The h Bar

3:02 AM

@Blue yeah, it's pretty cool

the prof i'm collaborating with had a good laugh when I wrote down 553664 as the number of vertices :P

ZeroTheHero

4:06 AM

Has anyone every heard of “Dirac observables”? It seems related to Quantum Gravity, about which I know very little.

Q: Doubt regarding expression of angular momentum

4:56 AM

I dont know why this question is still closed, even after being edited

-1

Two thin circular disc of mass $m$ and $4m$, having radii of $a$ and $2a$, respectively are rigidly fixed by a massless, rigid rod of length $l = \sqrt {24}$ a through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that angular...

Pretty obvious question regarding the doubt of the angular momentum.

Anonymous

5:20 AM

@AjayMishra Hmm, that's the angular momentum question from JEE 2016 :P

Anonymous

They'll find the answer if they search the net well. C.f. this

Anonymous

That aside, when asking such questions you need to boil it down to a single concept

Anonymous

There's excessive numerical detail in the first paragraph (it's better to generalize the problem using variables $M_1, M_2$, $a_1, a_2$ and so on)

Anonymous

And too less research effort shown

Anonymous

I appreciate the effort you put in to edit that question though (the initial version was absolutely terrible)

Anonymous

5:26 AM

But it requires a bit more work (like giving it a more searchable & descriptive title, showing some research, etc)

Anonymous

Nevertheless, keep in mind that PSE does not intend to be a physics "help" site. It's supposed to be a reservoir of high quality, "easily-searchable" Q&A

Anonymous

Imagine: someone else, who doesn't know about the JEE, is stuck with a similar angular momentum problem, in the future. If they type in "two disc system + angular momentum" on google, they'll most probably not land up on that thread

Anonymous

It's our collective duty to transform the problems into more generalized ones so that it can be of help to a larger set of people

2

I think, it is doubt regarding the definition of the angular momentum, like overcounting the same rigid body

There is literally nothing involved in there, it was basic definition question, so I thought it would be great if someone has trouble getting the idea with sine component of position vector of mass element, and distance from the axises might get help.

Anonymous

5:42 AM

@AjayMishra As I said, we are not a physics "help" site. There's a separate chat room for that. Encouraging such poorly researched questions would only be a downhill ride for us.

I agree one would get solution from the books and internet, and I think the person who asked the question did so, that why he had the doubt regarding the expression of angular momentum.

indeed.

Anonymous

> I think the person who asked the question did so

Anonymous

Then they'd have to clearly express what they did and what exactly they found while doing so

Anonymous

In its current form it lacks research effort + is too localized + lacks a good title

Anonymous

Once that's fixed, I think you can ask people to reopen it

5:46 AM

@Blue may be or may not be

okay.

Anonymous

In my personal opinion, it's next to impossible for a site to accommodate high quality research-level or grad-level physics questions alongside these undergrad/high-school level physics problems. If we have to encourage the former it's absolutely necessary to keep a high bar for the latter. Or else we'll just end up becoming another Quora.

Anonymous

Imagine a professional physicist landing up on the main page of the site and noticing such JEE type problems all around. They're sure to go - 'tis not the place for serious physics, and leave the site for good (I half-believe that's already happening :/). Add to that the terrible question formattings.

5

7:24 AM

@Blue I mean that's kind of the reason Physics Overflow exists

Anonymous

@SirCumference Physics Overflow is dead

Oh, didn't know

Anonymous

It's in the ventilation now with recycled questions from Physics SE which hardly anyone ever answers there

Well you could bring it up on meta. There used to be a theoretical physics SE that got merged with this. Perhaps it's worth considering another one of those

Anonymous

I'd love a Theoretical Physics SE now

Anonymous

7:27 AM

But I don't know if SE has sufficient manpower to get that to private beta

Anonymous

Physics SE already doesn't have much experts around

Anonymous

So I don't know if such a site will survive without external sponsorship

Anonymous

The easier alternative is to ban homework and undergrad level questions from PSE and bam - you have a site for experts

Anonymous

But that's probably not gonna happen....because reasons

Anonymous

The middle ground is to keep a high bar for pre-grad level questions

7:31 AM

Well we do have MathOverflow and Theoretical CS surviving as distinct sites from Math and CS (although MO does predate Math.SE) Regardless I think there ought to be a place for lower level questions and expert ones, just not necessarily the same SE

I probably wouldn't have gotten into physics if I didn't find low level answers to some questions I had

Anonymous

Well, one could always try to propose a new site on Area 51. But whether it will survive the Area 51 stage is something we'll have to wait and see

