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Anonymous
7:19 AM
Any idea about this question?
 
Anonymous
The answerer seems to have completely missed my point...
 
Anonymous
@blue, I think I see your point. Your issue isn't with reaction order, but the rate constant definition. To summarize your argument: say our reaction is $\ce{A -> B}$ and $k$ = 10 s$^{-1}$, but if our reaction is $\ce{2A -> 2B}$, then $k$ would be 5 s$^{-1}$. The half-life of species A remains the same in either case, being $t_{1/2} = \ln 2/k$ in the former and $t_{1/2} = \ln 2/2k$ in the latter, but the reaction rate constant is different. Is that right? I think your argument is sound, but I'd like to see what others have to say. — a-cyclohexane-molecule 54 mins ago
 
user228700
@JohnRennie I uploaded one :-)
 
user228700
I think I know what happened; I used a software to change some of the details of the books which may have "corrupted" them.
 
7:26 AM
@Kaumudi.H YHM
Pro-tip: .epub files are actually just .zip files renamed.
 
user228700
What did u change..?
 
If you rename them to .zip you can extract them, make any changes you want then zip them up again and rename them back to .epub.
 
user228700
Also, I should mention that another reader also didn't recognise it.
 
@Kaumudi.H The file you uploaded opens fine with Aldiko on my tablet. Does the version I mailed you about open on your phone?
 
user228700
@JohnRennie Yes, it does...
 
user228700
7:39 AM
Does it really open in ur Aldiko? (The one that I sent)
 
@Kaumudi.H Yes. Weird - I'm not sure what was going on there. In any case your version has the line breaks messed up.
 
user228700
:-( I have twenty such books! Not even the HP books are being recognised!
 
user228700
Sigh. I bet it's that stupid program "EPubor Ultimate" that screwed me over.
 
I wonder if the file name has a space at the end i.e. it's ".epub<space>"
 
user228700
Huh? O_o How to discern if it has a space at the end?!
 
7:43 AM
The curious thing is that I don't think the Import screen in Aldiko opens the files until you actually tap the Import button. It should just all files that end in .epub regardless of what they contain.
 
user228700
That's the problem! It doesn't even show any files!
 
Download ES File Explorer. You can use that to see exactly what is in the Downloads folder.
Or connect the phone to the laptop and use the laptop to see what is in the Downloads folder.
 
user228700
I'm able to see on my phone that they're present in the downloads folder when I check outside of Aldiko, like I said before...
 
"If the universal cover is not taken, (p, q) anti-de Sitter space has O(p, q + 1) as its isometry group. If the universal cover is taken the isometry group is a cover of O(p, q + 1)"
 
user228700
Also, YHM!
 
7:46 AM
What is the cover of anti de Sitter D:
 
My recommendation is to use the laptop for downloading books. I think I installed an epub reader on the laptop, so you can open the downloaded files to check them. Then copy the files over to a folder you create for the purpose e.g. /Books and use Aldiko to import them from there.
 
user228700
Wokay. Thanks for all this help :-)
 
Oh wait
I guess the way AdS is defined in physics usually, it is rolled up, if you will
 
Anonymous
Why is Kinetic Energy equal to Potential Energy for waves on a string?
 
Anonymous
Is that statement true at all?
 
7:50 AM
So the universal cover is the actual hyperboloid sheet
 
@GPhys Who cares, because the quantum apple is super delicious!
 
user228700
@JohnR: Why are so incredibly helping/generous? :-P
 
Last night dream most weird thing: An interstellar fashion tsunami that flows upside down above our heads
 
@Kaumudi.H I wouldn't say I was incredibly helpful, just everyday helpful :-) It's not as though it costs me anything but time, and I have plenty of spare time since I quit full time work.
 
user228700
Gah, your modesty is irritating at times. There is no denying that it was kind of you to choose to help me in that spare time rather than do literally anything else.
 
