The h Bar

Obliv

01:48

I'm working on a forced harmonic motion with damping lab i.e., using $$m\frac{d^2 x}{dt^2} = F_0 \sin(\omega t) - kx - R\frac{dx}{dt}$$ as the EoM

but I don't understand how the amplitude \[
A = \frac{F_0 / m}{\sqrt{(\omega_0^2 - \omega^2)^2 + 4\gamma^2 \omega^2}}
\] is only a function of $\omega_0$

or does that inherently assume the oscillator is in phase with the forcing function

like even if $\omega_0 = \omega$, we could have a $\pi$ phase shift so that the forcing function is opposing the displacement of the mass?

phase shift is $$\tan\phi = \frac{2\gamma\omega}{\omega^2-\omega_0^2}$$ with $\omega_0 = \sqrt{k/m}$ and $\gamma = R/2m.$ $\gamma$ is called a damping constant.

wait I think this is what my TA was talking about when he said this model/theory assumes/doesn't assume some initial conditions

when I asked about the time it takes to equilibrate when changing $\omega$

Obliv

02:09

I think it has to do with transient motion dying out and reaching a steady-state solution that doesn't depend on any initial conditions. Could be wrong though

Obliv

02:52

This happens for $\gamma>0$ though, so if a system is minimally damped (such as in the lab), we should be careful about the initial transient motion of the SHO before changing driving frequencies..

which we didn't do. Great

Whatever I don't think it matters that much. Even if the phase shift is such that the driving force is initially out of phase and destroys the energy in the system, it'll get back in phase naturally I think.

Sir Cumference

03:14

@Slereah it's unfortunate that I constantly feel embarrassed to be part of this country

like why are we way behind the rest of the world in so many things

not a good thing for a country with so much geopolitical influence. means the rest of the world feels the ramifications of whatever the hell's going on here

alright that's the most i'll vent on it here

WaveInPlace

03:32

Yeah, I've been fighting back an urge to blurt things out all day.

Apropos of nothing, what's a better name for a charge that's flickering in and out of existence, Marty McFly-on or, Ion McFly?

Lucky Chouhan

@Mr.Feynman you should write from your phone more often :P

@SirCumference are you talking about France or US? because Slereah is French and US isn't behind the world at all.

naturallyInconsistent

@Obliv This is correct

Sir Cumference

@LuckyChouhan by "we" I meant americans

naturallyInconsistent

The result is only applicable to the steady state. This is the same kind of shit that we do with Ohm's Law and so on; generations upon generations of students fail to notice that we are never talking about the transients and are instead asking students to focus first on the steady state, and then they would get themselves confused. It is another kind of Sissyphean hell just like ACM in hbar.

Sir Cumference

@LuckyChouhan it just feels like so many of our policies are antiquated by this point

healthcare is terrible, we're one of (if not the only) western country that has capital punishment, we're one of (if not the only) country that still uses an electoral college, etc

WaveInPlace

03:52

I don't think anywhere else has an electoral college. Most countries use Westminster-style legislatures.

Sir Cumference

also I came across this the other day, why are we one of only two western countries that legalizes mutilating our pets

Cropping (animal)

Cropping is the removal of part or all of the external flaps of an animal's ear. The procedure sometimes involves bracing and taping the remainder of the ears to train them to point upright. Almost exclusively performed on dogs, it is an old practice that was once done for perceived health, practical or cosmetic reasons. Veterinary science states there is no medical or physical advantage to the animal from the procedure, leading to concerns of animal cruelty over performing unnecessary surgery on animals. In modern times, cropping is banned in many nations, but is still legal in a limited number...

naturallyInconsistent

@SillyGoose Miao miao had a row here in hbar with RR about it. In the end it was ACM and Slereah who came in and pointed out that the issue is down to definition of words. The issue is that GR tells us that acceleration has to be revisited whenever gravitation comes into the picture, and so a lot of us have a heightened sensitivity when people treat acceleration in SR.

Sir Cumference

it just feels like most of europe has been more progressive than us in a lot of areas

why can't we just look at what other countries do correctly

e.g. the nordic countries are consistently at the top of a bunch of quality of life lists, while we're usually somewhere in the upper middle. shouldn't we be taking notes on what they're doing?

this has also been a historical issue too. most western countries had abolished slavery before the US finally did it

it just feels like this country is so slow to make progress

naturallyInconsistent

@ACuriousMind I fully concur with you that photons are not localisable and all, but this "surface crossing function", can we use it to define the photon's wavefunction? If so, is it the Riemann–Silberstein vector? Want to hear your opinions on this matter.

