The h Bar

@EmilioPisanty I don't know if I'd say that. I think a good picture shouldn't be cranked out in 30 minutes - but most of the time is spent figuring out what you want the picture to look like, not actually implementing it. For a lot of diagrams TikZ isn't really much slower than an graphical editor.

Danu

@yuggib You clearly have no idea about (low-dimensional) geometry ;D

yuggib

@Danu I have an idea, and hence the reason why I am saying to avoid it ;-D

Emilio Pisanty

1:58 PM

Anyone around with Mathematica chops?

David Z

@EmilioPisanty a little bit

why?

Slereah

2:13 PM

B)

Emilio Pisanty

@DavidZ Trying to puzzle out what's going on here

Show[{
DensityPlot[Sqrt[(x - 1)^2 + y^2], {x, 0, 2}, {y, -1, 1},
ColorFunctionScaling -> False,
ColorFunction -> Function[r, Directive[Black, Opacity[1 - r^4]]]],
Plot[5 Sin[x + 0.4], {x, -4 \[Pi] - 0.4, -0.5},
PlotStyle -> {{Darker[Red, 0.2], Thickness[0.01]}},
PlotRangePadding -> Scaled[.1]] /. {Line[x__] :>
Sequence[
Arrowheads[{{.02,
1, {Graphics[{Thickness[0.01],
BezierCurve[
3 {{-1, -0.5}, {-0.7, -0.2}, {-0.3, -0.07}, {0,
0}, {-0.3, 0.07}, {-0.7, 0.2}, {-1, 0.5}}]}], 0.1}}}],
Arrow[x]]}
}

where if I remove the blob

Show[{
Plot[5 Sin[x + 0.4], {x, -4 \[Pi] - 0.4, -0.5},
PlotStyle -> {{Darker[Red, 0.2], Thickness[0.01]}},
PlotRangePadding -> Scaled[.1]] /. {Line[x__] :>
Sequence[
Arrowheads[{{.02,
1, {Graphics[{Thickness[0.01],
BezierCurve[
3 {{-1, -0.5}, {-0.7, -0.2}, {-0.3, -0.07}, {0,
0}, {-0.3, 0.07}, {-0.7, 0.2}, {-1, 0.5}}]}], 0.1}}}],
Arrow[x]]}
}
, PlotRange -> All
]

The arrow goes back to normal

David Z

By "normal" you mean without the dark tips on the ends?

MathsIsHard

IS anyone here good with force balances? (newtonian mechanics)

Emilio Pisanty

@DavidZ Yeah

Also the tip sharpens properly

Didn't come out in the previous one for some reason

David Z

Hm, my knowledge doesn't cover that

Emilio Pisanty

2:23 PM

Why would adding graphics change how the arrow looks?

I'm just completely baffled

David Z

Yeah, that's weird

ACuriousMind

@Slereah Relevant SMBC

@yuggib I second that

Slereah

2:42 PM

What are the non-perturbative methods in QFT anyway

There's LFT

There's the Dyson thing

books.google.fr/…

Hm

Might be cool mb

Though it's one of Those books

Just a string of unrelated papers

amazon.com/Classical-Solutions-Quantum-Field-Theory/dp/…

mb this

Why are most instantons about vacuum solutions, though

There are non-vacuum soliton solutions!

amazon.com/…

also this mb

Slereah

3:11 PM

vzn

@Slereah did someone say solitons? =D

Slereah

solitons indeed!

What soliton is your favorite soliton

I like $\text{dn}(px+\theta, \frac{1}{\sqrt 2})$ because it's a solution to $\varphi^4$ theory

vzn

not an expert but think they might be an awesome GUT candidate! have been tracking the area (loosely) for decades

Slereah

Aren't solitons just a class of solutions?

instead of a theory

vzn

@Slereah nobody sees it as a unifying theory yet but have long thought it has massive potential.

imagine all particles as just "space solitons"!

Obliv

3:20 PM

@slereah do you know where 0celo7 has been lately?

vzn

anyway thx for posting weinberg ref hadnt heard of it. have a few others too. cant beat that for credibility/ status... alpha male getting into it, maybe where theres smoke theres fire... =D

Slereah

@0celo7 has been banned for a month

That's another Weinberg

Obliv

wow.. that's so shitty. rip

vzn

@Slereah what?

