this a general thing?

ACuriousMind

@Danu It's generally low among students who are not philosophers or archeologists, in my experience

Danu

It's extremely high among med-students.

ACuriousMind

wat

Never met a med student who smoked

Danu

Like 75%+ type of high

In Amsterdam

ACuriousMind

@Danu Yeah, not here

They'd have to leave the library to smoke :P

Or whatever practical they're having

Danu

9:02 PM

Interesting.

I have one friend who is doing cancer research, he always makes jokes about this.

He is also a smoker :P

ACuriousMind

The med student will also take great pleasure in describing the time they saw the lung of a chain smoker to anyone who smokes :D

user507974

@ACuriousMind yep

dmckee

@Danu I can't say about students in the last five or ten years. When I was a grad student it was more true about US and Canadian students than about Europeans (and especially eastern Europeans). But I think it might be spreading.

user507974

oh that was a while ago

you guys mind if i ask a quick latex question?

Danu

@dmckee I'm thinking about physics students particularly

@user507974 You should go to the chatroom of TeX - LaTeX

But I can probably help you too, so give it a shot

(if it's easy)

The guys in the TeX - LaTeX chat will know the more advanced stuff

dmckee

9:09 PM

^ Yeah. We only do easy LaTeX questions.

user507974

@Danu How did you make tables bypass the two column formatting

Danu

@user507974 "the two column formatting"?

dmckee

@user507974 In revtex or something else?

user507974

@dmckee yea

dmckee

I know that figures have a figure* form in revtext that spans the whole page.

I'd assume there was a table* environment as well.

Danu

9:10 PM

Ah, you mean your entire text is two-column, but you want your table not to be

user507974

@Danu yea, exactly

Danu

32

Q: Page-wide table in two-column mode

I want a table that is as wide as the whole page in a document with option twocolumn. The table has to be inserted on the bottom of the page, but that is not necessary. I've tried: \begin{table*}[b] ... \end{table*} But that puts the table at the end of the document instead of on the same p...

user507974

something im sure all you have had to do all the time with papers

Danu

Google is your friend.

Specifically: "two columns" full width table site:tex.stackexchange.com

Learning how to properly google is really worthwhile ;D

ACuriousMind

@user507974 I'm not writing actual papers yet, but the papers I read (as well as stuff I write) aren't usually two column

Never really understood that format, it makes any equation that's a bit longer stick out like a sore thumb or unnecessarily span several lines

Danu

9:13 PM

Two column papers are only done if it's really required, usually.

user507974

@ACuriousMind really? I feel like thats the standard formatting, at in least Physical Review Letters it is and msot papers I've read are lik ethat

Danu

On arxiv, >99% is single column, I think.

dmckee

I've started using revtex4-1 for a lot of my general purpose physics writing because it reads easily but still lets you use full width equations. Whoo! Hoo!

Danu

Why would you ever y write in two columns, dmckee?

dmckee

Using the whole width in single column mode usually results in lines that are too long for optimal reading, and I end up with a lot of printed material to carry around to I try to minimize the number of pages.

Danu

9:15 PM

Eh, you do realize that tex was optimized in terms of sentence-length, right?

David Z

Don't ask me about the logic behind it, but the APS journals (Physical Review A/B/C/D/.../Letters) do use two-column formatting. I think the likes of Science and Nature do as well, not that we physicists publish in them very often. Most other journals are single-column.

dmckee

And it is the format of the Phys. Rev. journals.

Danu

As in, the single-column format is optimized :P

dmckee

@Danu Yes. And it has big margins.

ACuriousMind

@dmckee I much prefer printing to A5 (i.e. two pages per A4) instead of A4 for the paper issue.

dmckee

9:16 PM

To use a lot of the page and still get optimized line lengths you go to two columns.

user507974

all i was missing was table to table* -_-

dmckee

Or 2-up the way @ACuriousMind says. But I'm getting old-man eyes.

2-up is hard for me these days. I'm going to have to get bifocals or something.

Danu

@dmckee Which is also pleasant!

I think crammed pages is one of the worst things one can do in terms of formatting

e.g. Hatcher's book is just ruined for me (in terms of design, not content!) because of this

I do make the margins a bit smaller often, but still keep a lot of space.

