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02:00
One example he gives is "The elliptic space, or projective model, $\bar D^n = D^n/Z_2$"
What's $D^n$
@Slereah Commonly the n-disk
OR n-ball, whichever name you prefer
Hm
"THEOREM 3. The non-isochronous relativistic spherical space forms with n-dimensions are in one-to-one correspondence with the two-sheeted coverings of riemannian (n - 1)-spherical space forms. If n is odd, the only non-isochronous relativistic spherical space form is the projective model D" = D"/Z2, which is orientable but not isochirous. If n is even, such relativistic spherical space forms are isochirous but not orientable."
Blah
Okay, now I have 6.82. We're getting somewhere.
02:02
I hate it when they use a different terminology
@HDE226868 lol
Why didn't Einstein write HE
Couldn't he fix the terminology right when he made the theory
@0celo7 Let me walk though this step by step. Nobody interrupt.
I'll say it : Einstein ain't shit
We have $100=GMm$.
02:03
What counts as interrupting?
We also have $m=16\text{ pounds}=7.27\text{ kg}$
@ACuriousMind Nearly anything.
9.36 $\to$ 53 $\to$ 9.92 $\to$ 8.73 $\to$ 12.35 $\to$ 21 $\to$ 6.82
@HDE226868 NO
pounds are not kilograms
I have no clue if they mean slug
Therefore,$$M=\frac{100}{Gm}=\frac{100}{(6.674\times10^{-11}\times7.27}=2.06 \times 10^{11}$$
or want us to divide by 9.81
or they're just stupid and that info does not matter
@0celo7 I'm guessing they're skipping the fine distinction here. Let's pretend one way first.
02:05
He uses a lower case lambda for the cosmological constant
I am outraged
@HDE226868 DUDE
that distincion is huge
how can you convert a force to a mass
are we to assume that's on the surface of the Earth?
Divide by $g$
@0celo7 95% of the people on the planet don't think twice about it. It's fine for them.
@Slereah WHICH G
Okay, I'll start over.
02:06
the g spot
Now nobody interrupt unless I'm wrong. Got it?
this rule is wrong
"The Minkowski space Fn is the real number space Rn (a differentiable manifold in the usual way) with the flat Lorentz tensor"
Those slight differences of nomenclature disgust me
$$F_w=16=mg\to m=\frac{16}{g}=1.63\text{ kilograms}$$
@HDE226868 start banning people who interrupt
Oh wait
$D^n$ is De Sitter space >:|
02:10
$$k=100=GMg\to M=\frac{100}{Gm}=\frac{100}{6.674\times10^{-11}\times1.63}=9.19\times10^{11}$$
And $A^n$ is the anti de sitter space
@Slereah what
$$\mu=G(M+m)=(6.674 \times 10^{-11} (9.19 \times 10^{11}+1.63)=61.31$$
@0celo7 It's an old ass paper with weird terminology
ah
ass papers are the worst
old ones even worse than the worst
02:13
there is a linguist named "Ass"
Or was it "Butt"
I think Butt
Miriam Butt is Professor of Linguistics and Chair of the Department of Linguistics (Fachbereich Sprachwissenschaft) at the University of Konstanz. She is best known for her theoretical linguistic work on complex predicates and on grammatical case, and for her computational linguistic work in large-scale grammar development within the ParGram project. Butt earned her doctorate in linguistics in 1993 at Stanford University. She subsequently held research and teaching positions at the Institut für Maschinelle Sprachverarbeitung at the University of Stuttgart, University of Manchester Institute of...