8:17 AM
I suppose I have a missionary zeal to convert everyone in the world to a nerd (physics or computer flavoured nerd). And I have to concede it's gratifying to have others ask your advice on things. It implies a level of respect for one's knowledge :-)
 
Try the other way around, perhaps
try insulting him
maybe he'll compliment himself
 
user228700
@JohnRennie Indeed it does :-)
 
The Upside down tsunami:
The dream managed to fool me this looks normal because of how it extend all the way to the floor, thus can still be interpreted as the whole bulk of the water get sucked up and curved as follows due to the huge force in the tsunami, leaving a shallow puddle behind that still touches the floor
But if you think more closely, the centripetal and other forces have to be so large to overcome the downward pull of Earth's gravity, thus such a scene is highly implusible
(and yes, my head is briefly underwater because the (upside down) water surface is so low due to the travelling hump)
 
8:35 AM
The pdf of the new LHCb results is up! indico.cern.ch/event/580620/attachments/1442409/2226501/…
see indico.cern.ch/event/580620 for the seminar in 25 minutes if you're interested
summary slide, 2.2-2.5 sigma deviation from SM
here is the money plot
 
So what's wrong
Is it gonna be PCT symmetry again
Kaons always fuck up PCT
 
Brace yourself for about 1,000 papers proposing mechanisms for the discrepancy :-)
 
Is it gonna be a loose cable again
 
So, what is the expected $\mathcal{R}_{K^{*0}}$ if there is no new physics, is it 1.0?
 
@Secret the "SM" plot points here are giving calculated standard model predictions from various programs
 
8:42 AM
Also what is $\mathcal{R}_{K^{*0}}$
 
O sorry, I read too much into the colorful dots, I think I can see it now why it might be significant.

But until they can get that to $5\sigma$, it could fade away just like the 750 GeV diphoton signal
 
@Slereah it's a ratio of something in the measurements, I need to see the fuller paper or finish rereading the slides more carefully to tell you exactly
these slides tend to be arcane if you are not very well educated on the even the HEP subtopic, but the internal CERN notes are usually much better so I read those instead
the eventually published paper is okay, but the internal CERN notes contain all the stuff that's too "easy" to put into the published paper
@Slereah Here it is
 
Hmm so the results means the decay channel to electron is ~1.5 times more likely than the decay channel to muons?
 
So weak decay sort of ratio?
why is the weak interaction so awful
 
9:03 AM
webcast starting now indico.cern.ch/event/580620
audio man saves day \o/
 
Hi! I'm new to StackExchange!
 
9:31 AM
@JohnSmith welcome \o/
 
user228700
9:52 AM
@JohnSmith Hello and welcome! :-)
 
10:49 AM
hello, Im just having some doubts about how to make correct notation of my experience's result, using reglinp i've got my b coefficient and it's -6,83E-17 mV, while the uncertainty of this is 0,0086 mV
shall I write 0,0000(86) mV as a result?
 
I want off this ride
 
11:01 AM
Hello @JohnRennie
 
@Ramanujan Hi
 
@JohnRennie, Can three forces of 5N, 8N and 14N acting on a body produce a zero resultant?
@JohnRennie, 1). Yes, 2). no. 3). Depends on time. 4). Depends on mass
 
@Secret Gee, you're quite imaginative ;)
 
@Ramanujan I'm generally willing to try and explain some concept in physics, but you have a tendency to just post a question with no indication of what work you've done on it or how you think it might be approached.
3
If you explained what you'd tried and where you got stuck that would be a better way to approach questions like this.
 
@JohnRennie, I guess the answer is 'no'. But not sure
 
11:07 AM
@JohnRennie and people said him before too
 
"I'm generally willing to try and explain some concept in physics" How about my queries? Can I ping you (occasionally) too? [Disclaimer: My "Queries" are usually the long drawn out discussion-kind ones though ._.]
 
