The h Bar

0celo7

01:09

@Cows because it's beautiful i.gyazo.com/e98223cb184a5954614a31a16a2f1c41.png

diobuc eulb

03:07

@AccidentalFourierTransform are you actually in canada now?

diobuc eulb

03:23

@AccidentalFourierTransform are you at perimeter?

bolbteppa

03:33

Lubos defending the Dirac sea nicely

7

A: Does Dirac's idea of filled negative energy states make sense?

Dirac's explanation of the emergence of antiparticles such as positrons out of the Dirac sea, and the Dirac sea itself, is completely valid and legitimate, and you have described some non-quantitative aspects of it and differences between it and some condensed-matter situations. Dirac just began...

Secret

05:41

@AccidentalFourierTransform a lot of interpersonal issues are suffered from ordinary people too, which is why "interpersonal SE" is more encompassing and relevant

Secret

05:51

nature.com/articles/doi:10.1038/nature25029

Black holes cluster around supermassive black holes. I wonder how fast they are orbiting

2

Cows

06:27

Just picked up my brother at the airport. Things should be fairly more interesting around here

Perhaps I'd ask him about how to build a supersonic aircraft or whatever it is he does

hehe

Engineers

Slereah

07:02

mornin

Swapnil Das

mornin

John Rennie

0

Q: How do rocket scientists do iterative development?

In software, the general process for developing anything is code, test, fix, repeat. This is easy and cheap, because running a program typically costs an incalculably small amount of money. In rocket science, it's different. Each launch can cost tens or hundreds of millions of dollars, and scale...

rockets

Launch. Boom. Repeat.

3

Slereah

hopefully in simulations

fortunately the original rocket testing was all done on Hitler's dollars

John Rennie

The US rocket programme had its fair share of fireworks :-)

The Russians probably did too, but they were sensible enough to conduct their tests in secret :-)

Slereah

07:34

So

Given the FRW metric, we can check that the measurements performed on astronomical data checks out

But how certain are we that this is the only such metric to be so?

it's fairly hard to determine since the measurements mostly assume FRW to some degree

Since far off sources are measured assuming that the redshift corresponds to the distance

though I'm guessing that people probably checked a bunch of other metric classes, maybe?

John Rennie

The FRW metric isn't a single solution. It's a whole class of solutions depending on the matter/energy/dark energy present.

Slereah

I know

But still

it is a fairly big assumption

John Rennie

The only assumption is homogeneity ...

There have been studies of the dynamics if homogeneity is not assumed, but I'm not sure how much progress has been made.

The CMB tells us the universe was homogeneous in its youth so it's not that big an assumption.

In other news, time for my third (pint of) coffee. Some mornings are a struggle. God help us when the UK finally goes fully metric. I'll have to start drinking litres of coffee.

Bernardo Meurer

@JohnRennie You know, there is some beauty in languages like Python too

exercism.io/submissions/2a52c783757d4e06b6877045869d48dc

John Rennie

@BernardoMeurer :-)

I tend to distinguish between the core features of a language, its basic syntax, and the various APIs that go with it. Python kind of blurs the distinction since a lot of what would be regarded as extra APIs in other languages is built into Python.

That allows code like yours to be written so concisely in Python

Bernardo Meurer

07:49

Yeah, I agree with that

John Rennie

Whether that's a good or bad thing I don't have any strong view about

Bernardo Meurer

But I was just proud of my implementation :P

John Rennie

It's certainly elegant :-)

Slereah

@JohnRennie and isotropy

If you drop the assumptions of the FRW metric, measuring actual distances from redshift changes radically

John Rennie

@Slereah haven't you got anything better to do? :-)

Slereah

07:51

Also does the CMB actually say the universe was homogeneous?

The CMB implies isotropy

I dunno about homogeneity

Homogeneity is more from the 2dF survey

John Rennie

OK, the universe is inhomogeneous and the Earth really is at the centre of it.

Slereah

It could be!

Although I'm guessing people already tried fitting data with a spherically symmetric model around earth, just in case

let's see if there's a survey of all non-FRW fittings

Bernardo Meurer

Slightly improved: exercism.io/submissions/a064df7ccf8a4e0b976b3b2eef5e6ea1

Time for bed! Gnight!