I still think it definitely warrants a meta post first

Anonymous

I think such a proposal has already been made twice now, and been rejected by the SE guys

Anonymous

So unless we can convince them, it's going nowhere

Anonymous

@SirCumference Sure

Anonymous

7:35 AM

Anyhow, making a new expert site isn't gonna automatically improve the question quality on the existing Physics SE

Anonymous

Question level is a different thing from question quality

Anonymous

I don't have problems with the former, but I do have issues with the latter

Anonymous

Discussions related to newbie questions can still be excellent and insightful provided the OP puts in sufficient effort

Anonymous

You see there we have - MO and Math SE (one is an expert site). But still there's a huge controversy regarding PSQs (students posting homework questions without showing much effort and people still answering them) there, on Math SE

Anonymous

Nevetheless, this particular discussion is always frustrating. Most of gave up on the hw problem issue on PSE and MSE, long ago.

Anonymous

8:09 AM

On a different note, I've been trying to eat fishes (with tons of fish bones) with spoon and no hands - it's fun and I'm getting better at it everyday :P

8:34 AM

@Blue Math.SE hasnt become Quora.

Anonymous

@Abcd It's on the path there

@Blue as if.

Anonymous

You may disagree.

Anonymous

Anyway, if all you took from my huge essay is "Math SE is turning into Quora"...there's some miscommunication.

Anonymous

What I meant there was mostly metaphorical rather than literal

8:44 AM

The three little piggies should have used Lego

Whoa

We have a main site

We have a meta site

Why don't we have a hw site

Chemistry already has a homework issue

Math & physics as well

Anonymous

@AvnishKabaj In short, SE isn't gonna support a separate homework site. That has been debated ad nauseam, and been shot down by them every single time

Anonymous

Some Physics SE people previously made a separate site for hw. I think some of you are aware of it.

Quandaphysics?

Anonymous

@AvnishKabaj Yes

Homework questions do keep the site thriving

Anonymous

8:57 AM

@AvnishKabaj But there's only one guy who answers questions there

Anonymous

It's a desert

Well you could use researchgate

@Blue where ?

Anonymous

To keep such a site running and healthy you need more people

@Blue and only 3-4 people visit there

Anonymous

@AvnishKabaj qanda

8:58 AM

Physics Q&A

Sammy gerbil answers

And 3-4 people like koolman ask

Sometimes I ask too if no one is around :p

What's the link?

It's qanda

Oh

Anonymous

@AvnishKabaj physicsproblems.nfshost.com

Oh they have changed the name @Blue

Anonymous

@AvnishKabaj Research gate is not for students

Anonymous

@Abcd No, I think it's accessible from both links

9:00 AM

@Blue cant find other one

@Blue but isn't that what you wanted?

Only theoretical questions?

Anonymous

@AvnishKabaj Well, I wanted something like Math Overflow rather than Research Gate. Also on Research Gate you can't stay anonymous

@Blue area 51

You won't be able to change pse

Anonymous

And honestly, the Stack Exchange UI is way better than RG

Anonymous

@AvnishKabaj Yeah, I'm not hoping to :P

9:02 AM

Hands down

@Blue whaaaaaa

Then what's the point of all this debating whatnot

Anonymous

@AvnishKabaj There wasn't a point as such

Anonymous

Was just putting forth my views and observations about the site

O.o

Anonymous

Also someone asked why their question isn't being opened

Lol

Anonymous

9:04 AM

So that was an explanation of our philosophy

That's the reason

2:53 PM

On the subject of homework-like questions (he said to an empty room): I had to spend about five solid hours this week explaining to my ten-year-old the difference between his arithmetic class, which he hates and struggles with, and mathematics, which he finds amusing and is good at.

I read him the "musician's nightmare" section of Lockhart's Lament, without reading him the title of the essay, and he recognized immediately which academic subject was being parodied.

I also used that essay's examples of real math questions as ways to get him to experience the "oh! aha!" sensation of actually understanding something interesting about the way that logic works, and told him that that's what mathematics is like.

Since I've been helping him with long division, I've stumbled on a question about the repeating decimal expansions of fractions with prime denominators. I was able to explain that question to him, and to talk about how I might go about looking for an answer, but that I hadn't yet. And he got that, and agreed that the question was interesting.

And I pointed out that, even though he's having a hard time dealing with his arithmetic class, he knew enough long division to appreciate this thing that I was asking. I told him that long division is like an alphabet that he needed to be able to have the conversation with me.

