The h Bar

Semiclassical

12:06 AM

(Note: just because I don’t find something interesting doesn’t mean I think you’re wrong to find it interesting)

danielunderwood

12:23 AM

Does temperature even make sense as a concept in QM?

Emilio Pisanty

12:34 AM

↑ hep-th submission times over the years

look at that spike go!

danielunderwood

lol did they make a major change in 2010 or something?

Emilio Pisanty

@danielunderwood I'm not sure

I don't think so

the mailing structure has been around for ages

since the beginning, I imagine (though maybe @dmckee can confirm)

the spike is people submitting immediately after the daily submission deadline so that their papers will be listed at the top of the mailing on the next go-round

I don't know why that's not-so-noticeable before ~2007

but it's an interesting question

what I really want to know is how this behaviour changes from category to category

<html><body>
<h1>Retry after 600 seconds</h1>
The arXiv OAI service is unavailable due to maintenance</body></html>

↑ but this stuff isn't helping ¬¬

dmckee

@EmilioPisanty Man. That's actually before my time. I was around soon enough that the first few papers I got off the arXiv (then xxx.lanl.gov) were downloaded by ftp.

I think they accepted both email and ftp up loads, but don't quote me on that.

Emilio Pisanty

@dmckee heh

but was the daily mailing already a thing, though?

dmckee

@EmilioPisanty I don't know. Activity was pretty low by today's standards. (I'm talking about the early to mid 1990s when the sequence numbers were shorter.)

Emilio Pisanty

12:43 AM

fair enough

I guess the post-deadline spike is mostly a response to competition and more people reading it daily, as opposed to some discrete change in how arXiv worked

danielunderwood

Sounds like they should randomize the mailing list

And yeah it's quite active. There's a twitter account for hep-th that I followed and it made me stop twitter again lol

Emilio Pisanty

@danielunderwood it's not just the mailing list - it's how the results are presented if you just browse the website, say, going to hep-th/new arxiv.org/list/hep-th/new

though also the ordering is reversed in new vs recent

so I'm trying to figure out whether the categories that naturally give recent as opposed to new (specifically, the physics.* subcategories) have the same behaviour

dmckee

After all, the sequence-number are assigned ... well, sequentially.

Emilio Pisanty

12:59 AM

@dmckee the time-binning is additional to that, though

it could e.g. not sort by dates by default and always just give the x latest entries

danielunderwood

1:35 AM

Any chance there are any stats on the arxiv rejections? I can't seem to find any

But holy colors batman arxiv.org/help/stats/2017_by_area/index

2

Semiclassical

@danielunderwood if your quantum system is contact with a reservoir, certainly

on the other hand, temperature does not necessarily make sense (and I think generally won't) for a statistically-small system of particles

danielunderwood

2:28 AM

Ahh so it makes sense if you have enough particles? I was kind of thinking of a single particle in a box type system, which wouldn't have any statistical properties. We did talk a bit about bosons in my thermo class now that I think of it though.

Semiclassical

3:52 AM

@danielunderwood temperature isn't going to be a useful quantity for a particle in a box, no

vzn

4:18 AM

@danielunderwood a well concealed secret. swept under the rug. covered up.

user 2646

5:05 AM

> "Reality is that which, when you stop believing in it, doesn’t go away."

John Rennie

5:19 AM

Bit like testicular cancer then?

user 2646

That, my friend, would be a harsh reality.

ACuriousMind

10:12 AM

@user54826 I reject the question :P A black hole so massive that it has such a low density is so large that there is no continuous body of water in existence on which it could float.

Even if you have enough water, I question the idea that, with the immense gravitation of such a hole, you can still meaningfully treat the water being sucked in as a continous fluid to which ordinary hydrodynamics apply.

user 2646

10:24 AM

how's the ankle feeling pal @ACuriousMind

ACuriousMind

@user2646 still broken :P

user 2646

:P

user54826

11:19 AM

Thanks for your answers @knzhou and @ACuriousMind you both rock.

Nick

11:29 AM

I have something bugging me

Are there field particles that exert the electric force per coulomb of test charge in a given electric field?

