The h Bar - 2017-12-13 (page 4 of 5)

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4:00 PM

Or am I explaining poorly

"However it is a philosophically difficult issue. QM to be formulated needs completeness of the space of the states otherwise some fundamental results do not hold (the spectral theorem). However some of the states have no energy, no momentum etc. in a quite weak sense: the expectation values of these observables do not exist."

Or maybe he doesn't

Aaaah

I have the QM madness

@Slereah now you know why I deny physics

did Yariv write more than just his quantum electronics book? In Griffith's quantum book it states that in section 15.4 footnote 22 is a more detailed argumentation about why $\beta = \frac{1}{k_B T}$ holds for a variety of systems
but I didn't find any footnotes at all in section 15.4...

@DanielSank you're the quantum measurement guy

What do you think

Should a "real" quantum state be part of $$\bigcap \text{Dom}(A)$$

For all reasonable observables

Daniel probably does not know what domain means here.

I need to find this mythical unicorn that knows both linear functionals and experimental QM

4:12 PM

you got a physicist answer

very bad

yes that answer is not helpful

I could leave a nasty comment

Anonymous

@Felix.C Yes. It seems he has some other books. Just google...

There's no reason why $H$ should even have eigenstates

garbagio answer

-1

@Slereah No. If you "replace" the unbounded self-adjoint operators by their (bounded!) spectral projections, you can still ask all the same questions regarding what you're going to measure but the domain issue vanishes.

4:21 PM

only thing worse than QM madness is QFT madness

All states in the Hilbert space are in principle admissible physical states, but in case of unbounded observables it can be tricky to find the correct prescription for computing the quantities you usually compute by applying the observable to a state.

oh, lawd. hats have arrived?

@Slereah Hall p. 206 is what ACM is talking about

I think

@ACuriousMind I am aware that mods usually don't like to talk about suspensions, but ooolb's not sure why he got banned for a week. I must say I too am confused about it - the conversation prior to his ban was relatively civil. Can you clarify this so that he can know?

banned for a week? Jeez

4:25 PM

I haven't read Hall but I think this is how the $C^\ast$-algebra approach defends its claim to generality even though unbounded operators cannot be part of a $C^\ast$-algebra - you produce a bunch of bounded operators (either the one-parameter unitary ones from Stone's theorem or the spectral projections) from the unbounded operator and use these instead.

@ACuriousMind To clarify, your spectral projections are the spectral measure evaluated on some subset of $\Bbb C$?

@PrathyushPoduval Heyyy. That's pretty good.

@BalarkaSen We're currently debating whether we might reduce the duration, but one reason is because he kept bringing up his earlier 24 hour suspension claiming it was "ridiculous" and "unjustified" after being explicitly told the reason and told this is not up for debate, cf. the still pinned message.

@0celo7 Some subset of $\mathbb{R}$, yeah, and...I guess you have include all of these, i.e. it bloats the algebra terribly.

@ACuriousMind Ok R because it's self-ajoint?

aye

If you're only symmetric and not self-adjoint there's further trouble :P

4:30 PM

@ACuriousMind Symmetric isn't enough for a real spectrum?

Or you mean because the spectral theorem fails?

The latter, I think

I only know enough about this stull to sound as if I'm know what I'm talking about ;P

@ACuriousMind Thanks for the clarification. I guess that kind of makes sense. I personally didn't think he was being argumentative about it, more like clarifying it was jokingly made; good to know the mods are considering to reduce the suspension span.

PDEers (we really need a better word for that) worry about these domain issues too

PDEists

Is a PDEer not simply a subtype of "functional analyst"?