ACuriousMind

@Danu Have you read his notes on how it was done? I have a feeling most of these are really bad hacks you shouldn't do to TeX

Danu

@ACuriousMind Yeah, I think it's disgusting :P

His font is also BLURGHHH to me

ACuriousMind

9:22 PM

Then again, for some reason he also decided to use plain TeX.

@Danu !!!

Danu

I honestly think my notes look a lot better

ACuriousMind

I mean, I can understand not liking Computer Modern, but...that's not an improvement

Danu

His pictures are nice, but he "cheated" using Inkscape

His "inserting figures" method is also... suboptimal haha

ACuriousMind

@Danu Not Inkscape... Adobe Illustrator

Danu

Literally telling tex line-by-line how to change the paragraph, lol

@ACuriousMind Right, something 3rd party was the point ;)

ACuriousMind

9:24 PM

And creating rectangles as pictures over which the text is then laid to get shaded section headings...

I would never tell anybody if I did that

Danu

Hahaha right

shameful

Shamefur Dispray

►

0celo7

@DavidZ Can confirm Science is two-column.

Danu

^lol

That took you so long? :D

0celo7

@Danu No.

I was walking home.

Checked the log when I sat down.

?

@dmckee I'm drinking French vanilla -- why do I like this so much

It's heathen coffee

ACuriousMind

@Danu: Had a (physics, gauge) lecture today where the lecturer kept talking about the "complement" of a subgroup. I was a bit puzzled, but I thought he'd know what he was doing. Then he wrote $\mathrm{SU}(2) \setminus \mathrm{U}(1) = S^2$. I asked: "Do you perhaps mean the quotient?" He answered: "Is there a difference?"

Physicists really suck at group theory.

0celo7

9:30 PM

Is there a difference?

Or do you pedantically insist that there is a difference?

ACuriousMind

@0celo7 YES

@0celo7 NO

Danu

@ACuriousMind Hahaha, gauge theorist confirmed

0celo7

@ACuriousMind Hmm, did he mean to write $\mathrm{SU}(2)/\mathrm{U}(1)$?

Danu

@0celo7 Come on, you know that

0celo7

@Danu No?

Why would I ask if I knew.

ACuriousMind

9:32 PM

yesterday, by 0celo7

@ACuriousMind I want to say "to annoy you" but that would make me seem incredibly stupid.

Danu

Didn't you read books on gauge theory/string theory?

0celo7

I don't think you people believe me that my memory is absolutely terrible.

@Danu Yes.

Danu

Welp, okay then

0celo7

I don't remember a single word.

Danu

So that was a complete waste of time?

0celo7

9:33 PM

I can look back on convos I had here with ACM, don't remember them at all.

@Danu Yes.

Danu

Damn

0celo7

I got through six chapters of BBS, 9-10 of BLT.

Don't remember anything.

And I know I understood most of it at one point, because I used to have intelligent diuscussions with ACM.

Danu

lols

I gotta feel for you

0celo7

I don't even remember what T-duality is.

Danu

Yeah okay, but the basics of you know... quotients

0celo7

9:36 PM

I don't know what $\mathrm{SU}(2)\setminus\mathrm{U}(1)$ is, or why it would be called a quotient.

ACuriousMind

@0celo7 The point is that's not the quotient, that's the complement. But the complement isn't $S^2$.

Danu

Exactly

0celo7

Ok, well I know what a quotient of groups is.

Danu

see

The lecturer didn't apparently

0celo7

But I don't know why that quotient would be $S^2$.

Danu

9:37 PM

which is awful

@0celo7 I wouldn't be able to prove that quickly either

ACuriousMind

I thought he'd do some interesting thing with the complement right up until he wrote that $S^2$ on the r.h.s. Then I realized he just didn't care about the math at all.

Danu

Is there an easy way to even prove "simple QM" stuff like $SU(2)$ being a double covering of $SO(3)$?

0celo7

$G/H$ is $G/\sim$ where $g\sim gh$ for $g\in G,h\in H$. Something like that.

Danu

I saw a proof in Riemannian geometry but it was not easy

@0celo7 yeah, right

See, no problem :P

0celo7

And it's a group iff $H$ is a normal subgroup?

Danu

9:39 PM

Yeah

ACuriousMind

You have $\mathrm{SU}(2) = S^3$ and $\mathrm{U}(1) =S^1$. Seeing $S^3/S^1$ should remind one of the Hopf fibration $S^1\to S^3 \to S^2$.

