The h Bar

12:09 AM

@ChrisWhite Good evening

12:29 AM

@0celo7 Express a symmetric matrix as part of a quadratic form, then (as long as there are diagonal terms) just continually complete the square and you get a diagonal matrix, (if there are no diagonals just change variables until you get one then do it), use this to prove you can diagonalize a symmetric matrix, exercise.

0celo7

@bolbteppa The fact that Hermitian matrices can be diagonalized in an eigenbasis is proved in Shakar's QM book

Symmetric $\subset$ Hermitian

dmckee

1:42 AM

@MAFIA36790 The moderators have access to a suspension reason "consistently low quality questions over time", but we don't have one for consistently poor answers.

And we try not to be in the business of judging correctness in our official capacity.

In our capacity as users with the downvoting power is a whole 'nother matter, of course.

Secret

$$H=n\cdot\sigma\otimes I $$

\begin{align}
[H,\rho] & =\sum_{ijklm}n_i \sigma_{i,jk}\delta_{lm}\rho_{kp,mq}-\rho_{pj,ql}n_i \sigma_{i,jk}\delta_{lm}\\
& =\sum_{ijkl}n_i \sigma_{i,jk}\delta_{ll}\rho_{kp,lq}-\rho_{pj,ql}n_i \sigma_{i,jk}\delta_{ll}\\
& =\sum_{ijkl}n_i \sigma_{i,jk}\rho_{kp,lq}-\rho_{pj,ql}n_i \sigma_{i,jk}\\
& =\sum_{jkl}n_x \sigma_{x,jk}\rho_{kp,lq}-\rho_{pj,ql}n_i \sigma_{i,jk}\\
& +n_y \sigma_{y,jk}\rho_{kp,lq}-\rho_{pj,ql}n_y \sigma_{y,jk}\\
& +n_z \sigma_{z,jk}\rho_{kp,lq}-\rho_{pj,ql}n_z \sigma_{z,jk}

dmckee

As for your question "Is there a way to stop them...", well, a high enough downvote to upvote ratio brings the a-ban down on them for a while.

But these users tend to be very persistent. In some case that means patient and in other it means making new accounts to carry on.

Secret

and the compactified expression for Pauli matrices as shwon in wikipedia, it is still in some sense need to write out all 4 terms of it https://en.wikipedia.org/wiki/Pauli_matrices

Is that all I can simplify down to in index notation and then I must swtich back to computing them via the matrix way (by writing out explicitly all components?)

(grr, will massage this problem into one that can fit the main site's guidelines as per advice, and see how it goes. I am just so bad at indices)

0celo7

@dmckee I'm doing a guided reading course and my prof was supposed to email me yesterday with the problem set for next week

should I email him and remind him

dmckee

@EmilioPisanty Of all the users who rank high on that list I feel that Marty Green could have something really worthwhile to offer the physics community if he would treat it as a set of puzzles and interesting facts instead of trying to right a percieved wrong from a hundred years ago.

@0celo7 Depends. Does he have a history of forgetting stuff? Or is he usually on the ball?

In the former case you probably should, but in the latter give it a bit.

0celo7

1:49 AM

@dmckee He's not great about remembering things

0celo7

2:21 AM

@dmckee lol this structure:

does that even make practical sense

0celo7

2:40 AM

@Slereah You got destroyed here physics.stackexchange.com/questions/267916/…

bolbteppa

2:55 AM

I'm sure Shankar does it with eigenvalues, you can also prove it by completing the square, and there's a third quicker method when all principal minors exist

0celo7

Shankar does do it with eigenvalues.

bolbteppa

Look in Gelfand or Anastassiou for Lagrange's Method (complete the square) or Jacobi's Method when you get sick of computing all that stuff to get the answer

dmckee

@0celo7 Seems intended for a single, very tightly defined lift. Presumably at one end of a assembly line or something similar.

0celo7

Solving for all the reaction forces was not fun.

dmckee

I'm told that such specialized designs make up a surprising fraction of some engineer's careers.

@0celo7 Well, no. It wouldn't be.

0celo7

3:02 AM

Although there is something satisfying about finding that one equation that allows you to unravel the rest.

dmckee

But knowing from experience (a) that it can be done and (b) some of the tricks to make it go smoothly is part of the point, I'm sure.

0celo7

@dmckee The prof was an industrial ME, he secretly loves this stuff.

dmckee

::chuckles::

Not that secretly, I suspect.

