The h Bar - 2016-04-12 (page 1 of 4)

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0celo7

00:02

@ACuriousMind Why?

Not a troll question, what is there to be gained from this?

ACuriousMind

@0celo7 What is there to be gained from studying manifolds?

0celo7

@ACuriousMind Don't answer a question with a question. It's like tu quoque but not.

ACuriousMind

@0celo7 Okay, then what there is to be gained is that you can indeed define many differential geometric concepts in categorial language and then these concepts extend to the diffeological spaces.

I think it's a notion of geometry guided by the "functor of points" approach of algebraic geometry. You think of a space as not being defined by its points, but by its maps into it, and in particular it is already defined by the maps from the objects it is "modelled on".

A scheme is defined by maps from affine schemes, and a manifold is defined by maps from open subsets of $\mathbb{R}^n$.

But when you just look at spaces modelled on $\mathbb{R}^n$ in this sense, you find there are far more of them than manifolds - and the diffeological spaces are a much nicer subcategory of these generalized smooth spaces.

Oh, now that I'm talking about it, @Danu, you asked for motivations on sheaves, here is a different one: A covering space $C$ of $X$ is a space with a local homeomorphism $\pi : C\to X$ where every fiber is discrete and the same. If you now just drop the restriction on the fibers, you get what's called an étale space, and in fact every sheaf on $X$ is the sheaf of sections of some étale space $\pi : E\to X$.

So you might say a sheaf is a "generalized covering space" or "a space that looks locally like $X$".

0celo7

00:29

What.

@ACuriousMind I'm assuming this has nothing to do with Riemannian geometry or geometric analysis :P

ACuriousMind

@0celo7 Well, it is relevant to what is called "synthetic differential geometry"

0celo7

00:54

@ACuriousMind What would that be

dmckee

01:25

Hey @commutatertot, clever name. Made me chuckle.

commutatertot

@dmckee thanks d:

dmckee

Good avatar, too, of course.

0celo7

@dmckee Huh

I never read people's user names

I just recognize them

I do that a lot, especially with Pokemon

I tend to memorize the shape of the word, not the actual content

2

4 hours later…

Danu

05:15

@ACuriousMind It's étalé space in this case, is it not (tricky, I know!). This is also in Forster's book.

David Z

05:50

@Qmechanic If it's gotten to the point where locking is warranted, I think it would make sense to have a meta question devoted to the fate of this specific question.

anna v

06:08

I think the question is more general :" is chaos a physics theory"? Then the mathematics as tools of chaos theory should be within the allowed topics, unless the question is not connecting with physics variables. If I see space and time in the variables, I assume one is modeling a physics problem, and there is space and time in the question's formulas :) .

David Z

OK, I see. It could be reasonable to have a meta question about whether the topic of the question qualifies as physics - or really, whether it's on topic at the site, so it'd be slightly more general than just this specific question.

skill patrol

06:23

in The Biosphere, 3 hours ago, by James

For anyone remotely biophysics-y, this is an interesting arxiv article that disputes 3 nature papers on magnetism in biology. http://arxiv.org/pdf/1604.01359v1.pdf

Take home message: at least try a little bit to properly quantify your hypothesis.

Slereah

07:10

I think I found the solution to that contour business

It's another case where I can switch $\vec p$ to $-\vec p$

With nary a trouble

Slereah

07:20

Though I still don't know where that factor of 2 comes from

I need to redo this srsly

2 hours later…

DanielSank

09:33

@ACuriousMind made progress.

I can now ask a new question:

The states of a single particle in a 1D potential (often harmonic oscillator) share a formal degeneracy with the states of a single mode of a quantized field. Is this degeneracy an accident or not?

ACuriousMind

10:07

@DanielSank No, it is not an accident. The free quantum field is a sum of uncoupled harmonic oscillators in Fourier space, hence its space of states is the sum of spaces of states of harmonic oscillators.

@Danu Yeah, I never get the diacritics right :P Then I have no further motivation to offer you

@DanielSank If by "formal degeneracy" you mean just that a single particle in a 1D potential has a countable number of energy eigenstates that you can map to those of the HO or those of a mode of a quantum field (sending the ground state to the ground state, the first eigenstate to the first eigenstate, etc.), then that's also true, but has no physical meaning

It is merely a consequence of all quantum mechanical Hilbert spaces being separable, meaning they all have countable Hilbert bases. Since the energy eigenstates fom a basis by the spectral theorem, you can map any two Hilbert space to each other in such a fashion

2 hours later…

0celo7

11:59

Guten moooooorgen

skill patrol

Vietnam?

