The h Bar

ACuriousMind

20:00

@0celo7 And that concerns me how?

0celo7

@ACuriousMind oh, have I confused you for someone who gives a damn?

Slereah

@0celo7 None of us are without sine

Hari Prasad

@user36790 what are you doing?

John Duffield

@HariPrasad no, there are no naked singularities inside event horizons. The event horizon is the singularity. People say it's merely a "coordinate singularity" that can be removed by choosing a different frame, but I'm confident that they're wrong. It all starts with time. You have to understand what clocks really do. See this. After that there's two simple steps.

ACuriousMind

@0celo7 Apparently so

user116211

20:01

@HariPrasad reading Nernst equation.

Slereah

Speaking of

ACuriousMind

@Slereah That might be the worst pun I have ever read.

Slereah

Do Lamé polynomials form a full orthonormal set

0celo7

@JohnDuffield lol

you clearly have not read any literature on singularities

Hari Prasad

@0celo7 that's naked science

Slereah

20:03

Einstein didn't approve of singularities

0celo7

Einstein was WRONG

Slereah

:O

John Duffield

@0celo7 : but I have read the Einstein digital papers.

Hari Prasad

XD

0celo7

@JohnDuffield lol

Slereah

20:04

Since I'm in Finland I'm getting finnish ads

0celo7

QED is wrong because I read the Democritus digital papers!

Hari Prasad

@JohnDuffield Do you think the current theory of general relativity is rubbish?

ACuriousMind

@Slereah Funny? Weird? Incomprehensible?

Slereah

@0celo7 Obviously atoms are held together by tiny hooks

So sayeth Democritus

Hari Prasad

@Slereah lol

0celo7

20:05

Holy shit I didn't notice 2 Chainz dropped an album

Slereah

IIRC the oldest book on EM is from the 16th century

I think it was called De Magnete or something

De Magnete

De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth) is a scientific work published in 1600 by the English physician and scientist William Gilbert and his partner Aaron Dowling. A highly influential and successful book, it exerted an immediate influence on many contemporary writers, including Francis Godwin and Mark Ridley. == Contents == In his work, Gilbert described many of his experiments with his model Earth called the terrella. (Previously, it was thought that Polaris or a large magnetic island at the North...

Yep

Hari Prasad

@0celo7 What does "Holy shit" mean?

Slereah

De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure

0celo7

@HariPrasad Seriously?

Hari Prasad

@0celo7 yup

i need an answer

ACuriousMind

20:06

Learn to use google :P

John Duffield

@HariPrasad : no. I think General Relativity is one of the best-tested theories we've got. See Clifford M Will's paper. But I also think there are authors who don't understand it, and who have taught others a version of General Relativity that is in some respects wrong.

Slereah

It is odd that he wrote a book about both electricity and magnetism 200 years before the two were linked

Although of course he did not link them in the book

It's just a book about weird attractive forces

0celo7

Wow Gotta Love is already shit. Autotune and nonsensical lyrics.

Slereah

"Previously, it was thought that Polaris or a large magnetic island at the North Pole attracted the compass"

"Gilbert also made the claim that gravity was due to the same force and he believed that this held the Moon in orbit around the Earth."

Already he unified gravity and EM

Kaluza Klein

Hari Prasad

@JohnDuffield Does magnetic monopoles exist?

user116211

20:08

@HariPrasad Even if exists, it would be very rare.

Slereah

Current theory of QED predicts the possibility of magnetic monopoles, anyway

Depending on the initial conditions of the universe

But so far, no magnetic monopoles, no cosmic strings and no domain walls

Well, not quite true

Those exist within solids

Hari Prasad

@Slereah i need an answer from a Relativist

Slereah

But no fancy QFT topological defects

It is fun for a while to poke JD but you'll get sick of it pretty fast

Worst part about topological defects is that you can't make them in a lab

ACuriousMind

Stop starring those messages, whoever it is. Having the whole star wall full of slightly derogative comments serves no purpose.

6

Slereah

Since topological defects are associated with a conserved charge

Well, not exactly true

Some topological defect are not from exact symmetries

Hari Prasad

20:13

Good night.