John Rennie

No

Nick

Basically, what I'm asking is do electrons radiate particles that exert force.

John Rennie

Still no

You'll hear people say that the electrostatic force is due to the exchange of virtual photons, but virtual photons do not exist - they are just a computational device.

Nick

So, the concept is that I'm sitting in India trying to push you and you, who sits in the US, is pushed by my force because of our arbitrarily assigned opposite charge values.

A virtual photon taking an 18 hour flight to execute my will seems more plausible or atleast appeasing to hear to the rational mind.

John Rennie

We describe the behaviour of e.g. electrons using quantum field theory. The field has states called Fock states that describe the particles in the free particle limit i.e. when the particles are far enough apart for interactions to be negligible.

When particles interact we do a calculation to find out how the Fock states interact. This is where the virtual particles come in as we split up the calculation of the interaction into pieces that correspond to the exchange of the virtual particles.

Akash. B

12:03 PM

@JohnRennie sir?

Nick

neat. I guess I sort of understand.

Next, I'm off to figure the relation of the higgs boson to the higgs field. I guess one best describe it as the thug that deals the interactions of the field on its behalf. (This particle is no god of mine, tbf)

Akash. B

@JohnRennie sir are you free?

ACuriousMind

@Nick I answer the question of how to obtain the Coulomb force from the QFT description in some technical detail here.

Akash. B

12:47 PM

anyone?

Emilio Pisanty

1:01 PM

@dmckee @danielunderwood a zoom into that spike

for 2017+2018

you need to resolve it into intervals no bigger than 5 seconds if you want to resolve its structure

danielunderwood

wow

it looks like there may be a 0 before it too

though I suppose the zeroes aren't particularly abnormal

Emilio Pisanty

that looks like an artifact to me

the histogram is over-resolved at that binning width outside of the spike

but yeah, that 10-second spike is something like 10% of the yearly submissions to hep-th

but that said, this is the histogram for physics:physics

no monkey business there

danielunderwood

The hep-th folks have to get their papers out ahead of everyone else I suppose

Emilio Pisanty

or maybe the hep-th folks take things too seriously for their own good?

it'd be interesting to do a full analysis including all the categories and subcategories

... but I can't be bothered to scrape all of the API, it gets boring fast.

danielunderwood

Would hep-th authors have more programming experience than the rest? I kind of wonder if people have scripts to automatically submit at a certain time

Emilio Pisanty

1:08 PM

@danielunderwood you can't submit via API

danielunderwood

Ahh. Something was mentioned last night about ftp, but I didn't know if that was still a thing

Or they've gone overboard and written something that interacts with the website hah

Was arxiv originally for condensed matter? Or did it just drop off?

Emilio Pisanty

The thing that determines the submission timestamp is when you click that button.

@danielunderwood no. That graph is just telling you that cond-mat was broken off into several subcategories

danielunderwood

Ahhh that makes more sense

And so all you'd need would be something that triggers a mouse click? Or just set an alarm and stare at the clock

Emilio Pisanty

as of right now you cannot submit to cond-mat without selecting a subcategory

@danielunderwood it's infrequent enough that I imagine most people just stare at the clock

danielunderwood

And that would make the axis label make more sense. I thought they were separate and it seemed odd

user 2646

1:15 PM

@danielunderwood I saw a color graph like that for Nobel prizes

danielunderwood

Like per area of physics or something?

user 2646

Per country

On Wikipedia

people.idsia.ch/~juergen/all.html

@danielunderwood^

danielunderwood

hmmm neat. It'd be interesting to see a cumulative version

Physics Meta

1:30 PM

0

Q: Prematurely closed "duplicate"

This question, asking why oceans look blue but rivers don't, was closed as a duplicate of another question, which was answered with a good explanation of why large masses of water, including oceans and swimming pools, look blue. The "duplicate" does not address the main thrust of the new questio...

danielunderwood

I feel like diving into the arxiv stats would be a really interesting thing for a blog

user 2646

1:47 PM

@danielunderwood start at the main article, it's a fun site to browse :-)

Novalium Company

Hello guys, I thought the speed of light was constant, but then I hear that waves have different speeds in different mediums, why is that? And also, I've heard that red is slower than violet for example.

