The h Bar

5:52 AM

@loong my teacher told me about Eric do little as the first scientist to experiment that. :-)

Loong

6:49 AM

Eric?

Yup

Loong

?

Have a look at this.

jstor.org/stable/6845#metadata_info_tab_contents

@loong.

@JohnRennie hi.

7:08 AM

@YuvrajSingh... hi :-) I'm working for about half an hour ...

@JohnRennie :-)

So you remember regarding Linux?

7:43 AM

@YuvrajSingh... hi, yes I remember

8:35 AM

@YuvrajSingh... what with linux? if it's debian, tell mah

India's Wild Plan To Bring Cheetahs Back From Extinction

9:16 AM

►

9:35 AM

Doing the Olbers paradox with statistics is tricky

Trying to find the probability of number of stars versus probability of luminosity is annoying bc there may be overlaps

although at least fortunately all I have to show is that $$\forall K, P(L < K) = 0$$

9:47 AM

Hm

Actually

It may be trivial

The total luminosity is $$ \int \left( P(L_{i',j',k'} < K - \sum_{i',j',k'} x_{i',j',k'}) ( \prod_{i,j,k} P(L_{i,j,k} < x_{i,j,k}) \right) \prod_{i,j,k} dx_{i,j,k}$$

If $P$ is $< 1$ almost everywhere, that will go to zero right away

Or wait, is it

hm

10:38 AM

It's been a while since I've done probabilities proper

11:01 AM

What exactly are you trying to show? That an infinite number of stars really would predict a bright night sky?

@ACuriousMind Yes

Showing it for a continuous distribution or stars on a grid is easy enough

random distribution of stars is a bit more tedious

There are infinite convolutions involved!

I'd expect whether or not it's true depends on the specific distribution, no?

@ACuriousMind Sure, but I think it's basically true as long as the average star density is $> 0$

ie the expectation value over a volume is $> 0$

@Slereah FWIW, we had a thread about Olber's on Astronomy a couple of months ago. astronomy.stackexchange.com/q/34893/16685

Although of course, that's for a uniform distribution

Since the Olber's paradox can disappear for very specific distributions

But that will be the next chapter

11:08 AM

I don't think you need to worry about overlaps, assuming your model is an infinite uniform distribution of stars. Any light energy that gets blocked by a star isn't destroyed: it either gets reflected or re-emitted.

Oh I'm not even worrying about that now

The overlap is more

Statistics related

Just overlap of domains of distributions

which requires some intersection business

@Slereah True, Mandelbrot investigated that in Fractals: Form, Chance, Dimension.

The other hard part will be showing why we need a uniform distribution :p

Which involves Newtonian cosmology

Which is 100% not working

also I need to show the thermodynamics issues

Well, a uniform distribution of matter collapses, AFAIK, even in Newtonian gravity. I vaguely remember having a conversation about that with knzhou.

@PM2Ring I'm afraid it's much worse than that

A uniform distribution of matter doesn't make sense

There's no method you can use to calculate the gravitational field of a uniform distribution of matter

It will always have contradictions

11:20 AM

Which reminds me... this got bumped today. astronomy.stackexchange.com/a/19241/16685 I suppose Dewi is thinking that the Shell Theorem (& Birkhoff's in GR) prevents a homogeneous shell from collapsing. That sounds quite wrong to me, but I'm not having much luck finding a nice clear & simple online ref, although I see plenty of papers talking about the collapse of a thin shell, particularly in the context of black hole formation.

@Slereah Yeah. Here's the question I was thinking of earlier, physics.stackexchange.com/q/490829/123208 which links to physics.stackexchange.com/q/430419/123208

11:50 AM

Hm

Maybe what I need is like

a geometric argument

The sum of two random variable has a cumulative distribution which can be computed by an integral over a square

And a square in $\infty$ dimension of side $< 1$ has vanishing volume

Exercise: derive a formula for $\sum_{m=1}^n m^k$ for all $k \in \mathbb{N}$

I hope you like induction

MadSpaceMemer

Why is the frequency of the beat given to be the frequency difference of the both waves? i do not understand the explination of it being (double the envolope frequency) ?

