Thanks very much

@Jim: Only if the U(1) it belongs to is the electromagnetic U(1) :P

@ACuriousMind Where $U$ is the enveloping algebra?

Oh no the unitary group :(

@GaloisintheField No, U(1) is the circle group.

@GaloisintheField There is a mathematical formalization of the measurement schemes for QM, introduced by von Neumann, and given in a clear (for me) form by Ozawa in a paper of 1984

@yuggib I'll check it out tomorrow, thanks

@yuggib You managed to obtain it?

I recall you were upset because it wasn't easy.

Does $\epsilon_{jkl}\epsilon_{jnm} = \delta_{kn}\delta_{lm} - \delta_{km}\delta_{ln}$ use einstein notation on the right(or left or both)

@GaloisintheField Yes, sum over $j$ is implied.

@ACuriousMind yes

On the right both for k and m aswell?

in the end I bought it

just to discover that the university of Stuttgart where I am now has the subscription to the journal

@GaloisintheField No.

@GaloisintheField No, only repeated indices (in the sense that they are repeated in terms multiplied by each other) are summed.

(contrarily ot any other university I have been to)

T_T

You only sum if it's repeated in the same term.

but since it is a nice paper, that's ok

OH, well that helps a heap

Thanks @ACuriousMind

@GaloisintheField Of course you need to know some things about von Neumann algebras to understand it...

but probably maths is not your problem ;-)

I would like to see ACM in the hexagon with Weinberg.

@yuggib Haha sure, I'll try to understand it out of general curiosity, I'll get it in finite time

Oh hey, we have a chat session coming up

2.5 hours I believe?

@DavidZ Correct.

That's physics lab time.

someone has access to the historic of this (obscure) journal:

Mat.-Fys. Medd. Danske Vid. Selsk.

@DavidZ What does this chat session involve?

@yuggib wtf

Danish?

@GaloisintheField chatting

about physics

chatting about GDP

not very different from now...

@yuggib and sessioning

Like everyone can chat freely?

or rather, the lack thereof

more people attending

@ACuriousMind yes...

@GaloisintheField no if you break rules we break you

@GaloisintheField It's really just a time where more/different people than usual are here to chat.

@0celo7 Okay I'll make sure not to break the rules, I like being non-broken

where a very cited, and supposedly interesting, paper of Irving Segal has been published

and it is impossible to find

>implying you need anyone more than me

@yuggib How did it become so very cited then? :P

What percentage of the people citing it has read it?

@ACuriousMind that is a mystery

and it was cited in the 70s and 80s...

it is a 59 paper

You sure it even exists? :D

lol

well....never saw it

i read its second part

and refers to the first one

so....

@GaloisintheField it's just a time when a bunch of people try to get together here to discuss whatever happens to be relevant... if anything

surely it is not an existence theorem

This time we have a couple meta discussions we could talk about

Sometimes there is no particular topic

wait...interpreting I may have found the historic

sdu.dk/en/bibliotek/materiale+efter+type/hostede+ressourcer/…

maybe they have scanned pdfs...

I assume the author is dead

yes

and he was a great mathematician/((physicist))

did he increase GDP

?

HAH

sdu.dk/media/bibpdf/Bind%2030-39/Bind/mfm-31-12.pdf

found it

Segal was both a great mathematician and an action movie hero!

what does this paper show?

words

@0celo7 Y'know, that's what the abstract is for :P

Don't you know the order of reading a paper @0celo7

First the abstract

@ACuriousMind doing stuff

abstract is tl;dr

Then section two, to read the lagrangian/metric

Then the conclusion

hehe

Then back to section two to read the paper

papers in math rarely have a conclusion

often the last page before bibliography ends with the symbol meaning the end of a proof

I doubt most of them have a lagrangian, either

then they're useless

as it should be :D

what is the Lagrangian of the universe

But as a rule, you can pretty much always skip the first section

@Slereah

Unless you are looking for bibliography

:24822230

$+ \frac{\kappa}{2} R$

$+ \Lambda$ also, I guess

explain those terms

Okay

@ACuriousMind is string theory linear

First term is the kinetic term of the gluon field

@Slereah in less than 50 words

Second term is the self interaction of the gluon field due to the non-Abelian gauge

There are more than 50 terms

Gonna be hard

lol

you have only ~25 words of explanation left

well which idiot decided to expand everything

It was on some professor's website

For a laugh

actually not everything is even expanded

the Einstein summation is still there

yeah you could expand it further

he didn't even split left and right fermions

or flavors

@yuggib I find that very irritating. I mean, physicists do a bunch of things wrong, but I think the conclusion with a short reminder of what was shown and what would be interesting things to further look into is a better ending for a paper than just proving the last theorem.