Slereah

I assumed you're talking about Steven Weinberg

The book is from Erick Weinberg

vzn

3:24 PM

oops lol ok

ACuriousMind

@Slereah Strictly speaking, an instanton is not a soliton. The two are often related, but an instanton is a classical Euclidean solution, not a solution of the Lorentzian field equations. One cares about "vacuum solution" instantons because they represent natural starting points for perturbation theory

Obliv

Is it possible to define a square's area as the perimeter of the square divided by two multiplied by the distance from the end to the center squared (that would vary so it would be differential I think)

vzn

@ACuriousMind think there is some overarching theory for the variants waiting to be uncovered

ACuriousMind

@vzn I have no idea what that sentence is supposed to mean

vzn

@ACuriousMind lol sigh ok

ACuriousMind

3:26 PM

There is an "overarching theory" in many cases, it's called "topological invariants"

AngusTheMan

Sorry to interrupt, with what may be a stupid question, but when we talk of manifolds etc ... what underlying topology do we assume?

natural ?

Slereah

Canonical topology

ACuriousMind

Both instantons and solitons generally are some representants of non-trivial topological invariants, or at least of something "stable against perturbation".

Slereah

Basis of n-balls in $\Bbb R^n$

vzn

topology theory has some potential for generalizing/ abstracting it but am thinking of another approach

Secret

3:27 PM

I will get back to this later, as von neumann is needed to ensure I don't intepret this wrongly
http://science.sciencemag.org/content/352/6284/441

Slereah

The topology in $R^n$ induces a topology in the manifold via the atlas

ACuriousMind

@AngusTheMan By definition, a manifold is locally homeomorphic to $\mathbb{R}^n$ with the standard topology (e.g. induced by the usual Euclidean metric). Nothing further is assumed.

AngusTheMan

Thank you, that clears everything up :D

@ACuriousMind Does this happen to change depending on additional structure we endow the manifold with? e.g Symplectic .... etc

ACuriousMind

@AngusTheMan Well, no, the definition of a manifold doesn't change. However, e.g. the existence of a symplectic form of course puts restrictions on the manifold

(The most obvious restriction is that it has now even dimension)

AngusTheMan

I see now, many thanks chaps :)

vzn

3:36 PM

@Secret so you are tracking bell stuff? lots of recent news in area... try this one, am about to write some of this up phys.org/news/2015-05-quantum-emulated-classical.html

Jan 16 at 22:05, by vzn

> And therefore as a stranger give it welcome.
> There are more things in heaven and earth, Horatio,
> Than are dreamt of in your philosophy.

Noah P

4:05 PM

@Slereah @ACuriousMind @JohnRennie Anyone about for a further chat on Hawking radiation?

John Rennie

@NoahP Hi Noah

Noah P

Hi!

John Rennie

What did you want to ask?

Keep these mind

quantamagazine.org/…

Noah P

I'm quoting a general relativity textbook here

"Even the zero-energy vacuum of empty space exhibits quantum fluctuations in which anti-particle and particle pairs are created with tiny separations only to annihilate a tiny time later. Energy conservation prevents such fluctuations persisting in a flat spacetime."

John Rennie

4:10 PM

What text book is that?

Noah P

Gravity: An introduction to einsteins general relativity

By James B Hartle

Keep these mind

@NoahP Note the "flat" bit.

Noah P

"However consider Vacuum Fluctations (VF's) that create a particle anti-particle pair in the vicinity of a black hole" Hang on, we're getting there...

John Duffield

@vzn : LOL, some people have some catching up to do!

Noah P

"If the region is small enough, the geometry is indistinuguishable from that of flat spacetime. In such a region, sometimes a VF will create a particle outside the horizon and an antiparticle inside (or vice versa)"

From what you guys told me earlier, this isn't the case?

Keep these mind

4:13 PM

@NoahP What is this? Are you live-reading a book for the Internet people?

Noah P

@Keepthesemind The text in quotes were directly taken from the book, yes

John Rennie

@NoahP that book is aimed at undergraduates, and while it's a noble effort to introduce GR at an undergraduate level it necessarily has to simplify some aspects of it. That description is not something you will find in any graduate level quantum field theory book.