0celo7

@dmckee Nah, he's pretty chill. But he lectures without notes and has a bunch of horrible machine designs memorized.

So he probably enjoys it.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Hello people :-)

0celo7

3:16 AM

hello

I made some sign errors -.-'

Found it!

Yashas Samaga

4:28 AM

Anybody knows a good experiment (IRL not an animated) video which shows the properties anode rays?

Bernard Meurer

@YashasSamaga Yes, but it's NSFW

user218912

what?

Yashas Samaga

no problem. I just need one :P I don't have the aparatus in the lab (perforated plate) and I am not going to make one.

Just need to know how it looks in IRL. Youtube spams with all cartoon/animated videos. -__-

Bernard Meurer

@YashasSamaga Sorry, I read anal rays, no I don't

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

-_-

Yashas Samaga

4:39 AM

I have a question about this video. youtube.com/watch?v=2xKZRpAsWL8

Why do you see blocks/patches of light in the tube?

Why isn't it continous?

Gas exists everywhere in the tube? Hence, the electrons should excite the atoms everywhere and hence one should see a continous line of light (wrong terms but I guess you understood what I am trying to convey).

user218912

@BernardMeurer anal rays are related to fish.

user218912

I discovered.

Bernard Meurer

@3750 You're pretty brave if you googled that

user218912

xD

user218912

I searched it on google books.

Bernard Meurer

4:44 AM

Well, those were not the anal rays I was referring to though

user218912

The anal ray is a flap in the area at the bottom of a fish.

user218912

anal ray

user218912

where A-B is.

Bernard Meurer

Not the ones I was talking about still

user218912

._.

John Rennie

4:54 AM

@Obliv yes, you just need $10^{36}$ protons and wait for a year.

@JohnRennie Hai

Morning

Top of the morning.

@JohnRennie Innit a bit early over there?

user218912

@JohnRennie you're an early bird.

John Rennie

4:59 AM

I start work at 05:30!

user218912

woah.

John Rennie

But then I only work until 09:00 :-)

Bernard Meurer

@JohnRennie Aren't you retired?

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

:O

user218912

@JohnRennie what do you do all day then? answer questions on pse? or...?

John Rennie

5:00 AM

And to be honest I only do a couple of hours work during that period. The rest of the time I spend surfing the Physics SE.

@3750 that's a hard question to answer because I don't have a routine (apart from the few hours up to 9 a.m.)

Bernard Meurer

@3750 He cooks nice food and posts it on facebook

John Rennie

I spend a lot of time on the PSE, but I read, exercise (walking or cycling), listen to music, watch TV. The time passes ...

@BernardMeurer I've stopped posting the pictures on Facebook since everyone got bored with it :-)

Bernard Meurer

@JohnRennie Awwww, I think they're pretty cool

John Rennie

At the moment I'm scratching my head and trying to research this:

0

Q: Electron Beam does not appear to be continous (CRT Experiment)

https://www.youtube.com/watch?v=2xKZRpAsWL8 Why do you see patches of purple in the tube? Shouldn't there be continous lines of colour? As far as I know, you see the rays because some of the electrons knock the electrons out of the gas contained in the tube. When the excited gas atom de-excites...

There has to be a simple reason why you get something that looks like a standing wave, but at the moment I can't think what it is.

Yashas Samaga

:D It doesn't happen in my lab.

probably apparatus related...

John Rennie

5:05 AM

@YashasSamaga my guess is that it's pressure related. Note that the pattern changes as the air is being pumped out.

'kin 'ell I've got a server down! Excuse me for a few minutes ...

user218912

you guys should check out noise music.

user218912

I posted a few links before.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Where?

user218912

Aube - Low Spin Drift

►

user218912

am I the only one who likes this kind of music?

user218912

5:20 AM

because I listen to this genre everday.

Bernard Meurer

I guess it's cool if you're so high on synthetics you've gone death

user218912

It's cool period.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Unique comes to mind.

user218912

aube died in 2013.

user218912

I'm in process of listening to all of his songs.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

5:37 AM

Have fun :-)

He preferred to call them "designs," btw.

John Rennie

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ for a small and rather select subset of meanings of the word fun :-)

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Pink Floyd was once called "noise."

John Rennie

Not by me they weren't. Though come to think of it I suspect my parents may have referred to them as that bloody noise a few times.

Actually my Mum quite likes Dark Side of the Moon, and she's 83 :-)

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Interesting.

John Rennie

She's not so keen on Hawkwind though ...