Slereah

Hello

skill patrol

hi

Tomáš Zato

12:13

Is it ok to ask question regarding how my simulation behaves?

(I already asked, but want to make sure)

I implemented formula, and I don't like the results. I'm not sure whether the fromula is wrong or I am.

David Z

@TomášZato you can ask here in chat, for sure.

I'm not sure if that would be on topic on the main site.

ACuriousMind

I think he means this question

Tomáš Zato

Yes, exactly

I get some behavior and Im quite sure the code is correct, so I am afraid the problem is in my expectations or the formula used

ACuriousMind

Well...the answer already given is correct - you're trying to simulate a 3D collision with a 1D formula, that won't work. It's still a borderline question though, because one has to look at and understand your code to see what exactly the error is.

I'd prefer the question to be written in such a way that it can be answered without looking at the code.

Slereah

Oh boy

almost finished chapter 2 of Peskin

Only the questions left

skill patrol

12:22

how many are there?

Slereah

3 exercizes

EM field, complex KG and doing a propagator integral

David Z

@ACuriousMind okay, that's fine.

Secret

Hey guys I have a weird question:
What is our current most accurate illustration of a proton, i.e. if we are going to make an illustration of it, what illustration will be closest to what we know about quantum field theory and the standard model?

ACuriousMind

@Secret No illustration. You can't draw quantum states.

Secret

ok, I see

skill patrol

12:27

yet

Andreas Bonini

Hello, I'm a medical student and I'm studying the electric physiology of neuronal cells which can be considered an electrical system composed of a resistances and capacitors. The formula we were given to know the intensity of current (I) going in or out of the cell when the voltage (V) changes is: I = 1/R * (V1-V2) + C * dV/dt

However the 'd' notation has always confused me. Is dV the same as ΔV?

Can I write the formula as: I = 1/R * ΔV + C * ΔV/Δt ?

Tomáš Zato

@ACuriousMind I'll try to think how to edit it,

I did some deal of googling and I just can't find plain formula that gives you $$

that gives you $vx_a$, $vy_a$, $vx_b$ and $vy_b$ for inelastic collision of two objects

Isn't that a basic thing...?

ACuriousMind

You just have to think a bit about the formula, but it is not hard to derive.

David Z

@AndreasBonini not exactly. How much do you know about calculus?

Andreas Bonini

Nothing :/

Tomáš Zato

12:35

Neither do I. Quite frankly, I want to make a game, not do math

ACuriousMind

@TomášZato If you want to have a physically correct collision, you'll have to do a bit of math

Secret

$\Delta(something)$ means a small but finite difference. Usually for anything other than introductory physics text it implies $something_{final}-something_{initial}$

whereas d(something) is a infintesimal, which is the limit when the above $\Delta(something)$ tends to zero

d implies an instantaneous change. in you case, writing the above equation in terms of d will mean the equation holds for process that are very fast. Depending on what the equation describe, it may or may not be true

How fast is a typical neuron current?

Andreas Bonini

(Okay that was an exaggeration.. I have a lot of very vague notions we are sometimes randomly given)

David Z

@AndreasBonini In that case it might be a little difficult to explain. I would recommend learning the basics of calculus somewhere, at some point. But the idea is that if you make the difference denoted by $\Delta$ smaller and smaller, the ratio $\Delta V/\Delta t$ gets closer and closer to the thing that is meant by dV/dt.

Tomáš Zato

@ACuriousMind Why can't I just google up formula? :( Deriving formulas people have derived many times before costs me time that could be spent adding features and art to the game...

ACuriousMind

12:39

@TomášZato Oh, of course you can. I found how to proc a sphere-sphere collision with google in less than a minute.

Andreas Bonini

@Secret: the capacitive portion of the current is extremely fast, a fraction of a millisecond. i.imgur.com/Atg16hR.png

David Z

@TomášZato I edited out your code to make the question clearer. Since this is not a programming site, there isn't much need to have the code available.

Andreas Bonini

@Secret and @David: so to make sure I understood you correctly, 'd' is used when the change is very quick, while Delta is used when the change happens relatively slowly?

David Z

@AndreasBonini no, that's not really correct.