4:33 PM

@ACuriousMind not really

to me a "functional analyst" is someone who works with operator algebras

Ah, that's the other major subtype

@ACuriousMind mhm, but I don't know any PDE people who would describe themselves as functional analysts

Well, one of them taught my functional analysis course! ::curses Sobolev spaces::

I wish I knew functional analysis

@ACuriousMind Oh yeah, we're functional analyzers

@ACuriousMind Honestly I feel bad for that. There's so much interesting stuff they could have done instead

So much stuff that's related to PDE and QM. It makes everyone happy

4:40 PM

What's a bit strange about the usual textbook QM e.g. position wavefunctions is that, on the one hand, it's basically where every QM book starts

but in terms of applications, I feel like what most people end up needing is just finite-dimensional stuff

holy crap this show sometimes

or at the very least is just countably infinite (e.g. tight-binding models of electrons on a lattice)

I am at last watching some movie that is not completely insulting my intelligence

Captain Bohemian

is functional analysis ever taught in physics department/ particularly for physics students?

@CaptainBohemian no respectable physicist has any need for it

4:47 PM

@Sid What are you watching

@BalarkaSen 15 minutes? Is there some really easy proof I don't know about?

These proofs are all long (2+ pages)

Long? I don't remember it being long

given the implicit function theorem it's like 5 lines

but one of them is always long

It's applying the Banach fixed on $\phi_y(x) = x - f(x) + y$

I know

4:55 PM

I don't understand why it should not be 15 minutes then. It's a couple lines

the proof in Lee is 2 pages

hmm

Am I underestimating?

there's a technical bit about the inverse map being smooth

I guess

4:58 PM

@0celo7 I do wonder about that a bit. It seems like there should be places in applications where this actually is an issue, but I don't know them

9

Q: Does mathematical sloppiness in quantum mechanics ever produce incorrect predictions?

Does mathematical sloppiness in standard quantum mechanics ever produce predictions that don't pan out? I'm not talking about things like the WKB approximation, but instead subtle functional analytic issues, such as assuming every Hamiltonian is self-adjoint, has an eigenbasis of bound states, do...

quantum-mechanics experimental-physics mathematical-physics

oh, nice

@BalarkaSen Dubbed Telugu movie- Dangerous Khiladi

@Semiclassical the answer seems to be a resounding "no, but it's not unimaginable"

hmm

5:00 PM

@Sid Jesus

GSauce

@ACuriousMind if you have a state that isn't in the domain of $x$ but is in the domain of $e^{isx}$, what is the "equivalent" of its position?

Or is nothing weird about it

@BalarkaSen It sounds bad but trust me, it doesn't insult your intelligence as much as others do

Like what is $$\ln(\langle e^{is\hat x}\rangle_\psi)$$

Anonymous

@Sid What's the theme ?

@0celo7 one thing I notice about the papers which the one answer cites is that they all concern the classical limit

which has in common with my earlier remark that nothing is really a problem if one considers a finite-dimensional system. it's the transition from finite to infinite that makes things weird

5:06 PM

@Secret Traditional particle physics instrumentation was crude enough that particle identification and event character were basically statistical claims in all but the most easily identified cases, so trying to construct deeper correlation was a losing game: any correlation that existed was washed out of the data by the uncertainties associated with individual events.

"traditional" makes it sound like there's been some innovations in that regard?

Recently data has become somewhat more precise but in many case this has been taken advantage to allow the processing of denser data rather than deeper understand of a few limited events.

I.e. in the big LHC detectors they are taking three digit multiplicities!

Which makes sense because a lot of their analyses are luminosity limited.

The analogy that would come to mind: Doing perturbation theory to first-order with respect to multiple perturbations at once vs. doing perturbation theory to higher-order with respect to one perturbation

with the first one, you're just doing a bunch of linear approximations. with the latter, you have a combinatorial explosion of possibilities

I don't know enough about experimental particle physics to know if the above is a reasonable analogy, though @dmckee

Can someone point out where I'm messing up? I'm trying to compute the electric field $z$ units above the midpoint of a line charge of length $2L$. I carried out the following integral: $$\frac{\lambda}{4 \pi \epsilon_0}\int_{-L}^{L} \frac{1}{l^2 + z^2} \,dl$$. I want to go from scratch and not exploit symmetry.

so the world hasn't ended yet...what's the deal?

5:14 PM

@Slereah Don't do that. The expectation value of position is simply undefined.