Captain Bohemian

Wolfgang Pauli in a letter to Heisenberg dated October 19, 1926: “One can see the world with the p-eye, and one can see it with the q-eye, but if one opens both eyes, then one becomes crazy.”
Perhaps the pair of mathematical rigor and physical intuition should be added as another example of two mutually exclusive qualities. You can look at the world with a mathematical eye or with a complementary physical eye, but don’t dare to open both. https://www.quantamagazine.org/how-quantum-theory-is-inspiring-new-math-20170330/

Novalium Company

Maybe since the speed of an em wave is calculated by wavelenght * frequency, maybe their multiplication is always equal to the 299 792 458 m / s. That's why we say it's constant?

But then why do people say that red is slower than violet, it's just that their wavelength and frequency differ, but their speed is the same?

Hmm...

Secret

2:06 PM

Opens both eyes and met cthulu

humans are sooooooo overrated

Captain Bohemian

@NovaliumCompany the wavelength of red light is shorter than that of violet light; the frequency of red light is lower than that of violet light, but the speed of red light and violet light in vacuum is the same. While in medium, the speed of light varies with the susceptibility of the medium.

Novalium Company

@CaptainBohemian Did you mean "the wavelength of red light is longer than that of violet light"?

Captain Bohemian

@NovaliumCompany yes, sorry, I mean longer.

Novalium Company

Cool, thanks, but I've also heard that in the prism refraction experiment, white light breaks because of the different speeds of the colors, but as you meantioned, their speed will be the same, does that mean that frequency or wavelenght somehow effects how much the different colors bend in refraction?

Captain Bohemian

their speed of different-color lights in medium is not the same.

Novalium Company

2:21 PM

Why?

I mean, what causes for example red and violet colors to have the same speed in vacuum but different speeds in mediums?

John Rennie

@NovaliumCompany light slows down because it interacts with electrons in the medium.

The light is an oscillating electric field, and that exerts a force on electrons in any medium the light passes through.

In general the strength of the interaction between the light and medium depends on the energy of the light i.e. its frequency, so the amount the light slows down also depends on the frequency of the light.

Captain Bohemian

different-color lights in a given medium have different reflective indices.

Novalium Company

So since red and violet light have different frequencies, that means that they (and everything from the em spectrum) will exert different amount of force on the electrons in the medium, which causes their speed to differ?

John Rennie

Yes

@NovaliumCompany You know that light can cause electron transitions when its frequency matches the transition frequency?

Novalium Company

Umm, no sorry?

John Rennie

2:33 PM

Really?

Novalium Company

Ohhh, yes, I know sorry.

John Rennie

Shine the right frequency light on a hydrogen atom and it can excite the electron in the hydrogen atom?

Novalium Company

Yep, remember now.

And will emit photon/s when the excited electron comes back to it's stable state.

John Rennie

Yes.

And you gt electronic transitions in solids like glass as well, though they tend to be broader.

Anyhow, the interaction of the light with the solid basicaly depends on how close it is to the right frequency for an electronic transion.

Novalium Company

Everything we see actually reflects light because of this? The sun shines the ground for example, and the ground atom's electron's get excited and then de-excite and emit photons with the desired frequency, something like that?

John Rennie

2:36 PM

If the light is actually the right frequency for a transition then the interaction becomes very strong and the refractive index changes wildly.

@NovaliumCompany no, simple reflection does not normally involve electronic transitions.

Novalium Company

@JohnRennie Hmm, we see everyday objects because they reflect the light from a source (lamp, sun...) is that right? But that reflection is not the electrons getting excited and de-excited to emit light?

John Rennie

@NovaliumCompany correct. Excitation is something that happens only at specific wavelengths. In fact when the frequency is just right to cause an excitation the material absorbs the light so it isn't reflected at all.

@NovaliumCompany have a look at this related answer of mine:

14

A: Why does the refractive index depend on wavelength?

You have in fact put your finger on the reason for the refractive index change. It is related to moving electrons in the direction of the fields. NB dispersion is a complex phenomenon, so this is necessarily going to be an arm-waving explanation - do not take it too literally! There is a discuss...