Danu

@ACuriousMind Okay but then prove $SU(2)=S^3$ first?

ACuriousMind

@Danu Ah, yes, I remember that one being tricky

0celo7

@ACuriousMind Oh! $S^3/S^1=S^3S^{-1}=S^{3-1}=S^2$. Got it.

ACuriousMind

but I guess you can just do it "explictly" by using the properties of the Pauli matrices

0celo7

9:41 PM

@ACuriousMind You write down the $\det M=1$ thing.

ACuriousMind

@0celo7 what?

0celo7

If you use Pauli matrices it just becomes the sphere equation.

Danu

@ACuriousMind Also "easy" $\neq$ Hopf fibration

I want to say that I can somehow use the unit quaternions for the $SU(2)\cong S^3$

But that's on the level of algebras probably...

I don't know.

0celo7

Weinberg does it simply.

Is that not rigorous enough?

Danu

Sorry, what does he do?

0celo7

9:43 PM

One can show that the 2x2 special unitary matrices with parameters $x,y,z,w$ satisfy $x^2+y^2+z^2+w^2=1$.

ACuriousMind

@Danu Yeah, my way now would have been to write $\exp(\mathrm{i}k_\mu \sigma^\mu)$, and observe that the power series gives you (due to $\{\sigma^\mu,\sigma^\nu\} = \delta^{\mu\nu}$ or something) something like $ f(k)\mathbf{1} + g(k)_i \sigma^i$ for functions $f$ and $g$ and identifying each of the $\sigma^i$ with one quaternionic $i,j,k$

Danu

Okay, both ways seem possible

ACuriousMind

(and $f$ and $g$ have $f^2+g^2 = 1$ because they're sine and cosine or something)

Danu

@0celo7 I guess in the two-dimensional case it's really feasible to write all of them down

(though it's not super elegant)

ACuriousMind

@0celo7 That works, too

0celo7

9:45 PM

@Danu There's a simple form for the most general special unitary 2x2 matrix.

ACuriousMind

But I avoid writing out a matrix whenever possible :D

Danu

@0celo7 That thing with those two angles you mean?

0celo7

@Danu No. Look at sect. 2.7 of Weinberg.

I'm not TeXing a matrix :P

ACuriousMind

@0celo7 How can you say you don't remember a thing and then come up with this? :P

Danu

Yeah, lol

0celo7

9:47 PM

@ACuriousMind What?

Just because I know Weinberg by heart does not mean anything

ACuriousMind

There's your problem. Having your heart filled with that notation would drive anyone nuts

0celo7

Is there an intuitive reason for $S^3/S^1=S^2$?

@ACuriousMind I'm not nuts

Is there a similar thing for $S^2/S^1$?

Maybe that one can visualize?

ACuriousMind

@0celo7 Nope

$S^1$ doesn't act freely on $S^2$, and $S^2$ is not a group.

DanielSank

@0celo7 Gross.

ACuriousMind

So one can't even define the quotient property without getting some weird object

0celo7

9:50 PM

@ACuriousMind Act freely? That's definitely something I used to know.

@Danu Get this: I read Nakahara and did all of the exercises, now I don't know a single thing about algebraic topology or complex geometry.

@ACuriousMind How would you translate "Cheers" into German?

DanielSank

Dudes, my research group has come upon a very difficult and interesting problem. Suppose you have a quantum 2 level system where the energy splitting is fluctuating in time. You'd like to measure the power spectral density of this fluctuation. This is hard because you're detector only has 1 bit of resolution (it's a two level system) and is stochastic (i.e. the result of a measurement is random, but the probabilities depend on the noisy parameter).

Do any of you know anyone who is good with this sort of problem?

0celo7

@DanielSank Mine has an interesting problem, too

DanielSank

We've made progress but we're still stuck.

0celo7

How do we hook up more shit into the power sockets without the safety people getting mad

DanielSank

I'm looking for a possibility to collaborate directly with an expert because I don't think this would get answered on the main site.

@0celo7 Don't.

ACuriousMind

9:52 PM

@0celo7 As a salutation while drinking or as the "Cheers!" used as a greeting/goodbye/whatever

0celo7

@ACuriousMind No, the word

Danu

@DanielSank Seems like my corner of physics

ACuriousMind

@0celo7 Dude, it depends what you mean by it.