@ACuriousMind but then why is the expectation value of the exponential defined

@Slereah Why shouldn't it be?

Is it like $\ln(0)$ or something?

Well, no, but you have no reason to believe that the logarithm of the expectation value of the exponential there is the expectation value of position.

@ACuriousMind Is there anything that goes wrong on an intuitive level

Like is the value divergent or something

or non-real

5:16 PM

@gian It looks like you haven't taken into account that the electric field is a vector. (Or, at least, you haven't done so correctly)

@Slereah I don't understand what you mean by "intuition". States and/or observables that are "intutive" in any sense will never show these issues.

so long as one has the correct kind of intuition :P

So I should include $\frac{\mathbf{r}}{\sqrt{l^2 + z^2}}$

right.

But note that "the expectation value is undefined" is not a "quantum" phenomenon - it's easy to write down probability densities whose expectation value is undefined, and no amount of manipulation you can do on these will make that any better

5:18 PM

Yeah I'm aware

The Saint Petersburg paradox!

But that's because it's a divergent value

Is the expectation value of the position divergent?

a practical example is the Cauchy distribution

I guess the question is like

If I looked at the PDF of such a state

it's got a well-defined center and scaling parameter, but its mean value and variance don't exist

Where would it be peaked

What would it look like

@Slereah that's different than the mean, though

5:22 PM

True

user image

and as the Cauchy distribution shows, you can have a PDF being symmetric and unimodal without it having a well-defined mean value

Now I'm getting $\frac{\lambda}{2 \pi \epsilon_0} \cdot \frac{L}{z^2 \sqrt{L^2 + z^2}}$...

Quite unfortunate!

(see the bit on "Estimation of parameters")

\cdot may serve you better than \bullet, fyi

@gian what was your integral?

5:25 PM

@Blue Hero foils the villain's plan

$$\int_{-L}^{L} \frac{\mathbf{r}}{(l^2 + z^2)^{3/2}} \,dl$$

@EmilioPisanty ~~Well, there are 39 items in there for me.~~ nvm, that'S Academia The red dot has the same behaviour as the old "number of flag indicator" - it might also light up when there's no item you personally can act on

I guess I'll stop complaining about the red dot on PSE lighting up for three LQP reviews

@ACuriousMind on closevotes?

@ACuriousMind yeah. The academia red-dot does seem to have some mild hysteria problems.

@Slereah Well, go and look, then!

@gian Can you include the rest of that?

5:27 PM

That's after taking out the constants.

@ACuriousMind Well I'm guessing the Cauchy distribution is probably one!

@EmilioPisanty "academia...does seem to have some mild hysteria problems." -EP

@Slereah Is that a probability density that arises from a square-integrable wavefunction, though?

@ACuriousMind Maybe?

huzzah for selective quoting :P

5:28 PM

Hm, wait, you can literally just take its root as the wavefunction :D

How does that translate, experimentally, though

So yes, there.

@Semiclassical I was going to say I agree with that, but frankly, the stuff that gets us in a huzzle does tend to be worth the panic

If I measure the positions of such a state $n$ times

in fact, we tend to under-panic as a rule

5:29 PM

Will the mean of those positions just not converge?

it depends on what we're talking about

@Slereah I don't think that's a well-defined question.

Well the wavefunction collapse doesn't help, certainly

If you make actual measurements, nothing has to "converge"

@Semiclassical well

p-hacking

reproducibility crises

5:29 PM

You have N measurements, you take the mean, there's no convergence anywhere

in both psychology and biomedical sciences

@ACuriousMind Yeah but as $n \gg 1$, should it converge to anything

Geoff Marcy and his ilk

Or will it just be all over the place

@Slereah some good stuff here: physics.stackexchange.com/q/369138/55641

@Slereah not for cauchy, no

5:30 PM

That's fine

Principle is the same

Publishers nicking our IP and selling it back to us at exorbitant prices

@EmilioPisanty in the US context, the main alarm is at the tax bill

@Semiclassical on a four-week kinda timespan, yeah, I guess

right

@Slereah No, it will diverge - if it converged to anything, that anything would be the expectation value.