John Rennie

But if you drop homogeneity then you have a density-distance function that is effectively a free parameter.

Slereah

I didn't say it would be easy!

John Rennie

07:54

How are you going to do anything useful with initial conditions like that?

You can just choose any initial conditions to suit whatever scatterbrain theory you come up with

Slereah

I'm not sure, I guess you can probably fit that parameter from observations

just find out the redshift induced on radiation from stars

@JohnRennie Well it still has to fit observation

John Rennie

But as you said, we don't have a good way to determine the distance to really remote objects except from their red shift

Slereah

yeah, but I know it has been done for some metrics

I know that the Planck survey checked if the Godel metric fit observations

John Rennie

There has been so much work done on studying the CMB it seems hard to believe any significant deviation from the FRW assumptions wouldn't have beenspotted

Slereah

(it did not for any measurable value of rotation)

Oh I'm sure it's been done, but I would like to see a survey of such things

Attempts to fit data to spherical, cylindrical, axisymmetric universes, etc etc

because as it is it's a bit tricky to justify

John Rennie

07:58

Is the axis of evil still an unresolved issue?

Slereah

I think it was shown to be wrong?

But I didn't really follow all that much

iopscience.iop.org/article/10.1088/1475-7516/2011/07/029

Tanuj

08:19

@JohnRennie How is the mean free path related to Volume ?

John Rennie

@Tanuj Mean free path is dependent on density rather than volume

Tanuj

@JohnRennie okay , how ?

John Rennie

Like this

It's basically area of a molecule / number density give or take a few constants

Qmechanic

@AccidentalFourierTransform : Does a bird get offended if you flip the bird? :)

John Rennie

My walk home from an evenings drinking takes me along the canal path, and there used to be three ganders that hung out on the canal path as a group. They would attack me when I walked (staggered) past them. They'd peck me on the knees, which was bloody painful.

Eventually I had enough and aimed a kick at the nearest gander. Luckily (for the gander) I was too drunk to aim properly, but anyhow all three of them fled squaking.

They avoided me after that :-)

Jaime Gallego

08:40

@ACuriousMind And @BernardoMeurer still owes me that drink...

Emilio Pisanty

09:08

How Not to Land an Orbital Rocket Booster

►

BTW, it appears I am now officially the discussion-est non-moderator user on our meta.

though to what extent that comes from votes on Community Ads threads vs spending too much time discussing on meta is unclear to me.

John Rennie

Launch, land, boom, repeat :-)

Secret

And this video shows why we need the private sector

John Rennie

Well, it shows why we need people like Elon Musk.

The private sector is responsible for lots of money wasting failures as well.

Secret

09:28

Yeah, they made up the other significant portion of technological development

Secret

Here's a wild idea: Suppose there's some competition which task companies to provide solutions to rapidly improve the education of the developing world, then I think the competition generated by that could could be wreckingball enough to get an actual plan moving

Slereah

Why did the 2dF survey only cover like half the sky

why didn't they do a 4 pi cover

Secret

because half of the hemisphere is blocked by the horizon (it's ground based, right?)\

Slereah

09:43

indeed it is

Put it in space says I

For all we know the universe is only homogeneous on those two slices!

Dawood ibn Kareem

10:11

@JohnRennie It may have been a sign of affection. I have a pigeon who enjoys nibbling on human fingers, but he's not trying to hurt anyone.

Anonymous

@DawoodibnKareem Tfw "affection" hurts like hell ;)

Dawood ibn Kareem

Well, it would if he were the size of a gander.

Anonymous

I surely wouldn't want a tiger or lion's attention for that matter

Dawood ibn Kareem

Tigers and lions can be tame and affectionate. But most aren't.

John Rennie

@DawoodibnKareem :-)

Ganders are notoriously aggressive.

For some reason it's only domesticated geese that are aggressive to humans. I guess any wild geese that attacked humans would quickly have found themselves in a cooking pot. For some reason domestication has caused the aggression.

