The h Bar - 2016-08-02 (page 3 of 4)

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5:00 PM

@EmilioPisanty though you don't do that by starting with the TISE and solving it. You calculate the dipole moments of the ground state and do a few integrals to calculate the transition probability.

@JohnRennie Sure. But that's just mathematical scaffolding to put your experiment on.

@EmilioPisanty actually I think I agree. The chemistry courses did leave me blind to the allure of time dependence. The point is that for doing real calculations you didn't need it.

Maybe you rely on someone else already having done all the TDSE stuff that needed doing, and the real work is in the details of the TISE stuff.

@JohnRennie Sure. Operationally, the TISE might be all you ever see. But your molecule lives in the time domain and its response will be there even if you later choose to Fourier transform it.

Tangentially related: I think the entire idea of the wave function approach to QM is very misleading and actually causes a lot of harm in terms of people who keep thinking classically---in some sense the conceptual presentation in e.g. Feynman's lectures is much better.

@ACuriousMind so basically, an electron, a photon, and a higgs will all have their phases transform in 3 different ways when one do a poincairé transform around them, and the value of the spin labels the 3 different ways the phase will behave under the transformation?

5:03 PM

@Danu As opposed to?

Edited^

@Danu maybe.

Where you just start with the amplitude as the main thing

I think it depends in whether you're interested in QM for its own sake, or whether you just want to use it as a tool.

@Danu I found feymann's approach very straightforward and it give a nice taste on what path integrals will look like

5:05 PM

@JohnRennie Right---the wave function approach is much more hands-on and you're directly able to calculate.

But all the misunderstandings... sigh

Alarming though it may be, there are a lot of chemists out there who just want to calculate molcular properties and couldn't give a stuff for how precisely QM works.

I was one of them :-)

--->I am obviously not one of them because of my passion for QM

and that annoys them

We can't all be perfect :-)

They should have taught that wavefunctions is just the components of the ray under some basis

that's what Susskind used

Do you actually need to know for chemistry

5:09 PM

some basics are needed when using molecular orbitals, but only the physical chemists and molecular dynamists will worry about calculating them

Do you think that if I have the field of Colombeau's generalized numbers $\Bbb K_f$, I can define Colombeau's generalized functions as $f : \Bbb R^n \to \Bbb K_f$

organic chemists will just mess with orbitals and the linear combination of them in a qualitative manner (unless you are a physical organic chemist, which also does the hardcore calculations)

user image

for example

user image

that does not work on me, because I am both a physicist and chemists (all types) (my degree said so)

@Slereah that triggers chemists

5:12 PM

The early 80s were a really fun time because it was just beginning to be possible to do big wavefunctions. These days it's all got a bit routine.

(Joke) I am a superposition of all knowledge, this is the most common misconception that people had on me

Big wavefunctions?

From personal experience I'm not sure I'd call you a physicist

@0celo7 more than two atoms :-)

Can you even do two atoms?

5:13 PM

We did two atoms once in class

The dihydrogen molecule

As I recall $H_2^+$ has an analytic solution

At least in the Born-Oppenheimer approximation.

But that second electron messes things up so it's back to the computer.

Probably

Maybe using like

Bispherical coordinates

@JohnRennie I've been meaning to ask

you follow Jonathan Pie?

This isn't Game of Thrones!

There is a solution to the wave equation in bispherical coordinates

@EmilioPisanty Never heard of him. But then I watch very little TV, online or otherwise. I'm a fanatical book reader.

5:16 PM

Have you read

@JohnRennie He's mostly online

The Good Book

(By which I mean Hawking Ellis)

Well, in terms of the actual ability demonstrated, I suck at physic intuition, I am just passionate with it on par with chem (and tried to learn but improvement is v.e.r.y.s.l.o.w.)

Acuriousmind also found I am bad at computation

And to top that my mind is incoherent, (Evidence: Acuriousmind often said "What?")

One of my GR friend describe me as follows: I have the mindset of a theorist but the tools of an engineer

My mindset is actually closer to a mathematician, due to the reluctance of taking shortcuts nor approximations

The Large Scale Structure of Spacetime?

Do you know any other Hawking Ellis

There aren't a lot of real Hawking books

Hawking Ellis and Hawking Gibbons

5:17 PM

No, but I'm not that familiar with the literature, so that proves nothing.