Novalium Company

@JohnRennie Ok, thanks. So when electron transition occurs, the energy that the electron/s have received is basically stored as kinetic energy/heat?

John Rennie

In an isolated hydrogen atom the light causes the electron to move to a higher energy state. In an isolated atom there isn't anywhere for the energy to go, so eventually the electron returns to the ground state and emits a photon again.

danielunderwood

So about that question about the speed of light, would quantum effects cause a very slight effect on the speed of light and speed dispersion even in vacuum?

John Rennie

2:49 PM

In a solid light is absorbed and again moves an electron to a higher energy state. However in a solid the energy can go into lattice vibrations in the solid - i.e. heat - and it is not re-emitted as a photon.

Novalium Company

@JohnRennie Makes sense, thanks.

John Rennie

@danielunderwood no, the vacuum is just a vacuum so there is nothing for the light to interact with. So in vacuum all light frequencies travel at the same speed.

Every now and then someone comes up with an argument that the vacuum should be dispersive - usually related to quantum gravity. But no vacuum dispersion effects have ever been seen despite much looking.

danielunderwood

What about fluctuations of particle/anti-particle pairs? Wouldn't there be a chance of a photon occasionally interacting with a spontaneously created electron? I'll admit that I don't know much of anything on the technical side of the process, so I may just be missing something.

John Rennie

Yes but that doesn't cause dispersion.

danielunderwood

But the reason that the speed of light is frequency-dependent in a solid is due to interactions with electrons in the solid, no?

John Rennie

2:57 PM

The electrons in the solid are in bound states i.e. bound to atoms. That makes all the difference.

Also, virtual particles don't exist. They are a mathematical device. The vacuum is not full of spontaneously created particles.

danielunderwood

Ahh. A free electron would be able to absorb a photon, but wouldn't have any need to go to a lower energy level and emit one?

I would ask why everyone talks in that way, but I have a feeling your answer would be "study QFT"

Novalium Company

@JohnRennie If we have a beam of red light and a beam of violet light in air medium for example, mathematically their speeds should be the same, but due to electron interactions and different frequencies, it's not?

Lozansky

If I have two identical $s=1/2$ fermions in the state $\psi = \psi_a(\mathbf{r_1})\psi_a(\mathbf{r_2}) \vert 0 0 \rangle$, where their spins are interacting with the potential $V = \dfrac{A}{\hbar^2} \mathbf{S_1} \cdot \mathbf{S_2}$ for some constant $A$ and with $H \psi_a = E_a \psi_a$, how can I find the energy eigenvalues of $\psi$?

Novalium Company

Also, why red is slower, it's frequency is less, meaning, less bumping into electrons? Where violet has higher frequency, bumping into electrons more, meaning slowing down more?

John Rennie

I need to break off to eat lunch. Back in a bit.

Novalium Company

3:06 PM

@JohnRennie Ok, I'll wait, have a nice lunch :-)

Captain Bohemian

@JohnRennie I am also too hungry to think well now, but it's close to midnight here now, far different from your time.

John Rennie

I am eating a risotto made with butternut squash and chilli, and it is excellent :-)

Novalium Company

@JohnRennie Enjoy! :D

Novalium Company

3:25 PM

@Semiclassical If we have a beam of red light and a beam of violet light in air medium for example, mathematically their speeds should be the same, but due to electron interactions and different frequencies, it's not? Also, why red is slower, it's frequency is less, meaning, less bumping into electrons? Where violet has higher frequency, bumping into electrons more, meaning slowing down more?

Physics Meta

0

Q: Suggested edits button in red?

What does this mean? The circle beside suggested edits was red, and "suggested edits" was bolded. Why?

support suggested-edits

Novalium Company

3:47 PM

@Blue Hi, how are you? Can I ask a question?

Anonymous

@NovaliumCompany Yes? I'm a bit busy now, but if it's a short question...go on

Novalium Company

@Blue If we have a beam of red light and a beam of violet light in air medium for example, mathematically their speeds should be the same, but due to electron interactions and different frequencies, it's not? Also, why red is slower, it's frequency is less, meaning, less bumping into electrons? Where violet has higher frequency, bumping into electrons more, meaning slowing down more?