DanielSank

@Danu I can't tell if you're joking.

0celo7

@ACuriousMind goodbye

Danu

9:53 PM

@DanielSank I'm a mysterious person.

0celo7

@DanielSank Maybe you should talk to someone who does quantum computing

DanielSank

@0celo7 This is why I put you on ignore some times <3

0celo7

@DanielSank That was only half troll

Why not email someone at another lab?

ACuriousMind

@0celo7 I tend towards Mach's gut!, but it's difficult to say

DanielSank

@0celo7 Yes. There is another group with expertise on this and I am trying to contact them.

0celo7

9:54 PM

@ACuriousMind Hmm, did Mach have too much beer?

ACuriousMind

@0celo7 What? The address while drinking would be Prost!

0celo7

@ACuriousMind Sigh

Beer gut

gut = big belly

Stupid pun, forget it

ACuriousMind

...did you ask me that question only to try and make a silly joke that doesn't even really work?

0celo7

@ACuriousMind Ok, I ask because Lang always ends his emails with Cheers

Danu

@DanielSank Power spectral density... What does it even mean in this context? Some kind of Fourier transform thingy?

0celo7

9:56 PM

and one of the grad students, who is not German, just sent me something and ended the email with Cheers

Which I thought was strange

Danu

I end my emails with Cheers decently often

0celo7

Maybe he's picking up a trait from his adviser

Danu

(I got it from my prof. who graduated from Princeton, so it's not a European thing)

ACuriousMind

@0celo7 I think if Prost! was considered a greeting/goodbye here, we would use it all the time since it reminds us of beer ;)

0celo7

@Danu Well I might be getting it from my Prof who graduated from Hberg!

Danu

9:58 PM

@0celo7 I couldn't find what you were talking about with the $S^3$ thing. Can you be more precise?

ACuriousMind

As an ending to a mail, I am really at a loss how to translate that remotely faithfully

0celo7

@Danu I don't have the page number memorized

page 88

Danu

Ewwwww, Weinberg writes $S^3$ as $S_3$ (which is the permutation group on 3 elements)

@0celo7 Thanks.

That was more low-brow than I thought :P

DanielSank

@Danu It means exactly what it sounds like... the thing you integrate to get power.

0celo7

@Danu Which is why I was surprised you thought it would require Riem. Geo.

DanielSank

10:03 PM

@Danu Suppose I have a two level system whose Hamiltonian is:

Danu

@DanielSank "spectral"

0celo7

Of course, the best way it to construct $\mathrm{Spin}(2,3,something)$.

Danu

That sounds like "mystical" to me

0celo7

I think Jost contains that proof.

Danu

@0celo7 Oh, it doesn't, but we did it in Riem.

DanielSank

10:03 PM

$H/\hbar = - \omega(t) \sigma_z / 2$

0celo7

@Danu Hmm, what did you do?

Danu

(please don't write out $\hbar$ Daniel)

DanielSank

@Danu I want to know the power spectral density of $\omega(t)$.

Danu

@0celo7 Long story

@DanielSank What is the power spectral density :P

DanielSank

@Danu Ok fine, from now on $\Omega \equiv H/\hbar$.

Danu

10:04 PM

hahaha

You and your anti-natural unit rage :D

DanielSank

@Danu It's sense, not rage.

If it makes you happier we can define $H \equiv H/\hbar$.

How's that?

Danu

It's unnecessary for those who know what they're talking about. We went over this; I agreed it's not pedagogically optimal, but it works

Sure thing

DanielSank

@Danu The Fourier transform of the autocorrelation function, if you want.

You know what I mean, why are you harping on this?

Danu

@DanielSank Yay, so a fourier transform :D

@DanielSank No, I genuinely didn't

DanielSank

@Danu Yes.

Danu

10:06 PM

I think I heard about it at some point but that was long ago

So the Fourier transform of $\langle \omega(t)\omega(t')\rangle$?

DanielSank

@Danu Ok, so this isn't your area of expertise then? You were joking before?

@Danu Yes.

Danu

@DanielSank I most definitely was joking, lol.

I thought it'd be obvious

DanielSank

@Danu Ok, see you later.

Danu

@DanielSank oh come on

You don't even want to explain it to me?

That's weak

I was serious about wanting to know what it was about. The short text you posted seemed comprehensible enough.