@0celo7 Define "linear".

To the (mostly) matehmaticians: which QED symbol do you prefer?

@ACuriousMind ask @yuggib

@ACuriousMind Yes, maybe. But the main theorem is often stated in the introduction, and the end is just to provide the tedious details

@yuggib huh?

@0celo7 @ACuriousMind I said that as a quantum theory, ST should have a linear evolution operator

@yuggib $\square$

oh

My favorite is $\dashv$

I thought you meant quantum electrodynamics :P

was about to put $A_\mu$

that has recently surpassed $\blacksquare$

FWIW, I agree with Bajoran

@yuggib Uses too much ink ;)

@ACuriousMind Yes, but $\square$ goes so easily unseen

@yuggib I prefer for proving lemmas $\square$ and for finishing the entire proof $\blacksquare$

and $\dashv$ is so logic-style

@GaloisintheField wow...never made a distinction

and had some nested instances too within proofs

What's the one with three dots

that is to sum up what there was above

not to end a proof I think

Well whenever I need to preface my argument with, we want to prove 4), to do so we will need to use arguments 1) 2) 3) and then I get to $\square$ each argument and have a quick reminder of what we want, then move onto 2) and 3) and then $\blacksquare$ bam

@yuggib I am not sure the string theory has a "time evolution" in the usual sense.

@ACuriousMind explain

@Slereah therefore = $\therefore$ = $\therefore$ :P

@GaloisintheField exactly

@0celo7 The Hamiltonian constraint means that at least the Hamiltonian cannot generate a time evolution. Furthermore, do we want an evolution in the worldsheet time or in the target space time?

What could cause my internet speed to be good but for my browser to time out

@0celo7 Changes in internet state(i.e. if you are using internet from a phone plugged into the pc)

@ACuriousMind in the worldsheet

@GaloisintheField on wifi, 130Mbps but things are taking minutes to load

Windows works fine

something is wrong with OSX

@0celo7 No idea sorry, I just had the problem heaps with my phone internet

It was phone internet, from phone to the wifi though, so if you have a dongle for wifi or something could be that

@ACuriousMind well you're the one who read a whole book on constrained hamiltonian systems

so you tell me how we get time evolution

@yuggib That'd then be generated by the conformal Hamiltonian $L_0 + \overline{L}_0$. But string theory restricts the physical states to those of conformal weight 1, so they all are eigenstates of the time evolution.

@ACuriousMind Nevertheless, it is a linear evolution

the basic principle of quantum theories are mantained

fml I've forgotten everything about string theory

@ACuriousMind I'm not trying to learn everything

and it was just a silly joke with @0celo7... ;-)

I need to remember something

Yep. The actual "string time evolution" lies in the perturbative definition of the string partition function, I think.

Saying that you don't just take the overlap of the states in one possible conformal theory, but that you have to sum over all the worldsheets is what is the evolution here is, I think. It's very suspect that I cannot find any string text really talking about the time evolution of string states, not even stating there is none.

@ACuriousMind :-D

well...string theory is so keen to metaphysics that time evolution becomes subjective

:P

I think Gödel's ontological proof is less metaphysical than string theory

You're lucky no string theorists frequent this chat

:-D

I know

but I never said I do not like metaphysics

I like meatphysics.

Not so sure about metaphysics, though.

@ACuriousMind so you've decided not to do string theory?

@0celo7 I am not currently a string theorist. That's all I'm saying.

I do not know how many string theorists are hired nowadays...

not many I presume

@yuggib Godel's ontological proof is basic logic

The axioms are the questionable part

ok, wth is this ontological proof

why is everyone going crazy about it

MATLAB is going to take an hour to download...

Gödel was trying to formulate a logical proof of god's existence

for me, more than the axioms is what is called "God"

and, ok the fifth axiom is not so convincing

what are the axioms

The proof : dl.dropboxusercontent.com/u/19940612/…

> Axiom 5: Necessary existence is a positive property

wtf does that even mean

eh

that is the point XD

God is the collection of all positive properties

god killed millions of people

not positive in my book

you are just giving you own definition of god

that is not the one of Gödel / Leibniz

feel free to do that

what is a positive property

and also, the proof of Gödel has an error (that can be corrected)

and in that form yields that there are no contingent truths

but also that could be avoided

what?

and is founded on the axiom s5 of modal logic

stop saying words that have no meaning to me

and also this axiom is disputable

@yuggib I was just kidding about that of course :)

@Danu :)

I sometimes feel the same however...

but then I remember my origins

and my degree

IIRC Tipler was way into Jesus as well

> Axiom 4: If a property is positive, then it is necessarily positive

::scratches head::

@0celo7 : This one isn't very hard

You have a set of axioms that differ from the original...

