The h Bar

Las Vegas Raiders

05:20

Apparently not.

Fawad

06:09

Hi

Why can’t on some point Y (on extended AO) potential be 0?

John Rennie

06:20

@Fawad: if you write down the equation for the potential as a function of the distance $x$ from $O$ to $Y$ it should be obvious that it cannot be zero (except at infinity).

Slereah

09:27

Doing GR with units is hard

I always seem to be missing a $c$

Help me solve this math problem

John Rennie

@Slereah great lies of our time: factors of c and G can be reintroduced using dimensional analysis

Slereah

@JohnRennie Well it's not wrong, but it's not trivial in GR

Because there's several conventions

You have to decide what units $g$, vectors, the stress-energy tensor, etc have

John Rennie

@Slereah OK, gross oversimplifications of our time :-)

Slereah

even worse, specific components of vectors

Does $[x^0] = [T]$ or $[L]$

gotta decide which one you pick

I need to do a section on this, I think

user228700

11:33

Jul 4 at 8:21, by John Rennie

It's all coming together then! Scary!

user228700

@JohnR: Yes. We were out shopping today; bought a duffel bag, a backpack and everything...

Las Vegas Raiders

When will you buy a school shirt?

Secret

0

Q: Two opposite rotating clocks in Special Relativity

Time dilation experiments in centrifuge demonstrate, that rotating clock dilates according to predictions of Special Relativity. Clock hypothesis states, that acceleration does not affect time dilation. https://en.wikipedia.org/wiki/Clock_hypothesis We put one observer (1) with clock on one ar...

special-relativity

↻↺↺↻↺↻🗘●

Anonymous

@LasVegasRaiders "School" shirt? :O

Las Vegas Raiders

yeah, a shirt with your school name on it

Anonymous

11:45

@LasVegasRaiders Universities and colleges don't have any dress code as such in India.

Anonymous

Upto high school they have uniforms though...

Las Vegas Raiders

It's not a dress code, it's just a shirt with the name of the university on it.

Anonymous

Oh, yeah. But it's not compulsory to buy those. They give them out during college fests and stuff like that :P

Las Vegas Raiders

For free?

Anonymous

@LasVegasRaiders During college fests? Yeah

Anonymous

11:50

Otherwise you can buy them...but not compuslory

Las Vegas Raiders

Neat.

How's your lung condition? @Blue

Anonymous

@LasVegasRaiders What? :O I don't remember having any issues with my lungs...(?)

Las Vegas Raiders

Oh? Sorry it must have someone else.

Anonymous

Maybe you mistook me for someone else :P

Balarka Sen

@Blue you have chronic broncho-paracetahepaoctahedritis.

You just forgot all about it because cocaine

Anonymous

11:57

@BalarkaSen lol....maybe XD :: tries to remember ::

Las Vegas Raiders

you can tell Balarka has slept well when he uses long words :P

Balarka Sen

I just woke up from a smallish nap.

The master of long words is still at large: chartrain.org/PDF/Finnegans.pdf

Las Vegas Raiders

You made me load 849 pages for that!

Balarka Sen

sorry :p

Las Vegas Raiders

np

Balarka Sen

12:07

Well, at least, you have loaded 849 really good pages

Las Vegas Raiders

indeed

You should join the literature.SE

Their chat room is very lively

Balarka Sen

I get the impression that their goal is different from my interaction with literature. They're book-buffs, similar to the screening room people being movie-buffs. I don't think I belong to that collection of people.

Las Vegas Raiders

yeah, you don't strike me as the "buff" type

m.imgur.com/iovgTNf

Secret

Last night dream:

0celo7

13:27

@JohnRennie @ACuriousMind My computer won't start...

It crashed in the boot screen

user685272

before you OCed it?

0celo7

I did not OC

are you = @LasVegasRaiders

you both give god awful advice

user228700

@Secret Dude, what is that?

user228700

@LasVegasRaiders Huh?

Secret

@Kaumudi.H It's a weird type of bird of the size of cassowary (and the baby chick of it) seen in last night dream

It's beak has a spongy structure, presumably for suction like an octopus

user228700

13:40

Wow, I see.

user685272

Aren't you going to buy a shirt with your school's name on it?