5:32 PM

frankly, I see the US tax bill thing and I can do little more than shrug

@ACuriousMind alright

the US wants to destroy its standing in science and technology research?

I guess that's fine by me

Anonymous

@Sid ...

>_>

@EmilioPisanty Well, you're not one of the people in the US getting destroyed with it :P

5:32 PM

I mean, it isn't great for science overall

@ACuriousMind indeed

the people I worry about are those who are midway through their phd

I'm guessing this is due to very high variance/kurtosis, maybe?

@Slereah variance doesn't exist for Cauchy either :P

but there's a bunch of other things in the US that do have much wider ripple effects

@Slereah How could the variance exist if the expectation value doesn't?

5:34 PM

@Semiclassical Its spread then

If you prefer

though the sample variance should reliably blow up to infinity, I think

How do you talk about the spread of a distribution if the variance doesn't exist?

@ACuriousMind well, you don't know where it is, but you know it's on average about yea long away from there

I mean by eyeballing

@EmilioPisanty ~~Hm? I was thinking of the simple fact that the definition of the variance includes the expectation value of the variable itself, so it fails.~~ nvm my joke detector is a bit off today

5:35 PM

You can tell if a distribution has a center or how it spreads

Is there a mathematical version of eyeballing

@Blue That was the theme. The Plot is basically on how the hero manages to trick the villain. What is good about the movie is that it pays attention to details and at least there is some logic in how everything unfolds

@Slereah again, see the discussion of parameter estimation on the wiki page

thx

@ACuriousMind =P

the cauchy distribution is defined with pdf $\displaystyle p(x)=\frac{1}{\pi}\frac{1}{\gamma^2+(x-x_0)^2}$ with scaling parameter $\gamma$ and central value $x_0$

5:37 PM

@Semiclassical cauchy is a great-sounding adjective

what's it mean?

Cauchy

it sounds like it'd be onomatopoeia for something but I can't quite tell what

it's a person's last name

Cauchy means it has much cauch

e.g. Cauchy's various theorems in math

5:39 PM

@Slereah much cauch as in it's very gauche?

Gauchy distribution

but in a harsher way, I guess, signified by the hardening of g to a k sound

user image

"the sample mean of a large sample is no better (or worse) an estimator of x0 than any single observation from the sample"

the horror

yup

@Slereah though, also take a look at the characteristic function for Cauchy

that exists despite the mean and variance being ill-defined

hmmmmm

user image

them ellipses would go mighty well with my ellipses

5:51 PM

I guess a question would be like

Do physical measurement actually look like unbounded operators, in real life?

I'm not sure

@Slereah I'm pretty sure they're not

I'm not really sure what a bubble chamber or wire chamber looks like, mathematically

there's been analyses of how a bubble chamber works w/r/t quantum mechanics / heisenberg uncertainty

some numbers here: physics.stackexchange.com/q/107397/55641

basic conclusion being that, while the tracks look sharp, the track width and typical momenta are large enough that it's entirely consistent with the uncertainty principle

folks, btw, might I interest you in upvoting this answer?

16

A: Professor refusing to write recommendation letter to make student work longer

Your professor is not obligated to write you a recommendation letter. You should think about getting a letter from someone who will write a good recommendation for you. Your professors' attitude is highly unprofessional and needs to be exposed to their academic community. When you're clear, file...

the top-scorer in that thread is deeply wrong, I think

or at least, nowhere near right enough to deserve to ride on the rails of HNQness

I forget, what's HNQ mean?

5:59 PM

@Semiclassical Hot Network Questions

the Devil's sidebar

ahh

ohai

a.k.a.

Sep 14 at 14:11, by ACuriousMind

"SE-Wide Advertisement for General Enlightenment"?

lol

Well I guess that technically, I don't think any detector could measure an arbitrarily large position or momentum

6:01 PM

@Slereah hmmmm. any arbitrarily large position or momentum can be detected by a sufficiently range-y detector.

more like, for any detector, there are sufficiently large positions that it cannot measure.

