The h Bar

Slereah

06:51

morning

Abhas Kumar Sinha

@PM2Ring Hey, there, you gave me a question yesterday, the question is to find the cone of smallest size that can have a unit size Sphere in it, the progress I've made till now, confirms that it must have the length $l=2$, is that correct? Note it's not perpendicular length, it's length of the slope of cone

Morning

@Slereah you live in Egypt or Israel?

Or France...?

Slereah

07:08

@AbhasKumarSinha Odd question

Abhas Kumar Sinha

Hehehe see replies to this tweet (so called handcrafted tweets received great replies) twitter.com/realDonaldTrump/status/1137051097955102720?s=20

John P

08:17

Guys, would someone please help me figure out how to pose me question physics.stackexchange.com/questions/484784/… better? I'm basically interested in what happens if a ball tied to a rope falls down in a pendulum like contraption, but there's some object in the way of the rope.

PM 2Ring

@AbhasKumarSinha A unit sphere has radius 1, so its diameter is 2. So any cone containing a unit sphere must have a perpendicular height >= 2. And the sloping height of a cone must be greater than its perpendicular height.

John P

Maybe the situation could be better described (thought this problem is a bit different) by a double pendulum? Initial conditions would be the two objects $A,B$, just hanging, where $A$ is vertically above $B$. Restrict the movement of $A$ to only one plane. What happens if we apply a small force to the object $B$ ? If the direction of this force is perpendicular to the plane in which $A$ can move, it should be true that $A$ will simply stay still, and $B$ will start rotating around it.

(By plane I mean perhaps the $xz$ plane). Maybe this problem is difficult - I'd be happy to know that's the case, but I'm afraid I'm missing some simple explanation for what happens. But maybe this is quite complicated - I'm not even sure what happens if I apply a force to the lower object in a hanging-resting double pendulum, for say force $(1,0,0)$. I would expect that would cause the pendulum to simply reduce to a simple pendulum/sphere, but I don't know.

@JohnRennie any opinions please?

John Rennie

08:34

@JohnP if you restrict the motion to one plane then it's an easy problem since all that happens is the length of the string changes when it hits the barrier. So the SHM divides into two parts with different frequencies.

But as I recall your question the barrier was slanted so the string would slide along it i.e. the edge would produce a force out of the plane. That makes the problem considerably more tedious.

John P

Oh right, by plane I meant various planes (like the one generated by $(0,0,1)$ and $(1,1,0)$.

Maybe I should mention that I'm not necessarily interested in some precise/analytic explanation, just a way of how I could numerically simulate it for example (approximating how fast the string will slide is enough for me).

John P

09:12

(also in the explanation above I meant that only the upper object is restricted to a plane, the other isn't). In some sense I would expect that the distance covered by the rope must be efficient in some way if there is no friction. So maybe for example it can't happen that the rope goes from $(0,0,1)$ to $(0,0,0)$, and then from $(0,0,0)$ to $(1,1,0)$, because the rope could also reach the point $(1,1,0)$ by going from $(0,0,1)$ to $(1/2,0,0)$ and then to $(1,1,0)$. Does that make sense?

Either way thanks for the response @JohnRennie , at least I know the problem is probably a bit tedious, I was afraid I'm missing some very simple trick (like maybe the thing I just wrote above, but I doubt it's true ... it might be an ok visual approximation though).

user8718165

13:40

Hello @JohnRennie

pss 1

14:01

Hello ....anyone here?...what exactly is thermodynamics...what we deal with in it? We study Clausius calyperons equation...we study contact angle kinda related and gases...and lot more....can anyone just say what exactly we study in thermodynamics....does the name and the topics match

ACuriousMind

@pss1 Sometimes one says that thermodynamics is the study of statistical systems in equilibrium, but sometimes that's too restrictive. See physics.stackexchange.com/q/476554/50583, where an asker had a similar question about the extent of "thermodynamics".

skullpetrol

see also the forces associated with heat

Pritt Balagopal

Hi

skullpetrol

hello

ACuriousMind

@skullpetrol "forces"?

Pritt Balagopal

14:08

When they say that mass increases with speed in special relativity, is it inertial mass or gravitational mass?

and hi hows you

ACuriousMind

@PrittBalagopal neither

Pritt Balagopal

oh

then what does it mean?