Oh wait, there's also Hawking Israel

I tried the book early on in my learning of GR and it was much too hard for me. That put me off it and I've never gone back to it.

It's quite amazing that Hawking is still alive

I used to see him around Cambridge occasionally.

(Weird question) Is it possible to measure the overall spin of my iphone (or there are simply way too many atoms)?

5:19 PM

Put a stick in his wheelchair wheel

Odds are good that the average spin of an object is 0

At least if no magnetic effects are involved

@Secret yes, put it in an NMR machine.

The NMR spectra will probably be too broad to read

Might fry the phone, though

the peaks all mushing up

(assumign the phoen survives)

Oh wait

There's also Hawking Penrose

It's not that interesting a book, though

5:21 PM

@ACuriousMind: your downvote finger is twitchy tonight :-)

@JohnRennie That wasn't my downvote!

oops!

It occured while I was writing that comment, but I didn't vote on that question either way

@JohnRennie when do parents stop being embarrassing

@0celo7 When they're dead.

5:23 PM

@0celo7 speaking as an uncle not a parent, we do it deliberately because it's funny

Although we love our children/nephews they are a real pain much of the time and revenge is sweet.

I'm an uncle

@ACuriousMind What's nerdier? Reading an analysis book or reading Harry Potter

Harry Potter is mainstream nowadays

Nerd culture has been washed down by the normies

@0celo7 Reading HP is pretty mainstream, unless you read it so often you know it by heart

(Another weird comment)I will be excited if there exists some experimental way to demonstrate the lagrangian (up to some divergenceless vector field) before it get integrated into the action and then made stationary to give the equations of motion

I mean, (given discussions a long time ago) if the real world has no problem demonstrating the arbitrariness of setting the 0 baseline of some potential, then surely there must be a way to demonstate gauge invariance in a physical way somehow

The Lagrangian isn't an observable

5:27 PM

@Secret You're, once again, not making sense. What does "demonstrating the Lagrangian" actually mean? Sure, you can measure kinetic and potential energy and compute $T-V$. But what does that tell you?

@ACuriousMind so?

@0celo7 So unless you're reading the analysis book because you have been assigned that reading, that's nerdier :P

@EmilioPisanty Welllllll, it turns out quantum mechanics works just fine for collective degrees of freedom.

In our systems, the individual electrons are all in the ground state (superconductor), so those little arrowheads of each electron never change state.

Therefore, you can completely ignore them in any dynamical considerations.

The lowest energy single particle excitation is at ~40 GHz, but the circuit itself has a resonance at ~6 GHz.

That resonance is a collective motion of the charges in the superconducting state.

I swear, by experimental experience, that if you just analyze the quantum mechanics of the collective degree of freedom, you can understand the circuit, complete with control pulses, entanglement to other circuits, violations of Bell's inequality, etc.

@ACuriousMind you're colluding with her

this is mutiny

I am not a nerd.

@0celo7 I'm colluding with whom?

Your mother? Your girlfriend?

5:31 PM

What kind of tool doesn't prepublish his paper on arxiv

@Danu Well, I've never prepared said peppers myself, I've only consumed them. I recommend looking up a procedure.

@ACuriousMind Why would you collude with yourself?

@0celo7 Right, your mother it is, then.

theproofistrivial.com

@ACuriousMind and me are officially dating

5:33 PM

I mean, something along the lines of

how you can demonstrate the spin of an object by checking how its phase changes when you poncaire transform the particle (e.g. if you get different values like 1 ,1/2, 0 etc.) perhaps using some kind of inferometer set up (because we can only ever see phase difference) (assuming I have correctly understood you explanation on spin is a label of the representation of the group in question)

So I am guessing, if we can find something that play the role for that arbitrary divergenceless vector field term that you can add to any lagrangian but can be demonst…

And if I understood correctly, I think a poncaire transformation is quite easy to do (just move and rotate the set up)

>àlgebra

Your Spanish is seeping in, J. Aragona

@ACuriousMind you're sleeping on the couch until you cut your hair

@0celo7 if a blackhole suddenly (or perhaps in a long period of time) radiated/disappeared, would the structure of the space-time that it inhabited be different from the surrounding topology? I.e would a really strong deformation to the structure permanently deform it?>

@Secret A rotation is not a mere phase change except in the simplest of situations!

