@AccidentalFourierTransform Does that mean mods do like butts?

Re: 2. I think one possible way to think about what $U_i$ is doing there is that we have two particles, they undergone some unitary interaction, but we are uncertain what unitary interaction they undergone and the best we know is that all possible interactions that can happen follows a probability distribution, thus this result in the $U_i$ to form an ensemble, analogous to how we use density matrices to represents an ensemble of states

idk, let us ask them

Did making the time evolution probabilistic violated one of the postulates of quantum mechanics?

@Secret Well, that's just admitting that you're not doing quantum mechanics. Even in quantum statistical mechanics, there is no such thing as "being uncertain about what unitary interaction particles undergo".

This simply is not a possibility - the Hamiltonian, and hence the time evolution, is part of the definition of "a system".

(removed)

uh I think I don't fully understood. So you mean since the hamiltonian is part of the definition of a system, it cannot be probablistic (for reasons that I am not aware of)?

Why would you think the Hamiltonian can be "probabilistic" in the first place?

That is, very simply, not how quantum mechanics works.

And I refuse to debate possible extensions of quantum mechanics unless I know all participants have a very firm grasp of how quantum mechanics works.

@Secret "I thought quantum mechanics allow me to turn anything into an ensemble" [citation needed] You have violated no specific postulate, your construction simply doesn't make sense within the framework of quantum mechanics. By the postulates, states are well-defined density matrices and they evolve through well-defined Hamiltonians.

@AccidentalFourierTransform odd comment from someone whos gender is still TBD o_O :P

nothing in my comment refers to a specific gender

in case you didnt know, butts are fun to look at for everyone ;-P

@skullpatrol lol! knuth 80 party coming up!

@AccidentalFourierTransform when you read those two you can move on to Cartesian Currents in the Calculus of Variations

2 volumes for those too

my time is very limited yknow

@AccidentalFourierTransform lol, an old sentiment that goes back to the greeks & further! a facetious teenager tipped me off on this dictionary.com/browse/callipygian

Eh, why on earth are "butts" comments being starred?

@vzn heh, fun word, I didnt know it

@AccidentalFourierTransform what country are you in anyway? Madrid?

@vzn Spain, unfortunately (?)

yeah, Madrid, Spain

@vzn Madrid is not a country... :P

@Sid lol thx for the tip man

@AccidentalFourierTransform did you ever see this one? slereah posted it long ago mathematica.stackexchange.com/questions/66538/…

:-P

Wait a sec..., taking $e^{-\frac{iH}{\hbar}}$ gives $e^{-\frac{iH}{6\hbar}}e^{-\frac{2iH}{6\hbar}}e^{-\frac{3iH}{6\hbar}}$ which means 3 unitary evolution operators acting in sequence

but not sums of unitary operators

@AccidentalFourierTransform so what are you up to in madrid these days besides derriere-spotting/appreciation

@Secret assuming they commute...

nevertheless $H=\frac{1}{6}H_1+\frac{2}{6}H_2+\frac{3}{6}H_2$ seemed a pretty valid hamiltonian, it is self adjoint as required

why will quantum mechanics disallow that and think it is nonsense?

@Slereah "P.S. And yes, I believe Slereah's comment is wrong and misleading."

Wow

@vzn lol. Im at my parents house, Ill be here for the summer. In dont know what Ill do after that.

@0celoñe7 which one

@AccidentalFourierTransform did you graduate recently?

yep, masters degree

a couple of weeks ago

@AccidentalFourierTransform So you have nothing but time...

Oh wait, is it because...

@AccidentalFourierTransform cool, congratulatoins, physics? your undergrad in physics also? whats your thesis topic?

I know there's a relation between $T = 0$ and conformal symmetry

But it only goes one way

@ACuriousMind Yo

So maybe I got it the wrong way around

@0celoñe7 I have a family to feed

@ACuriousMind People are saying TW3 has outdated gfx. What's the gfx powerhouse nowadays?

@AccidentalFourierTransform kid(s)?

@vzn yes and yes

@vzn He has several baby mamas.

and my thesis is on my uni webpage, so I dont really want to disclose the topic, bc it would be trivial to find out what my real name is :-P

@0celoñe7 lol, seriously doubt that! sounds like something a rapper-admirer would joke about, which reminds me did you hear about r.kelly?