Slereah

10:41

They are the most entitled animals

Secret

11:25

It still annoys me that not only there is no literally dark photons, but we cannot even make something that resembles them

because that will mean creating an object that divert all electromagnetic radiation not only at the object's surface, but also some distance away. The issue is that ambient radiation is consisted of a continuum of frequencies, thus meaning there is no easy way to invert them or divert them as the inverse problem cannot be solved within the limited response rate of any object

John Duffield

11:46

@bolbteppa : the Dirac sea is a discredited Space is not some infinite sea of particles with negative energy. Have you ever actually read Dirac's paper a theory of electrons and protons? He said this:

"We shall have an infinite number of electrons in negative-energy states, and indeed an infinite number per unit volume all over the world, but if their distribution is exactly uniform we should expect them to be completely unobservable".

Some of these negative-energy electrons have infinite negative energy. The "be nice" policy here prevents me from giving my true opinion of that. Doubtless you will try to justify it by claiming that I don't understand the math.

skullpatrol

hello

...in mathematics you don't understand things. You just get used to them :P

Anonymous

12:09

@skullpatrol Which is a statement having multiple interpretations...

skullpatrol

I agree, completely.

I once attempted to find out more about the specific context of the statement; but, alas, ended up down a rabbit hole :-)

John Duffield

I don't. In mathematics you do understand things. Or you should. People who don't end up believing in garbage like the parallel antiverse.

Anonymous

Oh, the irony :)

John Duffield

@Blue : or believing that I made up the mass deficit.

Semiclassical

I’d be more willing to casually reject the weirdness of QFT were it not for the uncomfortable fact that there’s so much experimental support (eg the minutely verified corrrections to the electron magnetic moment)

Anonymous

12:19

@Semiclassical Are you well-versed with BJTs ? I had a few questions

Semiclassical

given that I don’t recognize that acronym off the top of my head, probably not

Anonymous

Well, this. I guess I'll ask in the EE SE then

Semiclassical

People talk about the challenges of interpreting QM, but it doesn’t seem like there’s been nearly enough work on the sane for QFT

Slereah

QFT isn't that hard to interpret

it's hard to define properly, but it's not really any less intuitive than QM

Semiclassical

Ah, I’m no help there @Blue

Anonymous

12:22

Np

John Duffield

@Semiclassical : I don't believe in weirdness. I've read up on the "weak measurement" work by Aephraim Steinberg and Jeff Lundeen, who says wavefunction is real. See physicsworld. Sadly that dates from 2011, and there's more woo now than ever.

Slereah

Np junction indeed

Anonymous

@Slereah lol

Semiclassical

I should note that I am subject to tremendous ambivalence when it comes to how QM ‘should be’ interpreted

John Duffield

@Slereah : there are more issues with QFT than you appreciate, grasshopper.

Semiclassical

12:25

I don’t really buy any interpretation that would require altering the experimental predictions of QM, though

Slereah

well if you change experimental predictions that's not really an interpretation

John Duffield

@Semiclassical : I'm not. We do physics to understand he world, not the shut up and calculate. Especially when those calculations result in retrofits rather than predictions.

Slereah

that's a different theory

John Duffield

@Semiclassical : what experimental predictions of QM?

Semiclassical

@Slereah yeah. I’m more saying that I don’t think one can evade the philosophical problems

Slereah

12:28

I don't trust philosophical problems

everyone thinks their philosophy is the most obvious one

and any deviation is a problem of the theory

Semiclassical

@Slereah including the philosophy that there are no philosophical problems :}

Slereah

The old "shut up and calculate" interpretation of QM, as it's called

Semiclassical

Statistical predictions are still predictions

Slereah

SUAC

Not saying that there are no philosophy problems, of course

but my point is

if you really have a problem with the theory

Make a theory that has the correct predictions

(usually they cannot!)

Semiclassical

Plus, a huge portion of chemistry is basically applied QM

John Duffield

12:32

Here's what I think: "Then Schrödinger’s cat, which illustrated the absurdity of the Copenhagen interpretation, was hijacked by the peddlers of mysticism to demonstrate just how “spooky” quantum physics is. Such people even advocate the many-worlds multiverse. What happened? More to the point, what didn’t? What didn’t happen at the 1927 Solvay conference was a discussion of what the photon was, or what the electron was. Then Bohr sold his pup to the world, and it was all downhill from there."