What do you mean by "black hole"

5:36 PM

And I still don't know what you're talking about with the Lagrangian.

@DanielSank ...ah

That's a shame.

@slereah an object that is within its schwarzchild radius

still wrong

..

If you mean the maximally extended Schwarzschild solution, then beware that it's very hard for spatial topology to change

5:38 PM

schwarzschild has no dynamics, how could it radiate

Vaidya metric does, tho

@slereah what do you mean by maximally extended?

Maximally extended is the blackhole with a wormhole topology

With the white hole in the past

what is a white hole

time reversed black hole

5:40 PM

Ok, so spin labels what representation a Poincaré group on an object is and thus tells how it behaves under the actions of the group.

What happens in the most general case, since phase change is just a special case of it?

It's Poincaré

what about just a regular non-wormhole topology blackhole then? Could one deform a manifold to no longer be locally euclidean or something else

can't type the é, forgot shortcuts

Manifolds are always locally euclidian

That's the point of manifolds

@Secret A rotation is just a unitary transformation in the general case. That's what being a unitary representation of the rotation group means

5:42 PM

So in the general case, if I have an electron and I look at the same electron when in some rotating moving frame, I will not only expect its phase to change, but its state vector also?

The spinor isn't measurable, @Secret

All observables relating to spinors are bilinear in the field

Which means that the 360 rotation doesn't matter

Anyone have a drill/tap chart that doesn't suck?

@Slereah One can measure the relative phase of that 360° rotation if you "rotate" one electron with a magnetic field and the other not, but that's not a "true" rotation if we're being nitpicky.

@Secret Yes. As another reminder, the state vector itself isn't really measureable either.

Yeah, about phase in the experimental sense, I always thinkg about relative phase, since we can observe that

for the state vector, that's easy to fix, we get probabilities that depends on it in the experiment

@ACuriousMind
as a side note, what kind of transformation is "applying a magnetic field to an object". Why it can always done a lot of weird things such as causing energy levels of a system to split, changing phase etc. From what you said that it is not a true rotation, it seems to be not a poncairé transformation?

Hm, found a not terrible one.

5:48 PM

The only certain thing I know abotu magnetic fields is that they are electric fields in a boosted frame

because of relativity

With spins there are magnetic fields that can't be boosted away

@Secret The standard spin-coupling is a term like $B(t) \cdot \sigma$ in the Hamiltonian, where $\sigma$ is the spin operator. Therefore a changing magnetic field can essentially act as rotating the state.

I see

You'll have to do the math/look up the specific experiments to see how it's done in details.

I think I saw a similar term in Susskind when he told us to do an exercise on two qubits in a constant magnetic field

5:51 PM

I almost did my thesis on that kind of shit

Because as you know

Some systems of particles in magnetic field can be described by supersymmetric operators

is that a mathematical coincidence similar to how some condensed matter stuff happened to have the same mathematical form as string theory stuff?

or is there some deeper explanation?

there is already a connection between condensed matter and QFT

A model of QFT being connected to condensed matter isn't that odd

ok

"Topologies dans les espaces de nouvelles fonctions géneralisées de Colombeau.
C-modules topologiques"

Hon hon hon

a countryman

Man, this → physics.stackexchange.com/posts/271271/revisions is worrying on so many levels

5:56 PM

A man's gotta eat, @EmilioPisanty

I've done a lot of jobs I didn't know shit about

@Slereah Other men gotta worry, though

@slereah How would the size of the space-time affect a massive object? The energy density would be infinite if the size of spacetime was $0$, right? It would only decrease as spacetime expanded? Would this just be a measurement that is taken, or would it impact the evolution of the system?

what

(Joke) It is kinda sad we can only see a hilbert space via its probabilities, like a higher dimensional lion being trapped in a lower dimensional cage in order to have some parts of it visble to us human beings

@slereah an analogy would be increasing the size of a trampoline while an object remained at rest on it? idk

6:03 PM

https://en.wikipedia.org/wiki/Lagrangian_mechanics

O that reminds me, the lagrangian also have units of energy (although that discussion is too ancient to matter)

*continue re-reading*

@Obliv how far are you in Zee

"As a rule, the proofs are be omitted."

that lazy bum

@ACuriousMind In the end, I won.

