The h Bar

@0celo7 Shouldn't you be on a date?

@BernardMeurer no

crap, $i_X\omega$ need not be positive.

@ChrisWhite Is there anything special, in general, about the dot product of a timelike and a spacelike vector

@ChrisWhite Lol, Wald and Carroll claim opposite things regarding this.

@ChrisWhite I think I can get Wald's result, actually.

But not Carroll's

@ChrisWhite Ok, proof of what Wald says. Suppose the normal vector is timelike and we're looking at the divergence of the vector $X$.

Then either $X$ is timelike or it is normal to $N$. (not sure about this, working on a proof)

if it is normal, then we're done because the integral vanishes

Suppose it is timelike. Then if it is future directed, we have $\langle N,X\rangle<0$ by some theorem.

But then $i_N\omega$ is not a positive form.

Hmm

Continue to ignore me while I figure this out...

Ah! Split $X$ as $X^\top+X^\bot$, then $X^\bot=\alpha N$, $\alpha >0$.

Then $i_X\omega$ is positive!!

But since $i_N\omega$ is negative, we must really take $i_{-N}\omega$ as the positive thingie

but by a theorem in Lee this is the inward pointing vector

@ChrisWhite I'll write the proof shortly and answer the question.

2:57 AM

@ChrisWhite crap! Now I've just moved the sign to the orientation of $X$

@ChrisWhite How crazy it is it to just say "Wald is wrong"

o.o

Hawking-Ellis contradicts Wald

And THAT'S the result I can prove

Berkeley's funding me pretty well

I'm back to being confused now...

@FenderLesPaul I think Wald has a mistake

:/

I know Carroll does

There's the same theorem appearing in the three books and each says a different thing

I can prove the HE version.

but this is actually pretty strange.

the orientation of the volume form should not depend on this random other vector CRAP

also this approach will fail in the spacelike case

so maybe HE IS wrong

@FenderLesPaul Holy shit Wald AND HE are correct

@ACuriousMind I've proved it :D

100% sure this time

user54412

3:33 AM

@FenderLesPaul o.O

user54412

go to Berkeley for a couple years, then ragequit and switch to UCSB

user54412

we can move around cali together ;)

@ChrisWhite hahaha

yusss

that would be pretty dope

If I join will either of teach me how to cook?

I don't know how to cook

user54412

3:35 AM

@0celo7 Pretty sure there are spacelike vectors with nonzero time component in Minkowski...

Well but you hold the hand-writing selfie technique

user54412

I've been looking for an excuse to cook more.

I'm a human grinder

As in I eat a lot, not that I grind humans

user54412

One summer in college a group of us got together to cook every day (they didn't feed us during summer). We vowed to never eat the same thing twice. I miss those days.

user54412

Right now though I live alone, and too many ingredients are only sold in bulk.

3:38 AM

I liked the weather in Cali, you never sweat

A: Stokes theorem in Lorentzian manifolds

0

Not surprisingly, this has to do with the signature of the spacetime metric not being positive definite. Furthermore, this issue is very subtle. We will need a slew of theorems to understand it. We first state the preliminaries, proofs of which may be found in the excellent, J. Lee, Introduction ...

Comments appreciated.

I'd comment "first"

user54412

ur mathjax. it broke

@ChrisWhite where

but then I'd lose my precious little points

user54412

3:40 AM

ninja'd

I pulled a scumbag

"the other cases are left to the reader"

I'm sure there's some simple proof

I think mine is rather brute-force

Or deeply flawed...

someone gave me a +1

user54412

wonder who the OP is -- don't get many people asking advanced things but never giving answers

@ChrisWhite Did you read it? Are you convinced?

wait a moment, is this even right

where the heck does it actually depend on the metric not being positive definite o.o

No, this is the proof

I don't care any more.

user54412

"But since $\langle N, X \rangle$ is negative"?

@ChrisWhite so?

user54412

3:49 AM

I'm answering your question

the dot product can be negative on a Riem. manifold

SHIT

@ChrisWhite I think this is wrong

user54412

maybe that should be $X^\perp$?

@ChrisWhite doesn't matter because $\langle N,X^\top\rangle=0$

user54412

yeah, okay, so only in Lor. manifolds can the inner product between one vector and the part of another vector aligned with that one be negative

@ChrisWhite mb

ok, that's true.

well, no, it's not

AHHHHHH

I give up

@ChrisWhite Do you think the proof is correct?

user54412

3:55 AM

it's probably not flawed in any serious way :)

@ChrisWhite ok

now papa ACM needs to read it

Q: Quantum Theory just lazy physics?

4:09 AM

0

Is it true that physicists decided that because they couldn't predict with certainty the location of an electron at any given time, that they just created equations using probability instead, still allowing them the ability to invent new technology and other things without actually stripping away...

quantum-mechanics

~sigh~

@0celo7 Glad the daddy title stuck.

@DanielSank please read my proof

@0celo7 no way both Wald AND HE can be correct

those books are antagonistic as fuck

:P

@FenderLesPaul I'm super-dooper busy at the moment. Shouldn't even be typing this.