Let's finance an infinitely long accelerator

eh, I think you could take the detector to be a spherical shell

how long's that.

in which case I think you'd almost always detect an outgoing particle?

e.g. put a sample of radioactive uranium-238 inside a spherical shell

Can you guarantee that if it's inside the shell at some point, and outside the shell at another, it gets detected at the shell in between though

6:12 PM

depends on the thickness of the shell, I should think

it's basically a barrier penetration problem

that, and to say that it gets detected is basically a statement about whether it interacts with the shell

there's presumably some probability that it won't interact with the surface on its way through, so yeah

there's a detection loophole right there

6:27 PM

Can't we just go back to classical mechanics

ewww mechanics

@EmilioPisanty Boy, some of the comments there are over the top. My opinion would be that a mentor should always be willing to write the best letter they can (but that if that letter would be harmful they should be willing to tell the student that), and that they should intervene with a student who is on the road to not living up to a good letter soon enough for them to do something about it (assuming they have the wherewithall).

@dmckee mine, answerer, or someone else's?

the problem is the quid pro quo involved

@EmilioPisanty I'm looking at the comments under Nicole's answer, mostly.

6:39 PM

@dmckee yeah, figures

@dmckee extra *'s on your comment btw

Your answer looks good to me. They have to deal with the situation as it is, but the organization needs to know if there is a problem.

@dmckee not my answer

this is me on academia

E.P., Barcelona, Spain

4.2k 23 50

publications arxiv citations copyright ethics journals open-access

There was a story in my graduate department, about a committee conveining and graduating a student while the advisor was on vacation because the sense of the whole department was that we was exploiting her talents for his own gain.

including many of the comments under Nicole's answer

huh

6:41 PM

@0celo7 @BernardoMeurer He's back!!!!

@dmckee yiiikes

@dmckee while advisor was on vacation?

@EmilioPisanty Yep.

wow, things must've been baaaad

though I guess her thesis would've been essentially completed?

The professor in question had lost his wife, had a bit of a breakdown in the aftermath and return with a changed personality.

6:43 PM

@dmckee =/

He was a more than competent theorist, and continued to do good work, so no one wanted to get rid of him, but they had to do something for the student.

Future students were quietly warned off.

how'd he respond when he came back?

Apparently there were heated discussions at the School of Arts and Sciences administration level.

sounds about right

Paul Simon Gumboots

6:45 PM

@dmckee Was the sense justified?

?

@Sid Before my time, but when I was around he would drop in on (other professor's) grad students who had taken his advanced classes and give them assignments. These sometimes lead to papers and he generally took first authorship even if the student did most of the work.

@dmckee "give them assignments"?

yeah, I feel like I'm missing something.

His advanced class examined current papers and methods, and he'd drop in, discuss a recent paper and a new avenue he'd thought up and end with something like "Get it done over the weekend".

6:49 PM

...

Some students did it because it led to papers.

:/

Others ignored him.

@dmckee even if it did lead to papers I'd be like

yeah no

ask nicely next time

^ That.

If you didn't do it a couple times he'd stop asking.

6:51 PM

Though I guess I do know enough examples of comparable pathology that I'm not that surprised

@dmckee if they guy was good and the questions were interesting then I guess that'd make it more of a shame

He was productive, and had a reputation for having been a powerhouse in his heyday.

It also matters what expectations were conveyed

"here's this nice intellectual avenue! where does it go? to a dysfunctional relationship with a faculty member with a known-as-problematic track record"

i.e. if the student understood from the outset that they'd be getting the second author slot

@dmckee key word being "heyday"?

@Semiclassical yeah

6:52 PM

One of my office mates had gone along with it for a while and then quit so he could focus on getting graduated. He said the assignment were almost always interesting and exciting.

yeah, that's tricky

@EmilioPisanty The sense I got was that he wasn't breaking any new ground but was filling in a lot of interesting details right behind the current leaders.