@0celo7 Who's that?

https://en.wikipedia.org/wiki/Lagrangian_(field_theory)

ok... so it seems the lagrangian is the sum of all interactions in a system in the most general case

For classical mechanics, the interactions are the kinetic energy and the potential energy (will revise later why it is minus and not plus)

For relativistic mechanics, the interactions are the rest energy (corrected by time dilation along some path (represented by $\frac{d\tau}{dt}$ term(?)) and whatever itneractions due to its trajectory in spacetime

6:17 PM

@BernardMeurer Since ACM is my girlfriend, it must be my mom.

isn't it the other way around

@0celo7 It's not your parents, that's for sure

@Obliv No, ACM is both

@BernardMeurer How do you know

and I told you I'm not continuing with Zee until I've finished multi-var calc (i'm on lec. 8/36 using mit open courseware)

"Don't forget to ask your parents..."

6:18 PM

(The plan) Well then, in that case, start with the classical mechanics lagnrangian first, and try to "project" as many of its mathematical properties and degrees of freedom into real space by some relevant experimental set up that immitate those mathemtical relations

and I'd prefer learning the geometry with a math approach before trying to learn gr but maybe I'll read zee right after

Why would you do that

because i don't know how to math yet and zee assumes u do

Zee is the best GR book

@Secret Are you referencing this?

6:19 PM

Zee assumes calculus and linear algebra

@Danu I thought you had him blocked.

@Danu Not exactly, (some variations of) it is a common phase used by Machio Kaku in his book Hyperspace. It is also mentioned in some popsci stuff whenever string theory is mentioned

Basically the idea on why we put 11 dimensions in our theory is to be able to use maths to 'see' the higher dimensional lion in its unmangled form when projected into just 4 dimension, at least that's how the saying goes

@0celo7 What a non-constructive comment.

@Danu Almost all comments are non-constructive.

@EmilioPisanty oO

@ACuriousMind ???

6:23 PM

@ACuriousMind What do you think of Elsevier?

@Danu Gotta say: "constructive" is not a criterion we usually hold this chat to :P

@0celo7 He unblocked me at least 3 week ago, reason is not important atm

@EmilioPisanty I agree with you that that's worrying.

Only civil engineers need to be constructive

@BernardMeurer oooooo

6:23 PM

@BernardMeurer I rarely think of them

@ACuriousMind :(

And I must say that I have far too little knowledge about the structure of academia in general and that of publishers in particular to offer a qualified opinion.

@ACuriousMind So you hate them?

What the heck is a Hilbert transform

@BernardMeurer My hate is a finite resource, and directed at other entities :P

6:26 PM

user image

Actually, while I have rely less on pictures to visualise things now, (because of some recent inspiration) I put "visualisation" on a more abstract level:

If you have some set up in real life that is arranged in a way to simulate (as many as possible) the mathematical properties of some mathematical object, then you can "visualise" it and make laymen understand it with its full rigor presented

Side effect of this project is an increase in the number of questions and thinking on how to experimentally demonstrate something

Is it normal to list religion and marital status on a resume in India O.O

@ACuriousMind What do you hate?

@0celo7 @ACuriousMind Do you guy's think these will look good on me?

@BernardMeurer Who wears a watch these days?

@ACuriousMind ::looks at wrist::

6:28 PM

The cool kids?

::raises hand::

It's not just any watch, it's a calculator watch

No, that's a crappy looking watch

@BernardMeurer I don't want to have another discussion characterized by negativity from my side.

that seems a bit too technical to be stylish @bernard but If you accompany it with headphones, maybe fingerless gloves and a scarf, you'd look like a pretty cool cat

6:29 PM

@ACuriousMind Yikes

I do want to taunt you by saying I'm going to Wacken tomorrow, @BernardMeurer :)

What is Wacken

@ACuriousMind I hope you ~~die~~ have a great time!

@0celo7 The world's largest metal festival

It's the single most awesome festival

I gotta go next year

6:31 PM

will rammstein be there @acuriousmind

@ACuriousMind I'd say "don't get too wasted", but please do

@Obliv No

I think not at least

@Obliv no

(cont.)
Mathematically speaking, I suspect "can be drawn on paper" can be defined as follows:

There exists a map (or something more general) $f$ and some object $M$ (in order to avoid the trap of vagueness, let's stick with mathematical objects) such that $f: M \rightarrow S\subset \mathbb{R}^2$ such that the properties of $M$ is preserved by the map $f$

There's still a vague element: Interpretations. Suppose I draw a line on a piece of paper, it can mean many things, and different people will have different interpretations of it

@ACuriousMind Never heard of it.

they're a pretty old band. I wonder if they still tour. What about eisbrecher

6:31 PM

@Obliv They're fascists

@BernardMeurer what a stupid thing to say

wat

@Obliv wacken.com/en/bands/bands-billing

@Obliv They do, and they were in Wacken in 2013. They're not really metal, though.