Sadface

Never seen Daniel ragequit like that before

ACuriousMind

@Danu Well...he did ask for help in earnest and all he got were two people making fun of him.

Danu

10:12 PM

@ACuriousMind No, I was genuinely interested in learning about this.

Of course I made the joke bout not knowing shit about it, but yeah whatever

I WANTED TO UNDERSTANDDDD

ACuriousMind

@Danu You did not really communicate that you wanted to learn, and while I was pretty sure you didn't actually know what he was talking about, I also would rather tend toward assuming someone tells me the truth when they say "this is my kind of physics".

Danu

@ACuriousMind Given that I've never every discussed anything even remotely related to this?

ACuriousMind

Because it would be potentially really insulting to assume someone doesn't know shit about something they actually care about

Danu

Haha

That's true.

So in light of the above @DanielSank I didn't mean to make fun of your (seriously, interesting!) problem.

And I'd like it very much if you could explain it to me

But I guess that's not an option any more :P

DanielSank

10:39 PM

@Danu Dude, just busy.

Sorry to hurt your feelings.

I'll explain it later. I need to write it up nice so I can explain it to people who might be able to help me!

Danu

@DanielSank Oh no you didn't! I was just afraid I hurt yours

But good to see that that's not the case---we'll talk about it more later.

DanielSank

@Danu Jeezus, that's like something from a middle school romance.

Danu

@DanielSank Who says I'm not a middle school romantic (do note the ":P" though)?

0celo7

@ACuriousMind Two?

DanielSank

@0celo7 @Danu and his sock puppet.

Danu

10:47 PM

My sole friend

FenderLesPaul

@GPhys sup?

Qmechanic

2

Q: How much QFT do I need to get started on String Theory?

I want to get started learning String Theory (most likely from David Tong's lecture notes) and I would like to know which topics I need to know from QFT. In particular, if I were to follow Peskin, which sections do I need? Can I do without part 3?

quantum-field-theory string-theory soft-question education

Primarily opinion-based?

ACuriousMind

@Qmechanic Yes.

(On the topic of the question, I say that someone asking "which sections of Peskin do I need" should learn QFT, not think about String Theory :P )

Danu

Ah @DanielSank so you agree that, strictly scientifically speaking, there is no measurement problem anymore since the decoherence story?

Up to the "relatively minor" (not so minor, of course) subtleties you mention

Hahaha, a nice description of AdS/CFT:

"Gauss/divergence/Stokes theorem on steroids"

user54412

11:14 PM

@Danu Noooo. Those margins. :(

user54412

@Danu I picked it up from Europeans/Australians

Danu

@ChrisWhite Globalization :D

Sir Cumference

Does anyone know the answer to this?

0

Q: Will gravitational waves too far away ever reach us?

Gravity is the curvature of spacetime, and its effects travel at lightspeed. However, space is expanding; eventually, light from distant galaxies will become more and more redshifted, and we will no longer be able to see them (source). As such, there is a limit to how far we could ever possibly ...

gravity expansion gravitational-waves dark-energy fate-of-universe

ACuriousMind

I tend towards saying no, stuff beyond the observable universe will not have gravitational influence on us. But stuff beyond the observable universe would not have gravitational influence on us simply because it is so ridiculously far away to begin with, so the question's moot.

user54412

@user36790 As a test, can you see this or this answer?

ACuriousMind

11:25 PM

Note, though, that gravity is different from gravitational waves. Just because gravitational waves can or cannot reach something, that doesn't mean gravity can't reach it.

Sir Cumference

I was thinking yes, but for a different reason. Even if it's the slightest gravitational effect, a lot of distant objects still affect us

DanielSank

@Danu I've been reminded recently that philosophical questions are an absolutely essential part of science.

From that perspective, I do think there is a measurement "problem"... but only sort of.

Sir Cumference

My question is whether these objects will eventually have no effect on us

DanielSank

From a very strict scientific method point of view, there isn't really much of one to speak of.

Danu

@DanielSank Sure, but I think the "but wtf Y U NO deterministic" is just something that belongs in the past, so it doesn't properly qualify

DanielSank

11:26 PM

@Danu Agreed.

Danu

I'm sensible to philosophy of science generally though, yeah

DanielSank

@ChrisWhite put it incredibly well a while ago. He said something like "Folks need to just come to accept that probability distributions do not always come from a lack of information".