@yuggib Wiki

it's similar to $\vdash \phi \rightarrow \forall x. \phi$

wtf

@0celo7 original manuscript (in its translated form)

@yuggib I'm looking at Wiki

ok

nevertheless

can someone explain

> Axiom 5: Necessary existence is a positive property

It means that if something is true, then it is necessary that it is true

@Slereah well no shit

It's part of the whole modal logic set of axioms

It's not very useful for meanings

it actually means that positivity, implies necessary positivity

But it is useful for proofs

i.e. that there are no contingent positive objects

if god has all positive qualities and existence is a positive quality

??

my brain

Eh don't bother

It's not all that interesting

the one that @Slereah is saying follows from the context of the proof indirectly

It's a very old proof

Like at least goes back to medieval times

When people mostly used logic for that

and means that no truth is contingent

but that could be modified

just add that to the list of stuff I'm ignorant about

not that it was ever in the list of stuff I'm not ignorant about

necessary existence is positive

not existence

what

there is difference between existence (the common one)

and the necessary existence of the proof that involves essences

@0celo7 : Look up modal logic first, maybe

Basically modal logic is about like

Probabilities, sort of

possibilities

It has a symbol for necessity, similar to $\forall$

the idea is that apart from the usual logic quantifiers

why is the installer using 1% of CPU

use ALL and get this over with

you have also a symbol $N$ for necessity

$\square \phi$ means that $\phi$ is necessarily true

and one $M$ for possibility

they obey some rules

this makes zero sense

$\square \neg \phi$ means it is necessary that $\phi$ is false

wtf is "necessary"

What is the meaning of the rhombus? commons.wikimedia.org/wiki/File:Rhombus_1.svg

$\neg \square \neg \phi$ means that it is not necessary that phi is false, ie, it is possible

@0celo7 The CPU is not the bottleneck for installers. It's just copying (and possibly decompressing) files.

@0celo7 : It varies, it is used in several contexts

For instance it can be statistics

Something with a probability of 1 is necessary

the rhombus is a muon going in a dirac belt loop

@ACuriousMind the disk is only being used 2%

whatever that means

@Slereah what about $\square\neg\square\neg\phi$

It is necessary that $\phi$ is possible :p

it means that it is necessary that $\phi$ is possible

stereophonic answer :D

what about $\lim_{n\to\infty}(\square\neg)^n\phi$

No limits :p

I have a nice book on modal logic if you want, though

@Slereah why

set $n=100$ then

what does that mean?

that you want to complicate your life

"Modal Logic" by Brian Chellas

@0celo7 Logic deals with a limited alphabet. $\lim$ is just not an allowed symbol.

make a 6th axiom then

and under axiom s5 of modal logic, it actually means only $\lnot\square\lnot\phi$

There are totally theorems with double necessities, though

$\lim_{n\to\infty}(\square\neg)^n\phi$ means $\phi$ is stupid

Like $\diamond A \rightarrow \square \diamond A$

@yuggib what is S5

that is not a theorem, it is axiom s5

never said it's a theorem

Well axioms are theorems :p

the one @Slereah just wrote

not in the system without the axiom :P

well, just another thing I'm bad at

whatever

not necessarily

I'm quickly running out of maths that I'm not bad at

S5 implies that if you have a chain of those symbols, you only take the one closest to the statement

makes everything easy, but the semantical meaning is disputable

what is $\rightarrow$

Well as said, you can assign several semantic meanings to modal logic

logic inference (in this case)

@0celo7 : basic logical implication

not usual symbol used however

what is $\implies$ then

$A \rightarrow B$, if A is true then B is true

and $\diamond$

$\diamond$ is possibility, $\neg \square \neg$

what is $\square$ again?

Similar to how $\exists$ is $\neg \forall \neg$

wtf...

$\square$ is necessity

@Slereah explain

lol, @Danu abusing mod powers to fix @Slereah's TeX

and $\cdot\lor\cdot$ is $\lnot (\lnot \cdot \land \lnot\cdot)$

@0celo7 : Well, $\forall x. \phi$ means that for all elements x, then $\phi$ is true

seriously, this stuff is messed up

$\forall x. \neg \phi$ means that for all elements x, then $\phi$ is false

$\neg \forall x. \neg \phi$ means that it is not true that for all elements x, then $\phi$ is false

this means that for one x, it could be true

Or several x

or all x

Basically it means that there exists at least one x such that $\phi$ is true

how do you know