The h Bar

Al Nejati

03:38

Lots of highly downvoted questions recently.

Anonymous

04:38

@Lozansky I don't really see how you conclude that the bound volumetric charge resides at the "center of the sphere"

Anonymous

Remember that $\rho_b$ is your is bound volumetric charge "density"

Anonymous

For homogenous isotropic dielectrics, it turns out to be 0

Anonymous

But not otherwise

Anonymous

Anonymous

Notice $\rho$ there ^

Anonymous

04:43

@Lozansky Oh, I see you get a $\delta^3(\mathbf{r})$ in the expression for $\rho_b$. Didn't notice that earlier.

Anonymous

Interesting

Anonymous

05:00

@Lozansky Hmm, I'm finding it a bit difficult to believe that that is the volume charge distribution. $\chi_e$ is a scalar in your case, right?

Anonymous

05:40

@Lozansky Okay, hmm. It doesn't follow from "susceptibility = $\chi_e$" and "radius = $R$" that your polarization is of the form you wrote. For isotropic media the direction of the macroscopic electric field is same as the direction of polarization (which is not radial in general)

Anonymous

However, if you do assume that your sphere has a radial polarization of that form, the volume charge density is of that form.

Anonymous

Such a polarization has a non-zero diverge and it becomes obvious that the negative bound charge is concentrated at the centre.

Anonymous

Draw any spherical surface within the sphere. Physically you can imagine the negative and positive ends of consecutive dipoles lining up in radial direction, making the net charge density on that surface zero.

Anonymous

^ I meant spherical surfaces having the same centre as the original sphere.

Anonymous

And then you can see the negative ends of the dipoles getting concentrated at the centre of the sphere.

Anonymous

05:48

What doesn't make sense to me is your sentence "It's a straightforward task to show that ...".

Emilio Pisanty

07:58

-2

Q: Could I express the electromagnetic field as an expression of the rest energy of a proton?

We suppose to have e Proton of mass $m_p$ moving with speed $v_p$ in a constant magnetic field $\vec B$ perpendicular to the speed. Then we can write: $$\frac {m_p v_p^2}{R} \hat r=ev_p \times \vec B$$ expressing $v_p =\omega_p R$ we obtain: $$m_p \omega_p = eB$$ where we eliminated the vecto...

How did this last so long without a single close vote?

John Rennie

@EmilioPisanty because it is completely incomprehensible?

Anonymous

08:22

93

A: Efficiently find binary strings with low Hamming distance in large set

Question: What do we know about the Hamming distance d(x,y)? Answer: It is non-negative: d(x,y) ≥ 0 It is only zero for identical inputs: d(x,y) = 0 ⇔ x = y It is symmetric: d(x,y) = d(y,x) It obeys the triangle inequality, d(x,z) ≤ d(x,y) + d(y,z) Question: Why do we care? Answer: Because ...

Anonymous

This answer is gold! Took me 2 days to find it :D

Emilio Pisanty

@JohnRennie that's what UWYA is for, though, innit?

John Rennie

@EmilioPisanty well yes, but there's a difference between this doesn't make sense and I don't understand this - the latter does not necessarily imply the former especially in my case. To determine the difference requires a certain amount of effort to read the question and try to understand what it is asking.

user129412

10:11

Would anyone be able to point me towards a plot of transition matrix elements vs offset charge for a cooper pair box?

Semiclassical

11:40

@JohnRennie “this doesn't make sense to me” vs “this wouldn’t make sense to a reasonable reader” I guess

Huzzah for contextuality

Captain Bohemian

11:55

is the landscape in string theory just the multiverse theory?

John Rennie

Not exactly ...

The landscape is the idea that there are many metastable vacua, but that doesn't posit any mechanism for those vacua to occur in nature.

Typically the idea is linked to eternal inflation. The idea is that different parts of the inflating universe undergo compactification independently of each other, and compactification results in one of the vacua in the landscape being chosen randomly.

So there is a single universe but there are different regions of it it that are (a) in different metastable states and (b) causally disconnected from each other.

This is referred to as a multiverse because it has causally disconnected regions in different states, but it is still a single continuous manifold so there isn't really anything multi about it.