Any links or articles to help me?

hyperphysics.phy-astr.gsu.edu/hbase/Sound/beat.html

In QM when we represent some operator in matrix form and we act on a wavefunction written as a column vector, are the components of the wavefunction "vector" eigenstates of the operator in some basis?

If the matrix can be written as a diagonal matrix of its eigenvalues is only then the wavefunction vector components the eigenstates in that basis? What if we choose a basis that isn't an eigenfunction of the operator?

12:07 PM

@Charlie I'm afraid I don't really understand the question(s) - the components of a vector are just that, components, not states in themselves.

Not every basis is an eigenbasis of a given operator right

MadSpaceMemer

@bolbteppa well tbh thats not a detailed explination. Problem with todays world is that people make alot of assumptions while expaining concepts. Which is either a sign of teaching immaturaity or arrogance or unable to actually get a detailed in depth grasp of the subject. It makes me furious reading senteances such as : usally is, given thru .. etc etc i am sure you know the struggle

Anyway i find a good video from Khan academy.

I'm not sure I quite understand this enough to formulate a coherent question, I might have to just read a bit more and come back

If you're in an eigenbasis, then of course all vectors whose components are 1 in one component and 0 in all others are eigenvectors.

That makes sense

Hmm actually I'll keep reading for now until I can ask more precisely

MadSpaceMemer

12:11 PM

youtube.com/watch?v=pI6iJg_W1ug here is the video if you are interested

12:28 PM

wrong... sorry. my bad.

Ah yes, there wego

as long as the probability of the luminosity being inferior to some constant is inferior to $1$ eventually, then the Olber's paradox holds

@Slereah wut?

$$P(L_{\mathrm{tot}} < K) \leq \prod_{i = 1}^n \int_{[0,K]} (P(L_{i,j,k} = x_{i,j,k}) dx_{i,j,k})$$

That's the stuff

Question?

which question your solving?

Olber's paradox

12:33 PM

@AbhasKumarSinha hi :-)

astronomy related?

@YuvrajSingh... hello bro :-)

@PM2Ring hi sir.

@PM2Ring Hello sir :-)

@AbhasKumarSinha sorry for yesterday my Internet connection had some fault:-(

@YuvrajSingh... same here....

During lockdown, 4G behaves like 2G.

12:37 PM

@AbhasKumarSinha yup

@YuvrajSingh... What are you doing now?

@AbhasKumarSinha a physics book!

Writing or reading?

Lol reading

@YuvrajSingh... what?

physics?

which topic?

12:39 PM

Hi @Yuvraj & @Abhas.

@PM2Ring Is there lockdown there well?

A book on quantum mechanics and mathematics!

@YuvrajSingh... Ian Stewart?

No.

then who?

12:42 PM

Lean A. Takhtjan.

@YuvrajSingh... heard him somewhere.... dun remember.

@YuvrajSingh... I'd suggest Shankar and Shakurai

@AbhasKumarSinha book is good.

yep.

@YuvrajSingh... I'm doing something very big.... beri big....

@AbhasKumarSinha I will see! But book I am reading is also good.

OK?

k

12:45 PM

need a second opinion on an E&M statement

@Semiclassical Good Evening sir...

good morning here

@Semiclassical E&M?

What big, meeting to a Corona patient without mask or going out with no reason infront of police? @AbhasKumarSinha

electricity and magnetism

12:46 PM

@Semiclassical Good Morning sir...

though really just dielectrics and electrostatics

'very hard... I read Irodov's ...

i'm holding a Zoom discussion session today, and my students' formula sheet includes the following:

$E =E_0/\kappa$ (Field in dielectric placed in an external field $E_0$)

@Slereah I think you're referring to Joseph Kittinger's glove accident. en.wikipedia.org/wiki/Project_Excelsior#Test_jumps

@Semiclassical Gauss' Law

12:48 PM

Zoom discussion?

video streaming software

but my recollection of that formula is that $E_0$ is really the free field, i.e., the field due to free charge and not bound charge

@Semiclassical doesn't matter. Gauss Law is applicable to both

distribution of charge doesn't matter

okay? that's not at all what I'm asking, but thanks

@semiclassical please post the question if you have?

the issue is whether one still has $\vec{E}=-\nabla V$

12:50 PM

@Semiclassical refer Basic Laws of Electromagnetism By Igor Irodov it's free on internet

@Semiclassical yap

that's what I'd say too

@Semiclassical So, $\nabla^{-1} \vec E = -V$

@Semiclassical For Cartesian Coordinates, it's simple integration...