@vzn im OP here

@AccidentalFourierTransform NICE

@AccidentalFourierTransform Oh, you have sockpuppets. :P

@AccidentalFourierTransform !!! whoa, dude. afaik DNA tests are not too expensive, and highly reliable, do you have some objection to one?

I am almost 100% sure he is trolling.

@Secret There's nothing wrong with that, but that's not what you said you were doing and it has nothing to do with "ensembles".

@vzn I'm 99% confident he's not being serious.

oh, the nice thing is, you'll never know for sure ;-)

@ACuriousMind "not serious" aka lying?

I don't have kids.

@AccidentalFourierTransform (sigh) your endless facetiousness seems to border on discourteousness sometimes (to say the least)

@vzn it's irony rather than a delibrate attempt to deceive

or, you know, maybe you are slightly too naive/gullible :-P

@ACuriousMind I am not sure if I misunderstood. In that example clearly $\frac{1}{6}+\frac{2}{6}+\frac{3}{6}=1$ thus the coefficients fullfill the requirement of a probablity distribution. Thus $H$ can be interpreted as being in an ensemble consists of $H_1$, $H_2$, $H_3$. Why is this way of understanding not valid, and instead we simply treat those coefficients as coefficients and not probabilities?

@JohnRennie ?!? it seems nobody here really knows the situation exactly except AFT and s/hes not nec to be taken seriously

@Secret Why would you treat them as probabilities? You haven't given any argument for that.

@JohnRennie Irony? Is that the polite term for trolling?

I wouldn't mine being called an ironologist.

@0celoñe7 I think the point of trolling is that do it to annoy someone.

While the point of irony is that you do it to amuse people.

and sarcasm?

@JohnRennie Can one not mix the two?

@AccidentalFourierTransform you heard the story when you were young about the boy who cried wolf right?

@0celoñe7 Annoy one person to amuse everyone else? Isn't that bullying?

^

@JohnRennie its a fine line sometimes

@AccidentalFourierTransform You need money and you have a lot of free time, and also need some adventure after your Masters. Go find that treasure then.

@vzn dude, dont take it so seriously. If I annoyed you, I apologise. Its an online chat, nobody really cares about anything.

@Mostafa lol, I aint reading no poem!

@AccidentalFourierTransform "Its an online chat, nobody really cares about anything."

Really?

Shhh!!! Time out.

@JohnRennie No.

@Mostafa what?

@0celoñe7 what then?

@AccidentalFourierTransform nobody really cares about anything??

Ironic trolling.

DNE

@Mostafa nobody cares about anything anywhere. Why would a chat be any different?

@AccidentalFourierTransform took you seriously when you said you were OP (didnt scan post closely). now realize it likely isnt posted by you. but dislike the nihilistic philosophy in chat. however, agreed cyberspace tends to reinforce it in many ways.

@vzn that post is so out of character for AFT that no-one who had shared the chat room with him for long would have taken his claim to be the author seriously.

@vzn no, Im not OP. I assumed it was clear enough that I wasnt OP. Apologies for wasting your time. Can we move on, please?

@ACuriousMind Well, you can have the quantum states being two isolated electrons, and have a device controlled by a random number generator consists of three polariser such that there is a 1/6 chance polarizer 1 is set into place and thus rotate the electron spins to point in the $\pm x$ direction,

2/6 chance polariser 2 is set into place and thus rotate the electron spins to point in the $\pm y$ direction and 3/6 chance polariser 3 will be set into place and thus rotate the spins to the $\pm z$ direction.If I want to describe the hamiltonian of how the

electron spins are rotated, then since each polariser's action corresponds to some hamiltonian if they are the only ones present, then naturally the overall hamiltonian to be wrote down will be a weighted sum of the 3 hamiltonians by their probabilities?

@AccidentalFourierTransform since you dont wanna be serious about anything, lets talk about rkelly instead... you can take some pointers from him :P dailymail.co.uk/news/article-4703768/…

@AccidentalFourierTransform OK, let's move on

Or is there a way to write down the hamiltonian of this system given how the electron spins are rotated are determined by a random number generator that decide which of the three poarisers will rotate into the path of the electron beams?

Behumbole @0celoñe7

@skullpatrol I don't know what that is supposed to mean

@vzn taking the Daily Mail seriously is one of the few things more unwise than taking AFT seriously.

@JohnRennie lol (am well aware of your dailymail aversion, thx for reminding me...) go ahead an tell me exactly what is inaccurately reported in that article. it should be easy given its terrible rep/ incompetent standards, right? am waiting :P

@ACuriousMind Who is watching?