Anonymous

> If we have a beam of red light and a beam of violet light in air medium for example, mathematically their speeds should be the same

Anonymous

Not true

Anonymous

See:

Anonymous

3:49 PM

12

Q: Do all frequencies of light have the same speed?

Is there any speed difference between blue or red light? Is there ever a speed difference? Or do all types of light move at the same speed?

electromagnetic-radiation speed-of-light frequency wavelength

Anonymous

> Also, why red is slower, it's frequency is less, meaning, less bumping into electrons?

Anonymous

9

Q: Why does red light travel faster than blue light?

I know that light of all frequencies travel at the same speed in vacuum. But I wonder why their speed differ in any other medium, why does red light travel faster if it has less energy than blue light?

visible-light speed-of-light refraction

Novalium Company

@Blue Thanks, will read :-D

enumaris

4:04 PM

hmm

enumaris

5:21 PM

my long meeting got canceled today...hmmm....

danielunderwood

5:34 PM

you sure do have a lot of cancelled/changed meetings

wooo I finally got work to let me do some data stuff...once I get all the backend work done to actually collect that data

enumaris

haha nice

I'm gonna be exploring a new data source today, so that's fun I guess

enumaris

5:55 PM

finally getting my hands on some clinical data muahahahaha

danielunderwood

Is 20% of it missing? haha

That seems to be the case with the handful of data sources that I've gotten to look at so far

Or maybe there are some 2000 year old patients in there or something

Lozansky

6:25 PM

In an exercise, I have to compute $\langle H \rangle = \dfrac{1}{2m} \int_{-\infty}^{\infty} \psi^{*} p^2 \psi dx$ for $\psi: \mathbb{R} \mapsto\mathbb{R}$ and in the answer sheet they say this is equal to $\dfrac{1}{2m} \int_{-\infty}^{\infty} |p\psi|^2 dx$, how is this justified?

danielunderwood

If $\psi : \mathbb{R} \to \mathbb{R}$ then $\psi^* = \psi$

Semiclassical

That’s not the pertinent point

enumaris

I'm sure there's a ton of data missing

Semiclassical

Note that $|p\psi|^2=(p\psi)^*(p\psi)$.

enumaris

Clinical notes are not gonna be passed with 100% accuracy to the patient's EMR...and then the patient's EMR probably does not have 100% transmission to our systems

Semiclassical

6:32 PM

But what is $(p\psi)*) in the position basis ?

enumaris

Generally $\psi:\mathbb{R}\rightarrow\mathbb{C}$

Novalium Company

6:56 PM

Quick question, I see people do this $x^{-1}$, is this equal to $\frac{1}{x}$?

enumaris

Yes

Two ways of writing the same thing

Novalium Company

Cool, thanks.

enumaris

np

Lozansky

@Semiclassical Sorry, I had to go pick up my food. $(p \psi)^{} = \psi^{} p^{*}$

Semiclassical

7:12 PM

Actually, no. In the position basis, you’ve got $p\psi(x)=-i\hbar \psi’(x)$

So $(p\psi(x))^* =i \hbar \psi’(x)^*$

And therefore $|p\psi(x)|^2$ is a product of first derivatives

By contrast, $\psi(x)^* p^2 \psi(x)$ contains a second derivative

user54826

can someone tell me whether the following is a misconception? the slowing of light in a medium is due to absorbption and reemission of the photons

it's listed as a misconception in a physics forums and it makes sense to me that this is wrong, but I see it repeated every so often here on PSE that I start to doubt

for example here by enumaris physics.stackexchange.com/questions/422921/…

ACuriousMind

7:28 PM

@user54826 It's a classic lie-to-children, a story that makes sense of what is otherwise unintuitive QFT

In truth, light in a medium is simply a different kind of excitation from light in a vacuum. On the level of photons, the photon state in a medium is a different state from the photon in vacuum, just like a phonon in one medium is not the same as a phonon in another

enumaris

Well, I'll delete my answer if you guys think it's a lie. I think generally speaking, it's still a good model for what happens.

