The h Bar

1:21 AM

👍

1:55 AM

@0celo7 "the final solution" :( not something to joke about (for anyone with empathy) eh? dailymail.co.uk/news/article-5227677/…

vzn

2:23 AM

oh yeah and that reminds me of this! o_O psychologytoday.com/blog/born-love/201005/…

0celo7

Turns out if you leave potatoes in the cupboard for a month they liquify and produce a smell that can kill a small cat.

Captain Bohemian

2:43 AM

have never had experience with potatoes but kiwis, which put uneaten over one month liquify and taste rotten.

Sir Cumference

3:25 AM

Hey

Anonymous

4:19 AM

@Mithrandir24601 What type of noise are they talking about when they say "Unfortunately for analog computation it turns out that when realistic assumptions about the presence of noise in analog computers are made, their power disappears in all known instances; they cannot efficiently solve problems which are not solvable on a Turing machine." (in Nielsen & Chuang)? Looks like they're speaking of thermal noise, but I'm not sure

Sir Cumference

4:36 AM

Vending machine gives me $3 worth of nickels, a bunch of pennies and then gives up on giving me the rest of my $5...

0celo7

@Slereah springer.com/us/book/9783540070115

Balarka Sen

4:52 AM

ＳＰＡＨＧＥＴ．ＭＰ４ 🍝🍝🍝

►

This is my spirit beat

ooolb

5:19 AM

@BalarkaSen you said you don't listen to edm

Balarka Sen

Frank JavCee is beyond EDM

Cows

6:42 AM

Wanted to switch things up a bit. Building an interpreter(a basic one ).

Then might return to some physics study, then programming project

In other news, I think I now understand what Taylor expansions are. I mean I've been doing them for years, but someone told me something about someone who did something awesome that changed physics and now I think I know what a Taylor expansion is about lolz :P

ok ok back to my super simple intepreter. Need to tokenize now or something like that , then label stuff

still in parser stage

Slereah

8:16 AM

@0celo7 ew typewriter

Hm

The switch from $$\frac{d}{dt} \frac{\partial L}{\partial \dot q^n} - \frac{\partial L}{\partial q} = 0$$ to $$\ddot q^{n'} \frac{\partial^2 L}{\partial \dot q^{n'} \partial \dot q^n} = \frac{\partial L}{\partial q^n} - \dot q^{n'} \frac{\partial^2 L}{\partial q^{n'} \partial \dot q^n}$$ involves the use of the total derivative formula and all

But how do you do it for field theories

Where it's all partial derivatives

Do we have $$\partial_\mu F(\phi, \partial_\mu \phi) = (\partial_\mu \phi) \frac{\partial F}{\partial \phi} + (\partial_\mu \partial_\nu \phi) \frac{\partial F}{\partial \partial_\nu \phi}$$

Oh I guess it's just the chain rule

Mithrandir24601

8:32 AM

@Blue I don't think they're talking about any single specific type of noise here, but yeah, it would most likely be thermal noise, (although this is actually very general - you couple the system to a thermal bath, then the type of interaction determines the specific type of noise, to my knowledge - this is known as 'non-Markovian' noise). The problem in QC is that the above noise generally don't have any nice sort of scaling with the size of the thing

Slereah

8:58 AM

Man I'm having troubles with indexes

What is gonna be $$\partial_\mu \frac{\partial L}{\partial (\partial_\mu \phi)}$$

Is it $$\partial_\mu \phi \frac{\partial L}{\partial \phi \partial(\partial_\mu \phi)} + \partial_\mu \partial_\nu \phi \frac{\partial L}{\partial(\partial_\mu \phi)\partial(\partial_\nu \phi)}$$

Anything I come up with seems wrong

Secret

A new paper about using the many world interpretation to resolve the black hole information paradox

I am still reading it, so no comments yet, even though I did had one in the pipeline

Mithrandir24601

@Secret Like each black hole contains a universe? - I've heard of that before, but I don't know how seriously people it...