WaveInPlace

American exceptionalism wrecks things in a lot of ways.

naturallyInconsistent

04:03

@qwerty Miao miao thinks it will be particularly helpful to consolidate a few facts. 1) Miao miao is with @Mr.Feynman on this issue: It is not just photons that are affected by the lack of position, it is all quantum stuff having the same sadness. It is just that if a NR limit of a QFT entity exists, then we can pretend to localise them.

@qwerty 2) This is actually more misleading than the fiction: Even though the classical Maxwellian solution corresponds to a coherent state and not to individual photons, the photon picture is extremely successful. Things that approximately behave as bosons tend to be treatable as single bosons doing this and that, and in the case of photons, it is even better than that, because photons do not interact with each other to the first approximation. As such, the fiction works in almost

every circumstance, and only when we explicitly need the anharmonics, e.g. SPDC, that we absolutely have to consider quantum corrections.

qwerty

04:36

@naturallyInconsistent when you say "this" do you mean part of ACM's take or all of it?

Slereah

06:28

@ACuriousMind Newton just thought it was a rotating little corpuscule

From what I remember there's a few ways you can approximate EM fields into null paths, although that is classical physics

but you can at least try

@SirCumference I think you're ahead

Fascism is creeping everywhere

Lucky Chouhan

06:53

oh @SirCumference it seems like you don't like being an American (?) There are problems in every country, I used to think US as a wish-granting factory but as you said there are also problems, but US is one of the powerful nations, and as you belong to the academia and US has best universities and professor and research labs.

Sir Cumference

@LuckyChouhan It's not that I don't like being American, it's just that I'm vastly disappointed by how such a powerful nation is dropping the ball in so many areas

I went to a top 10 US uni and all I really got from it was gigantic tuition fees

Lucky Chouhan

@SirCumference but why should it bother us?

Sir Cumference

Should've gone to another country instead in hindsight

@LuckyChouhan Ethics?

@LuckyChouhan Frankly having a nation be this powerful is a big problem when its citizens are so polarized

It means other countries constantly have to deal with our fluctuating stances

Which in turn affects them

And if fascism succeeds in creeping up in our nation, it has international consequences as a result

Slereah

Gwar - America Must Be Destroyed [music video edit]

►

Lucky Chouhan

@SirCumference that's not the problem only in the US everywhere people who wants power has an attitude "come what may", here in India political parties divide people by their cast and who does it better gets the seat.

Sir Cumference

06:57

@LuckyChouhan I'm not going to claim only the US has problems. It's just that many of the US' problems have already been solved in most western countries

2

or at the very least are far better off

Nobody's really solved healthcare yet, but the US manages to be one of the worst countries with regard to it

We seriously should be taking notes of what other countries do

Slereah

@LuckyChouhan I have recently learned that Indians nowadays call caste abolition "woke"

Rammstein was right, we're truly all living in Amerika

Sir Cumference

@Slereah Honestly I'm just hoping this doesn't become a trend every century

Slereah

@SirCumference you should look at european politics right now, it's not as impressive as you'd think

Sir Cumference

@Slereah Well I guess it's a "grass is always greener on the other side" situation

Lucky Chouhan

@SirCumference I don't know, but problem of one nation can't be solved by seeing how other nation(s) solved it. There are places where US is lacking but there are also places where no-nation is near to US. So...

@Slereah yeah, but it is still a giant issue on ground level,

Sir Cumference

07:02

Honestly if history is any indicator, fascism can show up anywhere

It's just scary that one country can have so much geopolitical power, since it's still possible for that to take root in it

Slereah

I mean it's not like the US was particularly good before

Sir Cumference

that is true

It's only as an adult that I've realized how much our education systems sugarcoat the messed up things the US has done throughout history

that really only makes us liable to repeat them

Lucky Chouhan

@Slereah whenever I read or hear "European Politics" I remember only two people Emanual Macron and Giorgia Meloni, lol

Slereah

Macron démission, as the French say

Lucky Chouhan

@SirCumference don't the give some native people wavier, I have heard of people who gets full wavier on their tuition fee.