She wrote a book with Tracy Holloway King
The Butt King book
$$r=10\text{ feet}=4.88\text{ meters}$$.
$$a=\frac{r}{1\pm e}$$In case #1, we use $+$, and$$a=\frac{4.88}{1.5}=3.25$$In case #2, we use $-$, and$$a=\frac{4,88}{0.5}=9.76$$
@ACuriousMind kek
hmm
$$h=\sqrt{a(1-e^2)\mu}$$In case #1,$$h=\sqrt{(3.25)(.75)(61.31)}=12.22$$In case #2,$$h=\sqrt{(9.76)(.75)(61.31)}=21.18$$
Also, this affair has spilled onto meta.SE
02:17
lol = $\mathrm{Ad}_1$o
@ACuriousMind wow
that Daniel Sank guy must be a real monster
he should know
He IS that monster
@HDE226868 dude, you're making this complicated
We have$$\frac{v^2}{2}-\frac{\mu}{r}=-\frac{1}{2}\frac{\mu^2}{h^2}(1-e^2)$$Therefor‌​e,$$v=\sqrt{2\left(-\frac{1}{2}\frac{\mu^2}{h^2}(1-e^2)+\frac{\mu}{r}\right)}$$
@Slereah have you fought an alpha deathclaw yet?
I got this awesome shotguin
le fusile terribles
does 180 damage
kills everything
I have yeah
02:20
I murdered the hell out of an alpha deathclaw
same here
actually I had to fight a deathclaw and an alpha at the same time
At some point you become too tough for enemies really
I found this camp
And the only danger is big mobs of enemies
02:20
it had a siren machine
when I turned it on a bunch of raiders and two deathclaws appeared
@Slereah even then, I have 250 stimpacks
if there's something really scary I'll get Elder Maxon's beast mark 6 armor
that thing has hundreds and hundreds of health
@HDE226868 I think that's what I have?
wait
I don't have $h$ in the denominator
In case #1,$$v=\sqrt{2\left(\frac{61.31}{4.88}-\frac{3758.92}{298.657}(.75)\right)}=7.62‌​\text{ feet per second}$$
In case #2,$$v=\sqrt{2\left(\frac{61.31}{4.88}-\frac{3758.92}{897.185}(.75)\right)}=13.2‌​\text{ feet per second}$$
I don't know if I plugged things in correctly for any of the steps, though. @0celo7, you'll probably want to check my work.
lol
fml
I have an exam on this on Tuesday
@0celo7 That'll certainly change something.
@HDE226868 alright
there's something wrong with something
now what is that
WAIT
why are you not getting a quadratic eq
a nontrivial one
@ACuriousMind Really? Thanks!
More set theory tonight!
02:28
what is the convex hull
In mathematics, the convex hull or convex envelope of a set X of points in the Euclidean plane or Euclidean space is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X. Formally, the convex hull may be defined as the intersection of all convex sets containing X or as the set of all convex combinations of points in X. With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces; they may also be generalized further...
@HDE226868 learn some real math
prove that the conjugate operation on a lie group is smooth pls
you know what you can do
you can check your answer
you know what's fun?
because $v_0$ is perpendicular to $r$
Looking at lists of ancient manuscripts
"Official letter in Greek mentioning a pickled goose (P.Duk.inv. 599)"
02:30
we have $h=rv_0\sin\alpha=rv_0$
It is followed by this one :
"Official letter in Greek mentioning a pickled goose (P.Duk.inv. 605 R) "
lots of pickled geese back then
@HDE226868 does that work out with your numbers?
@0celo7 I get $4$ and $6.96$. Both apparently wrong.
@0celo7 Smart.
and $h=blah$ follows from the cross product definition of angular momentum
Well, I most likely plugged in something wrong. At least you know how to figure it out, though:$$h=\sqrt{a(1-e^2)G(M+m)}$$Simple enough.
Let me know if you get anything that remotely makes sense.
Anyway, it's Saturday night, so time to party! read Arthur C. Clarke and sip hot chocolate.
02:36
@HDE226868 weird
@HDE226868 will you be around on Monday?
that's when I'll do more studying for my exam
@0celo7 Possible from UTC 21:00 to UTC 3:00.
Although I have to study for an AP Euro exam.
AP Euro
AP European History
I was remembering the failure
I completely bombed it
@HDE226868 who are the Medicis
Italian bankers and art patrons.
02:42
who developed the scientific method
Lorenzo's the most famous.
@0celo7 No idea, although I should know that.
Aristotle?
HSM modship going to be revoked.