ACuriousMind

Also, "they" don't really say that anymore, cf. physics.stackexchange.com/a/133395/50583

Modern relativity does not rely on the notion of relativistically increasing mass. It's an anachronism that it still appears in many introductory treatments

skullpetrol

That beginning students are stuck with.

Pritt Balagopal

Oh okay

user8718165

14:11

Hii ! Can somebody please tell me what does derivative of a cross product actually mean?

Pritt Balagopal

Thank you

ACuriousMind

@user8718165 What do you mean by "meaning" there? ;P

pss 1

@ACuriousMind thanks :-)

user8718165

@ACuriousMind I wanted to say is there some kind of visualization?...because in cross product a and b are constant only the angle $\theta$ between them changes so all we can do is take the derivative of $\sin\theta$...is it possible?

ACuriousMind

@user8718165 Wait, what are you differentiating this cross product with respect to?

pss 1

14:16

@user8718165 are the vectors constant in magnitude and direction?

ACuriousMind

The cross product on its own is just an operation on two fixed vectors, it has no inherent notion of a derivative because there's nothing varying there

pss 1

A specific vector do not change w.r.t anything tho...is it mentioned that the oneof the two or two vectors Ur taking product of is function of some variable?

user8718165

@ACuriousMind with respect to time...

ACuriousMind

@user8718165 So you're taking the time derivative of a function that is the cross product of two other, time-dependent vector functions?

user8718165

@ACuriousMind I'm trying to find relation between angular momentum and torque...

ACuriousMind

14:21

In that case the derivative is just a vector that point in the direction in which that cross product is changing, like with the derivative of any other vector-valued function. There's nothing special about the cross product there

user8718165

@ACuriousMind Thank you so much...got it:-)

skullpetrol

like Precession?

peterh

15:01

Chairs' account is now deleted!

skullpetrol

:O

@ACuriousMind dynamics means "other forms of energy" ;-)

ACuriousMind

(Even if that were true, I don't see how that's a reason to talk about "forces associated with heat", but)...not really. While the Greek dynamis means "force" or "power", today by "dynamics" we usually mean the opposite of "statics", i.e. an investigation of evolution rather than that of an unchanging state.

Semiclassical

you also see the kinematics/dynamics distinction. not entirely sure how to compare that with the statics/dynamics distinction

ACuriousMind

@Semiclassical There the original meaning is preserved somewhat, in that "kinematics" cares only about the description of motion, while (Newtonian) dynamics cares about the "cause" of motion, i.e. Newtonian forces.

Semiclassical

yeah, that sounds right

skullpetrol

15:13

"forces"? :P

::runs::

@Semiclassical are you back home yet?

Semiclassical

yeah

skullpetrol

@ACuriousMind how about "other forms of energy associated with heat"?

ACuriousMind

What do you think "heat" means?

What "forms of energy" are you talking about, and how is/was this supposed to help the user who inquired about what thermodynamics is?

skullpetrol

....does the name and the topics match

Semiclassical

i mean, thermophoresis is a thing

but i don't think the mechanism there is some kind of other force

(also, 'thermodynamic forces' do show up in the context of Onsager reciprocal relations, but that's hardly elementary)

skullpetrol

15:29

thermoplastic is a thing also :P

> Thermodynamics is a physical branch of science that deals with laws governing energy flow from one body to another and energy transformations from one form to another.

pss 1

@skullpetrol That’s good! Actually

skullpetrol

yup, it's a good start :-)

pss 1

Start?...meaning?

skullpetrol

It gets complicated fast.

pss 1

Oh..

Idk anything about thermodynamics except for the high school part!..XD..

skullpetrol

15:44

in high school they leave out all the calculus

danielunderwood

physics - calculus = :(

pss 1

Hmm...so u enjoyed a lot of it ha (idk what ur now)...of course Ido with mine(high school tho!)

skullpetrol

physics + calculus = 8-O

@peterh that's a pity

@pss1 learn calculus on your own!

skullpetrol

16:17

@ACuriousMind how would you define "heat"? (other than the energy associated with the motion of molecules :)

ACuriousMind

@skullpetrol That's not heat, as you would know had you bothered to read the very first sentence of the Wikipedia article on heat you yourself linked. Heat is not a form of energy, it's any energy transferred during a thermodynamic process by means other than mechanical work.

dmckee

The heat/internal-energy distinction is not merely overlooked among students, it is not universally attested in (a) historical sources or (b) source pertaining to other disciplines that care about energy. I'm looking at you, chemistry.

pss 1

@ACuriousMind I was taught heat is an energy in transit !

skullpetrol

^

dmckee

But it really (really) helps in clarity and communication to make a strong distinction between the state property (internal energy) and the process property (heat).