Slereah

don't make your philosophy problems my physics problems :p

Semiclassical

As is most of solid state physics, condensed matter Physics, etc

@Slereah Eh, my insistence would be that this imposes a very impoverished view of Physics

Slereah

I'm not saying that it can't be useful for creating new theories and all

But maybe at some point let it go

Semiclassical

(Mobile keeps auto-capitalizing Physics)

John Duffield

@Semiclassical : next you'll be telling me quantum mechanics gave us the transistor.

Slereah

12:34

If reality doesn't seem to agree the physics might not be the issue

If you want to find a new QM sure knock yourself out but you know, actually do it

and be aware that odds are slim

Semiclassical

I dunno about transistors (though I should) but understanding semiconductors does involve knowing QM

Secret

tunneling and field effect transitors sure requires QM

Semiclassical

Not a huge amount of it, but it is there

Secret

and they run most of our computers

Slereah

that's why I only use good christian electric relays

The classical transistor

John Duffield

12:37

@Semiclassical : it's one of those overhyped myths. QM did not give rise to modern computers etc Just as CERN did not give rise to the internet.

Semiclassical

There is a distinction to be made between “how were transistors invented” and “how did we git gud at making really really small transistors”

Anonymous

Transistors sure didn't need QM, to be discovered, but surely QM explains their working.

Semiclassical

For the former, I wouldn’t be shocked if it didn’t need QM

John Duffield

@Blue : no it doesn't. Go read the history.

Secret

yeah i was thinking about the hypothetical scenario where all our computers will switch off if suddenly someone decided to delete QM from our universe

Semiclassical

12:39

For the latter, though? You definitely need QM for that

Slereah

Semiconductors were discovered around the mid-19th century, from what I remember

But it was just crystals acting mildly weirdly back then

Anonymous

@JohnDuffield Oh really? My whole book on transistors is based on QM.

Slereah

Nobody really found it that interesting back then

Semiclassical

Plus, y’know, superconductivity

John Duffield

@Blue : oh really.

Semiclassical

12:40

Oh, and phonons

John Duffield

Can somebody give me some predictions of quantum mechanics?

Not postdictions.

Silence.

Secret

physicsforums.com/threads/…

as a chemist, I can tell those hyperfine structure stuff are discovered after QM is formulated

Anonymous

@JohnDuffield Yes

Anonymous

Read it up.

Secret

as well billions of molecular spectra and how to interpret them

Anonymous

12:43

The very first chapter is on QM

Anonymous

And it builds the whole theory from there

Semiclassical

If you insist on QM delivering predictions for things which QM is predicated on not being able to predict

Then no s***

Statistical predictions are predictions

Anonymous

If you can explain tunneling to me without QM, you deserve a Nobel Prize.

Semiclassical

Oh. Also, integer and fractional quantum hall effect

John Duffield

@Secret : Zapper's answer is risible popscience lies-to-children: "Atomic spectra, periodic table, the band structure of the semiconductors that you use in your modern electronics (i.e. look up a Solid State Physics text), MRI, X-ray spectra, the double helix structure of your DNA...." QM did not predict atomic spectra, the periodic table, the band structure etc.

Semiclassical

12:45

Quantization of conductance is neat

Secret

well if those are not good enough, then try entanglement, it is a uniquely quanutm behaviour and are now giving us quantum simulators and progressively more powerful quantum computers

pretty sure no one thought about entanglement before quantum mechanics, or any experiment on it as far I knew

Semiclassical

Bell-type experiments on the whole, really

Secret

Quantum computers and networks are a prediction that is coming true slowly, thus by definition, it is a prediction

John Duffield

@Secret : what have quantum computers delivered?

@Semiclassical : Bell-type experiments aren't predictions, and you should read up on Joy Christian.

Secret

sciencemag.org/news/2017/09/…

Semiclassical

12:48

Oh look, a bird flipping in flight

Secret

here's a nice one. It's still a small molecule, but the error correction and number of qubits are growing fast in these 5 years

John Duffield

@Secret : I work in computing. People have been talking about quantum computers for decades. Meanwhile electronic computers have advanced by leaps and bounds.