Sir Cumference

07:07

@LuckyChouhan Only under exceptional circumstances

Vast majority of people are spending hundreds of thousands of dollars

Some unis offer scholarships to particularly promising applicants, but top American universities won't do that

They figure they're already enticing enough to anyone who applies

Lucky Chouhan

@Slereah why? he says, "I'm centralist." And very good friend of Indian government. Do your and people whom you know like him?

Slereah

@LuckyChouhan did you not follow the politics

Last election the left wing won and he nominated a right wing prime minister, the losing party

Allying himself with the far right

Also Macron is "centrist" in the way of all centrists, he is a right wing person who does not wish to say it

His program is all about concessions to businesses and patriotism

Lucky Chouhan

@SirCumference One thing you don't understand is they charge fee because they provide students better facilities, professors, otherwise you can do your Bachelors and Masters in India with less than $1000 in many colleges but after doing that you won't get anything but just two certificates.

Sir Cumference

@LuckyChouhan Only thing I got from it was good research projects

The education was a joke. I ended up just learning from a textbook for all my classes

Lucky Chouhan

@Slereah oh, I didn't know this was the scenario, I follow some geo-politics but don't know so much about EU's internal politics.

@SirCumference hence,

qwerty

07:13

@LuckyChouhan there are plenty of countries which do not have the problems the USA has; and the US has the money and resources to actually fix those problems

Sir Cumference

@LuckyChouhan That does not justify over $200,000 in costs imo

Lucky Chouhan

@SirCumference everyone learns from textbooks :')

Sir Cumference

It's not like many European countries don't have good universities with far better tuition

Slereah

Macron is also very strongly in the MORE ORDER camp

I'm not quite sure what policy of his is meant to categorize him anywhere but the right wing

Lucky Chouhan

@SirCumference yeah, okay so what's the solution?

Sir Cumference

07:15

@LuckyChouhan I don't know if this is common in other countries, but American professors often demand you attend lectures (a "participation" part of your grade)

which just gets in the damn way if you learn from textbooks

Slereah

Macron is a centrist in the typical way that he believes his ideas are not "ideology" but Being Reasonable, which is the most alarming thing you can hear from a politician

Sir Cumference

(anger's not directed to you btw, it's to my bad memories of that)

Slereah

A sentence that emits Hitler particles

Lucky Chouhan

@SirCumference be a diplomat.

Sir Cumference

@LuckyChouhan Well from what I've heard European tuition is often free

Whatever they're doing sounds good

Slereah

07:17

My university was about 400 bucks a year

Sir Cumference

...

Lucky Chouhan

@SirCumference no no, I understand. So after paying high-tuition fee, does every student gets job or something equivalent which will make the paying tuition fee worth?

Slereah

Really for the price of American university, it would be cheaper for someone to study in Europe

qwerty

@LuckyChouhan no! lol

Slereah

Just spend a few years in sunny Europe

Sir Cumference

07:19

@LuckyChouhan not at all lol

I didn't get accepted into a grad school until my second year of attempt

and it's notoriously difficult to find work in a lot of fields these days

qwerty

university was free in Aus for the previous generation, then politics happened

Sir Cumference

ultimately education can only get you so far. What really matters is prior work experience, which is a catch 22 of sorts

Slereah

Extremely funny to hear the governments complain about the lack of scientific workers afterward rly

Lucky Chouhan

One thing clicked me suddenly is, US institutions charge too much fee because they're high in demand, @SirCumference

Sir Cumference

if you're looking for a good justification, there isn't one

Lucky Chouhan

07:21

@qwerty Was your tuition fee also high?

Slereah

They're all dumbfounded that they can't find workers for quantum computing to work for their spook agencies

Sir Cumference

there's nothing better about US universities than European ones

qwerty

@Slereah not as bad as the USA at all and not nearly as cheap as Slereah

Sir Cumference

many European universities like Oxford and Cambridge are just as well known as the very top unis here, if not more

Slereah

Oh our universities are better, but our research budgets? Grim.

Lucky Chouhan

07:22

@qwerty sure, if they have billions of dollars to pay to Israel and Ukraine but, maybe it is not in their to-do list.