Semiclassical

While I’m not a Tegmark guy, his categorization of different levels of multiverse is pertinent here:

“This categorization posits a nested hierarchy of increasing diversity, with worlds corresponding to different sets of initial conditions (level 1), physical constants (level 2), quantum branches (level 3), and altogether different equations or mathematical structures (level 4).” (lifted from the Wiki page on Tegmark’s mathematical universe hypothesis)

With the string theory notion of multiverse being at level 2 I guess

I find it hard to take talk of multiple universes very seriously, personally, except in the weakest (level one) sense

Secret

13:20

I want a level 5

vzn

13:54

more on the Strumia affair discussed 2d ago in here HIGH ENERGY PHYSICS COMMUNITY STATEMENT / Statement on a Recent Talk at CERN "particles for justice" via reddit reddit.com/r/Physics/comments/9lk5ww/… chat.stackexchange.com/transcript/71?m=47012006#47012006

also reminds me of this recent blog by gowers on math controversy wrt TP Hill paper Has an uncomfortable truth been suppressed? / gowers

Semiclassical

14:23

@Secret the Secret level

Secret

Wonder what level of infinity of the multiverse do fantasy live :P

Semiclassical

14:43

depends on what kind of fantasy

If it's got magic, I think you really would need something beyond levels 1-4

user 2646

is the human brain a multiverse?

Avnish Kabaj

Yes why not

Imagination is your creation

bolbteppa

15:16

@vzn good statement by P4J

vzn

@bolbteppa dont know whats going on lately, seems topsy-turvy. whole thing seems like overreaction to me. battle of the sexes o_O

bolbteppa

Think it's an under-reaction to his 'cultural m...' nonsense about women in physics

Semiclassical

I entirely missed that this was a thing

vzn

@bolbteppa seems to some degree putting attn on it can increase the notoriety. ie unintended consequences. english expr let sleeping dogs lie™

Semiclassical

tbh I think I was happier not knowing about it

user 2646

15:22

ignorance is bliss

Semiclassical

yeah, that's the thing

my ignorance of it was more comfortable. doesn't mean it's better to be ignorant about it

bolbteppa

Yeah, but this has been festering and building because it's been ignored, c.f. 2016 election for another example :p

user 2646

lol

bolbteppa

(Or the nomination from 30 minutes ago and the insane back story)

Semiclassical

ehhhhh. Strumia is European, isn't he?

vzn

15:24

another "elite sex misconduct scandal" in the news pulitzer prize dailymail.co.uk/wires/afp/article-5718857/…

Semiclassical

i'd avoid simply transposing Strumia's comments into the American political context

there are similar issues, to be sure

hmm

that's a fair point

vzn

lol sigh

user 2646

-_-

vzn

← comes here for freeform/ unfettered discussion aka free speech™, maybe increasingly unrealistically

user 2646

(removed)

Semiclassical

15:28

I think it's fair to say that there's a common 'far right' aspect to this

What's different in the US is the whole R/D split

there are certainly political factions in Europe, and a lot of commonality between the various parties

but I don't think there's an analogue for how polarized the US context is between R and D

For instance, with the whole Kavanaugh affair of late

bolbteppa

Thankfully things are not as bad in most other places :p

Semiclassical

Whatever one thinks about all of that, one outcome is probably that the R base is more energized than it previously was. hence the political stakes of Kavanaugh's appointment are quite stark

vzn

yes US really highly/ extremely (politically) polarized, fallout into other areas, maybe historic levels, just saw scientific study on that

"DEMOCRAT/REPUBLICAN DIVIDE IS WORST IT’S EVER BEEN" msutoday.msu.edu/news/2018/…

user 2646

in the US there is more religion involved

Semiclassical

i guess that's why I hesitate to put Strumia's comments in the same category. however bad they are, I don't think they'll have much political fallout

i dunno. i feel like I'm waffling

vzn

15:35

can anyone explain why it was necessary to start a substantial "P4J" "PAC"/ petition to respond to Strumia? maybe the "atiyah" model of embarrassed collective silence might have worked better...! o_O

bolbteppa

His comments fit into the q-anon wing of the Trump base more than the ignore-Kav-accusers base (which is the whole party admittedly)

He gave that talk at a Cern conference as an invited speaker during a women's conference to I think mainly a group of women and used n..i conspiracy theories to justify himself

Semiclassical

I do wonder how big the former actually is

bolbteppa

I think the physics community ignoring this would be unacceptable

Semiclassical

Oh, certainly

vzn

if hes never invited to any conference again, would that constitute "ignoring" it?