And long division, like the alphabet, is stupid and boring. Nobody talks about the alphabet as an interesting object with students who are older than about age eight. Instead, you use the stupid and boring alphabet to read clever and interesting books about dinosaurs --- or literally anything else.

The trouble with low-level homework questions on a website like ours, in my opinion, is that they come primarily from people who haven't yet figured out this distinction between "alphabet" questions and "dinosaur" questions.

I joined this community because I had a "dinosaur" question --- something counterintuitive about the correlation between density and redshift in the WMAP data set.

But if I had been looking for a place to ask that question and the front page here had been full of questions about coefficients of friction and inclined planes, I would have expected not to find an answer and left, forever, unsatisfied.

Anonymous

3:12 PM

@rob Very well summarized :)

Hello Sir, I am currently writing a research paper on Planar Bus platform Rotation for Optimum Commuter Comfort, and this is a small component of it. So is it still classified as a homework problem? — Steve Gordan 24 mins ago

Anonymous

Anonymous

@Loong Lol, I was just looking at that. I must say - Good luck writing a research paper with that kind of diagrams :P

Such diagrams seem to work for that xkcd guy.

@Blue That's a picture of an alphabet.

@Loong That's a joke about a dinosaur.

Exhibit A.

3:35 PM

i'm not familiar with the alphabet/dinosaur distinction

Anonymous

43 mins ago, by rob

On the subject of homework-like questions (he said to an empty room): I had to spend about five solid hours this week explaining to my ten-year-old the difference between his arithmetic class, which he hates and struggles with, and mathematics, which he finds amusing and is good at.

Anonymous

Starts there ^

ah, now I see it

the funny thing is that, while the alphabet is boring, the history of how the alphabet came to be can be plenty interesting

Anonymous

That reminds me. Someone once showed me that that numbers, as we write them in English (rather ancient Arabic iirc), originated because they had the same number of angles as the value they represented. Like 1 has one angle, 2 has two angles, and so on

huh

Anonymous

3:40 PM

But it gradually evolved

@Semiclassical Sure. I have successfully read texts (of varying lengths) in five different alphabets. Their similarities, differences, and common histories are interesting. That complexity is absent from "the alphabet song."

yep

which is understandable, to a point

Anonymous

hah, that's cute

though that's a very specific way of writing 7,8,9 :P

Slereah

yeah it's bullshit

Anonymous

3:43 PM

The person who told it to me, also said that was the initial way of writing it. But it gradually changed according to the convenience of writing

Anonymous

Sounds like a question for Skeptics SE

Slereah

I have a whole book on the topic of the history of mathematical notation

Anonymous

@Slereah Damn. A Google search says that it's a rumour.

this is an interesting table from wikipedia: en.wikipedia.org/wiki/Arabic_numerals#/media/…

"The evolution of the [Arabic] numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his Histoire de la Mathematique, which was published in 1757"

Anonymous

goodmath.org/blog/2015/07/21/…

Anonymous

3:46 PM

@Semiclassical Nice!

Anonymous

the 8 and 9 in there are interesting to me

Anonymous

> Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin.

Anonymous

Ah. I did expect they earlier used something like a tally chart.

Anonymous

3:52 PM

But then there were too many lines and they had to think of shorter symbols.

the 4 as + sorta makes sense--- 2-by-2

the rest make you wonder, though

@Semiclassical Which is interesting, since modern research suggests that four is the largest number of things that most people can recognize without counting. The research I read reported that chimps recognize numbers up to about nine without needing to count. I'm not optimistic about finding a link, though.

ACuriousMind

@rob How do you tell whether a chimpanzee needs to count?

@ACuriousMind That question is why I'm looking for a link. But I think it was about the amount of time that it took to respond.

Anonymous

Maybe it was an experiment with bananas

Anonymous

3:57 PM

:P

Anonymous

(Don't ask how)

ACuriousMind

1 banana, 2 bananas, 3 bananas, ::gulp:: 2 bananas, 3 bananas...

3

@ACuriousMind thunder and lightning

@ACuriousMind This one is close, but I'm not sure that's it. Linked from here.

> The numeric working memory of young chimpanzees is astonishing: Flash a random scattering of numerals on a screen for just 210 milliseconds — half an eye blink — and then cover the numbers with white squares, and a numerically schooled young chimpanzee will touch the squares sequentially to indicate the ascending order of the numbers hidden beneath.

> Don’t bother trying to do this yourself, Tetsuro Matsuzawa, a primatologist at Kyoto University, said at the scientific meeting in London on which the themed journal was based. “You can’t.”

