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1:16 AM
Heh, seems like you can get the "Still Fresh" hat just using the association bonus
Thinking about what kind of set can model the behaviour of bosons:
1. You can pile as many bosons as you like in the same state, until the energy density become so high that it becomes a black hole
Don't recall sets in set theory have this cutoff property
1 hour later…
2:24 AM
OK. Why has no one posted today's xkcd yet???
Both arXiv and archive.org are invaluable projects which, if they didn't exist, we would dismiss as obviously ridiculous and unworkable.
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
1 hour later…
4:06 AM
Has anyone every heard of “Dirac observables”? It seems related to Quantum Gravity, about which I know very little.
4:56 AM
I dont know why this question is still closed, even after being edited
Q: Doubt regarding expression of angular momentum

NishantTwo 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.
5:20 AM
@AjayMishra Hmm, that's the angular momentum question from JEE 2016 :P
They'll find the answer if they search the net well. C.f. this
That aside, when asking such questions you need to boil it down to a single concept
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)
And too less research effort shown
I appreciate the effort you put in to edit that question though (the initial version was absolutely terrible)
5:26 AM
But it requires a bit more work (like giving it a more searchable & descriptive title, showing some research, etc)
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
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
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
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.
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.
> I think the person who asked the question did so
Then they'd have to clearly express what they did and what exactly they found while doing so
In its current form it lacks research effort + is too localized + lacks a good title
Once that's fixed, I think you can ask people to reopen it
5:46 AM
@Blue may be or may not be
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.
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.
7:24 AM
@Blue I mean that's kind of the reason Physics Overflow exists
@SirCumference Physics Overflow is dead
Oh, didn't know
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
I'd love a Theoretical Physics SE now
7:27 AM
But I don't know if SE has sufficient manpower to get that to private beta
Physics SE already doesn't have much experts around
So I don't know if such a site will survive without external sponsorship
The easier alternative is to ban homework and undergrad level questions from PSE and bam - you have a site for experts
But that's probably not gonna happen....because reasons
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
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
I think such a proposal has already been made twice now, and been rejected by the SE guys
So unless we can convince them, it's going nowhere
@SirCumference Sure
7:35 AM
Anyhow, making a new expert site isn't gonna automatically improve the question quality on the existing Physics SE
Question level is a different thing from question quality
I don't have problems with the former, but I do have issues with the latter
Discussions related to newbie questions can still be excellent and insightful provided the OP puts in sufficient effort
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
Nevetheless, this particular discussion is always frustrating. Most of gave up on the hw problem issue on PSE and MSE, long ago.
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.
@Abcd It's on the path there
@Blue as if.
You may disagree.
Anyway, if all you took from my huge essay is "Math SE is turning into Quora"...there's some miscommunication.
What I meant there was mostly metaphorical rather than literal
8:44 AM
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
@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
Some Physics SE people previously made a separate site for hw. I think some of you are aware of it.
@AvnishKabaj Yes
Homework questions do keep the site thriving
8:57 AM
@AvnishKabaj But there's only one guy who answers questions there
It's a desert
Well you could use researchgate
@Blue where ?
To keep such a site running and healthy you need more people
@Blue and only 3-4 people visit there
@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 they have changed the name @Blue
@AvnishKabaj Research gate is not for students
@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?
@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
And honestly, the Stack Exchange UI is way better than RG
@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
@AvnishKabaj There wasn't a point as such
Was just putting forth my views and observations about the site
Also someone asked why their question isn't being opened
9:04 AM
So that was an explanation of our philosophy
That's the reason
6 hours later…
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.
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
@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
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.
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
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
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."
which is understandable, to a point
hah, that's cute
though that's a very specific way of writing 7,8,9 :P
yeah it's bullshit
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
Sounds like a question for Skeptics SE
I have a whole book on the topic of the history of mathematical notation
@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"
3:46 PM
@Semiclassical Nice!
the 8 and 9 in there are interesting to me
> 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.
Ah. I did expect they earlier used something like a tally chart.
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.
@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.
Maybe it was an experiment with bananas
3:57 PM
(Don't ask how)
1 banana, 2 bananas, 3 bananas, ::gulp:: 2 bananas, 3 bananas...
@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.”
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
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.
4:51 PM
Q: Feature: Subscribing to Questions

user27084It 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...

5:43 PM
Is exponentiation by a fraction defined for imaginary numbers?
@SirCumference What do you mean?
@Blue Well can $i^{3/5}$ be nicely defined
Or rather I'm wondering if there's a commonly accepted definition
Q: Understanding down votes on answers

AndreiI 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...

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
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}$‌​$
@SirCumference Actually your example is well defined - but just multivalued
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 $n = l + ...$
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 $i^{3/5}$
The number of values you can get for that expression can be directly found from the algebraic equation it satisfies I think
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 $z=i^{3/5}$
Right, right
@Semiclassical But from there can we say for certain that none of the solutions are overlapping?
yeah, there's a periodicity
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
6:19 PM
> 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.
@Semiclassical Aha, it makes sense now :)
@Semiclassical Huh neat, didn't think of that
So for positive fractional powers of complex numbers it's pretty easy
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 $i^i = e^{(5i\pi/2)i}=e^{-5\pi/2}$
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
@SirCumference Indeed. So five solutions on the unit circle again
$z^5=i^{\sqrt{3}}$ - five again
So the problem arises only when dealing with complex powers
you could also have something like $z^{\sqrt{2}}=i$
in which case....nope, ima gtfo
6:32 PM
Oh. We can't naively write $z=i^{1/\sqrt{2}}$ there?
@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/…
@Semiclassical Wolfram shows only one solution :O
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 $\sin(\theta\sqrt{2})=1$
So $\theta\sqrt{2}=2\pi(n+1/2)\implies \theta=\sqrt{2}\pi(n+1/2)$
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
@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.
@DanielSank huh
I thought all of those were just hawaiian skirts
@DanielSank halp
no, on second thought, no, I'd rather not set it down in writing
but this is lovely
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
how's things your side?
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
1 hour later…
10:07 PM
@Secret The truth in that sentence...hurts. :)
@Secret The exams are machine checked/marked (OMR sheets)
11:09 PM
'Indeed there is the story of a party at which the charming wife of an American physicist, on being introduced to 'Regge', exclaimed: "Ah Mr Pole! I'm so pleased to meet you at last."'

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