Semiclassical

15:38

I think it's hard to have a united front on that without public announcements

vzn

ok, some point there. seems like a statement by the conference organizers might have worked. and maybe be slightly )( less divisive/ acrimonious.

bolbteppa

One thing is for sure - we can predict what kind of phd students he will have a bias against, what about msc students and what if he has women in his undergrad classes, this is simply beyond the pale

Semiclassical

yeah

vzn

to me part of the story here with Strumia like Atiyah is generational. Strumia is a kind of old fossil, a type nearly extinct.

Semiclassical

eh. there's a difference between being wrong and being an a******

vzn

15:42

"sledgehammer to crush a fly™" comes to mind.

Semiclassical

you can be one without the other, or you can be both

vzn

agreed theres a difference but the point is, its 2 very old men behaving excessively foolishly.

bolbteppa

It's a sledgehammer against a fly until vzn applies for the anti-vzn job he really wanted and was qualified for but couldn't get because his emoticon was rouge-y and not blue-y (and his acccount didn't let him change his emoticon :p)

Semiclassical

How old is Strumia?

vzn

wow big news already. didnt notice hes already suspended. again maybe the obvious/ sufficient response theguardian.com/science/2018/oct/01/…

bolbteppa

15:46

I mean honestly, how far removed is this from him using phrenology to justify excluding minorities from university?

Semiclassical

looking around online, it seems like Atiyah and Strumia are about 40 years apart in age

bolbteppa

Implicit/unconscious bias is simply too difficult for mr. genius apparently

Semiclassical

@bolbteppa it's seemingly too difficult for a depressingly large fraction of the world

vzn

ok, thought strumia was older. looks maybe 50s th-dep.web.cern.ch/roster/strumia-alessandro

Semiclassical

yeah

whereas Atiyah is almost 90?

that's not to say it's not a generational thing, of course

just separate generations

vzn

15:52

anyway theres possibly some correlation between sexism attitudes + age, some of it is related to shifting attitudes/ strictness on sex harassment boundaries over decades etc, this is seen in kavanagh issue, just saw flaming editorial on it thedailybeast.com/what-the-actual-fck-republicans?ref=home

Semiclassical

one thing the whole Kavanaugh affair has me thinking about is drinking

I didn't drink at all during college

but I lived with people who did, quite a bit

vzn

@Semiclassical yeah my next door neighbor was ranting about the hearings and then asked him about the drinking, he waved it off, dont like that myself either, think his behavior is dishonorable

bolbteppa

The idea that one of the Vince Foster ringleaders would even be a judge let alone a SC judge is kind of unbelievable, what is wrong with the people who vote for this, it's insane

Semiclassical

I haven't really kept up with my college friends, but I do still consider them as such

vzn

← remembers the vince foster thing o_O

Semiclassical

15:56

@bolbteppa the cartoon I saw in the editorial section of our paper was pretty on point: startribune.com/…

vzn

lol this latebreaking editorial just popped up, kind of almost-hilarious-yet-utterly-depressing title, onion like We were Brett Kavanaugh’s drinking buddies. We don’t think he should be confirmed. washingtonpost.com/opinions/…

bolbteppa

Yeah

It was 100% predictable he would do what he did and that it would pay off

Captain Bohemian

@Semiclassical excuse me, what are quantum branches?

Semiclassical

Suppose you make a measurement of a quantum state, e.g. you send an electron through a Stern-Gerlach device to measure the z-component of spin angular momentum

you'll get one of two outcomes: the electron deflects up or down

however, before you've measured it, you've got a superposition of those two states

so in that sense, before you make the measurement, both are equally 'real'. the question is what happens to the state that you didn't observe

enumaris

it splits off another universe

duh

Semiclassical

16:02

each of those possible outcomes is a quantum branch

Sir Cumference

Ugh I feel awful

How did I get sick right before midterms

Semiclassical

with measurement processes landing you in one particular branch each time

enumaris

did the radius shrink?

Semiclassical

(note: the following is probably caricature based on my own ignorance). if you go down the many-worlds route, you insist that each possible outcome is in fact realized in some universe, i.e. each possible branch is in some sense real

John Rennie

@Semiclassical the original paper from Everett wasn't many worlds.

enumaris

16:05

@Semiclassical so for a continuous observation, e.g. position, do you get an uncountably infinite number of worlds?

John Rennie

Everett's paper basically said that we measure the position of the system in Hilbert space wrt some origin.

But you need to consider the bigger Hilbert space of both the system and the observer.

And during the observation the position of the observer in that big Hilbert space changes too.