But then again, I don't work in quantum optics :D

user54826

thanks @ACuriousMind and glad that you saw my message @enumaris !

enumaris

mhmm

Lozansky

@Semiclassical So how can they be the same?

ACuriousMind

@enumaris A lie-to-children is not the same as a flat - out lie. As you say it is simply a model that happens to be inaccurate once one "zooms in". Physics is full of these, and many of them are nonetheless useful

enumaris

7:33 PM

True, but I think the Physics SE is pretty stringent when it comes to being technically correct or not

I'm more in the camp of use a model if it's useful, discard it when necessary. But I think a lot of people are concerned about getting the details down absolutely correctly. I can understand where they are coming from though, so I can avoid these kinds of answers in the future.

user54826

then you'd be amazed to find that most people on PSE refer to the Drude's model of electronic conduction as the absolute truth while it's as "wrong" as the Bohr model

enumaris

It does make answering a question kind of difficult sometimes :P

user54826

honestly I'd be much happier if the answers starts by specifying that the following is an obsolete and wrong model albeit useful and then proceed

enumaris

I feel like that might just mean nobody reads that answer tho lol

I mean we know there's some fundamental wrong-ness with our currently accepted models - the Standard Model and GR...so it kinda comes down to if there's a better model out there than the one you're answering the question with...but meh. It's a bit too meta for me. XD

user54826

I agree. "All models are wrong, some are useful"

enumaris

7:43 PM

(Dunno if ACM is gonna come back at u with String Theory...) cough cough

danielunderwood

Sounds like most of physics education is a "lie-to-children"

Although I suppose a lot of professors will tell students where what they're learning becomes invalid

ACuriousMind

@enumaris with what? "String Theory is right, but it isn't useful"? :P

Semiclassical

@Lozansky well, you’ve got one integral of the form $\int f’(x)g’(x)\,dx$ and another of the form $\int f(x)g’’(x)\,dx$. How can you relate them?

ACuriousMind

@danielunderwood yes, it is. The trick is a) knowing when to drop a particular model and b) not evoking the impression in your students that the models are anything more than that

Semiclassical

I like the slogan “teaching is the art of telling smaller and smaller lies”

danielunderwood

7:54 PM

We got a fair bit of that in classical mech. I don't think our EM courses mentioned where it's valid at all. QM just mentioned why classical doesn't work, but not how far the QM we were learning went

Semiclassical

(a sarcastic inversion of that: academia is the art of piling BS higher and deeper)

danielunderwood

And somehow neither CM or EM mentioned SR in the required courses

@Semiclassical Is that was the PhD in PhD comics referred to? I always thought it was work being piled higher and deeper or something

Semiclassical

It’s part of an old joke. BS = bulls***, MS = more s***, and PHD = piled higher and deeper

enumaris

@ACuriousMind ...maybe...

Lozansky

@Semiclassical $\int f'g' = fg'-\int fg''$

enumaris

8:01 PM

@Lozansky make sure you include the limits :D

Lozansky

And the minus sign is negated by the $(-i)^2 = -1$ oO

enumaris

and then use the fact that $\psi(x)\rightarrow 0$ as $x\rightarrow\pm\infty$

Lozansky

Yup

But I'm too lazy to include limits :P

danielunderwood

$(-i)^2$ always has me doing some mental gymnastics to try to figure out what the sign is for some reason

Semiclassical

Right. But the wavefunction is square-integrable. What does that tell you about the first term, which is evaluated at the endpoints?

enumaris

8:03 PM

@Semiclassical already went over that :P

Semiclassical

@danielunderwood same tbh. I reflexively sort it as (-1)^2*(i)^2

Lozansky

@Semiclassical Ah, you want me to apply Riesz-Fischer? :P

Semiclassical

if that’s what “integrate by parts and realize that the boundary term vanishes” means, yes

Lozansky

What if I have something like $\psi(x) = x^2 e^{-x^8 \sin^2 x}$?

ACuriousMind

@Semiclassical @enumaris It is not true that being square-integrable implies vanishing at infinity.