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

5:48 AM

Floyd has an almost mystical appeal to all generations.

I still get goose bumps just thinking about "welcome to the machine."

Dunno what it is.

John Rennie

So, so you think you can tell
Heaven from Hell,
blue skies from pain.
Can you tell a green field
from a cold steel rail?
A smile from a veil?
Do you think you can tell?

Did they get you to trade
your heroes for ghosts?
Hot ashes for trees?
Hot air for a cool breeze?
Cold comfort for change?
Did you exchange
a walk on part in the war
for a lead role in a cage?

Some of Roger Waters' lyrics are almost painfully beautiful

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

6:05 AM

By the way which one of you is Pink?

John Rennie

Lime and limpid green, a second scene
A fight between the blue you once knew.
Floating down, the sound resounds
Around the icy waters underground.

Not all their lyrics make sense :-)

Still beautiful though.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

poetic

Speaking of poetry @JohnRennie I found this the other day, what do you think?

In the midst of life, it happens that death comes

and takes a measure of man. That visit

is forgotten, and life goes on. But in silence

the suit is being sewn.

Tomas Tranströmer, Black Postcards

John Rennie

6:30 AM

I have to admit I don't like poetry unless it's song lyrics. I wonder if anyone has set Tranströmer's poetry to music.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

I think it has potential. :-)

Perhaps, I'm reading too much into it.

koolman

6:54 AM

can anyone tell me what is the difference between voltage and emf of a battery?

John Duffield

@JohnRennie : Games where the point is to achieve an arbitrary target aren't that appealing to me. Reputation 190,176:

Yashas Samaga

@koolman There are essentially the same. E.M.F is the potential drop across the battery when no current is flowing whereas voltage is a general term.

koolman

@YashasSamaga when internal resistance is present

Yashas Samaga

Yes ^ the internal resistance will cause a potential drop when current flows through it which is why the external voltage you measure of the battery is ALWAYS lesser than the E.M.F.

^ not true if you are charging the battery.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

1.Emf is the total voltage in the battery while the potential difference is the work done in moving a charge against the electric field between two specific points in the circuit.
2.Emf is always greater than the potential difference.
3.The concept of emf is applicable only to an electrical field while the potential difference is applicable to magnetic, gravitational, and electric fields.

Yashas Samaga

7:00 AM

E.M.F is just a term used to differntiate between actual voltage across the battery and the voltage across the battery when there is no current.

If there wasn't a special term called E.M.F, we would have lot of trouble in describing circuits because voltage across a battery depends on the external circuit whereas E.M.F is a fixed constant for a given battery.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

How do you find that ironic? @JohnDuffield

John Duffield

@MAFIA36790 : As Emilio Pisanty is to Pentcho Valev, so am I to him. Don't forget that I'm the guy who's always referring to Einstein and the evidence.

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ : JR indulges in gaming here to get his high score.

user116211

@JohnDuffield Well, you talk some sense; that guy is surely a crackpot.

John Duffield

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ : No matter what system you make up; there are always going to be "gamers."

Yashas Samaga

Having high rep @ PSE might help with your resume?

user116211

7:07 AM

@JohnDuffield Well, you talk some sense; that guy is surely a crackpot.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Players gotta play @JohnDuffield

David Z

@YashasSamaga nah, not for academic jobs, but maybe in other fields

John Duffield

@MAFIA36790 : he's "misguided", Mafia. See this exchange where I tried to educate and inform. I didn't succeed. But there again, I didn't succeed with Slereah either.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Any publication date on your second book yet? @JohnDuffield

user116211

@DavidZ: I've seen a guy referencing his SE account in his letter_statement of purpose_ to foreign school for admission in phd course under other activities involved. Also, seen some math guy mentioning his activity at MSE in Linkedin.

user116211

7:15 AM

@JohnDuffield yeh; he lives in his own world outside of which all are fostered from conspiracy and all that stuff; I don't wan to talk about that anymore.

Danu

@MAFIA36790 It's under "Other activities" for me too ;)

user116211

@Danu Yeh, it's a nice thing to mention that, I suppose.

John Duffield

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ : hell no. I'm only on chapter 2.

Noted Mafia.

David Z

Well... okay, it might help a tiny bit, in the sense that professors don't want to be seen as encouraging research to the exclusion of all else. It's supposed to be good to have a couple filler items under "service" or "other activities" for that purpose. But in practice, they're looking at your research potential and everything else gets mostly ignored.