Semiclassical

@enumaris eh, I think that's a bit of a caricature. a realistic detector is a large but finite set of pixels, each with some sensitivity

so any realistic measurement of position won't invoke uncountable infinity

enumaris

so now we gotta consider the properties of the detector? D:

Semiclassical

welcome to contextuality :)

danielunderwood

Can we measure the combined wavefunction in a case such as a photon and detector? I've always wondered how that would affect the measurement problem, but figured a detector was too complicated to incorporate into the system

vzn

16:07

@Semiclassical is that a thing in literary analysis? :P

enumaris

so just countably infinite worlds then>

?

danielunderwood

Well not measure the wavefunction, but get to it mathematically

Semiclassical

@danielunderwood one problem there: how do you formulate the wavefunction of a photon?

enumaris

@danielunderwood afaik that's akin to what decoherence wants to do

danielunderwood

Uhh electron then. I admittedly don't know anything about photons in QM

Semiclassical

16:09

there's also the issue of: Do you treat the detector classically or as part of the quantum-mechanical system?

danielunderwood

I mean you'd have to treat it quantum mechanically if you wanted to see what happened when the particle and detector interact, correct?

Semiclassical

The problem is then how the system actually reaches a final measurement state

vzn

← sometimes feels current photon theory is modern version of "how many angels dancing on pins™"

danielunderwood

Yeah I suppose that would still be a problem as well. I've always been a bit troubled by the thought of a measurement causing wavefunction collapse when a measurement is generally going to heavily modify the potential in the problem

Semiclassical

Gotta deal with the measurement problem somehow

danielunderwood

16:14

Yeah and even if you incorporate the detector in the system, you're still going to have superposition of states and you're kind of back to where you started...hmmm

Semiclassical

decoherence is supposed to help make sense of that

whether it succeeds... shrug

vzn

@bolbteppa liked that ref, wanted to deconstruct more, are you giving up on Atiyahs physics completely? uv.es/~azcarrag/pdf/…

danielunderwood

Ahh I'll have to look into it. I've heard of it, but not familiar with it

Speaking of which, is QBism taken seriously at all?

bolbteppa

He doesn't have any physics haha

Semiclassical

@danielunderwood depends on the audience I suspect

the history of physics guy I've worked with has little patience for it

bolbteppa

16:16

Here is a thread on his 'physics' physicsforums.com/threads/atiyahs-arithmetic-physics.956055

vzn

@danielunderwood there is some new thinking on all that in scattered refs for any young enterprising/ openminded/ persevering students

@bolbteppa now suspecting you dislike him more for his bohmian affinity than deriving the fine structure constant :P

Captain Bohemian

@Semiclassical what a coincidence that recently I saw both the term "branch of the superposition" and the term "the component of the superposition" are used in the article regarding a proposal to test if gravity is a quantum force quantamagazine.org/… I just suspect "component" and "branch" mean the same. On the other hand, I also suspect

Semiclassical

for the record: I don't think taking the Bohm story seriously (if not literally) is as disreputable as the above might imply. But it definitely doesn't help with his credibility among mainstream physics

Captain Bohemian

"branch" is not a professional term, but is arbitrarily used. It turns out "branch" is professional term.

bolbteppa

His math is incredible, that commutative algebra book is something I've always wanted to sit down with, but there's no reason for him to make good arguments about physics

Semiclassical

16:19

And that's assuming his invocation/usage of pilot-wave ideas is sensible, which...not sure that can be taken for granted

vzn

@bolbteppa he seems to be pursuing solitonic ideas past/ lately but dont know the details would like to learn more on that. like his interest in trying to explain renormalization, a deep mystery that seems to show limitations of Standard Model... etc

Semiclassical

The weird thing with the fine-structure constant thing is how dated the mindset seems

bolbteppa

I think he was trying to do things like this in the 80's

Semiclassical

He has that quote of Feynman, and relative to that quote it makes sense

but that quote is how many decades old?

I'd guess that it precedes the notion of electroweak unification for instance

vzn

anyway Bt/Sc thx for your timely/ cogent Atiyah analysis that wknd, it was instrumental/ pivotal in my own thinking/ analysis vzn1.wordpress.com/2018/09/26/…

Semiclassical

16:26

hmm, looks like I'm wrong. that remark of Feynman is from his popular QED book, published in 1985

whereas the nobel prize for electroweak unification was awarded in 1979

to be clear, the quote I mean is this one:

>"There is a most profound and beautiful question associated with the observed coupling constant, e, the amplitude for a real electron to emit or absorb a real photon...It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it."