Sir Cumference

@LuckyChouhan In the modern day, what happens halfway across the world can still have significant ramifications to your own country

qwerty

@LuckyChouhan it's a question of politics, which is what started this whole conversation in the first place ;p

Mr. Feynman

@naturallyInconsistent that's precisely why I was objecting ACM's hate against photons :P

@LuckyChouhan 80% I'm here. I use my phone, unless I need to use many equations or write a question/answer

qwerty

@Mr.Feynman editing a message on phone sucks so much

Sir Cumference

well, i probably ought to head to sleep now

'night

Mr. Feynman

07:26

It sends it twice sometimes, unless you reload first

@SirCumference yeah me too

qwerty

@Mr.Feynman .. you didn't sleep? it's nearly morning over there, right?

Mr. Feynman

It's 8.27am. Basically dawn :P

I slept less than 7h

I have sore throat and my voice lowered, so I was testing it. It dropped about two-three semitones

qwerty

Do you sing... opera??

Mr. Feynman

No...?

But it would definitely be fun :D

qwerty

07:41

oh, sorry. I was wondering how much of chat.stackexchange.com/transcript/message/63818807#63818807 was true :P

Slereah

Family Guy - Peter and Pointy Water Cups

►

A beautiful language

Mr. Feynman

@qwerty I wish that was true though :P

Slereah

08:25

> It’s therefore helpful to think of sets as like groups with no group structure, or metric spaces with no metric, etc

arxiv.org/pdf/2005.05284

Gasp

What the hell is that page setting

it hurts my eyes

ACuriousMind

@naturallyInconsistent I can't currently find the links but there's an annoying debate in the literature about that - you can get a function that depends on position and does some of the things you want, but not all of them, and people are really split over whether or not that means you should call that function "the wavefunction"

Slereah

2

wise words

qwerty

08:42

@Slereah everyone's preferred level of rigour is their own: anyone less is being sloppy and anyone more is being overly pedantic

Slereah

All true, although I disagree that mathematicians are human beings

Ryder Rude

09:02

CU-Prime's 2nd Annual Physics Debate: What's Dark Matter?

►

The Omen is a good film. it is about anti-christ coming to earth

@Slereah these inconsistencies r only nitpicks

Ryder Rude

09:24

but i get the point. just like physicist math is nitpicked, one can nitpick mathematician math too if one is precise enough

Mr. Feynman

10:38

@Slereah even DG is hell if you don't abuse notation a little :P

Although, I wouldn't call that an abuse of notation myself. It is understood that if you see $\mathbb{R}$ as a subset of $\mathbb{R}^2$ you mean of course the subset $\{(x,y)\in\mathbb{R}^2: y=0\}$ (Ora any of the other isomorphic sets in there, but this is the choice we make in this context, of course I'm pointing out the obvious now)

So that at the end of the day, $x$ is just a condensed notation for $(x,y)$. There is no possible ambiguity. Instead, I would call an abuse of notation e.g. calling the composite function with the same symbol, as we do a lot in physics

ACuriousMind

@Mr.Feynman ...but that's exactly what the text means by an abuse of notation - using notation in a way that is clear to everyone but not technically correct

Mr. Feynman

Sure, I'm not saying the text is wrong. After all they are defining the concept of abuse of notation

I'm saying that my personal definition is not the same

I only call abuse of notation those things that are ambiguous, such as writing $g(y)=f(x(y))$ as $f(y)$, which physicists do a lot :P

Or also for Fourier transform, sometimes denoted with the same symbol as the function and a different name for the variable

ACuriousMind

I think your definition is just "abuses of notations are those inconsistencies that caught me off-guard before I realized what they were" :P

Mr. Feynman

Rather that catching me off guard, those things that make my head spin if I try to handle them properly

Like, I can write the transformation law of any tensor instantly, abusing notation. If I try to stick to consistent notation with compositions, local representations and so on, it takes several minutes

And I end up having to abuse notation to write it well :P

Slereah

I think the Kochen-Specker theorem's corner cases are coming to bite me in the ass

I'm trying to show an explicit example of a Bohr topos and like an idiot I picked $\mathbb{C}^2$

qwerty

10:54

@ACuriousMind *clear to everyone except perhaps a few uninitiated students

Slereah

And I'm starting to think that it's weird that no projector in there seems to be approximatable there, since either the projector is in there or they do not share an image at all

and then I think "Oh right this doesn't work in dimension 2"

Guess it's time to go with $\mathbb{C}^3$

Mr. Feynman

is that the same $\mathbb{C}$ as $E=m\mathbb{C}^2$

Slereah

Close

Lucky Chouhan

11:40

@qwerty he is cool Italian guy I guess,

@Mr.Feynman why once you said that "Never ask questions to Slereah?"