What are they

6:33 PM

Industrial rock

@0celo7 A variant of rock called Neue Deutsche Härte

Although what exactly is and is not metal is the subject of many holy wars

@ACuriousMind I thought they were categorized as industrial

@ACuriousMind I know what the Wiki article says.

That are eventually settled by all parties being too drunk to articulate an argument :P

@BernardMeurer I guess you can say that?

I've never been big on all the genre classifications

oh wow some big names going too. Dragonforce & iron maiden and rhcp :O
and vader :OO

6:35 PM

@ACuriousMind Do you know about my music OCD?

I do love Serbstorm :

Serbstorm - Fire and Flames

@Slereah Remove kebab

So generalising, a mathematical object $M$ can be physically demonstrated if there exists a map $f: M \rightarrow K$ where $K$ is a configuration in phase space restricted by $\mathbb{R}^3$ and then....

Error: Vagueness (Cannot define precisely real life and the set of all laws of physics), this computation will terminate

@secret you really are an A.I.

In imprecise words, however, it is easy to say. To demonstrate an abstract concept in real life, you need a set up that mimics it

6:37 PM

@Obliv Read carefully, those rhcp are not the red hot chili peppers ;)

Maybe @secret was an older version of @acuriousmind 's A.I. software

@BernardMeurer no?

well that makes much more sense @acuriousmind I wasn't sure why they'd be going to a metal concert. Lmao that name though..

@ACuriousMind My digital music library is impeccable, and I'm obsessed with it's organization. Like, can't sleep if I know an album has wrong metadata

Genres are crap to get right

I still don't have a consistent model for putting groups under genres

@Obliv Well...there's not only metal at Wacken. There's also Mambo Kurt

6:40 PM

https://en.wikipedia.org/wiki/Representation_theory

Argh, cannot make a joke based on that, since representation theory only map abstract stuff to vector spaces and modules, but what I want is something so general that map any conceivabel concept and their properties onto some configurations and interactions in real life (i.e. some physical construct)

@secret start defining your own math. I can see it now: "General representations of abstract concepts by physical constructions" I'm sure the mathematicians will love it.

No don't start defining your own math

Start by learning math

no they won't they will say I am not making sense and too meta

actually i don't think a mathematician would care for physical representations of abstract concepts

that seems to be a mathematical physics thing

learning maths is what I am doing as I study, and I acuallty like all those alien abstract spaces the maths live in

6:47 PM

@ACuriousMind What does a "generalized compliance" mean in the context of EM/thermodynamics?

To me, maths is exploring "alien spaces" with its own laws of physics the axioms

and thus doing algebra is in some sense moving in such space and interact with its elements

@0celo7 I have never heard that

"On the other hand, for elements of Colombeau algebras there is a very natural and direct way of obtaining point values, namely by inserting points into representatives."

Yesss

Take that, Schwarz

The most common complaint about maths from laymans is they they are too abstract and they don't get it
One of my personal wishes is to make people less fear of maths

@ACuriousMind what does $\delta\wedge\delta$ mean?

6:50 PM

@slereah hey would objects of greater temperature impose a greater gravitational force on other objects?

user image

Thank you Jesus

@Obliv Yes

that's stupid

You can totally define generalized functions as functions to generalized numbers

I hope I can make something out of this

Slereah theory, we'll call it

"it is obvious"

NO IT'S NOT

The proof is trivial, @0celo7

The reader can totally show

6:55 PM

"The proof is trivial and left as an exercise"
It is not trivial unless it is a one liner

This isn't even math

It's physics

user image

(Weird question) I wonder, if there exists nontrivial proofs that are actually one liners?

