The h Bar

ZeroTheHero

00:52

@ACuriousMind interesting. It’s a famous review. Out of curiosity, how d’you know these guys?

ACuriousMind

07:11

@ZeroTheHero I know Spekkens (among other interpretation-y things) from this series that Emilio Pisanty posted here a while back and Rudolph as the author of Q is for Quantum. I can't quite put my finger on what specifically I know Bartlett for, I'm afraid.

John Rennie

07:25

@ACuriousMind wow, there are 15 one hour lectures in that Spekkens series. I wonder if he's written notes that I can read instead of committing 15 hours.

Physics Meta

07:43

0

Q: Strict(er) adherence to homework guidelines?

Less a question and more of a heads-up. Due to the Covid-19 crisis, most higher education institutions (that I know of) are moving to online examination. Many of these examinations count towards degree classifications. In most physics departments (again, that I know of, in the UK), these exams ...

Stan Shunpike

08:09

Hello

Yuvraj Singh...

08:47

@ACuriousMind hi:-)

Morning

Sir if we have two duplicate tags so where we can send the request for deleting the duplicate tags?

Or some new tags which are useless

PM 2Ring

@YuvrajSingh... Hi. You can discuss such topics on meta, with the tags tag, eg physics.meta.stackexchange.com/q/12493/123208

ACuriousMind

@YuvrajSingh... Tags that are identical/pure subsets should be made synonyms. Sadly that page is very hidden and not many people know they can vote there.

@YuvrajSingh... Useless new tags should just be removed from all questions via edits. Once no question is tagged with a tag, it is deleted automatically some time later

Lastly:

2 days ago, by ACuriousMind

please don't call me 'sir'

PM 2Ring

I only learned about the tag synonyms page physics.stackexchange.com/help/privileges/suggest-tag-synonyms quite recently...

Slereah

09:03

Finally

Category theory for children

PM 2Ring

09:13

@Slereah I don't know much about category theory, but John Baez has a lot of introductory category stuff scattered through his old This Week's Finds In Mathematical Physics articles, which were originally posted to Usenet. There's a table of contents here: math.ucr.edu/home/baez/twfcontents.html This Week's Finds was essentially a blog before blogs were invented. ;)

Slereah

Does he have colorful diagrams, though

PM 2Ring

@Slereah No, he has ASCII art. :)

Slereah

Boo

PM 2Ring

He does have nice diagrams accompanying his recent stuff. But Usenet wasn't exactly a friendly environment for high quality graphics. When a high speed connection meant you had a modem that could do 14.4 kilobits / second, even small image files were a big load on the network.

See math.ucr.edu/home/baez for links to his recent works (as well as links to his old stuff).

Slereah

Maybe he should step in the 20th century and have a website

PM 2Ring

09:26

He is one of the founders of The n-Category Café

skillpatrol

21?st century

welcome back @DanielSank

Slereah

@skillpatrol No I mean 1990's internet

A website with images

skillpatrol

oh

PM 2Ring

Maybe this introductory article on category theory would be nicer with colourful diagrams, but IMHO the ASCII art diagrams are adequate.

3

skillpatrol

His home page is colourful.

PM 2Ring

09:44

FWIW, John Baez is friends with the Australian sci-fi author & programmer Greg Egan. Greg sometimes contributes animated diagrams to John's articles.

Slereah

heh

Egan does make neat stuff

skillpatrol

10:05

N.J. Wildberger hasn't updated his blog in a year?

(speaking of Australians :)

I think he burned himself out trying to reform the entire math education system.

Slereah

The real analysis people assassinated him

skillpatrol

RIP

user434058

10:47

Seems like Korea teaches quantum tunneling to its high school students...

ACuriousMind

11:03

@FakeMod I distinctly remember explanations like that from my physics school books as well.

In retrospect it strikes me as a regrettable pedagogic error to teach people to apply the uncertainty principle to all sorts of stuff it doesn't really apply to.

It's clear that it is like this because the actual math with states and operators is beyond the scope of high school physics, but I'm still not a fan

Slereah

They did teach us QM in high school, but only very basic stuff

Mostly discrete atomic levels

ACuriousMind

I think here most of the quantum stuff was for those that picked physics as a specialty, the "standard" physics course didn't include more than atomic levels and the Bohr model either

Slereah

It was mostly "Look, tiny steps make light!"

user434058

@Slereah Same here! :)

user434058

The deepest they've gone is to teach us how to interpret the Schrodinger equation in the terms of number of nodes and their location.