Noah P

@JohnRennie Okay, thanks for clarifying

John Duffield

@JohnRennie : very diplomatic.

John Rennie

@NoahP Virtual particles don't really exist. That is, there is nothijg you could point to and say aha, there's a virtual particle.

Noah P

4:15 PM

@JohnDuffield We've established by now that I'm well below this level - I don't mind this being stated!

@JohnRennie Okay. It is VERY frustrating that even Hawking himself (A brief history of time) uses this analogy

John Rennie

There is an energy density associated with the quantum vacuum, and it is generally calculated by modelling it as a sum of lots of different virtual particles. However these virtual particles are a mathematical device - theu are not real particles.

@NoahP because the real explanation is utterly impenetrable for anyone but quantum field theory experts.

Keep these mind

@JohnRennie Huh? Why would you find GR in a (graduate level) QFT book?

John Duffield

I do.

Secret

@JohnRennie The question is, why does this sum work, is it because the math theorem that ensure it will always converge to the energy density of the vacuum?

ACuriousMind

@NoahP Well, it's kinda the point of an analogy that it doesn't actually describe what is going on, and what is "actually" going on can only be expressed within the mathematical framework of quantum field theory. So, while I am annoyed by the pervasiveness of these analogies, I kinda see their point.

Noah P

4:18 PM

@JohnDuffield I'll do so now!

@ACuriousMind Are there no analogies that are horrificly incorrect then?

aren't*

ACuriousMind

I know of none

John Rennie

In QED it converges because each successive sum in the expansion is a factor of $\alpha$ smaller then the previous one, where $\alpha$ is the fine structure constant and is approximately 1/137. So the higher order terms fall away quickly.

ACuriousMind

That is not to say they don't exist, but no one seems to have found one that lets you actually usefully reason about the actual physical situation

Keep these mind

Analogy

Analogy (from Greek ἀναλογία, analogia, "proportion") is a cognitive process of transferring information or meaning from a particular subject (the analogue or source) to another (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises or the conclusion is general. The word analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily...

John Rennie

@NoahP search first as a question like this may well already have been asked.

ACuriousMind

4:20 PM

@JohnRennie It doesn't converge ;) All perturbative expansions are necessarily (well, there's at least a good argument for this) only asymptotic.

Keep these mind

@ACuriousMind What is the good argument? Is it perhaps an analogy?

John Rennie

Ok it appears to converge at first :-) I recall seeing an estimate of when the terms start to diverge, and while I don't recall the details it's not something that's going to be troubling us any time soon :-)

@Keepthesemind I think it was Freeman Dyson first predicted the expansion must eventually diverge

ACuriousMind

@Keepthesemind No. If the perturbation series converged, it would converge inside a radius of convergence, which, since we expansion is around zero coupling, would imply the series converges for negative coupling. But a negative coupling theory is utterly pathological (it creates cascades of particles out of the "vacuum"), it's not a well-defined theory at all and shouldn't have convergent perturbation theory.

John Rennie

@Keepthesemind See for example:

lassp.cornell.edu/sethna/Cracks/QED.html

Noah P

Question posted @JohnDuffield @JohnRennie

Keep these mind

4:26 PM

@JohnRennie Thanks!

ACuriousMind

@NoahP Please note that JohnDuffield's utterances generally do not reflect mainstream physics viewpoints, and tend to be completely wrong when it comes to quantum field theory.

Noah P

@ACuriousMind Ouch

amazon.co.uk/Aloe-Pura-Organic-Vera-Gel/dp/B0017TPE7C

John Rennie

4:43 PM

@NoahP I'll struggle to look at this tonight, but I'll try to have a think about it over the weekend. I am unconvinced there is a good explanation that can be given to someone who hasn't studied QFT.

Noah P

Okay, thanks @JohnRennie

Slereah

An intuitive model would most likely involve particles but the explanations behind the Unruh effect and Hawking radiation is very much the fact that particles aren't really a good fundamental thing

Noah P

@Slereah I'm not sure I follow?

Slereah

Well part of the problem is that in general relativity, particle number is a relative notion

In one frame, you may see no particles at all

Secret

Slereah

4:49 PM

And some particles in another

Noah P

Okay

John Rennie

NB these are real particles not virtual ones

Slereah

That's because in the end, particles are just an approximation in quantum field theory

Noah P

right

Secret

@Keepthesemind
The idea of a middle ground is pervasive. A lot of system seemed to achieve optimum far away from its endpoints.