Mr. Feynman

@LuckyChouhan One of the usual chat memes. Slereah is into pretty advanced and exotic stuff (at least for my meager understanding of math and physics), so most of the times you ask "what is that", you get a link which makes things worse :P

ACuriousMind

he's just expanding your horizons

Mr. Feynman

I guess that I'm not at the level of understanding required yet :P

Lucky Chouhan

@Mr.Feynman yeah, that's pretty much true because he sends so many links here :D

Mr. Feynman

He is a very powerful and fearful entity who exists out of space and time

and he's not a cartoon Frenchman

Lucky Chouhan

11:54

@Mr.Feynman is he your role model? :')

Mr. Feynman

Mhhh, I'm not interested in the same kind of things he's interested in

Slereah

To understand you must not-understand

Mr. Feynman

ACM is my role model :P

qwerty

never meet your heroes

Lucky Chouhan

@Slereah Hi, how you're this much smarter?

Slereah

11:56

Much smarter than who

Lucky Chouhan

@qwerty but @Mr.Feynman has chances to meet him, but please do it soon... :P

qwerty

huh?

Lucky Chouhan

@Slereah than me sir, how you study advanced physics along with philosophy and memes?

Slereah

Pretty low bar, I'm a huge dumbass

I just read a lot of things

Lucky Chouhan

Would you suggest me something to read?

Slereah

11:59

Any specific domain?

Lucky Chouhan

@Slereah yeah, in literature, philosophy or anything you like.

Slereah

Well I'm currently reading Red Plenty :p

Not exactly a scientific book, except as far as data science and the eternal science of Marxism-Leninism go

Lucky Chouhan

Thank you for telling me about Red Plenty, I have found its website

Slereah

> “There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.” -Karl Marx

2

A wise man

Mr. Feynman

12:29

@qwerty I don't have a clue of what he means

Soldier

@ACuriousMind Hi there! If you do not mind my curiosity to ask, how is mass operator $M$^2 in string theory related to zero mode Virasoro $L_0$?

(Can we compute the mass spectrum by knowing conformal dimension, in other words?)

ACuriousMind

12:57

@Soldier What difficulty do you have in deducing this from the general relation between the Virasoro generators and the modes?

Soldier

@ACuriousMind What a trivial question I asked, I apologize. Does this formula hold for WZW models too?

Say you know how primary field transforms under L0 (expressed in terms of affine currents). Then we know the mass spectrum from conformal dimension and excitation number

level*

Slereah

13:21

I'm trying to figure out the various SUBLATIONS of the Bohr topos but since I'm using a toy model with $C^n$ I am fearing that results may be trivial

I think the resulting topoi may be discrete and therefore have nothing interesting wrt cohesion

But on the other hand I'm not looking forward to making the infinite dimensional version

All the Gelfand spaces are just boring discrete spaces of the eigenvalues of operators

I mean I can still do the ground opposition of unity, I guess : nothing is nothing and something is something

Big if true

Lucky Chouhan

@Mr.Feynman Lemme clarify when you said, "ACM is my role model :P" then @qwerty said "never meet your heroes", after that whatever I said means "you have chance to meet ACM (your role model) and you'd meet him soon." :D

Silly Goose

Are defects in condensed matter treated by a stochastic schrodinger equation?

i read that defects are treated by introducing random (in space) perturbations to the hamiltonian. This sounds like introducing some noise, i.e. turning schrodinger into stochastic schrodinger

Lucky Chouhan

@SillyGoose I just asked this to ChatGPT see here

ACuriousMind

13:40

@LuckyChouhan Please don't put content from this chat into ChatGPT or other models without asking for permission first.

Lucky Chouhan

@ACuriousMind sure, unfortunately I can't delete it now :(

think_meaning_builds

@LuckyChouhan are you trying to start a new trend that mimics the "Let Me Google That For You"?

ACuriousMind

also please don't reply with AI-generated content to questions people ask in this chat in general; they come here to interact with humans, not machines.