Slereah

11:24

Learning can be fun!

Guru Vishnu

11:34

Which question (out of A and B) would you choose to close as a duplicate when both have great answers? What criterions do you use generally?

Yuvraj Singh...

12:25

@ACuriousMind I am not aware that what kind of people are eligible for '' sir'' tag in a European countries!

Slereah

Yuvraj Singh...

In India we usually use '' sir'' for our elders and our teachers.

Slereah

It does help quite a bit

Yuvraj Singh...

So today if anybody here can help me in understanding it?

@ACuriousMind

@PM2Ring thanks sir:-)

ACuriousMind

@YuvrajSingh... There is no comparable address in German at all, and I'm not really used to the formal address that we do have outside of official contexts, either. (E.g. we use the informal/familar address for company-internal communication, too)

I'm aware that it's meant to be a show of respect if someone calls me 'sir', but I still don't like the deference. We're all just people on the internet here, and I see no need to impose levels of formality or respect here.

Yuvraj Singh...

12:38

Ah! Right

B. Brekke

In a fermionic Feynman diagram with internal (imaginary) time variables, the sign of the contribution depends on the internal times and therefore changes troughout my integrations, right?

ACuriousMind

Sign of the contribution of what?

In general, I wouldn't think that you need to think explicitly about the different times, the propagator should already encode the correct behaviour for you

B. Brekke

12:54

Contribution to the propagator

So the diagram consists of many bare propagators, and these bare propagators can be both particle and hole propagaters, and for fermions they have opposite sign, or?

ACuriousMind

Sorry, I'm not really getting why you're worrying about signs here. The only "sign rule" related to fermions is that you have to include a sign when there's an odd number of "crossings" of fermion lines in your diagram

Otherwise you just use the Feynman rules to compute the diagrams

ZeroTheHero

@ACuriousMind Thanks for answering. I realize now this was a somewhat personal question to answer so I hope it didn’t cause you to wince too much.

ACuriousMind

13:09

It was an acceptable amount of wincing :)

ZeroTheHero

so of course terry rudolph is now gone private: ft.com/content/afc27836-9383-11e9-aea1-2b1d33ac3271

steve bartlett is still in sydney and rob spekkens still at PI.

PM 2Ring

14:00

How can we typeset nuclear reactions? I just did this physics.stackexchange.com/a/546102/123208 but it looks a bit ugly with the italic atomic symbols, and I'm not sure if that's the proper right-arrow. I tried using \ce{...} but I guess that's only supported on the Chemistry stack.

Secret

Looking at both diagrams makes me starting to suspect that colliding with the singularity is the same as colliding with the wormhole's neck

thus when the wormhole pinches off completely, there is no way but to collide to the "wall" of the wormhole halves, even if you travel at a spacelike trajectory

ACuriousMind

@PM2Ring use \mathrm for upright letters in math mode

user434058

BTW I just did this edit to make my integrals look better. Could anything possibly go wrong?

PM 2Ring

14:23

@ACuriousMind Thanks I actually did try wrapping the whole align block with \mathrm{...} but it didn't help. And wrapping each symbol would be rather tedious, especially on a phone. I was hoping for something easier...

user434058

15:21

@PM2Ring If you use \rm then everything that follows, gets converted to the text font.

user434058

For e.g. $$\rm abcdefg$$

user434058

@PM2Ring I suggested an edit which does this...

PM 2Ring

15:37

@FakeMod Thanks. That looks much better.

Yuvraj Singh...

15:52

@FakeMod I have ordered through big basket, do you know how it is?

Slereah

16:21

"The definitions themselves can be stated very succinctly. But like little onions, they have several layers, which we will peel away slowly to minimize the shedding of tears."

Category theory is like an onion. Peel it one layer at a time, sometimes you weep.

user434058

@YuvrajSingh... I have never ordered from Big Basket, so I don't know :)

PM 2Ring

16:40

@Loong Thanks. That's definitely better, but a bit more tedious to do on the phone. But yes, I'd rather not use obsolete LaTeX stuff, even if it's convenient.