Most professors have probably never heard of Stack Exchange, and if they know what it is, they're more likely to view having a high rep as a strike against you.

Danu

^

Oh, wait, no I don't agree it'd be a thing against you, ever

Just skimmed over

David Z

7:20 AM

Why not? I'm pretty sure more profs would consider it a negative than a positive contribution

Danu

What, really? It's "outreach", which I think shows passion more than anything

Trying to teach people physics in your free time...

John Duffield

@MAFIA36790 : Reminds me of a famous guy. You must be taking about Voldemort.

Danu

How would that be a bad thing?

user116211

@JohnDuffield :)

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

A lot of people call it a "cheating site." @Danu

Yashas Samaga

7:23 AM

"cheating" why? :-(

David Z

@Danu to the kinds of people who read and evaluate CVs, "free time" - or, time spent contributing to PSE - is just time you should be working on research but aren't

Danu

@DavidZ Cry evrytiem

I will now blame my rejection by the top US universities on this :D

user116211

@Danu oh, Jesus ;)

David Z

@Danu haha. Sure, why not.

To be honest, I doubt it really makes a difference, but in the few cases where it does, I do think the difference is more likely to be negative than positive.

Danu

Hmkay.

user116211

7:27 AM

David Z

Maybe like 95% of the time it doesn't matter, 4% of the time it counts against you, and 1% it helps you.

2

user116211

71

Q: Do Danish and Canadian militaries exchange gifts on a disputed island?

The following image is circulating on LinkedIn: There is an island which is disputed territory between Canada and Denmark. The militaries of both countries periodically visit to remove the other guy's flag and leave a bottle of Danish schnapps or Canadian whiskey. This is what happens whe...

military canada denmark

David Z

rough estimates

Danu

Fair enough.

user116211

That's how a war needs to be ;)

user116211

7:28 AM

@DavidZ noted

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

@YashasSamaga one could be given a take home exam and then post the questions on the site, right?

Danu

How are you @DavidZ?

Still in China?

David Z

7:45 AM

Yep

Danu

How's things there?

David Z

Hot, lately

Well, not so much today, but most of this week it was very hot

Danu

Mmm...

It cooled down very quickly here over the past days

It's like 12 degrees (Centigrade) now :(

user116211

@Danu WoW! when is summer?

David Z

@Danu sounds very nice

Here it dropped from about 35 to 22 over the course of one night

user116211

7:50 AM

Here 32 degrees Centigrade; raining :)

user116211

This is monsoon of India.

user116211

@DavidZ yep; sounding same like here.

Danu

@DavidZ Awright

22 is nice though

David Z

Relatively, yes

I guess 22 was earlier today; maybe it's up to like 25 by now

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Do you speak Chinese?

David Z

7:53 AM

Only a little

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

cool

user116211

@DavidZ Can you write some?

David Z

why?

I mean, 为什么？ :-P

2

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

:D

user116211

@DavidZ ;)))

hwlau

8:08 AM

OMG, see something weird here

user116211

@hwlau where?

hwlau

Nothing just see David Z writing cheinese

user116211

awooh

user3183724

9:15 AM

@vzn Sorry for the slow reply. Graduate level, our interest is in quantum simulation of photosynthesis. There's a bunch of proposals waiting to be harvested, most of them dealing with the fact that photosynthesis operates in a regime where quantum light harvesting is not optimal (decoherence mainly) and still manages to outperform pretty much everything we know classically, while at the same time showing some quantum signatures

@DanielSank Hi Daniel! So if I am not mistaken, you have quite a background in qubits and such. My main question is if you know of any research in which they have investigated the behaviour of single/multiple qubits under high levels of decoherence (introduced artificially I'd say). You can think of fluctuating magnetic fields for superconducting circuits for example. My worry is that for high levels of decoherence the linewidths will become super broad

So I do not know how one would then say, ah, the qubit has a decoherence rate of this amount of MHz. Moreover, standard T2 measurements won't work if the T2 is lower than the time it takes to measure your Ramsey or whatever

Of course, it is very counterintuitive because as has been pointed out most research aims to decrease the decoherence rate, not increase it

skill patrol

He's very busy this month.

FYI :-)

user3183724

Not sure if it is aimed at me, but if it is, that's fair enough! I'm trying to look into it myself as well, just thought that someone in the field might remember a specific reference or two

Danu

10:04 AM

Hi @user3183724

user3183724

10:54 AM

@Danu Didn't know you were still into physics Danu

user116211

12:51 PM

@DanielSank: Welcome.