Which even in 1985 seems out of date

vzn

nice survey A Critical History of Renormalization / Huang arxiv.org/abs/1310.5533

enumaris

just change the letter and it's all good

John Rennie

It's a tempting thought that at a high enough energy all the coupling constants have simple values related to some fundamental theory (string theory?) and the value we see at low energy is the simple value plus an infinite series of corrections.

bolbteppa

The value of $e$ is simply such an insane thing if you go back to the whole Dirac sea thing I've been saying here recently, the difference between bare and observed charge

Semiclassical

yeah. but even there you need some physics theory telling you how that unification would proceed

John Rennie

16:35

Viewed from that perspective what Atiyah is doing is working out a way to calculate all the messy corrections we get as the energy scale is lowered towards zero.

It's conceivable he's stumbled across a way to do that by chance.

Semiclassical

@JohnRennie the trouble is that it seems less like "working out the messy corrections" and "trying to guess the result"

bolbteppa

Then there is the whole electroweak stuff

Being able to re-express the coupling constant in terms of other constants

Semiclassical

the most generous interpretation I've been able to come up with: Suppose you didn't know about electroweak unification, and all you had was QED

John Rennie

Yes, it all seems like numerology. But it's just possible there is something akin to the amplituhedron structure hiding behind the standard model and there might be a way to short circuit all the tedious calculating of corrections to $\alpha$.

Semiclassical

Can you set up a field theory which reduces to QED at the energy scales to which we have access and where $\alpha$ has some nice simple form?

@JohnRennie yeah, tbh that's why I find stuff like resurgence theory interesting

the suggestion being: it's not that our theories are wrong, it's that we don't know how to extract the information from them correctly

...i guess. i dunno. there's a reason I never worked on this myself

bolbteppa

16:45

Atiyah does not even mention the formula for $e$ here motls.blogspot.com/2014/10/… in terms of $SU(2)$ group constants

Semiclassical

yeah

it really does seem like QED pre-electroweak

enumaris

I could imagine the coupling constants be geometrical in nature fundamentally

bolbteppa

In the PF forum post it seems that because $137 = 1 + 8 + 128 = 2^0 + 2^3 + 2^7$ with $0, 3,7$ gives numbers one less than the dimensions of 3 of the 4 division algebras and because they link to bott periodicity it is somehow not numerollogy

enumaris

in which case, it could make sense that they can be "derived" from a purely mathematical consideration given some geometrical features of space time...

Semiclassical

@bolbteppa which feels like the worst kind of numerology

just because it doesn't want to be called numerology, doesn't mean it isn't

bolbteppa

16:49

Yeah

enumaris

but my gut tells me that e.g. knowing only the structure of spacetime given by GR is not enough to arrive at such an answer...

Semiclassical

the best it seems like one could hope for is to find some convenient/natural way of approximating the fine-structure constant

enumaris

but perhaps he's seen through the veil and found some much deeper geometrical facet upon which one can derive the coupling constants...

Semiclassical

to hope that the fine-structure constant itself, as inferred from the amplitude for a real electron to absorb/emit a real photon, is going to have a tidy mathematical explanation

that just seems way too much

enumaris

seems so to me as well

but one can always hope

vzn

17:11

@Semiclassical in the pilot wave hydrodynamics analogy this is the relation between the pilot wave and the "bouncing" particle related to contact dynamics/ surface tension. there is an even deeper analogy in solitonic picture.

bolbteppa

17:23

What if I told you $SU(8)$ was a subalgebra of $E_7$

Semiclassical

hax

hax i say

enumaris

don't you mean $\mathfrak{su}(8)$ and $\mathfrak{e}_7$

gotta keep dat notation consistent

bolbteppa

You are lucky I did not say subgroup and mean subalgebra

E7 (mathematics)

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E7 algebra is thus one of the five exceptional cases. The fundamental group of the (adjoint) complex form, compact real form, or any algebraic...

enumaris

cries softly

Semiclassical

yuck

tfw you can't tell if the author is doing something clever or just careless

$L_1 \psi = L_2\psi$ does not imply that both sides vanish seperately

enumaris

17:38

o.o

Semiclassical

I think I see what they're doing now

but meh

enumaris

I ain't psychic

Semiclassical

lol

It goes like this. Suppose we've got $H=-\hbar^2 (d/dx)^2+V(x)$ and $H\Psi = E\Psi$

and you make the substitution $\Psi(x)=a(x,\hbar)e^{i \phi(x,\hbar)}$

enumaris

why are you putting hbars into the function slots

Semiclassical

You can reorganize that to $$(\partial_x \phi)^2+V(x)-E = \frac{i\hbar}{a(x,\hbar)^2} \left(i\hbar a(x,\hbar)\partial_x^2 a(x,\hbar)-\partial_x[a(x,\hbar)^2 \partial_x \phi(x,\hbar)]\right)$$

b/c that's what the paper does, if I'm honest

enumaris

17:52

looks weird

Semiclassical

the really weird thing imo is why they write $\Psi$ as just being a function of $x$ but not $a,\phi$

enumaris

is it doing some classical correspondence?