John Rennie

@Mithrandir24601 no

The idea is that information is conserved if you sum it across all the "many worlds"

But not that the many worlds doesn't actually mean there are many worlds

Mithrandir24601

@JohnRennie fair :P

John Rennie

It really means there are many relative vectors in the Hilbert space

Mithrandir24601

9:09 AM

(I haven't actually read the paper)

John Rennie

If you ever feel the urge to read a paper on interpretations of QM first you should do a few precautionary checks first. e.g. do your toenails need cutting? Have you hoovered the living room?

2

Slereah

Max Jammer is a pretty good source on QM interpretations

Although it's a bit old by now

I don't know what's a current reference on it

Mithrandir24601

@JohnRennie yep :) I need to make breakfast, finish a PhD in about 3 years-ish, then I've got ~250 books to read. At that point, assuming I don't have anything else to do, I'll have enough time to read it

John Rennie

:-)

Balarka Sen

9:28 AM

I see some physics stirring

Slereah

just wait for the caffeine to kick in

CooperCape

ola

Secret

10:13 AM

(finished reading)

Hmm..., if I understood correctly, the complementary view of a stationary observer seeing a stretched horizon while an inflating observer does not see anything weird at the horizon, and unitarity is preserved by black holes by having a global wavefunction consists of a superposition of black hole geometries, detector/observer states and the degrees of freedom inside and outside of the black hole.

In particular, the inflating observer inside the black hole and the stationary observer outside the black hole are located at different branches of the global wavefunction, where the former will see the inflating information get scrambled by the black hole, while the latter see nothing strange going on.

The hawking radiation emitted then serves to decohere these branches, thus this increase in the number of black hole and exterior environment spacetime geometries in the product state will then manifest itself as the black hole entropy

Or in other words, the black hole spacetime geometry, observers and any inflating information together forms a superposition, which is then decohere by the hawking radiation became entangled with the exterior environment as it escapes from the black hole

However I have two questions:

1. What about an infalling observer that is outside the black hole. Will the branches between it and the stationary observer be compatible (e.g. both seeing the state by using the information from their detectors as a nontrivial transformation of the interior state of the black hole which is the state of the stretched horizon)?

2. The models and the maths supported that by modelling the evaporating black hole geometry as a superposition of semiclassical spacetime geometries and then invoking decoherence, black hole complementarity, unitarity and the black hole entropy (in terms of bounds) are recovered, suggesting that the model indeed works. But suppose we managed to flew a space probe near a black hole, how can we test that it is indeed consists of decohered branches of a superposition of spacetime geometries,

that is, how can we distinguish this from other information paradox resolution models that does not invoke the global wavefuction (or an ensemble of spacetime geometries)?

The above are my thoughts after reading that paper for you guys to ponder about...

It would be interesting to somehow be able to keep a black hole in a superposition, then we can use diffraction experiments to show the existence of a superposition. alternately, we need to prepare many copies of such black hole with the same initial state, and then the information of our detectors should reveal some probability distribution of observables related to the nearby spacetime geometry that suggests the spacetime was once in a superposition before being decohered by hawking radiation

But either way, I like this idea of the superposition of spacetime geometries used in this paper

Slereah

11:26 AM

web.math.rochester.edu/people/faculty/doug/otherpapers/…

good cover

John Rennie

12:16 PM

@Kaumudi.H Done! :-)

user228700

Oops, didn't notice the ping :-)

Curio

1:13 PM

Is this a valid formula to calculate the period of a simple pendulum with large amplitude?

Slereah

Large amplitude pendulum are described by the Jacobi elliptic functions

The complete formula for it is rather complicated

Pendulum (mathematics)

The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations. == Simple gravity pendulum == A so-called "simple pendulum" is an idealization of a "real pendulum" but in an isolated system using the following assumptions: The rod or cord on which the bob swings is massless, inextensible and always remains taut; The bob is a point mass; Motion occurs only in two dimensions, i.e. the bob does not trace an ellipse but an arc. The motion...

for more details

John Rennie

@Curio yes, that's an approximation for when the amplitude is large but not too large

Curio

Is 60° okay?