Secret

Since my drawing is still not very good (as some user said the bird look horrifying), here's a pixar video which illustrate accurately the emotion you should expect to have when you saw that chick:

Piper Short animation film فلم الانيميشن القصير

►

user228700

@user685272 Who, me?

user685272

yup

user228700

No...

user228700

13:45

I hope to buy one during our technical festival but not before, no.

user228700

school shirt is not exactly a thing over here...

Secret

In the dream, that little chick is taken cared by me for some time, and the dream scene where it appears depict me having a reunion with it as I stroke its head and it portal jump across many tanks in some kind of biohabitat

As for the adults, they walk around casually in the theme park among people

Balarka Sen

you could buy a shirt and paint "Church of Scientology" on it

alternatively

user685272

custom t-shirts are popular

0celo7

@JohnRennie I was in my room reading, then I heard two strange noises coming from my turned off PC. Sounded like cracking. I turned it on, it crashed on the boot screen. The CPU light came on and I waited for a minute. I turned off the power on the back of the case. I turned it back on, repaired the disk, and it booted fine.

I'm worried about that cracking noise I heard.

user228700

13:48

@BalarkaSen Still thinking about ISI/CMI?

Balarka Sen

yeah i'm officially (whatever that means) preparing for them

user228700

Cool! :-) A good friend of mine is in her second year at CMI.

0celo7

Good god, my GPU scored 14,121 that time

user228700

@BalarkaSen Just those two?

0celo7

@JohnRennie Somehow my GPU benchmark is now higher than the Titan Xp

Balarka Sen

13:51

very nice. a friend of mine went to CMI this year

yeah just those. i dunno what else to take tbh

i mostly want to get in to CMI

user228700

@BalarkaSen Ooh, cool.

user228700

@BalarkaSen Ah, OK. It's excellent, I hear. My friend, however, is having a bit of a hard time there; she's the only girl in her class of 30-40 :-/

ACuriousMind

@0celo7 I'm at a loss what would make such a noise in a turned off PC - I'd guess it was just a cracking from some thermal stress in the case

0celo7

@ACuriousMind It hadn't been on since last night

Balarka Sen

yikes. i suspect that'd be hard.

not everyone has nonexistent social life like me

(aka not everyone is a madman)

user228700

13:55

It is. The last time we met, she specifically requested that we not talk about college.

Balarka Sen

heh

user685272

you said you had a friend?

Balarka Sen

"""friend"""

we are mathematical friends

user228700

We did, of course, just for a little, and she told me about how, even though her social life has pretty much gone to shit, the professors are next level amazing.

Balarka Sen

I have heard good things about the university academia

user685272

13:57

is it competitive to get in?

ACuriousMind

Is there anything in India that's not competitive to get into? :P

user228700

^

user228700

There are just too many of us; students and corrupt politicians, I mean.

user685272

^

ACuriousMind

@Kaumudi.H You're a student and a corrupt politician? ;)

Balarka Sen

13:59

it does not help that there are like 4 or 5 universities in all of india which has a decent math curriculum

@ACuriousMind we are all corrupt politicians, deep down

user685272

even survival is competitive for the poor

user228700

@ACuriousMind Dang, I phrased it wrong :-P

ACuriousMind

@BalarkaSen I may be corrupt, but I refuse to be called a politician!

0celo7

@Kaumudi.H i gotchu

ACuriousMind

Please don't joke about killing people. Again.

0celo7

14:01

does the ";)" not make it clear?

user685272

no

0celo7

Maybe not to you

Balarka Sen

rekt

ACuriousMind

@0celo7 Well, it's clear it's supposed to be some sort of joke. That doesn't make killing people any more an appropriate thing to joke about.

user685272

what's your problem?

0celo7

14:02

@ACuriousMind So, should I not worry about the noise? The only thing I'm worried about is the GPU power cable...it's touching the top of the case and pushing on the GPU slightly.

Balarka Sen

0celo is a nuclear engineer, he's allowed to joke about nuking

0celo7

@BalarkaSen god church

ACuriousMind

@0celo7 If it seems to be working fine now, I wouldn't worry about the noise any more.

John Rennie

@Kaumudi.H: hi, sorry I missed your earlier ...