@Blue : noted. I shall write about that.

Anonymous

@JohnDuffield I'll be waiting.

Secret

quantum computers suck at storage and other routine stuff, but excellant at simulations, therefore it is necessary for classicals computers to be still growing

Semiclassical

I do find the QC argument to be a weak one if I’m honest

Secret

12:53

Most people in the industry had that attitude that quantum computers is more like a module for calculating molecular chemistry and physics, run along side a classical computer

well, to be fair, you need at least 1000 qubits to do a calculation on pharamceutically important moelcules

and we are indeed still far from that

John Duffield

@Blue : I won't hold my breath, because you won't believe me.

Secret

I think the current record is 53 qubits with moderate error correction?

Slereah

that's because a quantum computer would be stupid for most calculations

diobuc eulb

@JohnDuffield well you sure spew out loads of other stuff daily regardless of whether anyone here believes you.

Slereah

most algorithms don't really benefit from quantum computing

Secret

12:55

yeah, it is really only specialised for simulations and molecular calculations

Anonymous

Since quantum computers are good at very specific things, pretty sure in the future they will be used alongside classical computers rather than as a replacement.

Secret

@Blue this is the current consensus for both academia and industry alike

Semiclassical

To put my own cards on the table, I really am not a fan of interpretations like many-worlds

It just seems too extravagant

John Duffield

@diobuceulb : that's because I know so much. Google on tunnelling evanescent wave.

Slereah

plus I'm guessing quantum computers are gonna be expensive

Not much point in having a quantum computer to run the OS

quantum linux

Anonymous

12:58

@Slereah Yup. They're very resource expensive

Secret

they do, unless someone managed to come up with room temp superconductors

actually wait, I mixed up something

Anonymous

Not all QCs need low temperatures

diobuc eulb

@JohnDuffield well if you keep telling us about all the things you know you'll run out of things you know!

you need a renewable source of new information because old papers are not.

Secret

@Semiclassical I am currently somewhere between psi ontic approaches and psi epistemic approaches, but not include many worlds

Slereah

Motl did an article on many world btw

his own version of many world!

Semiclassical

13:00

I’m sympathetic to Bohm stuff. But that’s predicated on it providing the same level of experimental predictions that the usual Copenhagen one does

John Duffield

@diobuceulb : not for a long while yet, because I'm learning about more things than I'm telling you about.

Slereah

motls.blogspot.fr/2018/04/…

Secret

@diobuceulb well at least for QM, he does cite stuff dating only back to 2011

John Duffield

@Slereah : many-worlds is woo.

Semiclassical

Which, in the setting of non-relativistic QM at least, it does just fine

From what I’ve seen, the supposition that Bohm does (or even could) provide different experimental predictions that QM does on its own is just wrong

Slereah

13:03

Well what is the actual prediction for EPR

as in done mathematically

Secret

> My version of the many worlds contains infinitely many worlds – they form a continuum with many continuous coordinates included in |ψ⟩,L,μ. I would claim that the splitting of the many worlds according to |ψ⟩ as well as L as well as some μ is necessary (my number is the minimum one) – you need to multiply the number of worlds both to deal with the Heisenberg choice and the Dirac choice. But you could increase the number of the worlds. For example, instead of depending "just" on |ψ⟩, the world could depend on a whole pre-history of measurements which remembers "how we got to |ψ⟩". In other…

Motl's wavefunction is so nonlinear

John Duffield

Bah, "my version of the many worlds contains infinitely many worlds".

Secret

that's motl, deal with it lol

Semiclassical

As far as I know, there’s no difference with QM. there’s more conceptual data with the pulitvwace account, but in terms of actual predictions it doesn’t differ

Secret

@Semiclassical I thought there's an arxiv mentioning how the peak intensity of the fringes in bohm will differ from QM?

Semiclassical

13:05

Yeah, well, there’s a lot of stuff on arxiv

John Duffield

@Secret : No wonder he thinks the Dirac Sea is fine and dandy.