@paracresol yes, of course.
 
in The Periodic Table, Jan 9 at 13:43, by Mithoron
@Ramanujan sigh could you stop asking bad questions?
@JohnRennie Yes!!! \o/
 
However bear in mind that I've forgotten much of the basic physics I learned 40 (!!!) years ago so my knowledge is a bit patchy :-)
 
@paracresol sorry but no question is bad
 
11:10 AM
^^ I'm still a high-schooler, so my physics is limited to those patches ;)
@Fawad There's no stupid question (generally speaking), but there are certainly very bad questions out there :]
 
@Fawad I disagree, though I probably wouldn't use the words good and bad. A question is useful if you will learn something from the answer. If you're just going to write that answer in your homework book then it wasn't a useful question.
2
 
@JohnRennie agreed
 
@JohnRennie, I am preparing for competitive exams and so don't have any formal classes to learn the concepts and thus directly go by exercises
 
@0celouvsky were you @0celo7 by any chance?
 
Why does everyone think that?
 
11:14 AM
@Ramanujan so explain how you approached the problem, then we can comment on whether your approach is correct or not.
 
Great, it's confirmed then! Hi 0celo7! o/
@JohnR Another query?
What is Planck's Radiation Law? By that, I mean the original statement that Planck (supposedly) provided, or is it even a "statement" at all? I've run multiple searches online, consulted several books but none of them provide any sort of statement though ._.
 
@JohnRennie, Actually I think that it depends on mass of body. Bcoz. It may be possible that a body has 0 acceleration. Suppose three men pushing a wall with forces 8N, 5N and 14N. The wall will have 0 acceleration.
 
Wikipedia mentions:
> Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T
My Oxford Science Dictionary says:
> This law gives the spectral distribution of energy emitted through black body radiation
^ Which isn't very different from the Wikipedia version.
Like I said, what bugs me is the absence of any explicit "statement" :(
I mean, I understand Planck's Law, but whenever I ask myself the question "State Planck's Law." I strongly feel like punching myself in the face out of frustration >_<
 
@paracresol: momentarily busy, back in a mo ...
 
^ Yeah I noticed, I can wait ;)
 
11:20 AM
> That is like comparing an uncountable set with a countable set, which is nothing compared to koolman's
(The above message is intentionally nonlocal)
 
@paracresol: this law?
Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900. It is a pioneering result of modern physics and quantum theory. The spectral radiance of a body, Bν, describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body for frequency...
 
^ Yeah, that one!
 
What are you asking about it?
 
Gimme a second
@JohnRennie I was hoping to find the "statement" of the law (if it exists). That sounds kinda obscure, sorry; for example, the "Statement" of Newton's 2nd Law goes like: In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.
 
@paracresol who are you
 
11:29 AM
@0celouvsky A guy you bugged/helped a long time ago ._.
 
???
Who
 
^ Um...me?
This is confusing...
 
Planck's law is actually an example of a probability distribution. So I guess it is a mathematical object rather than a simple law. It is analogous to the Fermi-Dirac and Bose-Einstein distributions.
 
^ Done! Thanks for confirming that!
Oct 12 '16 at 4:41, by Aaron Abraham
@DavidZ I have experience......he did it to me when I was inquiring about Noether's theorem :P @0celo7
 
Is there a metacresol?
 
11:33 AM
Well, there was a metacresol >_<
 
@0celouvsky writing out the boosted Alcubierre was a mistake
 
Morning
 
The horror
That's what happens when your metric isn't boost invariant
 
Why are you investigating the alcuberrie metric in a boosted frame?
 
that is the classic trick to form CTCs for the Alcubierre metric
 
11:36 AM
I see
 
@paracresol did you change your name?
 
Yep ^_^
I was formerly Aaron Abraham ._.
 
its illegal to change one's username
I flagged you
 
so I'm stuck with user400188 forever
 
Then we must send @0celouvsky to jail
 
11:41 AM
27 mins ago, by paracresol
@0celouvsky were you @0celo7 by any chance?
^ Oops
 
I changed my name too :P
I removed the surname off my username
 
0celouvsky and 0celo7 are two different people
and one of them is a jerk
 
@AccidentalFourierTransform O_o
@AccidentalFourierTransform :D
I noticed :3
 
I want a new username too
help me pick a new one
 
It is @0celo7's russian cousin
 
11:43 AM
AccidentalLorentzTransform
 
@AccidentalFourierTransform your name is quite good as it is in my opinion
 
thanks, I made it myself
 
AccidentialLaplaceTransform :P
 
@Yashas when have we ever accidentally realized we Lorentz/Laplace transformed something though?
 