0celo7

@ACuriousMind Is it not suspicious that it failed to boot?

user228700

14:04

@JohnRennie Hi! :-) Sure, no problem.

ACuriousMind

Depending on what "slightly" means, that cable may be a problem, but I think if the GPU is not bending under the stress or anything, I wouldn't worry about that either

John Rennie

@Kaumudi.H Buying stuff for college eh? Makes it all seem horribly real! :-)

user228700

Yep yep.

0celo7

@ACuriousMind I'm going to get an L-shaped power cable.

Balarka Sen

@0celo7 Satan is on your PC

- M. Night Shyamalan

ACuriousMind

14:05

@0celo7 A bit, but I think all of my computers failed to boot every once in while and I never found anything wrong with them

0celo7

Alright

John Rennie

@0celo7: if you get regular boot failures I'd be worried, but not after a single boot failure.

ACuriousMind

(Except for the one with the fried GPU, but that didn't have anything to do with booting)

0celo7

Ok. I need to figure out this power cable, for my sanity.

John Rennie

If it happens again check the diagnostic LEDs and see what they show.

user228700

14:06

@JohnRennie What's for lunch?

0celo7

I might be able to McGyver it

John Rennie

@Kaumudi.H I'll post a photo later. Did you see yesterday's lunch?

user228700

@JohnRennie No...

John Rennie

Lamb rogan josh with kitchari rice!

user228700

Wow. Was it delicious?

Balarka Sen

14:08

are you going to eat the keyboard too

/did you

user685272

you eat in front of the computer?

John Rennie

@BalarkaSen Only if I'm really hungry :-)

@Kaumudi.H Actually ... it was nice but not amazingly nice. The lamb had a nice flavour but I used a premade sauce and it wasn't that wonderful.

@user685272 it's the bachelor lifestyle :-)

Balarka Sen

@JohnRennie inner cyberpunk intensifies

user228700

@JohnRennie Ohhh, OK...

John Rennie

But I do like kitchari rice. It's basically a dahl pilau i.e. rice, lentils and spices cooked together.

user685272

14:11

you could have sprinkled some cheeze on it

John Rennie

@user685272 I did contemplate adding some cheese, but I thought it might detract from the flavour of the lamb.

user685272

right, right

0celo7

@JohnRennie do you eat vegetables?

user228700

No, he does not.

John Rennie

@0celo7 Yes. Monday to Friday I eat healthy meals - lots of green veg. I only splurge at the weekend.

user228700

14:13

LIES.

John Rennie

But I don't post pictures of the healthy meals because, well, they're boring. Who wants to see veg?

Balarka Sen

Coraline (2009) - Slime For Dinner - Movie Clip ★

►

John Rennie

@Kaumudi.H do you mind? I do a very nice vegetable risotto :-)

user228700

Ah, you and your risottos. I can't remember the last time your lunch wasn't risotto and had vegetables in it.

John Rennie

I had risotto once last week ...

0celo7

14:15

@JohnRennie where would I have installed that CPU maxing program?

Just need to check the water cooler

user228700

Except for that time you had a whole bag of apples for lunch.

John Rennie

C:\Program Files or C:\Program Files (x86)

@Kaumudi.H I did that again last Friday. Very nice too.

0celo7

@JohnRennie what is it actually called?

John Rennie

@0celo7 the CPU maxing app? Don't know.

0celo7

I thought you made it

John Rennie

14:16

Oh, EatCPU?

0celo7

yeah, can't find it

John Rennie

Probably in the downloads folder.

0celo7

and my computer won't search

I haven't figured out the Win 10 search

John Rennie

Or grab it from swarchive.ratsauce.co.uk

0celo7

is there some trick to it?

John Rennie

14:18

I never use the Win10 search. I've lots of hackeresque command line apps for that sort of thing.

Just win baby

hi peeps

0celo7

@JohnRennie it clearly doesn't work at all

Balarka Sen

why are you splitting your personality up in ten million chat users

0celo7

fuuuk that is blurry

Balarka Sen

that never ends well

0celo7

14:21

parkinsons, sorry

the windows 8 search was actually amazing

why did they break it?

even the file explorer full search can't find it

why is Windows so terrible?

John Rennie

@Kaumudi.H Today's lunch:

user228700

And what is this?