Slereah

Also I think I found out why some people claim that topological defects are nD structures

In the pop science

John Duffield

@HariPrasad : no. Because the E=hf photon is a singleton electromagnetic wave, not an electric wave, and we create charged particles out of electromagnetic waves in gamma-gamma pair production. Then the electron has an electromagnetic field. So electric charge is a misnomer, so magnetic charge is misguided. Particularly since it demands a rotating region of space, which can't happen because space is continuous.

ACuriousMind

What's an "nD structure"?

Slereah

It's because there is an approximation method by which they can be described

You know, cosmic strings as 1D structures

Domain walls as 2D

Etc

Real cosmic strings are nowhere close to 1D but you can approximate them by the Polyakov action

To first order

Same goes with magnetic monopoles or domain walls

0celo7

@JohnDuffield you do know electric/magnetic charge has a precise definition in terms of the Faraday tensor, right?

ACuriousMind

20:19

@Slereah Well, a monopole as a topological defect is well-localized in the sense that e.g. a BPST instanton has a clearly defined center out of which the "current" belonging to the topological charge flows.

Slereah

Well sure but a Gaussian also has a well defined center

Doesn't mean much!

It's no Dirac tho

ACuriousMind

@Slereah No, it's really well defined in the sense that the topological charge is 1 if you include that point in the integration over the Chern-Simons current and 0 if you don't.

Slereah

Hm

Well yeah the same is true for domain wall, I suppose

Still I wouldn't call them 2D structures

There's no discontinuity in the field or anything

user116211

@0celo7: @HariPrasad: @Slereah @ACuriousMind: o/ Bye.

John Duffield

@0celo7 : I know that the Faraday tensor is "a mathematical object that describes the electromagnetic field in space-time of a physical system". So what? I also know that "the electric and magnetic fields are better thought of as two parts of a greater whole - the electromagnetic field".

0celo7

20:22

@JohnDuffield So what? The electric charge is $\int_{S^2}\star F$ and the magnetic charge is $\int_{S^2}F$

ACuriousMind

@Slereah You might just have a different expectation of what is a "structure" than others

Slereah

Well I have Einstein and the evidence

When did topological defect appear, anyway

The study of it, I mean

Let's see

At least 1977

ACuriousMind

Perhaps in the '80s with 't Hooft's study of instantons?

0celo7

> The Holographic Ricci Dark Energy and Its Possible Doomsdays

Most ominous article title ever

Slereah

@0celo7 : I've seen worse

Plenty of big rip articles have fun doomsday titles

Also things related to vacuum collapse

Apparently Goto's original paper was "Relativistic Quantum Mechanics of One-Dimensional Mechanical Continuum and Subsidiary Condition of Dual Resonance Model "

ACuriousMind

20:31

Goto's original paper for what?

Slereah

The string action, I assume

0celo7

dual resonance was the historical name for string theory

Slereah

Not directly related to topological defects, tho

Damn, string theory is that old?

That paper is from 71

0celo7

Dual resonance model

In theoretical physics, a dual resonance model arose during the early investigation (1968–1974) of string theory as an S-matrix theory of the strong interaction. It was based upon the observation that the amplitudes for the s-channel scatterings matched exactly with the amplitudes for the t-channel scatterings among mesons and also the Regge trajectory. It began with the Euler beta function model of Gabriele Veneziano in 1968 for a 4-particle amplitude which has the property that it is explicitly s-t crossing symmetric, exhibits duality between the description in terms of Regge poles or of resonances...

Slereah

So many old models~

I remember the old timey weak interaction models

John Duffield

20:35

@0celo7 : please explain your expressions term by term. And please note that there is no such thing as a pure electric field. Somebody with no relative motion might say it's an electric field, but somebody with relative motion will say it's a magnetic field in part. This is because of the "screw" nature of the electromagnetic field. see Minkowski and Maxwell references here. Think twist and turn.

Slereah

Four fermion model, scalar vector, scalar tensor, scalar pseudo tensor, vector vector, tensor tensor, double trouble, truffle shuffle

0celo7

@Slereah holy crap, why is $\partial I^+(p)$ a null hypersurface

Slereah

I may have made up some of them

0celo7

I don't get it

ACuriousMind

I have yet to hear a good explanation of what a Regge trajectory really is

0celo7

20:36

@JohnDuffield no, I admit you're smarter than me

Slereah

Because that's the edge of the cone???