Although there's no combined analysis out of CERN yet, this surely puts C9 standard model violation at >>4 sigma
(>5 sigma?)
 
11:45 AM
@user400188 Not sure how can such an accident happen but that's what it literally means I guess.
 
and it's clear from the release that LHCb believes so as well
 
well; the fourier transform result happens a lot in digital signal and image processing
in fact there have been results which took years to solve; which turned put to simply be a fourier transform of some simple concept.
 
@JohnR Quick question: Assume you were to give a QM lecture. What would you mention first (and why): a) Stark effect, b) Zeeman effect? [ I'm relatively new to QM and atomic physics , and I'd rather avoid the disaster that would result by jumping into uncharted territory by myself]
 
Hello @yashas
 
@GPhys Is the result suggesting decay channels from kaons to electrons is 1.5 times more likely than that to muon channels (based on interpreting the diagram with $\mathcal{R}_{K^{0*}}$)?
 
11:49 AM
@Ramanujan hi
 
@paracresol Z. is way easier to calculate (and to understand intuitively)
Lorentz and Larmor calculated the expression for the Z. effect a couple of decades before QM
 
Can 3 forces of 5N, 8N, 14N produce a zero resultant? 1). Yes, 2). No, 3). Depends on mass 40. Depends in time @yashas
 
@paracresol I'm not sure I have a preference.
 
@Ramanujan if the sum of smallest two forces is less than or equal to the largest force, then you can
 
@AccidentalFourierTransform So as a beginner, I ought to go for Zeeman?
@JohnR What do you make of @Accidental's proposition?
 
11:51 AM
@Ramanujan The vector of largest magnitude you can make from two vectors is the sum of the magnitudes.
@Ramanujan The smallest you can make is the difference of the two magnitudes.
 
as a beginner, go for whatever your book/professor introduces first :-P
 
@yashas, i tried by drawing a cordinate axes such that F1, F2 acting along x and y axis and F3 acting at an angle if 225° then i got Rx=-4.898N and Ry=-4.1243N
 
@Ramanujan You can adjust the angle b/w the vectors to get a vector of any magnitude with the limits.
@Ramanujan 5 + 8 < 14
You won't find such a combination.
 
@AccidentalFourierTransform I'm...still in high school (don't laugh) ._.
 
@paracresol Are you from India?
@Ramanujan Haven't heard of triangle law of vector addition and triangle inequality?
 
11:53 AM
@paracresol I guess I agree. You are essentially just calculating the energy of a magnetic dipole in a magnetic field, which is classically easy to do.
 
@paracresol I don't bug high school students
So idk who you are
 
@yashas, I have only heard about triangle law of vector addition but not other one
 
@JohnRennie Alright then! So Zeeman it is! Thanks @Accident!
 
@Ramanujan If a, b, c are sides of a triangle, then a + b > c, a + c > b, b + c > a
 
@Secret I don't think I can effectively answer your questions on the specific meaning that number is set up to have without spending a lot of time with their internal notes (which I don't have access to :( )
 
11:55 AM
@paracresol np, and good luck w that
 
ok nvm then
 
@Ramanujan That result (triangle inequality) can be proved easily using vectors without invoking the triangle inequality itself.
 
@yashas is my attempt to solve correct?
 
@Secret but they have made it clear that they have constructed this variable so that if it disagrees with the standard model then this would suggest lepton flavor violation, and that in the direction observed would be consistent with the other analyses
 
Anonymous
11:56 AM
Yohooo
 
@0celouvsky A long time ago...asked around for help with getting started on Noether's theorem... you 0celo7 took me on a roller-coaster ride ;)
 
@Ramanujan The sum of two vectors is obtained by joining the head of the first vector to the tail of the second vector. As the three vectors form a triangle, their lengths (magnitudes) must obey the triangle inequality.
@Ramanujan I have no idea what you did.
 