0celo7

A lot of fish

Just win baby

Balarka Sen

@Kaumudi ghoti

John Rennie

14:28

@Kaumudi.H They are called slices in the UK. It's meat in puff pastry. The one cut open is chicken and bacon, and there are also spicy chicken and pulled pork slices on the plate.

Balarka Sen

aw i am wrong

0celo7

it looks like fish

are you sure it's not

Balarka Sen

I thought it was fish patties

John Rennie

They are really good. The pastry is really crisp and flaky.

0celo7

@JohnRennie I'm going to muck around with Cortana

this is ridiculous

user228700

14:28

@BalarkaSen Huh?

Balarka Sen

does Cortana actually work

Just win baby

Deep fried?

0celo7

@BalarkaSen haven't tried

but people are saying I need to restart Cortana

user228700

@JohnRennie Oh, wow, I see.

0celo7

she apparently control the search

peterh

14:29

@EmilioPisanty I wrote an answer which may be attractive for you. :-) And, also my query about the cross-network migration statistics is finally ready. It was a nice, productive day! :-)

Balarka Sen

@Kaumudi.H en.wikipedia.org/wiki/Ghoti

John Rennie

@BalarkaSen Cortana is generally considered to be pretty good.

0celo7

@JohnRennie ...

so I am just retarded?

is that the answer?

user228700

Creative respelling of the word fish?!

John Rennie

It's supposed to illustrate how illogical English spelling is.

Balarka Sen

14:31

GB Shaw was a genius, yes

but Joyce was a supergenius

"Gee each owe tea eye smells fish" from Finnegans Wake

John Rennie

@0celo7 I've never used Cortana - I always disable it

Secret

I almost want to prounounce Ghoti as "ghor-ti"

0celo7

Temperature stabilizing at 71C...cooler seems fine.

So who knows was the noise was.

Balarka Sen

i am saying it was the satan dude

0celo7

@JohnRennie What is this program doing, anyway? Harvesting my computing power for colloids?

Btw, the calibration was 1,481,000 today

My computer is getting faster, apparently

Balarka Sen

14:36

what are you going to do with your computer even

0celo7

@BalarkaSen See the second starred comment

Balarka Sen

sounds like you're building up some supercomputer to hack onto pentagon or something

0celo7

Oh, temp went up to 74C

John Rennie

static DWORD WINAPI CPUThreadProc(LPVOID Args)
{ int iterations;

// Start eating CPU

for (;;)
{

// Eat some CPU

iterations = EatSomeCPU();

// If we are calibrated pass info to main window

if (Calibration > 0)
MainWnd.SetCounters((100*iterations)/Calibration, iterations);
}

// Should never reach here

return(0);
}

static int EatSomeCPU(void)
{ int iterations, i, j;
DWORD endtime;

// Loop for two seconds

endtime = GetTickCount() + 2000;
iterations = 0;

for (i = 0; endtime > GetTickCount(); i++)

0celo7

75...

John Rennie

14:38

@0celo7 Those passmark scores aren't that precise. If you do them repeatedly you'll see a scatter of several percent. I wouldn't read too much into the change in the score.

0celo7

@JohnRennie Ok this is taking a while. Should I just leave it sit?

The temperature is creeping up

John Rennie

Run it until the temp stabilises or you get bored ... whichever happens first.

0celo7

I've gotta take a shower

I'm reading online

They say the temperature should be no higher than 60

it's 76 right now

John Rennie

I'm not sure I'd leave it running while you have a shower in case the temp gets too high.

Secret

Spacemind - Systems Functional

►

What a cave of crystals sound like

Abcd

14:44

0celo7

@JohnRennie 77...

Abcd

Can anyone here help me with the question?

0celo7

what's going on? I thought the temperature was supposed to stabilize

Abcd

PS: I know how to compare EA of atoms but not of ions.

Sid

@Abcd I believe that is Chemistry and not Physics...

Still... Do you know what is Electron Affinity?

Abcd

14:52

@Sid Chemistry stack exchange is generally inactive.

@Sid Yes.

Sid

Great. Now, You should now the Electronic Configuration of the ions..

(i suck at Chemistry. So, much of what I might be blabbering might just be wrong.. :P)

Abcd

@Sid yes I know that

@JohnRennie or @Secret do you know how to solve this one?