DanielSank

@user3183724 would you mind emailing me a description of what you're actually trying to do?

@MAFIA36790 hi

Danu

1:33 PM

o/

skill patrol

\o

Bernard Meurer

o/

I feel like if we ever did an h-bar meetup the first ten minutes or so would be slapping each other

Danu

^

Emilio Pisanty

whoooooooooo

physics.stackexchange.com/help/badges/132/…

2

ACuriousMind

@EmilioPisanty Welcome aboard :)

user116211

1:41 PM

@EmilioPisanty congrats :)

Emilio Pisanty

@ACuriousMind Thanks

There was a time where you and me were neck and neck on that one

but you beat me by a month

Bernard Meurer

@EmilioPisanty Nice! Congrats mate!

Y'all still gotta climb though, only John and Floris are famous down here :p

Emilio Pisanty

@BernardMeurer Who cares about fame? I can singlehandedly dupe-hammer now.

user116211

@BernardMeurer And Lubos but he never came here.

0celo7

2:23 PM

@ACuriousMind Any thoughts on my Morse theory question

ACuriousMind

@0celo7 You're reading the book, not I. And you seemed to have found a (partial) solution to the problem, so I did not spend time trying to solve a problem only to have you tell me "I knew that".

skill patrol

Jesus, I come into the elu room and say

in English Language & Usage, 9 mins ago, by skill patrol

Brext is a great topic.

and BANG a mod tells me to leave

>8(

ACuriousMind

@skillpatrol If you are surprised that politically controversial topics might blow up in some rooms, I envy your faith in humanity. Why would you say something like that if not to incite a heated debate, anyway?

skill patrol

These are all Americans.

ACuriousMind

@skillpatrol Who are "These", how do you know, and what has that to do with anything?

skill patrol

2:31 PM

Your reasoning follows if it was a mixed crowd.

I know them pretty well :-)

That particular mod has my number.

ACuriousMind

@skillpatrol Still, why would you insert that statement into an ongoing conversation about something completely different?

skill patrol

No, they were talking about it at the time

Moreover it is a great topic

At least for Americans

That and Trump :P

0celo7

@ACuriousMind What did you think when you were reading the book?

I don't understand step 1 of the proof

If we already have that in our hypothesis, why is he restating it?

skill patrol

Did you know @ACuriousMind that Trump proposed to build a wall between Mexico and the US to keep the Mexicans out.

Slereah

Well germans know all about wall building

user116211

2:41 PM

@Slereah The Berlin Wall?

user116211

The Atlantic Wall?

skill patrol

So do the Chinese

:P

0celo7

@skillpatrol Illegal Mexicans.

And other illegals, like ISIS operatives.

ACuriousMind

@Slereah That we do

0celo7

Don't misrepresent his policies.

Slereah

2:42 PM

ISIS operatives don't come from Mexico, though

ACuriousMind

We have a party lobbying to re-erect the wall between West and East.

0celo7

@Slereah They come through Mexico, allegedly.

Slereah

Allegedly.

user116211

Can't they use ladder to skip over the wall?

ACuriousMind

(They're a satirical party)

user116211

2:43 PM

And where would he get so much money to build the wall?

user116211

Let alone maintaining them.

0celo7

@Slereah They say they do, for what it's worth.

skill patrol

Politicians build walls

ACuriousMind

@0celo7 Rereading what you wrote, I do not understand your issue.

That $f^{-1}[c-\epsilon,c+\epsilon]$ contains no other critical points and is compact is part of the hypothesis of the theorem (as indicated by the "suppose that").

0celo7

@ACuriousMind I know.

So why is step (1) a thing?

Half-way down page 15.

ACuriousMind

2:45 PM

@0celo7 It's not "step (1)". It's one of the two conditions that $\epsilon$ needs to fulfill.

The hypothesis only gives you that some $\epsilon$ fulfill (1).

You are told to choose $\epsilon$ small enough so that both (1) and (2) hold.

0celo7

@ACuriousMind I'm not convinced.

vzn

@user3183724 did see a paper a few mos ago that probably would be relevant, let me try to dig it up, hopefully saved it, there was another guy in here looking into photosynthesis/QM models. anyway there are only a "few" labs in the entire world that are working with qubits, it would be helpful if you sketch out your experiment. also presumably your advisor or "principal investigator" has already tipped you off on some papers/ refs?