Yes it has.

dude. that's not the issue.

Then what?

It can be proved using Vector Calculus too...

12:53 PM

OK, it is not clear to what you want to ask.

yep... Not clear...

then maybe stop jumping to conclusions about what my question is

@AbhasKumarSinha Not yet, but there are various shutdowns in effect here.

Okay... Take your time and write a paragraph wise question...

@PM2Ring So you are going out?

my worry was whether students would assume $\vec{E}=-1/\kappa \nabla V$

12:54 PM

@AbhasKumarSinha I am mostly self-isolating, but I need to go food shopping in the next day or so.

in particular, consider a parallel-plate capacitor containing a dielectric with strength $\kappa$

then the 'obvious' implication would seem to be $E = \Delta V/(\kappa d)$

but that seems to be incorrect

Argh

Now I have to prove how many points are at the same distance on a lattice

@PM2Ring I'd suggest to postpone the idea if it's not very necessary.

@slearah ...infinitely?

@Semiclassical what's incorrect?

12:57 PM

@Semiclassical I doubt it!

I think I'll have to show how many points are within $[d, d+a]$ on a lattice

@Slereah first do $[d, + dx]$

$E=\Delta V/(\kappa d)$ for a parallel plate capacitor of width $d$ containing a dielectric of strength $\kappa$ subject to a voltage difference $\Delta V$

then integrate....

Obviously not

I think it should still be $E=\Delta V/d$

12:58 PM

Since this is a lattice

Not continuous

Plz @AbhasKumarSinha

okay then

k

I have literally never needed your advice

@Slereah could smear it out in order to get an estimate via integration, but that's probably not a good enough estimate

It's probably fine

I don't need an exact value

I just need a rough estimate

If I can just show that it's linear in the distance it's probably okay

right. then integration should be sufficient for an approximation

1:00 PM

Hm

Actually

Do I even need that

Maybe I can use the volume directly

probably, yeah

it'd presumably give you upper/lower bounds on the number of lattice points

and then it's just $N = (2n)^3$ are within a distance of $3n^2$

Solution: $S_n(k) = \sum_{m=0}^n m^k = \frac{B_{k+1}(n+1)}{k+1}$ where $B_k(n)$ is the Taylor coefficient of the function $t \frac{e^{nt}-1}{e^t-1} = \sum_{k=0}^{\infty} \frac{B_k(n)}{k!}t^k$ for example $\sum_{m=0}^n m^1 = \frac{n(n+1)}{2}$ is well known and $B_2(x) = x^2 - x$ but $B_2(n+1) = (n+1)^2 - (n+1) = n(n+1)$

sigh

@AbhasKumarSinha Food is necessary. ;)

1:03 PM

@PM2Ring okay.....

Ah, there's an idea

@PM2Ring Plus postponing it could theoretically be worse. You can't really know if you're less likely to catch something if you go out today, or 4 days from now. Best case scenario is just to be safe when you do have to go out.

The cube $[-n, n]^3$ only contains points at a distance inferior or equal to $3n^2$

The cube $[-(n-1), n-1]^3$ only contains points at a distance inferior or equal to $3(n-1)^2$

It's pretty bizarre to walk into our supermarket and see the cashiers inside makeshift booths constructed from wooden sticks and cellophane

Therefore, points at a distance superior to the one but inferior to the other are about $(2n)^3 - (2(n-1))^3$

Good enough for an approximation

Well, it's superior to that

But close enough

Actually, I'd better check the upper bound, too

1:09 PM

@ACuriousMind They went with big sheets of plexiglass here.

Hmmm

I guess the largest cube that would contain points at a distance of $3n^2$ is the cube $[-3n^2, 3n^2]^3$

Lower bound and upper bound

that will do

1:22 PM

That reminds me, In high dimensions, almost all of the volume of a ball sits at its surface.