Sid

Now, let's imagine stuff a bit and reduce our options..

John Rennie

@Abcd electron affinity is the energy released when an electron is bound. So for a cation it is the negative of the ionisation energy.

Sid

I am thinking it's Li+ though..

Secret

14:57

@JohnRennie wait, I thought electron affinities are more nontrivial compared to ionisation energies due to shieldings and the effective nuclear charge of the atomic species in question thus has no easy trend?

chemed.chem.purdue.edu/genchem/topicreview/bp/ch7/ie_ea.html

I mean complications like what is mentioned in this link. I am not sure how to put that into the level that Abcd's courses are on

John Rennie

Stephen Hawking is 75

Sid

Oh, he's still alive..

Slereah

Quite honorable for a man who was supposed to die 40 years ago

Sid

Some people tell that he is paralysed because he is an atheist...

Abcd

@Secret I have dealt with the exceptions in the periodic properties on the basis of EC, so not a big problem. You may explain

Anonymous

15:09

@Sid .....I'm an atheist too

The Dark Side

Hey @0celo7, I found something that might interest you:

165

Q: Did people think the Earth was flat?

I've heard it numerous times, that in the old days people thought that the world was flat. Most commonly I heard this in connection with the voyage of Columbus, that he believed the earth to be a sphere while most other people thought he must fail to reach India as the world is flat. Is there an...

history geography

Sid

@Blue I am not joking. I have actually heard people say that..

John Rennie

@Sid People say all sorts of things. Humans do that.

Anonymous

@Sid Well, people are weird things....

Balarka Sen

@Blue Atheism is clearly wrong

Anonymous

15:11

I remember my grandfather used to praise Hawking a lot but oppose his anti-religious views.

Anonymous

@BalarkaSen lel

Anonymous

Wrong isn't wrong though

Balarka Sen

Well, obviously

John Jack

Does anyone know the definition of the absolute value of a matrix $X$ defined by $|X| = \sqrt{X^2}$? I just want to confirm that if I was interested in taking $tr[|X|]$, then this trace is independent of the basis we choose for $X$?

Sid

@Blue My Grandpa hadn't even heard of Hawking. And neither did he care. :P

Balarka Sen

15:14

Here are my views on God

Anonymous

@BalarkaSen wtf....

Anonymous

lol

Balarka Sen

Think!

Sid

@JohnRennie I have heard people in the West refer to their fathers as "my Old man" and similar stuff. Is that some sort of cultural stuff or something else?

John Rennie

@Sid that's somewhat dated now. Referring to your father as the old man is the sort of slang used in the 1970s.

Anonymous

15:17

Zac Brown Band - My Old Man (Lyric Video)

►

John Rennie

My old man said follow the van

There you go, it dates back a hundred years.

Secret

Basically, electron affinity tend to be highest for halogens, and decreases down the group as the electron shielding increases. However period 2 elements tend to have smaller electron affinity than expected for a linear trend due to electron repulsion and thus it is often the period 3 element that has the highest electron affinity.

Therefore this leaves Na$^+$ and Cl$^-$ as possible candidates. I suspect the answer is a) but I don't seemed to understand the subject enough to explain why not Na$^+$ other than NaCl does not spontaneously form Na$^{2+}$Cl$^{2-}$ @Johnrennie might be able to s…

The Dark Side

101

A: What are some examples of colorful language in serious mathematics papers?

A paper of David Bachman-Cooper-White describes a proof that a hyperbolic 3-manifold containing large embedded balls has large Heegaard genus. As they say at the end of the introduction, a proper subset of the authors wish to subtitle this paper “Big balls imply big genus” whch is indeed t...

Sid

Some people are just too lucky...

Anonymous

@Sid That's nothing compared to most billionaires out there....

Anonymous

15:25

I don't like iphone 7 anyway XD

Balarka Sen

why would i want to buy a new iphone7 everyday for 964 years

Sid

Don't you see, 365*964= (Some big number)

Anonymous

@BalarkaSen No sane person would :P

Sid

He could give away that many i-phones everyday to different people.

Balarka Sen

i don't identify myself with sane people

Sid

15:26

We can then sell it and get money. Everyone's income increases. The world becomes richer. Poverty is reduced.. blah blah blah

Anonymous

Buy me a pizza everyday. I'll be happier.