See e.g. physics.stackexchange.com/q/331976/50583

enumaris

8:12 PM

@ACuriousMind I knew you would bring this up

Cramping my style bro

Lozansky

:D

Novalium Company

Sup guyz, quick question. Why when I shine a laser beam at night, I don't actually see the beam in the air, just the it's final destination?

ACuriousMind

@NovaliumCompany If the air is perfectly free of any other particlesm yes,

enumaris

You would only see the laser beam if the photons comprising it bounce off the atmosphere and into your eyes

since not many of them do, you don't see the beam

Novalium Company

So if I shine a laser at a wall, i see the dot at the wall because the wall reflects it into my eyes?

enumaris

8:15 PM

yep

ACuriousMind

Yes.

enumaris

@ACuriousMind too slow

bow chicka wow wow

Novalium Company

Why when the air is dusty, I see the laser, or when I shine it over fire?

Somehow the dust particles reflect the light to my eyes?

ACuriousMind

@NovaliumCompany Because there's lots of particles in the air reflecting the light in random directions, and so also into your eye

Semiclassical

Ugh. I find myself sympathetic to Griffiths footnote

enumaris

8:17 PM

@Semiclassical Me too

ACuriousMind

@Semiclassical Sure, saying "square-integrable functions that don't fall off at infinity do not occur in physics" is perfectly fine. What I dislike is the "Because it's square-integrable it falls off at infinity", which is plainly wrong.

Novalium Company

Cool, thanks @ACuriousMind and @enumaris for the help. :-3

ACuriousMind

And, besides, I've never heard a really convincing argument for why they shouldn't occur except that otherwise all the easy physics math doesn't work :P

Semiclassical

meh

enumaris

The statement would be "for square-integrable functions that occur in physics, integrability implies falling off at infinity".

Semiclassical

8:19 PM

I find it hard to care about statements which are only false for entities we’d never consider as plausible examples in the first placr

ACuriousMind

I mean, physicists are perfectly fine with saying that in one sentence and playing with plane waves extended to infinity in the next, so it's not as if compact support or something is something they always impose. If I'm allowed to pretend $\lvert x\rangle$ is a good state, why not these weird other states?

Semiclassical

Now that does bother me a bit

enumaris

"They"

ACM has distanced himself from the group

HE'S AN OUTSIDER! GET HIM!

ACuriousMind

@enumaris I always do when I don my mathematician's cap :P

Semiclassical

the justification for the delta function or the plane wave is really one of convenience, and I get that

But I feel like sources tend to be rather blithe about that, which indeed undermines any stance about certain wavefunctions being unphysical

enumaris

8:25 PM

hmm

danielunderwood

There are also the wonderful functions that go to 0 at infinity, but somehow their derivatives don't -_-

Semiclassical

I’m a bit biased on that, mind, because caring about dBB stuff gives you further reason to distrust “plane waves”

enumaris

Mathematical pathologies is an area I wouldn't touch with a 10 foot pole

ACuriousMind

@enumaris Good idea, they might leave a (Cauchy) residue on it.

danielunderwood

I find mathematical pathologies interesting, but I don't really understand them. Like I read about the functions that fall off to 0 at infinity but not their derivatives. I accept what I read, but it still seems weird

Semiclassical

8:31 PM

(Namely: if you do scattering off of a 1D potential step using plane waves, you end up with all Bohmian trajectories going in one direction; that doesn’t seem to match reflection / transmission at all. If you use a wave packet with finite width, by contrast, you end up with a reflected and a transmitted wave packet and corresponding reflected/transmitted trajectories)

Lozansky

Ugh, the inconsistency in the indexing of ground states for the harmonic oscillator/infinite well bugs me :>

Semiclassical

(So in the dBB story one indeed has good cause to view plane waves with suspicion)

@Lozansky you might look up Maslov’s index as a way to put them on the same footing

From that POV, the correct way to look at particle in a box levels is as (n+1)^2 for n=0 to infinity

Lozansky

Very neat

enumaris

8:58 PM

@ACuriousMind only if you poke it hard enough

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