In some sense, it often explains why researches in multi diciplinary fields are often more effective than the same research done by a single research field (probably because of pooling of resources)

Not sure if my experience reflects the actual situation though, for I do know some well know systems where the optimum is at the extreme scenarios

Slereah

4:52 PM

I guess the closest classical equivalent is...

I vaguely recall something in Feynman's book about the ambiguity of EM radiation in GR

About a charge in an accelerated frame

And he asks the question of whether an EM wave is dependant on the frame

Keep these mind

@Secret "researches in multi diciplinary fields are often more effective than the same research done by a single research field" Is there actually any convincing evidence for that?

Secret

@Keepthesemind which is why I am not sure, and I stress what I said above is based on my experience

But I do notice that in this century there are a lot of collabrations between different disciplines in solving problems

and it seemed to be a growing trend

Keep these mind

@NoahP Usually, a good explanation of a phenomenon at a certain level will be kinda totally wrong on a deeper level. That's the point of the deeper level. But 'we' still tend to accept the less-lower level explanation if it follows from the less-lower level theory.

@Secret What kind of problems?

Noah P

@Keepthesemind I was hoping for an explanation that would at least be acceptable at undergraduate level

Is that what you're referring to?

Keep these mind

@NoahP What I meant is that if there is an explanation at QED and GR level, then there is no real necessity to go further to QFT. (Like Newton is enough to explain an apple falling. No real need to involve Einstein.)

Slereah

5:02 PM

QED is QFT

Noah P

@Keepthesemind That would work for me!

Keep these mind

But I could be wrong, or rather, more knowledgeable people could disagree.

Secret

@Keepthesemind within the domain of science you ahve e.g. hydrogen production which involve engineers (to fabricate the electrodes, membranes and the cell), chemists and material scientists (to understand the chemical reactions involved and how the materials change when subjected to different environments), physicists and computational scientists (to model the performance of the system, the energy flow), the industry (what are the key issues to be addressed),
land users and the government (where to install the system), managers (integration into the grid, maintainence and labour etc), busin…

Keep these mind

@Slereah What are you saying? I know QED and know sh*t about QFT. You're saying they are the same?

Slereah

QED is QFT for the electromagnetic field

Keep these mind

5:04 PM

@Slereah I feel a lot smarter suddenly.

Secret

http://www.theguardian.com/artanddesign/2011/aug/21/collaborations-between-artists-and-scientists

@Keepthesemind and for arts x science, how artwork is frequently used to illustrate structures of biological entities, mathematical objects, physics phenomenon, which not only it is aesthetic, but allow scientist to gain further insights

Slereah

Either that or you don't know QED as much as you think :p

Secret

Keep these mind

@Slereah Could be. :)

Noah P

@ACuriousMind I've noticed a lack of activity since this...

Secret

5:08 PM

So I am guessing that as long those things that are true does not outrightly kill us, they effectively don't exist under the evolution pressure

Slereah

Oh true things that can kill us can also exert no pressure

If there is no alternatives that can be reached realistically

John Rennie

@NoahP I wouldn't pursue this subject if I were you ...

Obliv

guys how is the area of an ellipse $\pi a b$ ? if you multiply $a$ and $b$ don't you get a rectangle that has a greater area than the ellipse?

oh wait they are radii not diameter nvm'

Slereah

@Obliv $a$ and $b$ are half-lengths

The rectangle will only cover a quarter of the ellipse

Noah P

@JohnRennie Ah. I see.

Keep these mind

5:23 PM

@Secret I think that is nonsense. Yes, it also helps that physicists can use Word or Latex or Excel or computers or cars or whatever. That's hardly a contribution that 'counts' in a normal sense of doing physics. Or am I wrong?