Balarka Sen

@Sid wrong. you'd just end up creating a hedonistic mass hysteria

capitalism prevails

Avantgarde

Lol sorry

The Dark Side

Another old gem:

Truesdell is also the author of the single best Math Review ever: "In this paper are presented incorrect solutions to trivial problems. The basic error, however, is not new." — Allen Knutson Apr 25 '10 at 16:05

Sid

lol

0celo7

15:36

@Sid that doesn't seem like that much money

Sid

Hey @0celo7 ! Still messing with Cortana?

0celo7

No, was fooling with hardware. I think I got my PCI power cable issue sorted

hmm, it seems to find some apps but not others

@JohnRennie Ordered thermal paste and the extender for my radiator cable. I can't shake the feeling that my jury-rigged fan setup isn't cooling the radiator enough.

Maybe I'm crazy but it was only a few bucks

Sid

@BalarkaSen Capitalism is basically Darwin's law: Survival of the fittest.

Balarka Sen

15:51

@Sid a rather simplistic point of view

ACuriousMind

@JohnJack All traces are basis-independent.

0celo7

16:05

@JohnJack Do you mean $\sqrt{\mathrm{tr}(X^*X)}$?

John Jack

@0celo7 That's not how it is stated in the text but I would assume that's what is meant. Have you seen this kind of definition before?

0celo7

@JohnJack it's one of the standard operator norms in functional analysis

John Jack

@ACuriousMind I'm just confirming that $Tr[|\rho|]$ is basis independent based on the definition of $|\cdot|$ that I gave.

0celo7

you have to be careful with what "trace" means there

@JohnJack uh, wait

trace of a number?

Is $|\rho|$ supposed to be an operator or a number

John Jack

@0celo7 It's supposed to be a matrix.

0celo7

16:15

then no

and $\sqrt{\cdot}$ of an operator is trouble

John Jack

@0celo7 No to what?

0celo7

I have not seen it

John Jack

@0celo7 Oh okay. It's stated as $|X| = \sqrt{X^2}$ but then says that "equivalently it is the matrix obtained from $X$ making all it's eigenvalues equal to their absolute values". Does this make sense to you?

0celo7

Ok, so $X$ is a symmetric, finite-dimensional matrix?

ACuriousMind

@JohnJack The trace is always basis-independent. What sort of matrix you put into it has no relevance (unless your definition of $\lvert X \rvert$ was basis-dependent, but then it's not the trace's fault)

0celo7

16:19

If so, then that makes sense. Work in a diagonal basis to see that.

@ACuriousMind I'm getting waaaaay overleveled.

I still have lvl 15 quests to do but I'm 23

John Jack

Finite dimensional yes there's no assumption of symmetric matrix. Yes I see since it is basis-independent it makes sense @ACuriousMind Yes I understand.

ACuriousMind

@0celo7 Yeah, there are more quests for any given level than you need to outlevel them

0celo7

@ACuriousMind Now that I can play at 60fps, I have to say it's underwhelming. It doesn't look like it does in YouTube

Do you get the same feeling?

I recorded yesterday and watched the recording...it looked a lot smoother than when I was actually playing

Maybe it's because I can let my eyes wander when not actually playing

John Jack

@ACuriousMind I have just one more question if you have a second...@0celo7

0celo7

ok

John Jack

16:25

Will just take a second to type...

If we consider the operator $X = \rho - \sigma$ (where $\rho$ and $\sigma$ are density operators). Then $X$ is hermitian. We can also show $X$ can be written as the difference of two positive operators that have support on an orthogonal subspaces (support of an operator is the space spanned by eigenvectors with non-zero eigenvalues). Hence $X = P - Q$. Can you see from the definition of $| \cdot |$ why $|\rho - \sigma| = P + Q$?

Emilio Pisanty

Somebody please talk me out of taking the bait here

In fact, none of the questions can be voted as best or worst, a question is a question, I absolutely and without any doubt hate the statement when someone says "Yea...thats a good question" I mean it is just imbecile, what do you mean by a good question? Do you mean that we must think before asking questions? — Ajinkya Naik 2 hours ago

ACuriousMind

@JohnJack Because if $P$ and $Q$ are orthogonal, you can diagonalize them simultaneously, and then applying the definition yields the result.