A cute illustration of "almost all of the volume of a ball sits at its surface" is given by the well-known limit for $e$: $\left(\frac{n+1}n\right)^n$. This one converges a little faster: $\left(\frac{2n+1}{2n-1}\right)^n$. — PM 2Ring Apr 23 '18 at 14:19

So, if you live in 100 dimensional space, don't peel your apples, or you'll waste most of the fruit. :D

It's quite fortunate that I am dealing with the Olber's paradox

So literally the only two values I have to consider are $0$ and $\infty$

and $1$ I suppose

It makes the approximations much better

@PM2Ring or, at least, be prepared to peel really really thin

(and even thinner in 200d, etc)

Indeed! :)

1:38 PM

...who peels apples?

nitsua60

@ACuriousMind Olber.

I knew that guy was weird, but that weird?

Current bound is $$L_{N, d} \in [4 (3d^2 - 3d - 1) \frac{N L}{\pi (d \ell)^2}, N 4 (3d^2 - 3d - 1) \frac{N L}{\pi (d \ell)^2} ]$$

argh

The horror

I just need to show that it will not be of probability $1$ under $K$!

I probably should have split my space into concentric spheres, really

but who can resist the allure of a cube

But I guess that I can just show this by picking $N$ high enough, since it is of a non-zero probability

2:08 PM

samuel-lereah.com/articles/Physics/the-olbers-paradox#stats

Phew

There we go

I should rewrite it so that it is a bit more rigorous but that's the proof

So yes, the night sky isn't actually black

Get rekt astronomers

@Slereah Cleary, it's not black, if you can see in the microwave band. :)

@PM2Ring I mean the point of Olber's isn't so much that it's not black

More that it's $\infty ^\circ \mathrm{C}$

@Slereah True, it should be as bright as the Sun from a distance of zero metres.

Although of course

The proof I made isn't that it's true

But that having a bounded luminosity has measure 0

It could still happen I suppose

When I lived up north, the night sky was dark enough to see the Magellanic Clouds. The night sky here in Sydney is way too bright for that.

2:16 PM

Statistically it's still possible that every part of the universe has exactly zero stars!

2:28 PM

Space is mostly empty, even inside galaxies. Imagine compressing the Milky Way "vertically" into a thin disk with the same radius that it currently has, and a uniform density of 1 g/cm³. How thick do you think that disk would be? Please make a rough guess before doing a BOTE calculation.

3 cm

@PM2Ring Something silly like an atom thick?

Hm

Is there any other method of proving Olber's paradox

I think that's about all the main ones you can do using the standard assumptions

Very good! I get somewhere between 6 mm & 6 cm, depending on which size & mass figures from Wikipedia that I use.

Now to prove cosmologies that are stable and don't have it, I suppose!

but first, prove what kind of mass distribution doesn't collapse!

2:32 PM

@ACuriousMind people making apple pies

but otherwise, yeah. apple peel is edible

@JMac I wouldn't be surprised if it's that thin if we only include stars, and exclude all the dust, uncollapsed gas, and dark matter.

let's just vacuum all that dust

Hm

@PM2Ring I was even just thinking from the perspective of our solar system, there's a lot of empty space inside the solar system, let alone between us and the nearest other star. I just figured things would get really really flat when you had to fill all that area.

What's the theorem saying that any finite ball of mass distribution collapses

@Slereah I don't think it does. If the particles in the ball have enough KE, it evaporates.

2:43 PM

@PM2Ring Fine, a GRAVITATIONALLY BOUND ball of matter collapses

mister picky

Jeans instability

In stellar physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation, named after James Jeans. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter. For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to: d p d r = −...

Perhaps this

Mass segregation (astronomy)

@Slereah Yeah ok. But you did say any. ;)

In astronomy, dynamical mass segregation is the process by which heavier members of a gravitationally bound system, such as a star cluster or cluster of galaxies, tend to move toward the center, while lighter members tend to move farther away from the center. == Equipartition of kinetic energy == During a close encounter of two members of the cluster, the members exchange both energy and momentum. Although energy can be exchanged in either direction, there is a statistical tendency for the kinetic energy of the two members to equalize during an encounter; this statistical phenomenon is called...

Sorry I'm against mass segregation

I just need to show that a finite newtonian universe wouldn't look like ours, basically!

Are you also assuming that its age is finite?

How Trolls on Reddit Try to Manipulate You (Disinformation & How We Beat It) - Smarter Every Day 232

►

There is no talk about SE. So I think we too should start spreading misinformation!