Sure

@Secret How big a line

6:58 PM

Depends on how many lemmas you have before

Depends if you can put more than one statement on the line

@slereah what happens if two objects accelerate towards each other?

length=ttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

sounds reasonable eonugh
@ 0celo7 I see: "Proof: This is a corollary of <insert theorem>"

They bang their heads

i mean what happens to gravity

7:00 PM

Gravity bangs its head

facepalm

And now you bang your head

suppose a dipole $AB$ where $A$ and $B$ are massive objects. If they accelerate towards each other, would an object at some distance from $AB$ on the dipole axis be affected by gravity more or the same as if the two objects were moving towards each other at constant velocity?

https://en.wikipedia.org/wiki/Ring_(mathematics)

NB You cannot draw a general ring on a piece of paper using the same idea in the eigthfold way by using a lattice of points to represent all elements generated by some generator of a group and simply label the dots with some symbols a,b,c etc.

This is because the moment you start seeing shapes, there's a hidden constraint being imposed in your drawing that will make whatever ring you are representing less general

and say the acceleration is from $0$ to the constant velocity described in case 2

7:06 PM

The metric of those two situations would be different

how do you mean

Hi guys. The operator $\bar{e} \gamma^\mu P_L e$ can destroy and create a Left-handed electrons and positrons? Or the positrons have opposite helicity?

user image

example of a failed attempt in drawing a ring

@secret rings have to be commutative?

and why does that screw everything

user image

7:14 PM

nvm i don't get it

"the algebra of retarded distributions"

I believe we prefer to call them mentally handicapped these days

@slereah you never answered my question, and now I have class. shame on you

7:32 PM

@Secret Yes.

@Obliv no they don't

7:50 PM

@Slereah abelist scum

I think you mean "abelian"

8:05 PM

@Slereah Abel was one of my people

8:21 PM

@0celo7 Abel was an engineer-mathematician hybrid with an identity crisis?

@ACuriousMind Are you trying to burn me?

Is this what a """roast""" feels like?

I have no idea what a """roast""" is, I'm trying to discern what you meant by "my people" there :P

I also have no idea what the tripled quotation marks signify

@ACuriousMind You don't know what quotation marks mean?

@0celo7 I know that they mean ordinarily, but I don't know why you wrote """roast""" instead of "roast"

@ACuriousMind Ah, quotes have meaning modulo 2.

8:25 PM

maybe he is questioning the roastiness of your roast

@0celo7 That ""doesn't"" make any ""sense"" at ""all to"" me.

@ACuriousMind Clearly it does, since you just used the principle.

...that was a demonstration how silly that "principle" looks in action :P

Don't you mean the ""principle""?

No, those were scare quotes indicating I don't believe that to be an actual principle anybody uses

8:28 PM

Ah, well, not my issue.

I'm no "linguist."

Clearly not

Wow what a sick "burn"

@0celo7 You're only saying that because you can't french kiss

lol, how did you obtain that information?

My gf thinks I am a good kisser, shut up

::pouts::

@ACuriousMind Do you know anything about linear response theory?

8:35 PM

nope

$(u_\varepsilon)_\varepsilon$ is a bit of a redundant notation

What does $\mathcal C^\infty (\Bbb R^n)^I$ even mean

$I$ is the unit interval here

$A^B$ is a notation for the set of functions $B\to A$.

@ACuriousMind Ask rebecca

Oh I think it might be a family of functions with a parameter in $I$

@BernardMeurer I made her up

8:41 PM

@Slereah Yes, it's a function $I\to C^\infty(\mathbb{R}^n)$. A "path", if you will.

Well not really here

It's more of a family of regularized functions

A family of objects from a set X indexed by I is the same as a function $I\to X$.

That's the reason for the notation - you can conceive of $\mathbb{R}^n$ as functions $\{1,2,\dots,n\}\to\mathbb{R}$.

Thanks

@ACuriousMind what

@0celo7 What confuses you?

8:44 PM

@ACuriousMind Starting here; everything.

But what is confusing? Having the set of components $v_i$ of a vector $v\in\mathbb{R}^n$ is exactly the same as having a function $\{1,\dots,n\}$ that maps each number k to the component $v_k$.

...that makes no sense

@MarkMitchison is back, hah

How's the big T doing?

Loved this one btw

1

A: Dynamic Energy Dissipation (Qualitative question)

I'm afraid the statement is pretty vacuous, although technically true. Yes, systems dissipate energy to their environment. Do they do this in the "fastest way possible"? Well, they dissipate energy according to the laws of physics describing whatever process is governing the exchange of energy. S...

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