0celo7

you win

Einstein is right

Slereah

I dunno the proof

0celo7

@Slereah I see no reason why it should be a null hypersurface though

Slereah

@ACuriousMind Is that related to Regge calculus

0celo7

20:37

it's shown in HE that $\partial I^+(p)=\bigcup\text{future directed null geodesics eminating from $p$}$

Slereah

That sounds like the kind of theorem that you'd find in Penrose

You know

THAT penrose book

The HE before HE

Well wouldn't a surface of null geodesics be a null hypersurface

0celo7

@Slereah why?

Slereah

bc every point in it can be linked by a null curve?

0celo7

So?

ACuriousMind

@Slereah I...don't think so. It's to do with some masses running with the total angular momentum as straight lines or something, I never found a good explanation

0celo7

20:38

A null hypersurface is one with a null normal vector

@ACuriousMind total angular momentum in what frame though

I've never seen that explained

Slereah

Check penrose, mb

Sounds like the kind of theorem to be in it

ACuriousMind

But you often find statements like "A motivation for string theory was the phenomenon of Regge trajectories" and I'm like "??? You mind elaborating?" and the text/prof is like "nope".

0celo7

@Slereah ~~pirating~~ obtaining legally

Oh, ~~GR man~~ @JohnRennie

did I ask you the null cone thing

Slereah

I always buy my physics books at the physics store

And I give to the shopkeep flowers and a smile

John Rennie

@0celo7 No ...

Slereah

20:40

Thanks for the physics I say to the shopkeep

I will read this legally

0celo7

@JohnRennie why is $\partial I^+(p)$ a null hypersurface?

Slereah

Wait

You know where else you might find it?

THAT PAPER

You know the one

0celo7

link?

ACuriousMind

@0celo7 I'm telling you, the normal vector is just the null tangent. Like in the Minkowski case. You'll chase weird abstract definitions around for days only to find that that's it, I'm willing to bet

Slereah

arxiv.org/abs/gr-qc/0609119

^that paper

0celo7

20:42

@ACuriousMind ok, but how do you prove that??

Slereah

It's my favorite paper on the topic of spacetime topology and causality

John Rennie

@0celo7 $I^+$ as in the conformal infinity?

0celo7

I agree that it's true, @ACuriousMind

@JohnRennie no, chronological future

Slereah

Conformal infinity is the scri one

ACuriousMind

@0celo7 I have no intention of doing so. But here's a tip: You're attempting this too hasty. First: Why is the cone a codimension one submanifold at all, instead of just a jumbled mess of lines?

0celo7

20:43

@Slereah correct

@ACuriousMind Theorem in Hawking-Ellis :)

Also Wald.

ACuriousMind

Well, but if you know how to find the two other tangents, you might be able to show they're orthogonal to the null tangent!

0celo7

The boundary of the future of any set is a smooth codimension 1 submanifold

ACuriousMind

Saying "That is like that because of theorem" is not really a useful idea of a proof.

0celo7

@ACuriousMind I don't know how to find the two other tangents.

Slereah

Do you just go with gut feeling, @ACuriousMind

ACuriousMind

20:46

@Slereah Of whether or not the null tangent is the normal? Strictly speaking, yes, although it is true in Minkowski, and no other null vector can be orthogonal to it, so...if the cone is a null surface, the normal has to be the tangent.

0celo7

@ACuriousMind Well, it has to be true because the null vectors must be parallel

Slereah

I try to not go with gut feeling too much when I can

Because there are so many weird counterexamples

0celo7

so that just leaves the tangent to the geodesics

ACuriousMind

@0celo7 Well, then examine the proof of why the cone is a manifold to find out

0celo7

@Slereah but he's right in this case

Slereah

20:47

Of course I am p. bad at topology

John Duffield

@0celo7 : you will mean that once you understand that a "twist field" looks like a "turn field" if you're moving through it but don't know you're moving. Over and out.

Slereah

So I tend to go with gut feeling anyway

0celo7

@ACuriousMind ok

wait, it's not smooth

ACuriousMind

I don't guarantee it's there, but that is the first place I would look

0celo7

there is something about smooth submanifolds in one of these damn books

after a while the 50 theorems on spacetime topology start to blend

Slereah

20:49

But then you think you have a good gut feeling about something

And then a math guy will go

"What about this 37 dimensional manifold with infinite non-orientable handles!"