I'm going to guess Aristotle or Descartes or Newton.
Or there's no right answer.
I don't think anyone did
I think it was more
Because it's evolved over the years, and no single scientist in the past used it precisely as it's used today.
02:44
A process
The answer can only be an approximation to the truth
IIRC some islamic scientist is credited with some good advances on it?
@0celo7 Okay, what's the answer? Is there one? If not, I'm calling it a win for me.
I forget whom tho
@Slereah Alhazen.
No. Maybe not.
Wikipedia contradicts itself there (and yes, I looked there to look up Alhazen).
Okay, more research suggests it was indeed Alhazen.
aka Ibn al-Haytham.
02:49
@HDE226868 I gave that a while back
@HDE226868 5.48
So basically every spacetime with $R = 1$ is $D^n/\pi_1$
With $\pi_1$ some discrete subgroup of $D^n$
But
What discrete subgroups does it have!
@Slereah I don't think $D^n$ is a group :P
That's how the author calls De Sitter space
I don't think deSitter is a group, either
Are there any discrete subgroups of De Sitter space that aren't $Z_2$
Oh wait, I recall that there's weird polyhedral identifications on the sphere
02:54
@Slereah It's not a group, it doesn't have subgroups. Do you mean subgroups of its fundamental group?
"a properly discontinuous group of isometries of $D^n$"
Ah, that makes more sense
Although "properly discontinuous" is not a property of a group but of its group action on the space :P
@0celo7 I meant to the question about the person who first thought up the scientific method.
@HDE226868 O
Apparently to make de Sitter space non-time orientable you have to turn the sphere of its Cauchy surface into the real projective space D:
Look at this uncanny alignment
Three instances of "isochronous relativistic spherical space" aligned
Phew
For a moment I thought it was gonna be all topology wanking
But he has an actual example!
03:19
I think ACM wanks to topology
aw
No hotlinking
@0celo7 ಠ_ಠ
@ACuriousMind what
you're telling me you don't?
lie lie lie!
derivative derivative derivative!
@0celo7 Okay, for that, you don't get to complain about any of my puns ever again.
03:44
@ACuriousMind what
I don't complain about your puns
Oct 1 at 13:45, by ACuriousMind
@Slereah Must sinors repent?
Oct 1 at 13:45, by 0celo7
@ACuriousMind smh
that's not complaining
it was just a shitty pun
complaining would be
"stop making puns"
1
Q: What is the general relativity explanation for why objects at the center of the earth are weightless?

jheindelThe idea that as you move through the earth you get a symmetric cancelling of gravitational acceleration which approaches zero acceleration due to gravity at the center of the earth makes a lot of sense I think. I also think that is a pretty easy idea to understand physically. On the other hand,...

uh
I know this
But I can't remember D:
@HDE226868 do you know?
I know there's a shell theorem for GR
@0celo7 Nope.
@HDE226868 looks like it follows from Birkhoff
do you know what that is?
@Slereah so what is the different between static and stationary
@HDE226868 hmm
the twisty turny
03:53
@0celo7 Yes.
Is there a solution to geodesics in de sitter space?
how does the "there is no gravitational acceleration in the middle of the earth" come about classically
does it follow from the shell theorem?
@0celo7 : Shell theorem
@HDE226868 so what is the difference between static and stationary
stationary is a having a timelike killing vector
Static is time symmetric as well
03:55
@0celo7 I think they're the same, but I'm not positive.
Straumann defines static using the Frobenius condition
@HDE226868 they aren't
@HDE226868 I know that
when I was your age I knew!
What's the difference?
Do refresh my memory.
seriously, that's when I was reading this book :P
stationary is having a timelike killing vector
and static is when the killing vector is orthogonal to each spacelike hypersurface
maybe
03:56
that's it yeah
Basically it happens when you have some rotation going on
The twisty turny tips over light cones
@Slereah what do you mean by this
@0celo7 Well, when I was my age, I was learning celestial mechanics, so seems like we're king of in reverse lives.