ACuriousMind

@0celo7 What is there to be "convinced" of?

skill patrol

3:07 PM

\o @dmckee

Obliv

3:21 PM

I'm supposed to prove $x \to x^k$ is a surjective map iff $k$ is relatively prime to the order of $x$ in a finite cyclic group $G$. I don't believe being relatively prime to the order is required though

suppose $G = \{e,x,x^2,x^3,x^4,x^5\}$ then the order is $6$ and so the map $x \to x^5$ would be the only surjective map

I don't get it

ACuriousMind

@Obliv What do you not get? You haven't made any argument for why the statement should be false yet.

Obliv

For some reason I can't see what the map actually does with the elements. For a map $x^a \to x^b$ and setting conditions for the domain and target set/domain I understand

but doesn't this just map one elements of $G$ to an element of $G$?

ACuriousMind

@Obliv For a cyclic group, mapping the generator $x$ to something determines the images of all other elements if you demand the map be a group homomorphism (if you don't see this, prove it).

Obliv

@acuriousmind why would you need to demand the map be a group homomorphism? Why not just map the entire domain of $\langle x \rangle$ or whatever

ACuriousMind

@Obliv What?

Obliv

3:34 PM

I'm not sure I understand you correctly. Are you saying that $x$ gets mapped to $x^k$ then by a group homomorphism, you are able to map $x^2$ to $x^{2k}$ etc

ACuriousMind

@Obliv Yes, exactly.

Obliv

but then why must $k$ be relatively prime for this to be surjective?

ACuriousMind

@Obliv Well, that is what the exercise asks you to prove. Think about it.

Obliv

$x^{ak}$ for all $a \in \mathbb{Z}$ this element will be in the cyclic group so all of $\langle x \rangle$ will be able to be mapped to $x^{ak}$ no?

Physics Meta

1

Q: Why can't a question be deleted with answers while there is first a note given that it is only not advisable?

If you want to delete a question with an answer, you have an option to delete that question. But when you have made that option to delete the question it seems not possible. Is that a mistake of this program or is there an other reason?

bug questions deleted-questions

Obliv

3:49 PM

@acuriousmind I can't think about it if I don't understand the problem ;_;

ACuriousMind

@Obliv What do you not understand about the problem?

0celo7

Just cut up a 12''x12'' piece of copper into little pieces

my hands are blistered :(

and scraped up

workplace injury, can I sue?

Obliv

@acuriousmind I don't see what's stopping $x \to x^k$ and the corresponding group homomorphisms from being surjective.

wait give me a sec

ACuriousMind

@Obliv That's not "not understanding the problem", that's "not having the solution".

0celo7

lol

ACuriousMind

3:52 PM

@0celo7 Was that injury unavoidable?

0celo7

@ACuriousMind Convinced that any map has that property.

@ACuriousMind I could have worn gloves.

In hindsight, I should have

My hands are all banged up right now

got sliced by a rhenium sheet the other day

ACuriousMind

@0celo7 Then I guess that was a valuable learning experience but not something you can sue for ;P

0celo7

got my thumb caught in a sanding machine yesterday

Obliv

must have been a near death experience @0celo7

0celo7

@Obliv I'll grow my hair out and get it caught in the diamond wheel saw

Obliv

3:54 PM

you have a saw tipped with diamond?

0celo7

ACM would probably die in our lab

@Obliv yes

we need a new blade for it

Obliv

must be very expensive..

0celo7

and we're getting a diamond band saw too

should be coming any day now

Obliv

i thought you said hand saw for a second lol

ACuriousMind

@0celo7 What property? The claim is not that every $f$ can fulfill (1) and (2) - the claim is that for an $f$ that fulfills (1) for some small $\epsilon$, you can choose $\epsilon$ such (possibly smaller) that it also fulfills (2).

0celo7

3:55 PM

@ACuriousMind I'm not convinced that there is any $f$ that does that!

ACuriousMind

@0celo7 Why is that relevant?

0celo7

At least for $M$ noncompact

ACuriousMind

The theorem does not make an existence claim - it says that if you have such an $f$, then...

0celo7

I understand that

Obliv

if $\varphi : x \to x^k$ then $\varphi(x^2x^5) = \varphi(x^2)\varphi(x^5) = x^{2k}x^{5k} = x^k = \varphi(x^7)$ assuming the order is $6$. Then if $k$ were to be not relatively prime to the order, say $k = 2$, what keeps the map from being surjective

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