0celo7

lol

Slereah

And then you have to concede

By the way

0celo7

Ah!

@ACuriousMind I've proved it.

Slereah

A manifold with an infinite number of handles?

It is called a Loch Ness manifold

Because

0celo7

By Thm. 8.1.3 in Wald, $\partial I^+(p)$ is achronal. So it's either spacelike or null or some mix. If any part were spacelike, the normal would be timelike, which cannot be orthogonal to the null tangents. So it's null. $\Box$

Slereah

20:53

Did you know that the notion of mass from interaction dates ALL THE WAY BACK TO THE 19th CENTURY

0celo7

I think I have to justify the fact that achronal forbids timelike sections.

ACuriousMind

Congratulations, you have outsourced the part that was left to prove to some theorem :P

Slereah

It was part of the Lorentz ether theory that the mass of the electron was only due to the self interaction of the electron moving in its own magnetic field

This mass was

$E = \frac{4}{3} mc^2$

INTRIGUING ISN'T IT

0celo7

Ok, so a timlike hypersurface contains a timelike curve.

(Proof: can't be bothered, it's true.)

Slereah

IIRC you could get to $E = mc^2$ by adding a potential term to avoid the electron exploding

0celo7

20:55

lol

Slereah

Since you can't expect a spherical electron to hold together

It would blow apart under its own electrostatic repulsion!

0celo7

Ah!

Since the surface contains a timelike curve, and the future contains all the timelike curves, it contains a part of the surface.

So a timelike surface cannot be an achronal set.

@ACuriousMind Yup, proof complete.

@ACuriousMind That is how you prove stuff in GR.

Slereah

What about a timelike surface that is like

Slightly helicoidal?

Wait

I'm thinking of spacelike surfaces

0celo7

Any timelike surface contains at least one timelike curve.

Slereah

nvm

@0celo7 Well gee I hope so

Would be a weird name otherwise

0celo7

20:58

Proof:

Uh

Give me a moment for that one.

Slereah

Timelike surface is the one defined by a spacelike normal vector, right?

0celo7

Since the metric is Lorentz, pick any timelike vector field on the surface. Then draw the integral curve.

@Slereah yes.

Slereah

Then fuck I don't know

0celo7

so you're guaranteed to have a timelike vector field on the surface

and you can draw an integral curve of that vector field

Slereah

Sho'

0celo7

21:01

Ha, @ACuriousMind

My weird definitions worked out all right after all

@JohnRennie how do you like my proof

@Slereah Now how to prove that $I^+(p)$ is a future set...

Slereah

Isn't that its definition

0celo7

@Slereah Wait, isn't it true that $I^+[I^+(p)]=I^+(p)$?

Slereah

It is true, yes

0celo7

Proof?

Hmm, it should be trivial.

@Slereah Is $p\in I^+(p)$?

Slereah

I think it's just the proof that the junction of two timelike curves has endpoints that can also be joined by a timelike curve?

No.

Well, not necessarily

$p \in I^+ (p)$ means CTC business

0celo7

21:08

Right

Slereah

Basically that is the theorem I bothered you with a few months back

0celo7

Huh?

Slereah

With the geodesic trips and all

The proof that $p \rightarrow q$ and $q \rightarrow r$ implies $p \rightarrow r$

Hint : it involved THE NEIGHBOURHOOD

The hood

The Cauchy normal hood

Straight out of Cauchy

Semiclassical

22:08

@ACuriousMind fyi, here's the question as i posted it: math.stackexchange.com/q/1692164/137524

0celo7

22:52

@Slereah FWIW, my advisor said HE's proof of the Godel thing makes no sense

He also said Godel's proof is either wrong or not precise enough

0celo7

23:20

@Slereah if you're around, can you send me the link to Godel's original paper please?

0celo7

23:41

ignore ^ I found it.

NeuroFuzzy

@ACuriousMind I find this slightly derogative.

ACuriousMind

@NeuroFuzzy :P

0celo7

@ACuriousMind Welp, reading Milnor over the summer

Will have to turn in detailed summaries each week

And have discussions with the prof

@ACuriousMind can you lend me your brain

Or just the topology part

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