And the time direction tips over
@0celo7 : it is invariant by $t \rightarrow -t$
@HDE226868 I'm not learning celestial mechanics
I'm trying to solve this problem
that now 4 people have gotten different answers for
all wrong!
@Slereah can you give an example of a spacetime that doesn't satisfy that but is stationary
because stationary means you can find coordinates so that $t$ does not appear
so that's trivially time flip invariant
@0celo7 Did you try fiddling around with the last equation I gave you?
I'm ~90% sure that you were right about that.
04:00
@HDE226868 I'll work on it with my study group
I'm 90% right all of the time
so what was I right about this time
That using that equation for $h$ is much simpler than working with specific orbital energy, as I was trying to do.
@HDE226868 what equation
1 hour ago, by HDE 226868
Well, I most likely plugged in something wrong. At least you know how to figure it out, though:$$h=\sqrt{a(1-e^2)G(M+m)}$$Simple enough.
wait
can I set that equal to $vr\sin\alpha$
Yes. We established that, I think.
04:03
oh
maybe we did!
cocaine is a hell of a drug
So then the solution is obvious.
Anyway, gotta go. Let me know what you get.
@HDE226868 aight
@0celo7 Kerr
Basically whenever you have $dt$ cross terms
Because $t \rightarrow -t $ means $dt \rightarrow -dt$
oh
it's the components that are invariant
ah
static is what gives the -dt^2+dx^2 split
"In general relativity, a spacetime is said to be static if it admits a global, non-vanishing, timelike Killing vector field K which is irrotational, i.e., whose orthogonal distribution is involutive.'
04:25
what do any of those words mean
user54412
04:47
As I read the last 6 hours of transcript, I have just one question: How do you people chat so much?
3
0
Q: Non-time orientable quotient of de Sitter space

SlereahExamples of non-time orientable spacetimes are pretty scarce, but it seems the big one is quotients of de Sitter space of the form $dS^n/\pi_1$, where $\pi_1$ is some subgroup of the isometries of de Sitter space. The standard example, as seen in Hawking and Ellis (p. 130) and Calabi and Markus's...

plz halp
05:03
@ChrisWhite huh?
@Slereah using $dS^n$
why not $\mathrm{dS}^n$
Because go to hell
Hm
I think my example is probably not the adequate one
I think I misunderstood it
I think a proper example would be using null curves
06:03
@Slereah afaik you never get answers to your questions
so idk why you bother tbh
user54412
06:25
The conference paper was in 2002, while the journal paper is dated 2015. I think the more likely problem here is that if the papers are essentially the same, the new author on the journal paper had minimal contributions to it (he was apparently about 4 years old in 2002, when the conference paper was written.) — ff524 ♦ 6 hours ago
user54412
The plot thickens
4 years old
what the hell
user54412
Apparently this case of plagiarism/gift authorship has some interesting twists
a 17 year old is publishing in a journal?
lol
clicked the link
user54412
not the least being that the journal editor was the adviser of one of the implicated authors
user54412
06:27
I can see now why so many people are anonymous on Academia.SE -- getting on the wrong side of the editor of the journal in your field can't be good for a career.
@ChrisWhite that's scary
 
2 hours later…
08:53
I found it funny, how the development goes to more complexity in math, but less understanding in reality. I gave here an answer; physics.stackexchange.com/questions/180692/… but it was deleted, because it didn't answer the question! Though the question answered the question by itself; and the only think the asker missed, was the connection to reality.
I recall how it was once asked from a young engineer "How was the circumference of the circle calculated from the diameter?" and after answering C= pi x d, and then telling that pi is 3.14, the young Engineer was angry, as "Do you think, I am stupid, I KNEW PI IS 3.14", well yeah, he knowed the value, but didn't know what Pi is!
I mean how more simple the math can ever go? This is pretty exactly what Einstein ment by saying "Information is not Knowledge."
I have already encountered a similar situation with this question; physics.stackexchange.com/questions/159970/… I was able to give the OP what was needed, but yet the answer was found sort of incomplete. I mean how could you ever answer politely to the question like this young engineer once made?

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