Semiclassical

yeah. I think their tactic is to note that, if that equation is going to hold for all $\hbar$, then it'd better work in the limit $\hbar\to 0^+$

in which case the RHS goes to zero (so long as $a(x,\hbar)$ doesn't vanish....) and you just get the LHS equal to zero

which is the Hamilton-Jacobi equation

If that holds identically, then you need the RHS to vanish not just at $\hbar=0$ but for all $\hbar$

and therefore $$i\hbar a(x,\hbar)\partial_x^2 a(x,\hbar) = \partial_x[a(x,\hbar)^2\partial_x \phi(x,\hbar)]$$ as well

That's what I think they're saying at any rate

enumaris

if that holds identically...like if the Hamilton Jacobi Equation is always true?

no matter $\hbar$?

Semiclassical

If the Hamilton-Jacobi equation for $\phi$ always holds, yeah

enumaris

17:56

I feel like the RHS actually just measures the degree to which the Hamilton Jacobi Equation doesn't hold true lol

But sure o.o if you posit the LHS is always 0 then you can say the RHS is always 0

Semiclassical

Yeah

the weirdness really is in $\hbar$

and what it means to demand that it hold for any $\hbar$ as $\hbar\to 0$

enumaris

ugh, my hands are all messed up from doing BJJ yesterday...

-.-

Semiclassical

they're remarkably unclear on this unfortunately

bolbteppa

Why would you write it as a function of $a$ and $\phi$, it's just the decomposition of a complex number $z$ into $re^{i\theta}$ no?

Semiclassical

if they were assumed to be real, yes

but that doesn't seem to be what this paper is doing

bolbteppa

18:03

Why does it depend on being real?

Semiclassical

Because that's the only reason why the decomposition $z=re^{i\theta}$ would be unique

If they're not required to be real, then there's not a unique decomposition

bolbteppa

Just seems like they are solving $i \partial_t \Psi = \hat{H} \Psi$ by breaking the complex number $\Psi$ up into polar form then analyzing the two parts separately that both join up to give $\Psi = r e^{i\theta}$? $r$ is real and $e^{i \theta}$ is complex

Note this is how you do the quasi-classical approximation in QM with the action in the argument

Semiclassical

Well, in what sense do you mean 'two parts'?

the obvious way to get that would be to write $E=\dfrac{1}{\Psi}\hat{H}\Psi$ and take real/imaginary parts

bolbteppa

Well I guess it does not turn into a separable equation so one crazy part :p

Semiclassical

The problem is that the equations you get upon taking real/imaginary parts aren't the ones given in this paper

So that's not what they're doing

(the equations you'd get are the ones Bohm got in his 1952 paper: real part is an inhomogeneous Hamilton-Jacobi equation, imaginary part is the conservation of probability density equation)

bolbteppa

18:19

cqi.inf.usi.ch/qic/bohm1.pdf

Semiclassical

here's the relevant portion of the paper I'm looking at:

Note that equation (3) is just the classical Hamilton-Jacobi equation. By comparison, Bohm's equation (4) contains an extra term

(I'm taking the time-dependence to just be $e^{-i E t/\hbar}$)

What I'm trying to make sense of is their claimed 'equivalence' between the Schrodinger equation and eqs. (3), (4). With Bohm's equivalence it's obvious since you can take real/imaginary parts

bolbteppa

My guess is plugging it in with the gradient and divercenge in the Laplacian being treated one at a time

Semiclassical

What?

bolbteppa

18:35

Yeah not sure looks a bit weird (runs)

enumaris

21:13

hmmm

Hard to tell if the deep spelling corrector actually helped the named entity recognition or not...

danielunderwood

Add more layers for better results of course

enumaris

the spelling correction is probably about as good as it's gonna get

the errors it makes are like...weird abbreviations and crap like that that there's just no way around

but it seems like the named entity recognition performed on the spell corrected text and the non spell corrected text is not really any different lol

danielunderwood

Poorly spelled entities are still entities I suppose lol

enumaris