3:19 PM

I've just cycled into town (to go shopping) and it is uncanny. The place is deserted. It's as though the rapture has happened and I missed it because I was too busy chatting here.

indeed, sir, civilization has crumbled in less than a week @JohnRennie

@JohnRennie hi.

@JohnRennie Did you really expect to not be left behind after the rapture? ;P

2

@ACuriousMind don't you have to believe in God to be raised to the Celestial Host™?

It seems a bit cheeky to tell God I don't believe in him but can he reserve me a harp and a pair of wings just in case.

Cause the man from Mars stopped eatin' cars and eatin' bars
And now he only eats guitars, get up!

3:29 PM

@JohnRennie Yes? I'm saying you shouldn't be surprised to still be here precisely because of that!

I mean, you even have favourite cardinal sins...

(a disappointingly large fraction of the results for "sin" in the transcript are about trigonometry, btw :P)

cos?

There has to be something in the Bible that can be misinterpreted to mean physics nerds shall be exalted. I'll go look ...

Blessed are the electrical engineers for they shall inherit the earth

3

omg, blondie sang "rapture" in 1980?

googling, i'll go with Hebrews 3:4: "For every house is built by someone, but He who built all things is God."

so god as engineering expert

a higher form of "electrical" engineering

3:38 PM

@JohnRennie Bother. I must have mistranslated it to Blessed are the computer scientists for they shall inherit the earth

class MyEarth: public Earth

Hahaha! :'D

@Mithrandir24601 have you seen the user "Bue" around, lately?

@skullpatrol No... Should I have?

India is under lockdown.

3:47 PM

@JohnRennie Boo, everyone knows the universe is written in Lisp

None of that silly object-orientation :P

god is a hacker?

It would explain a lot. He coded hydrodynamics when drunk.

I mean, have you seen the platypus?

@Mithrandir24601 perhaps, in the next 21 days ;)

Loong

smbc-comics.com/comic/god-2

3:54 PM

mammals that lay eggs are plain weird

This Cat Got Stuck

►

That cat is trying to keep the house from ripping apart!

@skullpatrol I mean, the UK is under lockdown and I'm still online, so I'm struggling to understand why India's internet would suddenly drop off. If you're referring to Blue, I haven't seem him in over 2 months

@Loong smbc-comics.com/comic/a-group-project

@Mithrandir24601 I meant he should have a lot of extra time on his hands.

@PM2Ring Obviously not

Infinitely old

Secret

3:59 PM

Recently read some nonduality and beyond nonduality stuff

and my conclusion is:

Sure, I have experienced more than 12 Zen states already

But...

None of them will help me to finish my PhD!

Therefore: Spiritual practice is completely useless when it comes to solving concrete physical problems

@Secret ...is that a DoZen?

3

Secret

lol

Q: Is corona virus using Quantum tunneling to spread itself?

-2

Looking at the spread of this deadly virus, I am worried how much are we safe at home if Corona virus know about Quantom tunneling 😉. Is this virus small enough to cause Quantom tunneling that would cause community transmission in my country, even if people sit at home? I know it's always possi...

quantum-mechanics biology quantum-tunneling

lol

chad virus abuses physics to spread worldwide

4:04 PM

So quantum tunneling could be important for the operation of various receptors / channels in biology, but I don't think that is what is being asked about here haha

No I think he's asking if the virus is leaping from household to household with it lol

I'm pretty sure OP here is worrying about the virus teleporting into their home. Which, given some pop-culture explanations of quantum tunneling, is somewhat understandable but not really a well-defined question about physics

I just quantum tunneled the virus into the CIA mainframe and overloaded the... circuit board. Yeah that's it.

A: Is corona virus using Quantum tunneling to spread itself?

I am just trying to think of advice to give if this was actually the case. "Just make sure you keep measuring the position of the virus so it can't tunnel into you"

1

No, it cannot tunnel. This is a virus with genome size of 30000 nucleotides. Viral particle, of course, includes not only the genome, but also the coating and auxiliary proteins, so we are talking about something like a few hundreds thousands atoms. On the other hand, the most recent experiments ...

How did this answer get posted after the question was closed?