Tomáš Zato

@ACuriousMind Could you share your search query?

David Z

12:42

$\Delta$ is always used to represent a finite amount of change.

The $d$ is used for something else. Actually, you should think of $\frac{\mathrm{d}}{\mathrm{d}t}$ all together as one notation representing "rate of change".

ACuriousMind

@TomášZato Here.

Secret

only for expressions involving $\Delta t$ or $dt$ will the rate of the process that lead to the change came to play, as David Z elaborated

David Z

It just happens that when $\Delta t$ is very small, the ratio $\Delta V/\Delta t$ is very close to the rate of change of $V$.

Andreas Bonini

(Why is latex not displaying correctly? I see $\etc which is making it very difficult for me to understand what you're saying :( )

Secret

(@David Z, correct me if I am wrong)
@AndreasBonini For your equation
If whatever process that depends on the neuron current took at least an order of magnitude longer than a ms, then d might be a good enough approximation

ACuriousMind

12:45

@AndreasBonini Follow the link in the upper right corner of the chat room to activate ChatJax.

David Z

@Secret did you mean "...then $\Delta$ might be a good enough approximation"?

In any case, that might be true in practice.

0celo7

@skillpatrol What

David Z

The important thing is that you "zoom in" on a small enough region (of width $\Delta t$ and height $\Delta V$) that the function is nearly a straight line.

0celo7

It's what we used to say in the Grundschule when the teacher entered

@ACuriousMind Have you heard of the company Merck?

Secret

@DavidZ Yes you are right, I got that back to forth by accident

ACuriousMind

12:50

@0celo7 Yes, why?

Secret

Merck makes chemical reagents

0celo7

@ACuriousMind I think I need to procure a German phone number for them, but I can't access the .de webpage.

Ack, Petersen still can't be bought. Why, Springer?

ACuriousMind

@0celo7 ...what?

0celo7

@ACuriousMind They won't supply a certain chemical in the U.S. I've been tasked with ordering it and sending it to Darmstadt U and a colleague there will send it to us.

David Z

gist.github.com/bassup/93f78c0fac2a7be25086

3

Speaking of ChatJax, it reminded me, I use a userscript that does it automatically:

Secret

12:53

user image

0celo7

@Secret How the hell

Secret

this? and what chemical is that

0celo7

@Secret Can't tell you, it's new research.

Secret

ok

0celo7

@Secret It has a metal in it.

Oh, there we go.

It's msd.de

Huh

@Secret Danke

Andreas Bonini

12:55

Okay, I think I sort of understood it... Thanks!

Secret

hang on...

0celo7

Wait what

The German site is a medical stuff place

Valentin Tihomirov

I see that large magnet orients the small ones when they are placed into its field. Yet, stern-gerlach says that they should be simply deviated. Why is the contradiction?

0celo7

Is this even the right place?

This is a place for medical supplies o.O

Secret

I am actually wondering, isn't merck's logo blue, (I am searching again now...)

0celo7

12:58

Why would they have high grade esoteric chemicals

Secret

From my memory, Merck made a lot of metal complexes
It's kinda the opposit to sigma aldrich ,whcih make a lot of organic compounds

0celo7

@ACuriousMind How do I type out CaF in German?

@Secret ^ one of the chemicals

Loong

@Secret merck bought sigma aldrich

Secret

@Loong O, that I did not know, my experience came from my part time in an environment testing lab 2 years ago

Loong

@Secret ok, and yes, the logo was different then

Secret

13:02

user image

0celo7

@ACuriousMind Calciumfluorid?

Loong

merckgroup.com/en/media/…

@0celo7 do you mean CaF2?

0celo7

@Loong Yes, but that doesn't change the name.

Loong

@0celo7 in German: Calciumfluorid

0celo7

59 secs ago, by 0celo7

@ACuriousMind Calciumfluorid?

Well, looks like they don't sell it. And I don't know why they would, I can't find anything but pharmaceuticals on their webpage.

Loong

13:04

@0celo7 However, in colloquial language, you can still find Kalzium…

Secret

user image

i did not know it has so many susiderie back then

0celo7

Ah!

Merck Chemicals

There we go

Loong

@0celo7 Sigma-Aldrich has it: sigmaaldrich.com/catalog/substance/…

0celo7

@Loong Sadly not enough 9s in the purity for what we want

> Calcium fluoride, puriss., meets analytical specification of DAB, 99.0-102.0%,

102%?