Semiclassical

so, was helping a student with the following problem offline: You want to build a mass spectrometer that can differentiate between two molecules of nearly equal mass (CO vs. N2). To do that, you use the usual semicircle setup and require that the diameters of the two orbits differ by a specific amount. The computation is pretty simple.

However: How the heck are you supposed to do mass spectrometry on neutral molecules?

ACuriousMind

@Semiclassical Uh, afaik most spectrometers use special techniques to ionize the substance to be analyzed. The used mechanism of ionization depends on the kinds of substances the spectrometer is built for

Semiclassical

makes sense

problem didn't say anything about this, which is rather irritating

ACuriousMind

I'd say that's a technical detail completely irrelevant to the problem :P

Semiclassical

i mean

it's a technical detail which ensures that you get circular orbits in the first place

rather than just straight lines

ACuriousMind

16:52

Yes, but I wouldn't expect a specific problem that asks you to do "the usual semicircle setup" to mention it

Semiclassical

lol, it didn't even tell them that much

ACuriousMind

I would expect it to be mentioned at the point where the idea of a spectrometer was introduced, not in the exercises that assume you know what a spectrometer is

Semiclassical

fair

i don't have easy access to the textbook so I don't have an easy way to confirm/deny that

i mean, something as simple as "assume the molecules have been ionized to have a charge of -e each"

John Rennie

@Semiclassical you accelerate the ions into the mass spec with an electric field. Neutral molecules don't get accelerated so they don't enter the mass spec in the first place. I think an electron beam is typically used to ionise the molecules.

Semiclassical

right

via google books, i can see at least the first page for their textbook's treatment of mass spec

John Rennie

17:04

I'm sure Wikipedia has a relevant article ...

Mass spectrometry

Mass spectrometry (MS) is an analytical technique that measures the mass-to-charge ratio of ions. The results are typically presented as a mass spectrum, a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is used in many different fields and is applied to pure samples as well as complex mixtures. A mass spectrum is a plot of the ion signal as a function of the mass-to-charge ratio. These spectra are used to determine the elemental or isotopic signature of a sample, the masses of particles and of molecules, and to elucidate the chemical identity or structure o...

Semiclassical

and there, at least, it's explicitly stated re: atoms and more specifically ions

yeah, no sign as far as I can tell that their book says anything about this point

JingleBells

electronics.stackexchange.com/questions/375682/… I'm so proud

Loong

@PM2Ring no problem :-)

Physics Meta

17:27

2

Q: Add a link and hint to use Mathjax to the new question dialog

We like to see Mathjax used on Physics SE for equations but at present when you are typing in a new question I think there is no on-screen link to the Mathjax "guide" or a reminder to use Mathjax for equations. There is an old Q&A on Physics Meta which says that this has been implemented, but it...

feature-request

B. Brekke

17:38

@ACuriousMind So I interpret my diagram as a product of propagators. Suppressing the position or momentum dependence for now, they look like G(t1, t2)G(t2, t3)...G(ti, tj)... I integrate over the times, and in some domain of the integral I get G(ti, tj) with ti>tj and in some domain I get G(ti, tj) with tj>ti.

I am now thinking that the sign of G(ti, tj) is dependent on whether ti or tj is largest, since we are dealing with fermions and I think the propagator should be antiperiodic.

PM 2Ring

@PhysicsMeta Speak of the devil... :) Maybe we could have a simple "Intro to LaTeX / MathJax" page that has the bare essentials, and which links to the Math.SE MathJax page. That page is very comprehensive, but it's probably a bit overwhelming to newbies.

And there's so much on it that it's very painful to use on slower machines and phones. Also, I couldn't find anything useful on it for formatting reactions, which would've been nice when I was writing that answer I linked earlier about lithium burning.

ACuriousMind

@B.Brekke The fermionic propagator (expression for it e.g. here) is $\gamma$-matrix valued. It's overall sign does not flip when the times "switch position" unless the two spacetime points are at the same position.