ACuriousMind

16:24

@pss1 Which is the same thing I said, isn't it?

pss 1

Yeah.

ACuriousMind

@dmckee To be fair, technical terms whose meaning differs from their colloquial meaning always tend to fair poorly in this way.

pss 1

Internal energy isn’t a dynamic one(possession) so it’s not heat?and surroundings energy generally in in flow so...heat?

XD

ACuriousMind

"power", "heat", etc. - it's not that they're difficult concepts, it's that they are also ordinary words with a non-technical meaning that makes for confusing communication outside of explicitly technical texts

dmckee

@ACuriousMind Sure. Essentially every technical distinction that gets built on common words has this problem for a while.

Though I feel like this one is more common and persistent than some of the others.

skullpetrol

16:30

creating new words is not an easy task

Secret

such is more problematic for mathematical terminology, e.g. look at how "normal" is overused to the point that there is confusion even within maths disciplines

and then in business sectors, you have people sticking "quantum" to almost anything they can think of

skullpetrol

good point

pss 1

@skullpetrol why did u suggest me to learn calculus on my own.?,,..have fun u say?...I will ...

danielunderwood

16:45

If you had normally-distributed data coming in over time, would doing a binary classification based on a confidence interval around a linear regression be different than by doing it with a confidence interval in a histogram? I feel like counts and position should be different things, but I'm having a hard time convincing myself that that's the case.

(ignoring the bit about the histogram's bin size)

skullpatrol

@pss1 I said that so you can get the sense of amazement shown here:

58 mins ago, by skullpetrol

physics + calculus = 8-O

that^ is what is missing in high school

PM 2Ring

I find it bizarre that in some places, senior high school physics is taught without calculus. Ok, at my high school physics calculus was a bit sloppy, but that was ok, since we got a more rigorous version in the maths class.

skullpatrol

17:01

The same goes for biochemistry in the biology class compared to it being covered properly in organic chemistry.

danielunderwood

We didn't really even have calculus-based physics the first year or so of university, but I think that was due to some students coming in without any calculus knowledge

ACuriousMind

@danielunderwood We had a two-week math refresher at the start after which everyone was assumed to be able to do Taylor series in their sleep!

danielunderwood

Well there was some calculus, but you weren't really expected to work it out entirely yourself. Then a similar thing went on with differential equations in the later years. Like I don't think we really ever had to solve the infinite square well all on our own

I don't think I knew what a Taylor series was as an incoming freshman, even though I was one of the people with more high school math. Quite an education system we have here in the states

ACuriousMind

:/

skullpatrol

did you take AP?

danielunderwood

17:13

I think AP calc AB, though it wasn't the best. I think 3 of us actually took the AP exam

@ACuriousMind we also spent roughly half a semester of an EM course teaching vector calculus even though it was a prereq

skullpatrol

Wait, vector calculus before single variable calculus?

danielunderwood

And it's a bit of a shame that we didn't really go much into the theory side of EM since it's kind of a jumping off point for deeper theoretical stuff

@skullpatrol well by the time of that EM course, we were kind of assumed to know single variable calculus fairly well. That was an upper-level EM course and not the freshman level

skullpatrol

I see.

ACuriousMind

There was "freshman-level" EM that did not require vector calculus?

Every time I think I sort of understand how academic things are on the other side of the pond, I realize I just don't :P

Ajay Mishra

@ACuriousMind You can see walter lewin lectures, that’s without vec cal.