Lucky Chouhan

@think_meaning_builds Not at all, I get this thought many times that ChatGPT can answer most of the questions of Silly Goose clearly.

ACuriousMind

@LuckyChouhan Do you have the relevant expertise in condensed matter to judge whether ChatGPT's answer is correct?

think_meaning_builds

13:44

Long time ago we had a huge argument over LMGTFY

ACuriousMind

because otherwise you're being extremely condescending to Silly Goose's questions here without having a leg to stand on

Lucky Chouhan

@ACuriousMind Please don't be eccentric on such a fragile issue.

think_meaning_builds

Yes, it also involved condescending remarks

ACuriousMind

@LuckyChouhan I have no idea what you're trying to say.

think_meaning_builds

Let Me chatGPT That For You

ACuriousMind

13:49

But I guess that's a "no, I cannot judge whether the answer is correct", which means you just posted computer-generated garbage you can't even vouch for, pretending that's somehow a worthwhile contribution to a conversation

think_meaning_builds

@LuckyChouhan do you see the similarities

Slereah

Classifying projections in $\mathbb{C}^2$ was easy enough but doing so in $L^2(\mathbb{R})$ is quite another issue I fear

Even the one-dimensional projections are nasty

They're classified by... some Eilenberg-MacLane space, maybe???

naturallyInconsistent

14:08

@qwerty the quotation with classical wave = coherent state. It is correct, but the "not particularly useful" is very very very wrong. It is most of the time more than justified to argue using individual photons. Only very rarely is there a problem

ACuriousMind

@Slereah By "classifying" you mean exhibit another "better understood" space the space of projections is isomorphic to in a suitable sense?

Slereah

@ACuriousMind Well in the two dimensional case I can basically just label them by the 0 and 2 dimensional projections (both trivial) or 1 dimensional projections (labeled by the Riemann sphere)

And the abelian bon Neumann algebras are then just some assortment of those up to some rules

Easy enough to order

ACuriousMind

Yes (but also as you already mentioned the 2-dimensional Hilbert space is usually the worst possible example :P)

Slereah

quite the worst in this case really

Well, less so than $\mathbb{C}^0$ and $\mathbb{C}^1$

But still a little

$\mathbb{C}^3$ is a bit better but it doesn't really exhibit continuous spectrum, so it's not as good as it could be

ACuriousMind

The 2d Hilbert space is the infamous counterexample to a bunch of theorems - I'm immediately reminded of Gleason's theorem which also only holds from 3 dimensions on upward

Slereah

14:15

yeah, also Kochen-Specker

Basically all the good QM theorems that make QM special :p

I guess because fundamentally $2 + 2 = 2 \times 2$ [citation needed]

naturallyInconsistent

@Mr.Feynman literally said that am with ya on this

@ACuriousMind uugh, that is the kind of situation whereby it would be great if there is a listing of what the properties kept and lost are, so that people can judge for themselves!

Slereah

What is even the complex projective space CP²

The Riemann splonrg?

naturallyInconsistent

@Slereah And $\mathbb C$ is usually treated as one-dimensional, whereas $\mathbb R^2$ is two-dimensional.

Slereah

Whatever shape it is

"As a Riemannian manifold, the complex projective plane is a 4-dimensional manifold whose sectional curvature is quarter-pinched, but not strictly so."

Looks a bit trickier than a ball

Guess I can probably wing it and just use a few specific examples of ordered projections

Just need to find a few representative examples

Mr. Feynman

14:38

@naturallyInconsistent meow had just woken

naturallyInconsistent

The opposite is true. Miao miao just got back from stupid work

Most stupid, because it was way past work time, and only just to deliver stuff.

And it was most annoying because people were having sexy time at miao miao place when miao miao received the order to go deliver shit

Mr. Feynman

@LuckyChouhan I didn't know I would be meeting ACM soon. @ACuriousMind did you know that?

ACuriousMind

I didn't and the way it's phrased sounds vaguely ominous :P

Slereah

ACM is nigh

2

Repent

think_meaning_builds

LoL

Mr. Feynman

14:42

You shall fulfill my destiny

naturallyInconsistent

brings out measuring cups

think_meaning_builds

🍺🍹🍸🥃🍺🍺

🥛🚰☕🍵

Slereah