@JaimeGallego we need accurate information about AFT's identity. Can you help us?

That seems like a mean breech of privacy for no good reason.

It is certainly Not Nice.

^

Play nice guys

Eh, even if we meet each other, I won't reveal his identity

AFT is probably some 60 year old granny

@0celoñe7 AFT is Not Nice... sometimes

@AccidentalFourierTransform I am reading a calculus of variations book rn

it's pretty good

Eh, I have very accurate information of AFT. Or rather everyone does.

@vzn He is only Not Nice if you're naive

@JaimeGallego OH MY GOD AFT IS THE LAS VEGAS RAIDERS

I'll look for +--- t-shirts from now on, though

@0celoñe7 talking to you guys is certainly a good way to lose naivete quickly o_O

Remember there are drive-by flaggers out there

@0celoñe7 nice. I have it bookmarked, so Ill give it a look

@AccidentalFourierTransform No, not that one

A more specialized one

link.springer.com/book/10.1007/978-88-7642-443-4

same author

yeah, Im not gonna read that one

::shudders at the thought::

depends on how fit he is

Is that the American or British meaning of the word pants?

;-)

Or both!

Though that would get cold in winter

@AccidentalFourierTransform actually have been in a vaguely similar situation. long story. maybe got triggered some. o_O

What's the British meaning?

Aha! You're Scottish and wear a kilt!

That is why he lives in Spain

In fact, I just got back from borrowing Spivak in the Retiro library. Also had to acompany my father to the hospital for surgery.

@JaimeGallego Uh, wrong chat?

@JaimeGallego Your Dad's surgery? He is okay, we hope?

@0celoñe7 Why "no good reason"? Research has shown that people who use their real identity online use far fewer swear words, troll much less and are much more productive overall.

@Mostafa That's not a good reason.

@Mostafa Link on the research piece please?

far fewer swear words

@JohnRennie Seriously?

my real self use as much swear words as my online self

Is that ironic, trolling, or bullying?

@Sid Yeah, just some eye surgery. All of my family is myopic.

@Mostafa can you follow a lot of that nature article re waveguides? would like to dig into it deeper

@0celoñe7 That's Friday's grammar correction of the day.

@Sid Trying to find it. No sucess yet (but this is real)

Less = fewer

Wrong

Well, in British English anyway.

2<3

@skullpatrol Have you Googled it?

No

@AccidentalFourierTransform That is the secret identity of JR. :P

salutes

@Sid JR looks nothing like the President...

Wouldn't it better to do a bit of research before expressing an opinion?

I wager I'm the only one here who has seen him

Yes

@skullpatrol What?

@0celoñe7 true! Apart from the twenty year old phto I use as an avatar of course.

@0celoñe7 Where? In rallies or something?

@skullpatrol JR is right

JR is right

Ah, the pronoun game.

Yup

@Sid I tried to see him at a rally but there were too many people there!

silly question: how do you define raising and lowering indices intrinsically? given a non-degenerate tensor $\phi\colon V\times V\to\mathbb R$, you may define $v^\flat$ as the unique one-form such that $v^\flat(u)=\phi(v,u)$. But how do you define $\omega^\sharp$ for $\omega\in V^*$?

@vzn Yeah

@0celoñe7 Where, then?

I guess you need the inverse of $\phi$, but how is that even defined in a coordinate-free fashion?

@AccidentalFourierTransform Given $v\in T_pM$ define $\omega=v^\flat$ as the unique $\omega\in T^*_pM$ such that $\omega(w)=g(v,w)$ for every $w\in T_pM$.

yeah, that is what I said

what I want is $\omega^\sharp$, the inverse operation

the same way

Except you switch it around

For the other way around, do the same thing...given $\omega\in T^*_pM$ define $v=\omega^\sharp$ as the unique $v\in T_pM$ such that $\omega(w)=g(v,w)$ for every $w\in T_pM$.

Remember that a vector is a linear functional on dual vectors, too

@Mostafa is "chirality" basically referring to polarization direction? was googling it but couldnt find much yet... seems theres a startup called "chiral photonics" noising up the google results :|

hmm yeah, that seems to work

what was putting me off is that $g:V\times V\to\mathbb R$, and so I was expecting that one had to define somehow $g^{-1}:V^*\times V^*\to\mathbb R$, whatever that means

but I guess there is no need to do that at all

@0celoñe7 who, JR?

But what I said is intrinsic.