John Jack

16:53

@ACuriousMind I can see the first part but not how the simultaneous diagonalizing with the definition implies the conclusion.
So what I have is The first part you mention is: $$PQ~~\text{orthogonal} \Leftrightarrow PQ = 0 \Leftrightarrow [P,Q] = 0 \Leftrightarrow P~\text{and }~Q~~\text{can be diagonalized simultaneously.}$$

Then from definition $|X| = |\rho - \sigma| = |P-Q| = \sqrt{(P-Q)^2} = \sqrt{P^2 + Q^2} = |P + Q|$

What am I missing?

ACuriousMind

> equivalently it is the matrix obtained from X making all it's eigenvalues equal to their absolute values

John Jack

@ACuriousMind
So if I assume that $P$ and $Q$ are simultaneously diagonalized then I can simply add the conclusion as the final step: $|X| = |\rho - \sigma| = |P-Q| = \sqrt{(P-Q)^2} = \sqrt{P^2 + Q^2} = |P + Q| = P + Q$?

ACuriousMind

@JohnJack Well, you should understand why you can write that, and if you understand that you wouldn't write any of the $\sqrt{.}$ steps...

The reason is this: Since $P$ and $Q$ are positive and orthogonal, $P-Q$ is a block matrix with blocks $P$ and $-Q$ on the diagonal and otherwise all zeros. So applying the definition of making the eigenvalue all positive, this does nothing to $P$ and changes $-Q$ to $Q$ (since both $P,Q$ are positive). So you have the matrix which has $P$ and $Q$ on the diagonals and else zeros, which is $P+Q$.

John Jack

@ACuriousMind Since $P$ and $Q$ are simultaneously diagonalised, the sum $P + Q$ is a diagonal matrix with the sum of eigenvalues of $P$ and $Q$ respectively on the diagonal. Since they are positive operators, they respectively have non-negative eigenvalues hence it follows that $|P + Q| = P + Q$...?

ACuriousMind

17:09

Yes, $\lvert P+ Q\rvert$ because they're both positive, but that's not what you've got to use here. In fact, in what you wrote up there I don't understand why $(P-Q)^2$ morphs into $P^2 + Q^2$ - what happened to the $-PQ - QP$ term?

John Jack

@ACuriousMind They are both zero because $PQ = 0$ and $QP = 0$.

ACuriousMind

Ah, yes

Then that works, too.

John Jack

@ACuriousMind Okay thanks for checking. Out of interest, what are you using as your definition of positive operator, I am using an "Hermitian operator with non-negative eigenvalues".

ACuriousMind

Yes, that's what being positive means

John Jack

@ACuriousMind Does it follow then as a property that for measurement operators, say $\{ A_m \}_m$, we always have that $Tr[A_m P A_m^{\dagger}] \geq 0$?

ACuriousMind

17:19

@JohnJack If $P$ is positive and the $A_m$ are projectors, yes.

John Jack

@ACuriousMind Understood thanks.

0celo7

Bah, Witcher 3 broke again

this time it wouldn't let me alt tab at all

@ACuriousMind Why do you people get upset at America for using Imperial Units but not mad at @JohnRennie for driving on the wrong side of the road?

Sid

Wrong side of the road?

You always drive on the left side, no?

0celo7

Only backwards people do that.

Most people drive on the right.

Balarka Sen

@0celo7 Here's a relevant video:

Tom Lehrer - Decimal - The Frost Report

►

Sid

17:24

That is just.. wrong. Always drive on the left side. Less accidents.

0celo7

What

Sid

17:44

@dmckee No paternal leave for you? :P

dmckee

Delivery by C-section means I'm sitting in the hospital. Poking round the internet kills some time.

Sid

Oh, I hope both are okay.

(And as if a coincidence, I became an Uncle few days back..)

dmckee

@Sid Because I got a late start and my (younger, curse it!) brother got an early one I became a great-uncle a month before becoming a father.

For that matter the last diaper change I did before my daughter was on the mother of my great-nephew. I'm out of practice.

Sid

That sounds like very long ago...

Abcd

@Secret Thanks. yes, the answer is a) Li^+

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