That's some high grade shit

Loong

:-D

Secret

13:13

102%?, that does not sound right since it is >1 in terms of yield

0celo7

Keine scheiße

Loong

That's because of the uncertainty of the used analytical method.

Secret

ok

Loong

@0celo7 How pure do you need it?

0celo7

@Loong 99.999

skill patrol

13:14

can't you make it yourself?

0celo7

Apparently our German colleagues get it that pure.

@skillpatrol Not at 99.999.

skill patrol

what can you make it at?

0celo7

@skillpatrol I don't know.

We can get it at 99.99 in the US

But the prof said that's not good enough

Loong

@0celo7 this is close: alfa.com/en/catalog/010681

0celo7

@Loong Alfa was the first place I checked.

@Loong Mmm, it won't ship from SA for two months!

Hmm, wait, was that something else?

I've been on a chemical buying spree lately.

0celo7

13:32

@DanielSank Serious question, do you have any knowledge of high-temp superconductors like YBCO?

@FenderLesPaul Springer now shows the book metrics for Petersen, you should check again if it's available for mycopy :)

Tomáš Zato

14:27

Where do I put the coefficient of restitution in this elastic collision formula: en.wikipedia.org/wiki/…

>

I want to damper the bouncing, but I just reducing velocity is wrong - only relevant part of the velocity should be affected

Slereah

14:42

Hm

Tomáš Zato

I tried to put o.8 at several parts of the equation without success

surprisingly, some parts have no effect at all, even if I put 0.1 the program behaves all the same]\

Secret

15:03

user image

How I first learnt about the existence of muon catalysed fusion

Slereah

Chapter 2 is pretty much finished

Onto chapter 3

0celo7

@Slereah Really? You can't even do an integral.

Slereah

spinors and shit

you can't even do a logarithm

Some high school shit

What hope do you have of knowing anything

0celo7

I don't have a masters in physics

Unlike you

Slereah

And you never will B)

Do engineers get a master, or just a worker's cap

0celo7

15:06

Depends on how much green and pussy you get after the BS

@Slereah No, I'll go straight for the PhD.

Secret

15:22

4

Q: Can we write down a dynamical law of physics which is totally non-deterministic?

In classical mechanics, $F=ma$ tells us how to evolve a system at time $t=t_0$ to $t=t_0+dt$. In quantum mechanics, the Schrodinger equation gives us a similar recipe. These equations are, in a certain sense, completely deterministic. Is it possible that nature only appears to be deterministic ...

determinism laws-of-physics

Jan 28 at 2:50, by Secret

in Mathematics, 2 mins ago, by Secret

Is there are term for the most random thing possible?

Suppose we have a bunch of lights A,B,C,D,E,F

A blinks every 2 seconds
B blinks when A blinks 2 times
C dims and brightens according to the function sin^2(wt)
D blinks randomly in a way such that on average the probability of it is light follows a gaussian distribution
E blinks in a pattern that resembles a random walk
F blinks in a way that depends chaotically to A and B

Can there exists a lamp G such that it blinks so randomly that even when one tries to

I finally understood what I am trying to ask back then

> Interesting. I still feel that this is deterministic in some sense. By running Monte Carlo simulations, etc. one could in principle map out the probability distribution of this particle as a function of time. In this sense, it almost as deterministic as QM – hwlin Feb 23 '13 at 3:59

The term I am looking for is "non deterministic probability distribution"

Why do I have to experience so many random events on a span of weeks or months in order to find the terms I need to ask a question that can be understood by others...?

Grrr..

0celo7

@Slereah why are you learning QFT

Slereah

QFT is the best science, @0celo7

Much better than GR

What has GR ever done for you

ACuriousMind

@Secret That term doesn't mean anything.

Secret

Since in QM even probability evolves deterministically (because the state vector evolves deterministically by the hamitonian, thus $<\psi|\psi>^2$ must evolve deterministically as well), it then wonders me what can possibly be more random than that

barrycarter

@Secret You're saying the normal distribution isn't random enough for you?

Secret

15:37

@barrycarter Well for one thing, it has a well defined equation that describe it, even if it is just a probability distribution

barrycarter

@Secret So you want a probability distribution that has no definable PDF and no definable CDF?