John Rennie

@Curio you can check that for yourself

Slereah

Well, use the real formula, and compare

John Rennie

1:16 PM

The formula for the period can be written as a series expansion in the angle $\theta$

A fuller formula is given here

Slereah

60° probably is too large

You're gonna need about 8 terms of the expansion

John Rennie

The third term is $$\frac{11}{3072}\theta^4$ so see how that compares to the $\theta^2$ term.

NB you need to put the angle in as radians not degrees

Curio

@Slereah what is Tk?

Slereah

The formula of the period up to order $k$

Yours is $T_2$

as you can see it starts to get bad around 15-20°

at 60° it's almost 100% error

Curio

@JohnRennie what was that tool to read latex here?

John Rennie

1:20 PM

23

A: Any chance of MathJax in chat?

As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including: ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room. An altern...

Curio

what's k?

Slereah

The order

Curio

oh ok

what about T without subscript?

Slereah

That's the real period

Curio

ok

Slereah

1:23 PM

$$T=2\pi {\sqrt {\frac {\ell }{g}}}\left(1+\left({\frac {1}{2}}\right)^{2}\sin ^{2}{\frac {\theta _{0}}{2}}+\left({\frac {1\cdot 3}{2\cdot 4}}\right)^{2}\sin ^{4}{\frac {\theta _{0}}{2}}+\left({\frac {1\cdot 3\cdot 5}{2\cdot 4\cdot 6}}\right)^{2}\sin ^{6}{\frac {\theta _{0}}{2}}+\left({\frac {1\cdot 3\cdot 5 \cdot 7}{2\cdot 4\cdot 6 \cdot 8}}\right)^{2}\sin ^{8}{\frac {\theta _{0}}{2}} \right)$$

This is the formula you need

Or for short...

$$T=2\pi {\sqrt {\frac {\ell }{g}}}\left(1+\left({\frac {1}{2}}\right)^{2}\sin ^{2}{\frac {\theta _{0}}{2}}+\left({\frac {3}{8}}\right)^{2}\sin ^{4}{\frac {\theta _{0}}{2}}+\left({\frac {15}{48}}\right)^{2}\sin ^{6}{\frac {\theta _{0}}{2}}+\left({\frac {105}{2384}}\right)^{2}\sin ^{8}{\frac {\theta _{0}}{2}} \right)$$

Secret

Is it really finite or in full it is a power of sine expansion?

Slereah

It is an infinite series

Secret

figured

Curio

@JohnRennie @Slereah many thanks!

but why that subscript 0 next to theta?

Slereah

That's the initial angle

The angle at $t = 0$

Curio

1:42 PM

@JohnRennie why can't I always see the latex? For example I can see the last ones, but not yours " $$\frac{11}{3072}\theta^4$"

Slereah

because he inputted it wrong

The silly man

Curio

this site codecogs.com/latex/eqneditor.php reads it, I thought there were problems with my pc

Slereah

it does, but he put two dollar signs on the left and only one on the right

So Mathjax doesn't parse it

0celo7

2:19 PM

@Slereah what are you doing

skullpatrol

yo

Slereah

@0celo7 what u mean

Curio

@Slereah so in the image which you sent is k the maximum potence of sin?
You said that I'm in $$T_2$$ and in that formula there is $$sin^2$$. And in $$T_8$$ there is $$sin^8$$

Slereah

yes

Curio

nice, many thanks

Slereah

2:27 PM

Your formula uses the approximation $\sin \theta \approx \theta$

CooperCape

That's my favourite approximation.

Curio

@Slereah isn't that for small amplitudes?

0celo7

@Slereah why are these awful formulas up there

Curio

I mean, isn't $$sin(\theta)\approx \theta$$ used for small amplitude? Is 60° considered a small amplitude?

Slereah

@Curio yes, hence not a great idea

@0celo7 Pendulum

Curio

2:40 PM

Why then are we using that?

Slereah

We're not

you are

Curio

I am*

Slereah

I can't answer why you do the things you do

Curio

Is there an alternative to this formula then?

Slereah

The formula I gave is a correct formula

Curio

2:41 PM

but only for small amplitudes?