And that is freshman level too.

danielunderwood

17:22

Yeah there was a 3 semester sequence of CM -> EM -> QM that didn't really require calculus because people weren't expected to know it entering as a freshman. Then we had upper level courses that expected calculus, but people didn't typically understand vector calculus well enough to not get stuck on EM and for whatever reason we weren't expected to be able to solve any differential equations

ACuriousMind

As much as I'd love to dwell on my astonishment here, there's a party I need to be getting to.

skullpatrol

have fun

ACuriousMind

thanks, I will

Ajay Mishra

Do you mean QM was linear algebra based? As you said calculus weren’t expected.

danielunderwood

So the initial QM course only did stuff with square wells from what I remember. That was done with calculus, but it was more of "here's the answer" which is kind of what continued to be the case in upper levels when there was a differential equation. I don't think we even went much into the algebraic formulation in that course

skullpatrol

17:27

sounds like a lot of memorization

danielunderwood

I did do a funny thing in one of the upper-level quantum courses when solving the QHO on an exam. I didn't really understand the algebraic way, so I had a gigantic answer that was me doing everything in the position representation. I think my professor was just shocked that I went through so much unnecessary effort

It was some memorization, but it was like the type of thing where you'd remember that for square wells, you'd remember to have some combination of exponentials/modes and work out the actual details for the probably. Though we did have a lot of derivations in class that the only real requirement was to realize the result. It took me far too long to realize that the best way to remember the result was just to work it out from the beginning a couple of times

Emilio Pisanty

17:52

↑ unexpectedly nice-looking

(from here)

skullpatrol

+1

Emilio Pisanty

though now that I put it out of context, it kinda looks like an enormous mouth with an inordinate number of teeth

@JohnRennie well, that's a new one, for sure.

rob

18:27

@EmilioPisanty A quantum lamprey.

skullpatrol

with 50 teeth

Emilio Pisanty

18:43

@rob ugh =/

anyways

PSA: if you've been seeing a lot of questions (or other buzz) about the HBO show Chernobyl, and you're wondering "is it really that good?", then the answer is yes, it really is that good. Go watch it.

Tanner Swett

Hey there. So I'm trying to figure out how far away an aircraft or spacecraft's lights are visible, ignoring the effect of the atmosphere.

Now, I know that if a light is far away (so far away that it looks like a point source), then it appears dimmer the farther away it gets.

And I'm a little confused about all the various measurements of brightness. :D

Semiclassical

@EmilioPisanty ooooo

Emilio Pisanty

(OK, I dunno if I'd reaaally rate it as the absolute best ever, particularly given that The Wire is lurking just under GoT at no. 7. But still. Yes, it really is amazing.)

@TannerSwett those are confusing indeed.

Tanner Swett

It looks like the "amount of light per unit of solid angle" is the luminous intensity, measured in candelas.

(Or is the plural just "candela"?)

So I might talk of, say, a lamp which emits 5 candelas when viewed from the front.

Emilio Pisanty

@TannerSwett I take it you've found your way to the table at the end of this?

Luminous intensity

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit. Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions (photopic vision), the...

Semiclassical

18:51

@EmilioPisanty which potential is that with---just a disk with hard walls?

Emilio Pisanty

@Semiclassical yeah, nothing fancy. Just a Bessel function times a cosine

Semiclassical

gotcha

Emilio Pisanty

MM code in the answer's source if you're that curious

Semiclassical

I'm trying to remember where Mathieu functions show up in QM (besides a cosine potential)

I think it's with an elliptic disk rather than a circular one?

Emilio Pisanty

@Semiclassical if I ever start a mathematical physicist's list of Things I Won't Work With, then that's one of the top places you'll find Mathieu functions

Semiclassical

18:53

lol

Tanner Swett

@EmilioPisanty Yep, but it's taking me several minutes to think through all the implications of that.

Emilio Pisanty

@TannerSwett yeah, it's always a nightmare

What is it you actually know about the lights?

Semiclassical

@EmilioPisanty hard to avoid it entirely given that it's the simplest periodic potential (at least in the sense of momentum space)

Tanner Swett

I know that, from a particular angle, regulations require the lights to be at least 5 candelas.

Emilio Pisanty

@Semiclassical eight years or so, thus far, and I've managed just fine

Semiclassical

18:55

so you do see it in solid state, albeit mostly only the computations for the lowest bands

though if you think Mathieu is weird, I can do you one better

Tanner Swett

And then, since the "apparent brightness of a distant lamp" goes down with the square of the distance, I would expect this to be measured in... candelas per square meter?