Slereah

@Semiclassical Show me the money

Hey @JohnRennie

Semiclassical

Lemme see if I can find an accessible preprint

Slereah

According to Streater, due to being a classical probability theory, it cannot violate the Bell inequality

Hence it cannot work

John Rennie

@Slereah only poking my head in. I have to go shopping now. Oh well.

John Duffield

13:10

You know guys, in olden days some fat bishop of a charlatan would use Latin incantations to wow the suckers into believing in heaven and hell and sweet baby Jesus. Nowadays they don't use Latin, and the suckers don't believe in heaven and hell. They believe in the multiverse, and wormholes that lead to the parallel antiverse, and the holographic universe. And braneworld. And the evil twin universe where time runs backwards.

OK, lunch break over, I have to go. Nice talking to y'all.

Slereah

Hey @0celo7

0celo7

Hi

Semiclassical

@Slereah you do realize that, for better or worse, pilot wave theory is non-local? Plus, the predictions you get out of pilot wave theory still are consistent with the Born rule

Also, this is a frustrating paper: hal.archives-ouvertes.fr/hal-00862895/document

Slereah

@Semiclassical The proof of Bell's theorem doesn't actually require locality!

This was shown a little while back

Semiclassical

They talk about Bohm’s spin formulation of EPR but not the original one

Slereah

13:25

sciencedirect.com/science/article/pii/0375960187900752

Semiclassical

This is another nice one, though I don’t think it quite covers what you want: advances.sciencemag.org/content/2/2/e1501466.full

Slereah

^one of the proof is here, apparently

The Bell theorem doesn't require any reference to locality here

Secret

This region is strange. Is it detectable in principle by positioning the screen there, or it will just be pushed backwards when the screen is placed there?

Slereah

Trajectories are stochastic in Bohmian mechanics

Semiclassical

No they aren't.

Slereah

13:32

Don't read too much in a diagram

Aren't they?

At least in some versions

Semiclassical

The initial position of the particles is stochastic. But the trajectory is not, insofar as the wavefunction (and its time evolution) is known.

Slereah

I think the Wiener version is stochastic

Semiclassical

Here's my short summary of de Broglie-Bohm

Slereah

Well yes, but the point of Bohm is that the wavefunction isn't known, since it's generated by the universe :p

Hence in essence stochastic

Technically not but it is for all intents and purposes

Semiclassical

That seems dubious. If you don't know the wavefunction, then you're not in any position to make predictions in the first place.

Slereah

13:34

But how do you know it if it's non-local

Semiclassical

But tbh this is something I do find fuzzy.

Slereah

unless you know the position of every particle in the universe

Semiclassical

Here's the context in which I know how to make sense of de Broglie-Bohm.

Secret

if that region is detectable, then it will be evidence of bohm because usual QM don't have this in the fringes, and uual QM the fringes are predicted to spread out in strightlines

Semiclassical

Suppose I, in the usual QM way, can repeatedly prepare a single-particle state $\Psi_0$ at $t=0$.

To deduce that this wavefunction is well-defined, I should at the very least be able to repeatedly make measurements of the particle's location at $t=0$. If I'm indeed repeatedly preparing the same state, I'll get some probability distribution $\rho(x,0)$

Once I've determined to my satisfaction that I can do that, I can do the same after a time $\Delta t$ to get $\rho(x,\Delta t)$

and so on and so forth until I've got at least a rough approximation of my probability density and its time evolution

I should probably take $x$ to be a vector, not a scalar, since I want this to be a trajectory in space. But that seems like another detail.

From my approximate knowledge of $\rho(x,t)$, I can use conservation of probability to infer the probability current $j(x,t)$.

From this, I can write down the quantity $v(x,t) = j(x,t)/\rho(x,t)$.

Beyond Zero

13:42

Hi. I m getting issues on seeing the LaTeX part of the response. I m sorry its off topic. I m trying to make sense of this conversation but i m having issues to read the LaTeX . I am wondering if i m the only one ? i m using desktop.

Semiclassical

See the Mathjax link in the room desc

Anonymous

26

A: Any chance of MathJax in chat?

As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including: ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room. An altern...

Beyond Zero

ok. Thanks.

Semiclassical

Anyways. If you're doing regular QM, you could write down this quantity $v(x,t)$ but you'd assign it no meaning.