@Secret and that's about as much as I can say since I have a relatively small knowledge of this topic
 
@yashas so what is the easiest way of approaching such sorts if problems?
 
I already wrote an entire solution :|
Scroll up and read my messages again
And try to understand; don't just learn the final result.
try to understand how one can arrive at that result
 
11:59 AM
It means if there was 6N instead of 5N then it would produce a 0 resultant..
 
Googles "Zeeman effect"
 
@yahsas
 
It needn't produce a 0 resultant for every angle but there is an angle — when the vectors are anti-parallel — which produces 0 resultant.
 
Well, I probably have much less knowledge on particle physics, and trying to make sense of what they are presenting by looking for ratios and what channels they are considering.

Hmm,... lepton flavor violation, it seems that will suggest the leptons will participate in some kind of mixing, just as how we have found there is neutrino oscillation
But again I need to revise whether SM allows interconversion between two lepton flavors
 
@Secret The knowledge I do have is mostly from doing a lot of undergrad research @ ATLAS
 
12:02 PM
ATLAS?!
LHC?
 
and all the CERN analyses work the same and people use the same conventions and acronyms and the like
so at least I can get past that barrier (or at least interpret it), but you should expect me to have little knowledge beyond that
(for now, at least?)
 
@Yashas The LHC does many undergrad and postgrad projects
 
I should go buy some food ᕕ(ᐛ)ᕗ
adulting is boring
 
@Secret How many undergrads get a chance to do research there?
 
As always, I rarely pay attention to numbers, I only knew from the feedbacks it is a good project
 
12:05 PM
@AccidentalFourierTransform Oh, a child at heart? ;)
 
@yashas, i hope you mean this'
 
at least at my undergraduate (R2) university, who did research and who you got to do it with was up entirely to the undergrad
 
Anonymous
I think even Spacex has some undergraduate internships. Most big organizations do.
 
that is, the aspiring undergrad had to convince a professor they were worth their time themselves
 
12:07 PM
Hi all
 
I actually think I fucked over most of the faculty in this regard by convincing almost all the undergraduates below me that if they wanted to go to graduate school then they had to do research
 
@Ramanujan Such a triangle cannot exist because it violates triangle inequality.
 
Anonymous
@GPhys I'd like to know your story of getting an internship at CERN...
 
Anonymous
Did you apply yourself?
 
no no it's not like that at all
 
Anonymous
12:10 PM
Or some professor recommended you?
 
@yashas, If the sum of smallest forces is less than or equal to the largest force, then it can't produce a 0 resultant. Is it?
 
we had a new hire at the university who joined our university's high energy physics ATLAS group (which is now 3-strong)
 
Anonymous
@GPhys Ah! Then?
 
he had his PhD from Princeton doing dzero HEP-ex and then had been doing postdocs for ATLAS stuff at several universities and he was hired at our university the year after I started
 
@Ramanujan Sorry, that was a serious typo. I meant sum of two forces is greater than or equal to the largest force.
 
12:11 PM
the new professor decided he wanted to be the cosponsor for our university's society of physics students
 
becaz you asked this right now, it is an indication that you did not bother understanding what I wrote
 
this indicated to me that he at least did not abhor undergraduates, and I judged his personality would mesh fine with mine
 
you simply tried to apply the final result I told to the problem
this won't help you
 
@GPhys what?
Why did that fuck over the faculty
 
I knew I was interested in high energy physics, so after a SPS meeting I just asked if he would be interested in an undergraduate researcher and explained what my physics/math/programming background was
I think the programming background was somewhat important here
and, he said yes
and that's about it \o/
 
12:13 PM
@yashas, but in 2 other points you only talked about 2 vectors. HERe we have 3
 
Anonymous
@GPhys Oh, now I see =) There's a bit of luck involved there ;)
 
@0celouvsky in the sense that faculty who were never getting asked to do undergrad research are getting asked now
 
two vectors + resultant = 3
 
@GPhys so?
 