Sesame Street: The Count - Mailbags 1 to 12

►

4:08 PM

@Loong I remember being a kid and watching a skit where the Count announced that he was going to count all the way to one hundred. It was a big production. And when he got to the end, in addition to the usual thunder and lightening, it actually rained.

@rob reminds me of nothing so much as how counting works for the rabbits in Watership Down

"Notable traits include... the fact that cardinal numbers only go up to four, with any number above that being called hrair, "many", although the runt Hrairoo's name is translated into English as "Fiver" instead." (from Wikipedia: en.wikipedia.org/wiki/Lapine_language)

@Semiclassical Yes, although I assume that Adams invented that for his book. (It's a favorite of mine.)

yeah, it's a good book. I can see it on my bookshelf, though I haven't read it in a good while

Monty Python-Holy Hand Grenade

Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out.

Anonymous

►

Physics Meta

4:51 PM

1

Q: Feature: Subscribing to Questions

It happens to me very often that I see an interesting question that I'd like to know the answer to. I'll favorite it but then never get notified if there is a change. It would be very nice to have a "subscribe to question" feature, which sends me a notification if there is a new answer (or option...

feature-request questions favorites

5:43 PM

Is exponentiation by a fraction defined for imaginary numbers?

Anonymous

@SirCumference What do you mean?

Anonymous

Example?

Q: Understanding down votes on answers

@Blue Well can $i^{3/5}$ be nicely defined

Or rather I'm wondering if there's a commonly accepted definition

Physics Meta

0

I recently received two down votes in one day on an answer that was submitted more than a year ago (accepted answer), unfortunately without any comments. At the same time as the down votes, the question was marked as off topic (homework like question...). So I have two questions: Is there an ac...

feature-request specific-question answers down-votes

Anonymous

Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: b n = b ⋅ … ⋅ b ⏟ n × ...

6:05 PM

Regge theory

In quantum physics, Regge theory () is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer multiple of ħ but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1959. == Details == The simplest example of Regge poles is provided by the quantum mechanical treatment of the Coulomb potential V ( r ) = − e 2 / ...

@SirCumference the most obvious answer would be to write $i$ using Euler's formula as $e^{i\pi /2}$ and then take $$i^{3/5}=e^{3/5(i\pi/2)}=e^{3i\pi/10}=\cos\frac{3\pi}{10}+i\sin\frac{3\pi}{10}$‌$

Anonymous

@SirCumference Actually your example is well defined - but just multivalued

Anonymous

You can choose a principal value though

but you also have $i=e^{5 i\pi/2},e^{9i\pi/2},\ldots,e^{-3 i\pi/2},e^{-7i\pi/2}\cdots$

So complex angular momentum is not random or nuts, it falls out immediately from e.g. $E = 1/2n^2$ in the right units using $n = l + ...$

Anonymous

6:07 PM

Although the definition of principal value of not universally agreed upon

If you work through that list, exponentiating each entry appropriate, you eventually end up repeating the same things

so there's only a finite number of answers to $i^{3/5}$

Anonymous

The number of values you can get for that expression can be directly found from the algebraic equation it satisfies I think

Anonymous

I forgot how to do these stuff

which shouldn't be too shocking: $z=i^{3/5}\implies z^5=i^3=-i$

So there should be five answers to $z=i^{3/5}$

Anonymous

Right, right

Applying for a postdoc position - advice from Nobel Laureate Randy Schekman

6:11 PM

►

Anonymous

@Semiclassical But from there can we say for certain that none of the solutions are overlapping?

yeah, there's a periodicity

Anonymous

$z^5=e^{-i\pi/2}$

for instance, if you do $i=e^{i\pi/2+10\pi i}$, you get $i^{3/5}=e^{3 i\pi/10+6\pi i}=e^{3i \pi/10}$

So you effectively only care about $\theta$ mod 10pi when it comes to $i=e^{i \theta}$

Welp back

Slereah

6:19 PM

Anonymous

> The set of $n$th roots of a complex number $w$ is obtained by multiplying the principal value $w^{1/n}$ by each of the $n$th roots of unity.