Secret

is that some kind of velocity?

Semiclassical

13:43

The only thing dBB does is insist that this quantity (which will be a velocity vector field if I take $x$ to be a vector as well) is a real velocity field.

At the very least, you can verify that it has units of velocity.

I don't want to insist on more than that yet.

Anyways. What dBB would then do is have you look at this velocity field and look for its flowlines.

And it would have you say: If I prepare the system in the state $\Psi(t=0)$ and measure it at a position $x(t)$ at time $t>0$, then the trajectory of the particle is exactly the flow line which terminates at this $x(t)$.

Secret

Will I expect this velocity field (and hence the distribution of the trajectories) to change if I move the screen closer or further, or is moving the screen will not change the boundary condition of the problem and hence the velocity field will be preserved?

Semiclassical

That's a good question, and I don't know off the top of my head.

Measuring at earlier times shouldn't make a difference as such. But I'm not sure how the position of the screen would modify things.

Secret

I might have to do a calculation on that later to see what happens * jots notes *

Semiclassical

I think this is a very good reference: arxiv.org/abs/1210.7265

One thing I should stress about my account: Does it reproduce the Born rule?

Slereah

Born rule is the easy part

It's the lack of commutation of observable that's hard

Semiclassical

13:50

Well, depends on what time you're talking about

Secret

(typing too slow) but if the trajectory plot is fully determined by the $\rho(x,t)$ which is from the stochastic preparation of the particle and that the particular way the screen is moved does not change the boundary condition, then it might be possible for the screen to capture that bulge int the middle of the velocity field (as I don't recall usual quantum mechanics to have a bulge there in the distribution)

Semiclassical

No, that's really not an issue. You don't, in general, get the particle momentum in dBB by doing $(\hat{p}\Psi)/\Psi$.

The only case in which you do have that is for a plane wave

Sir Cumference

Morning

Semiclassical

If you want to get the expected value of momentum, you'd still do $\langle \Psi|\hat{p}|\Psi\rangle$

and that will still be subject to Heisenberg

Anonymous

@SirCumference Hie

Sir Cumference

13:53

@Blue How's life

Semiclassical

Mathematical detail: The probability density is given by $\rho(x,t)=|\Psi(x,t)|^2$

And the probability current is $\vec{j} = \frac{\hbar}{2mi}\left[\Psi^* \nabla \Psi-\Psi \nabla \Psi^*\right]$

Slereah

>he puts a vector on the $j$ but not on the $\nabla$

Sir Cumference

@Slereah I don't think most mathematicians even put vectors on the del

0celo7

putting a vector on $\nabla$? what kind of psycho are you

Secret

@Semiclassical so I won't get the bulge at all, or it will be smeared out by Heisenberg and hence undetectable? (I am currently having trouble following the replies as your response seemed to be equally continuous if it is responding to me vs responding to Slereah)

Slereah

13:56

@SirCumference well then don't put one on $j$!

Be consistent

Mathematicians don't put arrows on anything

Sir Cumference

But the $j$ needs the vector sign

idk convention sucks

Slereah

Except categories

Anonymous

@SirCumference 'xam blues

Slereah

Use $\textbf{j}$

Semiclassical

meh, I'm teaching E&M right now. Everything has arrows on it

Sir Cumference

13:57

^That's a case when I've seen dels with arrows

Bizarre

Slereah

I still put arrows on my vectors and hats on my operators

Semiclassical

I get lazy about the latter

Slereah

and both if required!

Secret

7 mins ago, by Semiclassical

No, that's really not an issue. You don't, in general, get the particle momentum in dBB by doing $(\hat{p}\Psi)/\Psi$.

Slereah

$\hat{\vec{p}}$

Secret

13:58

is this the response to:

8 mins ago, by Slereah

It's the lack of commutation of observable that's hard

Sir Cumference

Oh, that was a unit vector. Then yeah, the arrow is abysmal.

Anonymous

I think I had once seen a E&M book for mathematicians

Semiclassical

Yeah.

Anonymous

Forgot the name

Semiclassical

One notation I sorta liked for vectors was to put a single line under them

so $\Underbar{v}$

aww

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