Slereah

It's not like physics diagrams are that artistic

vzn

in theory salon, 8 mins ago, by vzn

$1B EU QM computing initiative + QM theory/ applied highlights Q1 2016 / Tmachine blog

↑ @Secret @FenderLesPaul @Martin @ACuriousMind =D

Secret

sciencedaily.com/releases/2016/04/160420111231.htm

vzn

5:55 PM

in theory salon, 21 secs ago, by vzn

The Quantum Computer Puzzle / Kalai, notices AMS

Secret

vzn

there was some earlier rejection around here of the idea of kuhnian paradigm shifts eg in all scientific fields incl esp mathematics, a thesis intermittently advanced by me somewhat. some "new/ old" material apropos to that

Secret

@Keepthesemind Ok here's a better one, where a designer and an artist is involved
http://www.echromi.com/

@Slereah edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0003oo

Slereah

yeah in real papers you don't really care about their artfulness :p

You just use the Latex library to make them

Secret

@Slereah Yup I understood that. I am just showing how there are so many examples where art crosses with science

@Keepthesemind If echromi is not striking enough microbialart.com (you literally cannot draw with bacteria wihout at least have some degree of understanding of their habits)

I an happy if someone can provide me a nice example in the recent decade where a pure field made great advances

because it is always nice to prove myself wrong

as it expand my view

I don't much problem letting go of realism, because I simply shift the realism to another level, by treating the wavefunction as a real object like a bunch of empty cabinets with only instructions saying how probabe is this cabinet contain that outcome, and that measurement is kinda like randomly selecting outcomes from this cabinet

and it is so far so good since wavefunctions evolve determinstically

thus pretty much kinda independent from the 'outside'

If you want anyone to believe that quantum has somehting to do with consciousness, you need to be able to wrote equations with the mathematical formalism and get consciousness as a result. But we don't even be ure what is consciousness

(REALLY hate that the editing expires so quickly, breaking my messages into pieces) and since it is commonly said that wavefunctions are only mathematical construct, I can easily shift back into the mainstream view by pretending to agree that the wavefunction is not real and do shut up and calculate as usual.

No experiments will be able to detect the difference between these two views, I claimed (to be tested)

The von neumann reading will help me to check whether my current interpretation will ultimately lead to contradictions with the experiments that will force me to abandon it

and only then, I will simply accept that to not waste time on trying to interpret quantum states

>Currently testing my understanding with this example:
https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_Mermin-Peres_magic_square_game

Slereah

7:11 PM

Hm

Let's see all the cheap physics books I have in my wish list

And do a bulk order

user507974

@Slereah you should post your list

im waiting on my LL stat mech to ship

Secret

https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_Mermin-Peres_magic_square_game

I cannot seemed to get $S_z \otimes I$ to commute with $I \otimes S_Z$ because I get $$\begin{pmatrix}S_z & 0 \\ 0 & S_z\end{pmatrix}$$ and $$\begin{pmatrix}I & 0 \\ 0 & -I\end{pmatrix}$$ respectively

What have I done wrong in calculating it?

Slereah

Let's see

Cheap ones are like

amazon.com/dp/0521260825/…

amazon.com/dp/0306423677/…

amazon.com/dp/0880292512/…

amazon.com/dp/0486469344/…

amazon.com/dp/0199680299/…

amazon.com/dp/0262028131/…

amazon.com/dp/0691037698/…

amazon.com/dp/3642118968/…

I could probably buy them all

Altho shipping might be a bit much

Slereah

7:47 PM

ouch

Shipping is a bit much

$24 per book

neverfuckingmind!

I'll try to find them on Amazon Fr

vzn

8:06 PM

oops got interrupted re this

2 hours ago, by vzn

there was some earlier rejection around here of the idea of kuhnian paradigm shifts eg in all scientific fields incl esp mathematics, a thesis intermittently advanced by me somewhat. some "new/ old" material apropos to that

Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World / Gerovitch, Alexander, notices AMS

think there have actually been many such "paradigm shifts" in math history but the "moving the goalposts" and "2020 hindsight" phenomena/ psychological bias tends to obscure them

Danu

8:30 PM

@Slereah Perhaps don't post such a long list of big amazon-links in the future, please.

user54412

physics.stackexchange.com/a/251369

3

user54412

^ A real LIGO-associated person who keeps giving great gravitational wave answers

Danu

Nice @ChrisWhite :)

Joe Stavitsky

I'd like to build a system that uses a small matrix of color-changing usb leds to project an enlarged rectangular image some short distance (<40 cm), but my optics-fu is weak. Where is it recommended that I start googling?

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