@AaronStevens Honestly, at that point I'd just admit humanity had a pretty good run and give up :P

4:08 PM

@AaronStevens quantum tunnelling? :P

@AaronStevens There's a "grace window" where clients - especially with poor connection - can still post answers even though the question is closed server-side if the client hasn't yet been notified that the question is closed. It's an old quirk in the implementation that seems difficult enough to fix that SE hasn't done so

or that^

:-)

@ACuriousMind Ah ok. Interesting. I suppose the answer isn't bad.

I think we can all agree that it's much more likely that the poster was an expert hacker who can backdoor into anything on the SE network.

Ignoring the fact that it happens all the time.

"if Corona virus know about Quantum tunneling..." It's not just a quantum tunneling virus. It is a sentient quantum tunneling virus

4:12 PM

22 mins ago, by skullpatrol

god is a hacker?

@AaronStevens Yeah, IDK why someone would be reckless enough to post that online where the coronavirus can read it.

@JMac Exactly. If the virus didn't already know about quantum tunneling, it sure does now.

@AaronStevens As soon as I read that post I started filling in all the quantum tunnels around my house just in case.

What's next? Parallel universe viruses?

Plot twist: We are the virus, and Coronavirus is trying to take back the planet that is rightfully theirs

2

4:17 PM

or, perhaps, wormhole coronaviruses

Seems pretty fair. We basically treat the world like it's ours... but I mean it's really as much the coronaviruses world as it is ours.

(assuming the coronavirus didn't quantum tunnel onto earth from a spaceship)

they could have been the seed for the Big Bang

The world has gone batshit crazy.

6

@JohnRennie Too soon :P

57 mins ago, by skullpatrol

indeed, sir, civilization has crumbled in less than a week @JohnRennie

I think the internet has intensified it

4:23 PM

It's been quite calm here so far. Only ~25 suspected cases in a province of 750,000, and people have been good at self-isolating and social distancing.

Quebec has been hit the hardest

@skullpatrol that was meant to be a silly joke about the origin of the virus, not a serious comment on the current response to it.

I'm in New Brunswick, sharing a border with Quebec, and we've done quite well so far.

Oops, I realized that later @JohnRennie sorry

Last I looked there had been just 46 cases in my area ( West Cheshire ). Even so I think the measures being taken are worth while. Given how deserted Chester is at the moment I can see the transmission here being brought to a standstill. Though I guess we're still vulnerable to cases being imported from other areas.

4:30 PM

Spain is in bad shape

::last virus update::

4:44 PM

In two days the tested cases went up by 0.1 million. When to expect 1 million? Or would that never be the case given our current capacity?

All hangs on how seriously people take the distancing orders

@Charlie when I was in town today people were stepping aside to keep 2m between them even when passing in the supermarket aisles. Well ... they were keeping 2m away from me, which may or may not have been due to the coronavirus scare.

@Charlie there is mixed response from the public over here. Many daily wage workers are now migrating from cities to the villages and they have to walk on avg. 200km to reach their homes.

200 km?

Due to the LockDown.

4:50 PM

I think a lot of people are taking it seriously, ofc media outlets will only report on those who aren't

I don't know what's become of the young of today - they can't even pirate textbooks for themselves.

@JohnRennie I was in a grocery store with tape markings all over the floor showing 2m intervals through each aisle. Seems to be working okay, especially with less people out anyways.

It was the top result on google when I checked lol

Yes, it took me several seconds to find a copy :-)

@skullpatrol yes. Most daily wage workers go to Mumbai and Delhi for their works. But due to the state borders being shut and public transport being at halt. They have to do so by walking.

4:52 PM

:(

@JMac yes, the supermarkets are doing that in Chester, and they also now have people on the door controlling entry to limit the number of people in the supermarket at the same time.

I didn't download many books in university really. Practically all the classes were open book, so instead I was buying international versions for like reasonable textbook prices.

The state I am in has 970 cases right now

I find it really hard to work from PDFs. I can see it's useful to have them for reference if only because they are searchable, but I'd always choose a paper book if it was possible.

About a quarter of those are in my city

4:55 PM

@AaronStevens 😱 are you OK?

@JohanLiebert I am doing fine. I haven't been out in a week, and that is because a week ago the only thing I did was go and get groceries

@skullpatrol Daily wage workers are more worried about starving to death than Covid-19

Might be going out for more tomorrow though