@DanielSank read my proof!!

4:22 AM

@DanielSank typing what?

haha

nvm I gotchu

@FenderLesPaul what?

I'm confused

5:04 AM

@0celo7 Question about projectiles, I don't get it

@DanielSank did you read my proof

@0celo7 Of course not.

@DanielSank oh come on why not

5:19 AM

@DanielSank :(

6:03 AM

@0celo7 Because I'm making slides for a talk I have to give tomorrow that I had very, very short notice on.

I have this thing called "job" that prevents me from doing what you want at all hours.

4

Frowny faces have no bearing on that. Sorry.

user507974

7:05 AM

@0celo7 proof for whay

Q: Quantum Theory just lazy physics?

8:08 AM

-2

Is it true that physicists decided that because they couldn't predict with certainty the location of an electron at any given time, that they just created equations using probability instead, still allowing them the ability to invent new technology and other things without actually stripping away...

quantum-mechanics uncertainty-principle quantum-interpretations probability

@0celo7 is that you

So anyway

How many exact solutions of $\varphi^4$ theory are known

I can think of two classes of solutions

Three if we include the vacuum

8:28 AM

Hm a basic solution of $x'' - x^3 = 0$ is just $x^{-1}$

I wonder if it translates to PDEs

eqworld.ipmnet.ru/en/solutions/npde/npde2101.pdf

user116211

8:49 AM

@Slereah: o/

user116211

@Slereah hahaha

Q: It is on topic to ask about computer software useful to do some particular task?

9:26 AM

Amazon wants to tempt me to buy "The global nonlinear stability of the Minkowski space"

They know what I like

Valentin Tihomirov

I can understand that 1 kilo of fish is equivalent to 5 euro, which I denote 1 kg of fish = 5 eur. Normally, you say that price is 5 euros per 1 kg of product? What do you mean by dividing 5 euros with the weight? I see now that it is equal to 1. That is, if 1 kgf = 5 eur then, dividing both sides by 1 kgf I get 1 = 5 eur per 1 kgf. What does it mean?

Physics Meta

10:21 AM

1

I want to plot some phase diagrams that look professional (Example). I don't really know what tools are usually used to do this kind of diagrams, I've been looking around and found some alternative but I would like to know what is usually used by professional researchers to do this. I have seen ...

discussion

apt software-installation

11:12 AM

http://physics.stackexchange.com/questions/1111/whats-the-difference-between-helicity-and-chirality

Chirality is determined by how the particle transform under the poncare group, on whether it is the right or left representation
-Paraphrased form wikipedia

This sentence sounds a lot less confusing ever since I learn some spectroscopy and symmetry groups

innisfree

11:35 AM

89

Q: Can't find clit

I have some lit files I want to convert from mircrosoft reader files to something my other devices can read. My friend says I should have clit, in $ which clit /usr/bin/clit but I cannot find it. I tried locate clit but the results are unrelated. So then I tried sudo apt-get install clit but ...

Puerile, I know :D

11:50 AM

By the way, I never understood that particular problem...honestly, it does not seem something so difficult to find

12:10 PM

@yuggib can confirm

@yuggib you should check out my proof

you are very anxious about your proof, but I have no idea which proof, and about what

@yuggib check my post history.

My latest one

I'm now going to shower, cleanliness is important.

12:31 PM

http://googology.wikia.com/wiki/Meameamealokkapoowa_oompa

For example, a large number

12:48 PM

@0celo7 seems ok, and quite boring as all geometric stuff

How is it boring

Coming from the person who does nitpicking math for a living...

I do fun math

geometry is boring

http://googology.wikia.com/wiki/Introduction_to_BEAF

*mind asplode*

Proof related

Do we really need numbers this large?

for practical applications or proof related things?

12:57 PM

@Secret especially when I can give you very easily a number that is larger than all of those: $\omega$

ah yes, the first ordinal

and one that is $\omega \uparrow \omega$: $\varepsilon_0$

and those are still countable

@Secret No

Graham's number is the largest that had maybe some use and it has only been used once

I can also give you $\aleph_{\alpha}$, where $\alpha$ can be any ordinal (finite or infinite)

but in the end...who cares? It is important to know that numbers are well-ordered, the rest is just having fun

Is that all that numbers really mean?

1:07 PM

numbers are of course important

especially when they constitute a field, or a group, or whatever

but writing down with some bizarre notation a very large natural number is not so interesting in my opinion

far more important is that no matter how large a natural number could be, there is always another one that is finite and bigger, and an infinity of infinite ones (that are also obviously larger)

How far can "well-orderedness" be extended?

what do you mean?

every set can be well-ordered thanks to the axiom of choice (even if the well-ordering may be "impossible to write down")

the well-ordering of ordinals is pretty natural

http://googology.wikia.com/wiki/Inaccessible_cardinal

o and it seems they use that notation for these infinite things also

============
On a more related note, is it safe to say that we can define everything in maths with just relations?

the well-ordering of reals is a nightmare

That's what I mean: "impossible to write down."