@Ramanujan I won't help you again if you don't make any attempt to understand the problem. You even ignore the explaination and wait for the final result.
 
12:14 PM
@0celouvsky and I don't mean it in any other sense
 
Maybe I'm an R1 scrub but everyone has undergrads
 
not at my (former) university
 
Were they getting pestered 24/7 or something?
And were these people expecting to get paid?
 
These are somewhat details questions for me on others actions
although, I did get paid
I have no strong opinion on the morality of whether or not the undergrads should be getting paid, in general
 
@yashas,
Two vectors + resultant = 3

(5N+8N) + (x)=14N

x=1N. Is it done then?
 
12:17 PM
.
 
?@yashas
 
maybe I will one day, but I haven't given it much thought or care at the current time
 
Let me explain again
You have two vectors, 5N and 8N and the question asks if there is any combination which gives a resultant which has a magnitude of 14N.
Let us solve the question for any two vectors $\vec{a}$ and $\vec{b}$
 
@yashas, its not 6. Its 8
 
I think what you have to understand about my undergrad university's physics program, @0celouvsky, is very little of the majors were going to graduate school at all
and the very few that did went to the same university
when I inquired about this, I was told only rarely did they have students seek much higher than this, and even then often only "moving up" to the R1 university of the state
 
12:19 PM
@Ramanujan The triangle law of vector addition states that the resultant vector is the vector draw from the tail of $\vec{a}$ to the head of vector $\vec{b}$ when the tail of vector $b$ and the head of vector $a$ coincide.
 
so I generally sought out and did all the things I knew I needed to do to get accepted where I did, e.g. Stony Brook etc
 
The length of the vector represents its magnitude.
@Ramanujan As the 3 vectors, $\vec{a}$, $\vec{b}$ and $\vec{R}$ form a triangle, their lengths must obey triangle inequality.
 
but I do mean to say I think I managed to sufficiently change the undergraduate physics culture/attitude at my university before I left
 
@Ramanujan Triangle inequaliy tells that $a + b > R$ and $a-b < R$.
 
@GPhys And you caused it all?
 
12:22 PM
@Ramanujan Sum of $\vec{a}$ and $\vec{b}$ can give $\vec{R}$ if and only if their magnitude satisfies the triangle inequality.
 
@0celouvsky it all? I mean we're talking needing to convince like 8 people here
 
@Yashas Do you know how to prove the triangle inequality?
@GPhys oh
 
@0celouvsky I know 3 ways as of today.
 
good
I'd be willing to bet many grad students would struggle
 
it's much less dramatic than it sounds like, but most of them really had no idea what they were getting into
 
12:24 PM
@GPhys I see
 
and it was a lot of work for me to figure out, so I thought it better if I just shared
but, my thesis advisor ended up on the committee that was reshaping undergrad physics major curriculum at my university during my senior year
and I'm glad I was able to provide a lot of input in that regard
because I felt like the required/optional classes were set up wrong
in the sense that the required physics major classes weren't even the reasonable classes you would expect to have to take if you're going to physics grad school (although they were offered)
for example, QM wasn't required for the physics degree
 
@yashas, is the explanation all.in all
 
?
 
and then there were some classes that were required that I didn't see a lot of other R1 universities requiring that were more obscure
 
like?
 
12:28 PM
4 physics lab classes, a sole class dedicated to optics
two mechanics courses (after physics 1)
 
@yashas, is the explanation finished?
 
Lagrangian/Hamiltonian mechanics?
 
lagrangian, in the second
the entire thing wasn't really set up to make it easy to fit in the courses graduate schools expected you to take
especially, for example, if you wanted to take, e.g., E&M before the GRE
 
@JohnR @Accident Could you have a look at this page for me? I'm not sure what M_j refers to here ( second paragraph, 7th line ) ._.
 