Loong

@PM2Ring A starting point is here: physics.stackexchange.com/help/notation

Slereah

Things are getting less pedagogical

bolbteppa

17:55

Soon you'll forget what you're trying to abstract

B. Brekke

@ACuriousMind I am not sure I understand what it means that it is gamma-matrix valued. Also I am actually considering a propagator at a single site, so maybe it does change sign in my special case. It is a strong coupling model with expansion in nearest neighbor hopping

Slereah

Well at least he uses examples

although it's the usual category theory problem

It gets a bit hard to remember what is what type

especially since the same symbol can mean different types

ACuriousMind

@B.Brekke Yes, if your two points are at the same site and only differ in time, then it flips sign indeed

bolbteppa

'Samuel Eilenberg and Saunders Mac Lane introduced the concepts of categories, functors, and natural transformations in 1942–45 in their study of algebraic topology, with the goal of understanding the processes that preserve mathematical structure.'

Slereah

I'm gonna read the rest of the site, I think

I don't rly have a good intuition on functors

PM 2Ring

18:02

@Loong Ah, right. I didn't know that page exists. Thanks again. :)

bolbteppa

These slides kind of showing how category theory arose seem good

Slereah

I dunno

B. Brekke

@ACuriousMind Then this will indeed be messy. Thanks alot though!

Slereah

As it arose from algebraic topology, I'm not sure that helps a lot to grasp it!

bolbteppa

"The first appearance of the notion ”category” in Samuel Eilenbergs and Saunders Mac Lanes paper”General Theory of Natural Equivalences“ (1945) came almost out of nowhere. There was only one and restricted to groups notation in the year 1942 in one of their papers.The title of their paper already suggests that they were more interested in natural transformations then in categories.

But they invented the natural transformation ”just” to study effects in homological algebra (e.g. effects involving homology groups $H_n(\cdot)$)."

It seems like learning category theory will help make a bunch of subjects easier, in reality you probably need to go through the subjects that motivated category theory to make it easier :\

Slereah

18:18

Well I can't learn everything

Though I am trying to learn algebraic geometry

bolbteppa

Even if you learn everything you'll soon forget most of it :p

Slereah

Also Gödel might disagree with learning all of math

"As Freeman Dyson would say, we need both birds and frogs to foster mathematical progress!"

Mysterious

bolbteppa

"Eilenberg was interested in understanding and computing various homology, cohomology and homotopy groups and Mac Lane was interested in understanding and computing group extensions. At first, these two topics seem to be unrelated. Group extensions belong to class field theory, a part of algebraic number theory. Homology, cohomology and homotopy groups are constructed from topological spaces and are aimed at translating topological information into algebraic, i.e. computable, data. Their function is to lead to the classification of topological

While Mac Lane was visiting the University of Michigan to give a series of lectures on group extensions, Eilenberg observed the surprising fact that Mac Lane’s calculations on a specific case of a group extension yielded exactly the
same result as Steenrod’s calculation of the homology of the solenoid, an important test case in topology. Eilenberg and Mac Lane’s long and extraordinarily fruitful collaboration – 14 years and about 26 papers – resulted from their attempt at getting at the bottom of this unexpected coincidence."

The last time I looked, I was trying to interpret homology and cohomology in terms of group extensions and obstructions, it seems like a lot of this is related to the idea of going from a group to a subgroup to a quotient group and back, which arises for rings, fields, lie algebras, etc...

bolbteppa

18:49

and in baby language:
"Homological algebra is a tool used in several branches of mathematics... It arose in the late 1800s in the following manner. Let $f$ and $g$ be matrices whose product is zero. If $g(v) = 0$ for some column vector $v$, say, of length $n$, we cannot always write $v = f(u)$. This failure is measured by the $\textit{defect}$
$$d = n — \mathrm{rank}(f) - \mathrm{rank}(g).$$
In modern language, $f$ and $g$ represent linear maps
$$U \to^f V \to^g W$$
with $gf = 0$, and $d$ is the dimension of the homology module

ICCQBE

19:06

Hello

I have a little question.

In that system, there is disc that is rotating due to the work done by gravity on the mass hanging on the pulley

There is no friction or any other non-conservative force on the system, so the energy is conserved.

The total mechanic energy of the system at the initial state is $mgh_1$.

at the last state $E_{f}=\frac{1}{2}Iw^2+\frac{1}{2}mv^2$

My question, are the linear velocity of disc and linear velocity of the hanging mass equal?

PM 2Ring

19:39

@ICCQBE Well, they have to be, if the string doesn't stretch. It's usual in such problems to state the string is inextensible and of negligible mass.