Sir Cumference

@ACuriousMind Aren't gravitational waves just from the propagation of gravity?

user54412

@SirCumference One has to be very careful about what even "object" means in this case.

Sir Cumference

@ChrisWhite Anything with gravity

I'm clearly focusing on very massive objects

ACuriousMind

11:27 PM

@SirCumference No, just as light is not just from the propagation of electromagnetic fields

Danu

Anything that contributes to the energy-momentum tensor?

Sir Cumference

Yep

Light, even

user54412

@SirCumference Too many people in cosmology questions like this implicitly have a notion of "present time" that gets wrapped up in their definition of an object.

DanielSank

Now @Danu, I do think it's important to try to understand what the hell happens if you put an "observer" in a closed box. When the density matrix diagonalizes from that observer's perspective, what happens from my perspective as the "outside" observer?

Sir Cumference

@ChrisWhite Er...I'm sorry?

DanielSank

11:29 PM

If you try to concoct an experiment on this subject, you can't really find anything interesting though... you always just find that quantum mechanics gives you the right answer if you keep track of all of the degrees of freedom.

user54412

user54412

^ @Sir this diagram is your best friend

Sir Cumference

@ChrisWhite Er...what is this?

user54412

6

Q: Is the cosmic horizon related to the Big Bang event?

The Universe expands according to the Hubble's law: velocity is proportional to distance. There must be some distance, therefore, at which the velocity reaches the speed of light. This defines the horizon. The Doppler shift is so huge that the length of waves becomes infinitely long: We can not s...

cosmology universe big-bang

user54412

One of many, many questions that can be answered with that diagram

Danu

11:31 PM

Lololol

Going way over da heads

user54412

@Danu there's no other way

user54412

In any event, focus on the third panel. The vertical lines are the worldlines of Hubble-flowing objects like galaxies. We're at the center where all lines meet.

user54412

Note our past light cone. The larger triangle labeled event horizon is what our light cone will approach as $t \to \infty$.

ACuriousMind

"We're at the center where all lines meet" Typical anthropocentrism!

user54412

Here's an important feature: for any galaxy whose worldline intersects our current past light cone (i.e. any galaxy we can see some version of), some part of that galaxy's worldline will always intersect our past light cone for all times in the future (i.e. we will always see some version of it).

Danu

11:35 PM

@ACuriousMind "cosmologists"

user54412

Even if a galaxy's worldline is partially outside our event horizon, any part of it inside our current past light cone is inside our domain of dependence, and always will be, so in some sense you can't escape its influence any more than you can escape your past.

Sir Cumference

OH, it all makes sense!

user54412

Oh good. I'm kind of surprised actually. This stuff shouldn't make sense ;)

ACuriousMind

@ChrisWhite lol, while I agree with the comment that plain o is wrong, it at the same time uses "Göthe", which is also just wrong because that name is always written with oe.

Sir Cumference

Damn good answer

But I'm still a bit confused. Why does our light cone go beyond the hubble sphere?

Danu

11:46 PM

@ChrisWhite This all is just saying that we're not traveling faster than light, right.

user54412

@Danu yes

user54412

@SirCumference let me think about a good way to answer that (or someone else can say something)

ACuriousMind

Easiest way is to turn the question around ;) @SirCumference, why do you think it shouldn't?

Danu

I recall that Mukhanov's book (chapter 3) has a very good discussion of this stuff.

Sir Cumference

Well, the hubble sphere is the point where astronomical objects recede faster than light

Danu

11:48 PM

It's all just a big tumble of definitions, but if you take an hour to sit down and write stuff out everything is simple.

Sir Cumference

Yet the boundry of light cone is the farthest we can see today

Wait, crap

Now I'm confusing myself

Wait, our light cone will grow larger until it approaches the event horizon, right?

ACuriousMind

@SirCumference Now. Since the Hubble parameter is not constant, it shifts over time. Only if the Hubble parameter were constant would Hubble sphere and light cone coincide

Sir Cumference

Er...I'm guessing the Hubble parameter isn't the same as Hubble's constant?

Danu

It is

The thing is not constant in time, but constant throughout space

Sir Cumference

All right, but I still don't see why the Hubble sphere and light cone would only coincide if it were really constant

Transcript for