Secret

and brownian motion also depends on what happens in the previosu time steps

Yes, basically, it might be a philosophical question. I want to know what true randomnessi s like

David Z

@Secret tip: \langle and \rangle

barrycarter

@Secret Well, the process you described above just seems to be combining probability distributions, so it would still have a PDF and a CDF, although they may be very ugly.

ACuriousMind

@Secret It's not even a philosophical question unless you define "true randomness".

You're again using expressions without checking that they actually mean anything.

barrycarter

15:43

@Secret Do you mean you want a distribution that can give you any real number with equal probability so you have no idea what the next number will be?

ACuriousMind

@barrycarter Such a distribution does not exist

barrycarter

@ACuriousMind Duh.

Secret

@ barrycarter and probability seemed not random enough. Even if each individual outcome you cannot predict in advance, you can still work out what happens in an ensemble (e.g. flipping coins, you expect on average 1/2 heads/tails, or for electron double slit experiments, you still see the interference pattern)

Chaos may look messy, but it it is deterministic

Probably, basically a process or something that you can only measure there are outcomes, but no matter how long or short time you took in measuring it, and how many or few replicates you have in the ensemble, you never can get a patte…

barrycarter

I was asking the question to see if @Secret sought something that didn't exist.

ACuriousMind

@barrycarter Juuuust making sure :P

barrycarter

15:46

@ACuriousMind I had one extra "duh" lying around, no offense intended :)

ACuriousMind

None taken

barrycarter

@Secret OK, so a binary experiment, where the probability of success does not converge with repeated experiments?

Secret

And I don't know if they can exist or not. My supervisors often said I have many ideas and thoughts but never can communicate it clearly to others.

you can simply have a look at my previous posts about I finally figure out what I am trying to ask 3 months ago and you will understand how hard it is I am trying to express what I want to ask

barrycarter

@Secret I think I understand what you're looking for now. Trying to come up with an example.

Secret

@barrycarter That's sounds like the thing I have in mind (unpredictable regardless of timescale or number of repeats, cannot be wrote into a pdf)

barrycarter

15:48

@Secret For a binary experiment, there really isn't a PDF per se. Just a percentage chance of success.

David Z

@barrycarter sure there is. They call it a probability mass function (PMF) when there's a discrete set of outcomes, but it's the same idea.

barrycarter

@DavidZ OK, OK. I meant the PDF isn't particularly useful when there are only two outcomes.

@Secret Now you realize the percentage of successes will appear to converge to some number as you do more experiment, right? (ie, success/number as number -> Infinity)

Secret

well, infinity is not a number (in the reals), thus we are good

barrycarter

That's why I used the little arrow thingy :) The limit as the number of experiments approaches infinity.

@Secret Your question seems valid, and I certainly can't answer it, and am not sure it's inherently answerable.

Secret

I found it quite embarrassing why you guys can often find the terms I want to ask about in my questions while I often have trouble even knowing what I am asking at times

ACuriousMind

15:54

Okay, @barrycarter if you claim the question is "valid", maybe you can explain it to me, because I still have no idea what he's asking.

barrycarter

@Secret That's actually pretty normal when you're starting out in a subject. You ask questions like "what do I google" for example.

@ACuriousMind OK, he wants to select plus or minus out of a bag, with the plusses and minuses in the bag defined in such a way that he has no idea what the percentage of success chance will converge to.

@ACuriousMind It's fundamentally a recursive issue, I think. Any given distribution for the bag means you'll know the long-term percentage of success.

If you choose the distribution itself randomly, whatever process you used to get that first set of random number will STILL determine the percentage.

In other words, even if we assume true randomness in a distribution, the long-term outcome is predictable.

ACuriousMind

that's kinda the definition of what a "probability" is :P

At least to a frequentist

barrycarter

Yes, but can you find a "truly random" distribution where the probability can't be computed in advance?

Even with quantum mechanics, you can give a probability distribution, even if you can't predict the results of a specific experiment.

ACuriousMind

@barrycarter That's a self-contradictory question. You can't ask for a probability distribution that gives no probabilities.

barrycarter

@Secret The only thing that comes immediately to mind is purely theoretical and can't be constructed.

David Z

15:59

This might be another way to think about it: You can always pick a sample of plusses/minuses out of a bag and compute the fraction of e.g. plusses seen. In frequentist probability, you use that fraction as a predictor of how many plusses you'll get in your next sample. If I understand correctly, what we're talking about here is a process where the fraction obtained from one sample is not a useful prediction of the next sample.

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