That is, the linear speed of the hub of the disc, where the string is wrapped, must be identical to the linear speed of the falling mass. That also assumes that the string is of negligible thickness, so that the radius of the hub remains constant.

ICCQBE

@2Ring thanks for the answer! I'm grateful to you.

Slereah

20:28

You know the enthusiasm for category theory strikes me as a little weird since a lot of it is somewhat reminescent of lambda calculus

Except lambda calculus never was that popular

ACuriousMind

@Slereah I think you overestimate the amount of people enthusiastic about category theory :P

Slereah

@ACuriousMind Well it is a bit like scientology or meth

Not that many, but the people who do are really into it

ACuriousMind

Lambda calculus is well-liked in certain comp-sci circles, category theory in certain math circles, but neither is really universally taught or applied

Slereah

But I suppose this is like that time my C# teacher told me about this amazing new feature of C#

The lambda functions

I've just received word that the Emperor has dissolved the MIT computer science program permanently.

bolbteppa

Yeah

the way they began with it, it was like a syntax
"They took the notion ”category” from philosophy, i.e. from Aristoteles, Kant and Peirce, but they defined it in a mathematical strict way.Their definitions contains the notation of classes and sets but they were rather a kind of meta calculus.They already denoted that the objects could be almost omitted and that the morphisms are much more important.In the year 1945 it was not clear that category theory is more then just a good syntax to describe effects in homological algebra"

Slereah

20:38

I don't really know why some math foundational ideas got popular and others didn't

History, probably

I think set theory was probably the first overarching such idea

that was worked out properly

bolbteppa

Ideology

Slereah

On the other hand, why ZFC and not the Russell theory?

Russell had that weird hierarchy, but then again, modern category theory also has a hierarchy

bolbteppa

I really don't know why people haven't just focused on factoring higher and higher order polynomials and finding special case rules where the roots can be found etc it's basically people following trends (motivated by physics, ahem)

Slereah

It's not like set theory was particularly uncontroversial

Space Otter

Hi everyone been a while but I am in dire need of assistance. I've written some code in python which solves the N-body problem. I'm now trying to set up some initial conditions which could replicate a rocket being fired from Earth orbit and then slingshot around the moon and return to earth orbit. How might I go about finisng these initial conditions?

I keep getting situations where the rocket isn't really captured by the moon

Literally any ideas or refrences for me to read would be so useful

tpg2114

20:51

A useful starting place could be an initial velocity that means the rocket reaches its peak altitude = moon orbit -- that would be a good sanity check to make sure there's not some bug or something

I assume the code gives correct answers for a low earth orbit and a low lunar orbit? I.e. that you've verified the limiting cases behave as expected?

Space Otter

Oh yeah good idea, I mean when I plug in initial conditions for lunar orbit it forms nice orbits as predicted so I assume the code works well.

tpg2114

It's always good to verify limiting cases (which it sounds like you did). But having the Earth-moon-rocket system with the rocket in stable orbits about different bodies is a good check

Then add more complex "simple" checks, like if the rocket gets to the lunar radius, does it fall back (if it's not aimed at the moon) or does it collide/get captured if it is aimed at the moon

Slereah

"But," you ask, "what is the Yoneda lemma? And if it's just a lemma then - my gosh - what's the theorem?"

:D

tpg2114

If all the code shake downs are good, then you're trying to find a free return trajectory: en.wikipedia.org/wiki/Free-return_trajectory which works with a little extra speed and pass in front of the moon, which slows the rocket down into a capture and leaves it behind to fall back to Earth

Space Otter

21:27

Okay I'm using $ GMm(r^2) = 0.5mv^2 $ to get some initial velocity to fire the rocket to a max alltitude of r and my simulation is now behaving badly

Ugh I forget how to use mathJax give me a minute to read that meta post

Space Otter

22:22

Yeah I think something is wrong with my code because given only enough velocity to reach lunar orbit then fall back it overshoots that distance by quite a lot

I don't understand why it produces stable orbits though

uhoh

23:25

0

Q: How to write this conservation of energy constraint in mathematical notation?

This is a question about equation notation. In a simple model for low energy electron scattering or LEED a single scattering events add a reciprocal vector from either the substrate's or adlayer's lattice to the transverse momentum of the electron. $$\Delta \mathbf{k_{xy}} = i \mathbf{g_1} + j ...

notation physics

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