Emilio Pisanty

@TannerSwett then you want the illuminance at the chosen distance over the pupil area, I should think

Semiclassical

Mathieu (cosine potential) is $-\psi''+\alpha(e^{i\theta}+e^{-i\theta})\psi=E\psi$

Emilio Pisanty

@Semiclassical I really don't understand what a cosine potential gets you that tight-binding doesn't

at a fraction of the complexity

Semiclassical

you're probably right in practice, yeah

but one of my first projects with my adviser addressed not only that but also stuff like $-\psi''+\alpha(2e^{i\theta}+e^{-2i\theta})\psi=E\psi$

(it wasn't actual a QM problem, but you could do some shenanigans to map it to that)

Emilio Pisanty

18:58

@Semiclassical that's ridiculous

Semiclassical

yeeeep

Tanner Swett

Hmmmm.

Semiclassical

the underlying problem was just classical stat mech, mind. coulomb gas stuff

Emilio Pisanty

non-hermitian and all?

Semiclassical

yuuup

Emilio Pisanty

18:59

ugh

on the other hand, it does have a nice bicircular feel to it

Tanner Swett

I'm going to do a Google search for "measurement of brightness of a star" and see what I get. :D Presumably whatever unit that is, that's the unit I'm interested in.

Emilio Pisanty

though you'd want to knock the first factor of two out

Semiclassical

note that it's a pt-symmetric potential (it's invariant if you do both parity and conjugation, but not either individually)

Emilio Pisanty

@Semiclassical you say that like it's helpful

Semiclassical

actually, that factor of two is handy. it ensures that the potential is harmonic at the origin

Tanner Swett

19:00

I feel like you're right, though, I feel like it's probably illuminance.

Emilio Pisanty

@Semiclassical yeah, I can see why you'd include it, but still

Semiclassical

@EmilioPisanty well, in the context of the problem, it is: it ensures that the eigenvalues are all either real or occur in complex conjugate pairs

Emilio Pisanty

Absolute threshold

In neuroscience and psychophysics, an absolute threshold was originally defined as the lowest level of a stimulus – light, sound, touch, etc. – that an organism could detect. Under the influence of signal detection theory, absolute threshold has been redefined as the level at which a stimulus will be detected a specified percentage (often 50%) of the time. The absolute threshold can be influenced by several different factors, such as the subject's motivations and expectations, cognitive processes, and whether the subject is adapted to the stimulus.The absolute threshold can be compared to t...

> A second absolute threshold for vision involves the minimum photon flux (photons per second per unit area). In this case the light covers a wide field over an extended period of time instead of being concentrated on one spot on the retina in a short burst. Knowing the pupil diameter and the wavelength of the light, the result can be described in terms of luminance (~0.000001 candela per square meter or 10−6 cd/m2) or retinal illuminance (~0.00002 Trolands).

Semiclassical

which ensures that the actual partition function you get (which would be something like $\sum_n e^{-\beta \lambda_n}$ where $\lambda_n$ is an eigenvalue of that potential) is real and therefore sensible

Emilio Pisanty

@Semiclassical no, as in: you say that you're doing PT-symmetric QM like it's not digging you further into a pit

Semiclassical

19:02

lol. well, there's a reason why I emphasize that this isn't really a QM problem

Tanner Swett

I dunno, this is too confusing for me at the moment. I'll look into all this later.

Semiclassical

and that's because I don't put a lot of stock in PT-symmetric QM as really having much to do with QM

the fun bit was that, despite the potential being non-hermitian, you could still do stuff like Bohr-Sommerfeld quantization and compute the level splitting via Gamow's formula

with the ground-state energy telling you, for instance, the pressure of the coulomb gas and the first splitting telling you about the energy barrier for charge transport across the (1D) system

that said, the functions involved in that are definitely weirder than Mathieu

simply by virtue of the non-hermiticity

There's a reason why we focused on what the eigenvalues were and not the eigenfunctions.

Emilio Pisanty

@Semiclassical yeah, that doesn't help them at all

It's like saying "oh, it's like a Meijer $G$ function but it's definitely weirder"

Semiclassical

i mean, you can still move to Fourier space and compute eigenvalues by numerical diagonalization. so computing the spectrum is not actually so bad

but getting an analytical handle on them? oof, no thx

Emilio Pisanty

@Semiclassical anyways, that's nicely close to the combination of RCP $\omega$ $+$ LCP $2\omega$ that's so close to my heart =)

Semiclassical

19:11

lol

we did a few other examples like (+3,-1), (+3,-2)

Emilio Pisanty

eh

I've never really seen anything truly nontrivial coming out of those

at least, anything that you couldn't get from (1,2)

Semiclassical

well, in terms of math stuff there's some neat stuff. for physics, though, you may be right

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