@dmckee any first-hand details on how justified the authorship ordering was?

Thqt's good science, even if it won't win you any prizes.

@EmilioPisanty No.

though really, faculty member pushing student out of first author is always dicey

like, what exactly are you winning with that

6:55 PM

@EmilioPisanty Yeah. In experimental particle physics the last author slot means "mentor" and implies guidance on the avenue of exploration.

@dmckee I thought experimental particle physics was more alphabetical?

@EmilioPisanty For big papers, yeah. (What can position mean across four hundred authors?)

seems to me like one should approach that scenario like contract / freelance work

But you usually publish some small papers, too, 3-5 authors.

but that's not easy to do as a grad student

lol, just saw this on a comments board online:

"I have often found that some of my most brilliant ideas had been stolen by someone else years before I had them."

3

7:11 PM

more hats

Mithrandir24601

@dmckee This is the really, really cool bit of physics though :) like when your supervisor has an idea, only to discover that someone else did it a couple of months ago, but missed some assumption or made the argument way too complicated or something

I'm running into something sorta similar right now, actually

I got to be the first author in both my papers so that was cool :P

it's a bit of math which, as I discovered after doing it, was already known to specialists, but is sufficiently visual/cute that it might make some inroads for a different audience

@Mithrandir24601 how is that cooler than your team having an idea, then confirming that it's not in the literature and being the first to publish?

7:14 PM

eh, it means you get to say "someone already did this, but they didn't do it right"

@Semiclassical that's my third paper right there

lol

or pretty much anything with explicit citations in the abstract, really

yeah

Mithrandir24601

@EmilioPisanty I think I just have a personal preference of filling in the missing details, but maybe that's because I'm a newbie PhD student and haven't yet got to grips with doing properly original stuff?

7:16 PM

sciencedirect.com/science/article/pii/S0040403900714523 being, of course, the most egregious example around

though that's a bit of a different beast

> Comment on a paper by Samir Chatterjee.

> All claims in the paper cited (Tetrahedron Lett. 3249 (1979)) should be accepted as fact after, but not before, verification by independent experiment.

(h/t, as always on chemistry stuff, to Derek Lowe)

...huh

yeah

can you say

"them's fighting words"

lol

@Mithrandir24601 I'm not saying that filling in the details is bad

there was a sheet of paper posted on the wall where our high energy theorists had offices, listing "roberts rules of order for theorists"

7:19 PM

just go into an area of physics so niche that nobody has published anything about it before

one of which was to avoid fighting words like trivial or inelegant

I just don't quite see "discovering that your fresh new idea just hit print two months ago" as the coolest bit of doing science

maybe neutrino spin oscillations in curved space-times with torsion

@EmilioPisanty yeah, it's a bit of a weird feeling

on the one hand, you may well be seeing something there which the original discoverer didn't. so it can be a discovery within a discovery

but you're still in a place where others have been before

The ultimate example of that is probably non-Euclidean geometry

Lobachevsky: so here's some interesting geometry I've been doing...
Gauss: Oh, nice, I had that same thing a while back but decided it wasn't worth publishing.

@Semiclassical yeah, well, but if you're competing with Gauss then you might as well just accept that you-getting-second-place is something that's going to happen.

7:25 PM

lol

@Semiclassical He did the same thing to Jacobi

not surprised

J got quite pissed off

actually, it seems like it was Bolyai not Lobachevsky in the above

right

bolyai was a good friend of gauss

prior to this incident

7:27 PM

lol

one thing I don't get, as I think on it: I can understand why discovering hyperbolic geometry took a while, but what about spherical geometry?

I mean, spherical trig goes back a long ways owing to its relevance for sea travel and navigation by the stars

@BalarkaSen ok so I'm gonna do the classification of 1-folds because I only have two lectures

indeed, the History portion on the spherical geometry wiki page lists quite a bit

@Semiclassical p sure spherical precedes hyperbolic

@0celo7 ahok

yeah

I guess I'm wondering when 'spherical geometry' would first have been described as 'non-Euclidean.'

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