Anonymous
@Ramanujan A friendly warning. The approach of "going by the questions/exercises" is a very bad one. You'll end up wasting a lot of time in gathering scattered bits of knowledge from here and there.
 
12:31 PM
it's fine for the physics major program to accommodate people who are not intending graduate study in physics, but a program that actively impedes it by requirement is just silly
 
@paracresol page?
 
@GPhys yeah I see that
 
@blue, so what should I do? Could you suggest
 
@GPhys My department (nuclear engineering) is a little similar. They have a lot of mandatory reactor courses, but 75% of the graduate research has nothing to do with reactors.
 
12:32 PM
Thought I put that in >_<
 
There's a medical physics track but no nuclear materials track
(which is the interesting bit)
 
@Yashas Nah, this is different ._.
 
I made the case that it should be set up for smooth sailing for those intending to do graduate study in physics
 
Anonymous
@Ramanujan If you are self studying then go and buy some good books or video lecture courses. Or if you can, join some good institute/teachers. Learn all the concepts properly first. Problem solving is the easy part after that.
 
and the decision they finally decided on for the new structure of the physics major was successful in this regard
 
12:34 PM
good
 
oh no
I am trying to prove a thing but it involves the transversality theorem
 
oooo
I can help
Homotopy transversality or jet transversality?
 
Not a clue!
 
what's the context
 
Trying to prove that every non-compact manifolds admits a vector field with only finitely many zero (or isolated zeroes, I'm not sure which)
only zeros at singular points, that is
 
12:37 PM
@paracresol I think $J$ is the total angular momentum and $M_J$ is the component of the angular momentum along the $z$ axis, where in this case the $z$ axis is defined by the applied field.
 
6
Q: Every manifold admits a vector field with only finitely many zeros

user15464Let $M$ be a smooth manifold. I am trying to prove that $M$ admits a vector field with only finitely many zeros. This will follow if we can find a function $f : M\rightarrow \mathbb R$ such that $df$ has only finitely many zeros, but I cannot find such a function with this property either. My i...

 
every noncompact manifold admits a vector with with zero singularities
 
I get this
 
that for compact ones you can only get finite is a corollary of Morse theory
 
Though I guess the exact number of singular points isn't much of an issue
 
12:38 PM
@Slereah the transversality theorem says that an arbitrarily small homotopy can make your map transversal
 
i need it to prove that all non-compact manifolds admit a nowhere zero vector field
 
@Slereah let me know when you have that proof
 
Geroch proves that but he uses the fact that every manifold has almost everywhere zero vector fields
Basically he shoos the singularities off to infinity
 
@JohnRennie Wait...normally wouldn't a component of angular momentum in, say, the z-axis be denoted as J_z, assuming J is the total angular momentum? (I speak from whatever little experience I have in Classical Mech... not sure if QM nomenclature is very different ._.)
 
it's not clear to me what $f_\nu(x)$ is
Maybe $F(x,v)=f_v(x)$
 
12:41 PM
Sounds like it yeah
"A classic method - I think of Steenrod - is to triangulate the manifold then form the vector field whose singularities are the barycenters of the triangulation."
Are all manifolds even triangulable?
(also lol steenrod)
 
@Slereah He took that proof from page 148 of Guillemin & Pollack, btw.
$\mathfrak M$
our manifolds should be $(\mathfrak M,\mathscr g)$
@ACuriousMind help, presheaf of modules makes no sense
 
$\mathscr{M}$
O'neill defines the Lie derivative weird
 
"more generally, $\mathcal S(E)$ is a sheaf of $\mathcal S_X$-modules for an $\mathcal S$ bundle $E\to X$"
Jesus
@Slereah page?
 
46
I mean it's fine, but he never even defines it as like
The derivative definition
$$\mathcal{L}_V T = \lim_{t \to 0} \frac{\phi^*_{-t} T - T}{t}$$
 
he will probably give that definition later when talking about Killing vectors.
lol, locally free sheaf
this terminology
 

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