Slereah

It's correct for up to angles in the range 70-80°

10% error at 80°

John Rennie

@Curio ah, I made an error typing the Latex. There is a dollar sign missing. That's why it won't render.

Curio

Why did you say that the formula uses the approximation $\sin \theta \approx \theta$? Is 60° considered a small amplitude?

Slereah

I said that your formula does that

Curio

@Slereah do you mean this one?

Slereah

2:48 PM

@Curio I mean this one

Curio

ooooh misunderstanding

thanks again and sorry if I'm annoying

0celo7

3:20 PM

@Slereah yo

apparently if you write out the GR action relative to an ADM splitting, it's identically zero for any field config

that's much better than saying Gauss-Bonnet and hoping no mathematician is listening

Anonymous

@Mithrandir24601 I was wondering if they were referring to noise is a more generalized setting. Like even if we get rid of the conventional noise - like industrial noise, vibrational noise, thermal noise (or reduce them to negligible levels), still noise could refer to the uncertainties in amplitude, phase, etc, which arise due to the underlying quantum mechanical nature of the system.

Anonymous

The Turing machine concept doesn't take into account this type of noise, which is impossible to get rid of, in any practical scenario. But then again, we can't even totally get rid of the classical sources of noise - like thermal, vibrational, etc in any practical scenario.

Anonymous

However, I think I more or less get it now. Thanks

Slereah

@0celo7 Yeah

GR is all constraints

0celo7

for 1+1 I mean

Slereah

3:22 PM

o

I should try to prove the Gauss Bonnet thing someday

0celo7

for lorentzian spaces?

Slereah

yeah

0celo7

I would read that

that book I sent you seems interesting

Slereah

does it

What's it about

The few pages available aren't very helpful

0celo7

analytical mechanics for fields

Slereah

3:29 PM

o

Is it the Legendre bundle stuff

0celo7

symplectic banach manifolds

scary stuff

there's too much to learn

Slereah

that there is

You think you're doing good on a topic then you find out some 800 pages book on some aspect you've never heard of

I still don't know what instantons are

it's apparently pretty important

0celo7

@Slereah oh jesus christ this guy writes the metric as a series

you can do horrible things in physics

Slereah

3:45 PM

what do you mean

Like a Taylor series?

0celo7

like some weird exponential series with poisson brackets

Slereah

know what's awful tho

Non-commutative geometry

Captain Bohemian

@Slereah are solitons important compared to instantons?

Slereah

They are

Emilio Pisanty

4:22 PM

@Slereah could be worse

I got hit with "isn't your work just a derivative version of instantons" on PhD Student Presentation Day on my second year, while presenting imaginary-time approaches to tunnel ionization (as described e.g. here)

in the end, it isn't, but I'd never heard of the things

didn't look very good =|

Curio

@Slereah is that formula infinite, right? So are there infinite graphs which go from 0° to 180°?

A graph: error curve of $$T_k$$

John Rennie

4:38 PM

@Curio for $\theta > 90º$ the equation of motion will change again because the string will go slack. But yes the equation does have an infinite number of terms and yes with an infinite number of terms it describes the motion correctly for $-90º \le \theta \le 90º$.

0celo7

just cleaned up a salmonella outbreak

John Rennie

@0celo7 if this is more info about the functioning of your lower bowel I'm out of here! :-)

0celo7

@JohnRennie I had a leaky package of chicken that I threw in the freezer before the break. thought it would be easier to deal with when frozen

it was, but was still a nightmare

John Rennie

Ugh

Curio

@JohnRennie wait, what do you mean with -90°? Consider the pendulum motionless
, I mean it doesn't move. The wire of the pendulum forms two 180° angles, one right to the wire and one left. I mean, if the angle is 200°, it doesn't make really sense because truly it's 160°

0celo7

4:48 PM

@JohnRennie it was 6 packages of 2 breasts each connected by plastic bits but the leaked juice got everything stuck together

thankfully it was all in multiple bags so the freezer is safe

unless it was airborne

welp, rip me

John Rennie