Anonymous

@Semiclassical Aha, it makes sense now :)

@Semiclassical Huh neat, didn't think of that

Anonymous

So for positive fractional powers of complex numbers it's pretty easy

Anonymous

Now say we have $i^{-3/5}$

6:21 PM

@Blue Well that's just 1 over the list of values from before. Then you can just rewrite it by multiplying top and bottom by the complex conjugate

where it's annoying is stuff llke $i^i$

there's actually an infinite number of answers to that

@Semiclassical $=e^{iπ/2}^i=e^{i^2 π/2} = e^{-π/2}$, no?

sure, if you take $i=e^{i\pi/2}$

wth latex

but you also have $i^i = e^{(5i\pi/2)i}=e^{-5\pi/2}$

$e^a^i$

6:24 PM

All right no idea why the latex is funky

yeah, e^a^i doesn't work

should be (e^a)^i: $(e^a)^i$

hmm, {e^a}^i: ${e^a}^i$

that works, but looks kinda crap

e^{a^i}: $e^{a^i}$

anyways. in this case, you end up with an infinity of real answers that don't loop back in on themselves

Anonymous

@SirCumference Indeed. So five solutions on the unit circle again

Anonymous

$z^5=i^{\sqrt{3}}$ - five again

Anonymous

So the problem arises only when dealing with complex powers

well

you could also have something like $z^{\sqrt{2}}=i$

in which case....nope, ima gtfo

Anonymous

6:32 PM

Oh. We can't naively write $z=i^{1/\sqrt{2}}$ there?

vzn

@Blue the vast majority of professional scientists seem not to use social media much/ are averse to it. the publication/ conference system still not too much changed by cyberspace roughly serves their (communication/ networking) purposes. feel cyberspace potential is underutilized by them. there is some great extended discussion in this book by Nielsen, Reinventing discover, the new era of networked science amazon.com/Reinventing-Discovery-New-Networked-Science/dp/…

Anonymous

@Semiclassical Wolfram shows only one solution :O

Anonymous

Am I missing something?

no idea

Is there a specific definition of exponentiation that can just answer these things?

Well that's probably something I should just look up

6:36 PM

if we take $z=e^{i\theta}$, we need $z^{\sqrt{2}}=e^{i\theta\sqrt{2}}$

So we need $\sin(\theta\sqrt{2})=1$

Anonymous

So $\theta\sqrt{2}=2\pi(n+1/2)\implies \theta=\sqrt{2}\pi(n+1/2)$

Anonymous

Yes, that seems like a good approach!

And $e^{i\sqrt{2}\pi n}\neq 1$ for any $n$

Oh neat, exponentiation can be generalized to any monoid, not just $\mathbb{C}$

6:38 PM

So you get an infinitude of solutions

bottom line is that exponentiation by rational numbers is nice in complex analysis

whereas exponentiation by real numbers is pain

Anonymous

@vzn That looks like a nice book

7:47 PM

@rob Hmm, I'd be a bit careful. Telling someone that their school work is not real mathematics (even though you're right) could demotivate someone from their academics

At least it probably would for me if I thought that my school work was useless

8:02 PM

@SirCumference This is why I ended up with the alphabet analogy. My son and I were trying to find 15.98/2.35 = 6.8, and found it so frustrating that he burst into tears. That particularly stupid homework computation wasn't worth tears.

But the skills he was practicing by doing that stupid and frustrating problem let us have an interesting conversation about why the decimal expansions of n/7 have one pattern with length six, while the decimal expansions of n/13 have two patterns of length six, and whether there's any way to those patterns.

I think he's too motivated by academic concerns at the moment: he is convinced that his struggles with this not-great arithmetic class make him an inferior person.

Hats!

@DanielSank huh

I thought all of those were just hawaiian skirts

heheheh

@DanielSank halp

hmmmmmm

no, on second thought, no, I'd rather not set it down in writing

but this is lovely

facebook.com/fritz.wiese.1/videos/2286409201429758

with some really nice beats at about 1min in

@EmilioPisanty That's an innovative way to play handbells.

8:25 PM

@EmilioPisanty Halp?

@DanielSank I've been given a task that ordinarily people shouldn't do

?

but I'd rather not set it down in public in permanent

@EmilioPisanty I didn't see it. Was on another tab.

Hit me up in Google hangouts if you want.

@DanielSank don't worry, it's not that important =)

8:33 PM

k

how's things your side?

Secret

15 hours ago, by Blue

Imagine a professional physicist landing up on the main page of the site and noticing such JEE type problems all around. They're sure to go - 'tis not the place for serious physics, and leave the site for good (I half-believe that's already happening :/). Add to that the terrible question formattings.

JEE is an adbomination that have give anyone nothing except misery

i imagine it will be pretty screwed for those marking the exams

Anonymous

10:07 PM

@Secret The truth in that sentence...hurts. :)

Anonymous

@Secret The exams are machine checked/marked (OMR sheets)