1:14 PM

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ nevertheless, there is a well-ordering of the reals

https://en.wikipedia.org/wiki/Well-order

cannot wrote it down

@Secret relations are not enough to define "everything" in math

@yuggib have you watched any of professor Norman wildberger's vids?

relations are just something that is defined in mathematics (more precisely, in logic)

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ no, who is he?

He's done a lot on YouTube about the real numbers being a myth.

1:18 PM

why should they be a myth?

The reals are not proven to exist

?

why would that be?

You should check it out on YouTube :)

nah...I'm not interested in b******t

I stopped watching too.

They call him a hyper finitist

Infinity does not exist either.

1:24 PM

that is just a matter of axioms

He refuses the axiomatic approach

ok, so how could he get a position? (assuming he has one in mathematics, and not in philosophy)

Dunno, he works in an Australian university and has a PhD from Yale.

To be precise, my university
Though for me, I found his idea interesting

as I am that kind of guy who likes to collect ideas everywhere to analyse

Norman Wildberger

1:31 PM

what is his approach then? what is a mathematical theory? something pre-existing in the platonic world of universals?

The biggest cardinality is the cardinality of the universal class, of course

If I recall, he is mostly interested in using surds to derive everything in trigonometry

$\text{Card}(V) = \text{Card}(P(V))$

I once, out of curiosity , entered his office to check out his rational trigonometry idea

Having said that, I am not a finitist because I like the weirdness of infinities

Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions...

user507974

1:33 PM

@Secret that sounds absurds

The idea seemed useful enough in case you want to compute unit cell angles, at the cost of squaring all your length measurements

constructivism in mathematics is something that is not new

as well as intuitionism and finitism

however people in those worlds usually aim to try and reproduce everything (or most of the times just something) that mathematics has already proved by their different means

a work that is very well credited on this is the following by Bishop:

projecteuclid.org/euclid.bams/1183531480

it is of the late sixties, so nothing extremely "new"

I have a book by a dude who built Newtonian mechanics without numbers or functions

indeed

Only Euclidian geometry

1:39 PM

@slereah O_O

(Well technically Hilbert's axioms)

It's not terribly useful

Someone can argue I sometimes think like an Intuitionism
Recall those crazy diagrams that I drew last year, one of these is a (foolish) attempt to draw one squary looking thing so that everything we know about linear algebra can be derived by geometric consideration on that diagram

intuitionists are not people that use intuition ;-P

and then some time later, when reading new scientist, I learnt the necessarity of need to go beyond our intuition that is hard wired into our brain in ordee to have chance to discovery even more weird mathematical objects

essentially, they reject everything that is not constructive and also the law of excluded middle

1:43 PM

@GPhys are you done with everything?

@yuggib so multivalued logic?

@yuggib upvote scrooge

Begging for up votes?

@yuggib what is the cardinality of the plane

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ yes

@Slereah why do you have this book

Put a link here and maybe you'll one from me pal.

1:47 PM

I'm not that desperate

I answered a question that had 10 upvotes, I expected more than two :V

For any questions, I only worry about downvotes
Because for each downvote I received, the more likely I will be question banned

otherwise I don't realy care if someone downvotes me

it's just a number

People shamelessly advertise their questions and answers all over the network.

Hi all

Hi all + 1

:-D

Has anyone here had magic mushrooms before?

1:54 PM

Yup

How was it?

Just like pot.

I did it twice last week and it's awesome. I had a different trip to weed. Really something everyone should do.

Awesome stuff.

Have you tried hash oil?

Would like to try acid, have never had that. But I here that the trip is much longer than shrooms, I prefer the duration of shrooms. 6-7 hours is enough.

No I haven't tried that.

1:59 PM

Work your way up slowly pal.

Yeah for sure. Hash oil not really something I have connections for.

A big part of addiction are those so called "connections."

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ yeah damn those horizontal distributions

What are those?

2:21 PM

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I edited the answer, it's on the front page if you wanna take a look

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I think this answer suffers from "very technical syndrome"

A: Do any quantum gravity theories deal with closed timelike curves?

2:36 PM

0

Do any quantum gravity theories deal with closed timelike curves? No. As far as I'm aware, there are no quantum gravity theories that deal directly with closed timelike curves. As far as I know that's correct. Some of them (like canonical QG, CDT and LQG) forbid them outright, ...

@Slereah :DDDDDD

You got an answer

@Secret no, not essentially

they just refused the implication of excluded middle

@0celo7 the plane $\mathbb{R}^2$ has the same cardinality as $\mathbb{R}$, i.e.: ......?

@0celo7 Hm

He doesn't get awarded the bounty if he has 0 votes, right?

Not sure I'll get any real answers really :p

Igael's answer is probably the best I can hope for I think

2:53 PM

http://philosophy.stackexchange.com/questions/32409/why-did-only-science-and-religion-became-widespread-instead-of-magic

they should really terminate downvoting if the question is closed
now I am in danger of gettign quesiton banned on philosophy stack exchange