The h Bar

Silly Goose

01:29

is jostling a bottle of water to increase the temperature of the water a work based transfer of energy (as opposed to heat)? I am thinking yes

why is specific heat capacity still refered to as such when it is really a relationship between energy and temperature generally

naturallyInconsistent

02:14

@SillyGoose because physicists will fight any change in terminology from the standard even when it is vastly superior

Silly Goose

02:53

well that is just ridiculously stupid xD
it is simply and utterly wrong

so the oft quoted formula from intro chem classes is just wrong / a special case (i.e. $Q = cm\vartriangle T$)

naturallyInconsistent

Yes, it is a source of confusion for generations upon generations and it is also not a tightly hidden fact, but because it is not generally taught that this is a mistake, students will not necessarily realise that it is actually a bad name

not to mention that we have not changed the pre-university textbooks to stop using such a stupid name, and so it will be continually enshrined in the general conception

Silly Goose

03:44

is the reason that atoms are often considered to be occupying energy eigenstates not due to decoherence?

Relativisticcucumber

@ACuriousMind awhile ago you linked a post about why things are found in energy eigenstates. do you recall what this post was? i cant find it

Ryder Rude

08:11

hi

Should Airships Make a Comeback?

►

it is from Derek

Sir Cumference

08:26

on a related note it's weird how there's now only 25 blimps left in the world

i could've sworn i'd seen some as a kid

Ryder Rude

08:39

the lift of these ships come completely for free

it is beautiful how physics work out to give free stuff, even to the extent of free flying

@SirCumference the video mentions a hydrogen airship that burned and crashed

many companies are trying to revolutionaise travel and transportation. airships, hypertubes, flying cars, etc

in the end, all but a few of these ideas will look terrible in retrospect

but the few that will make it will also look like horrible ideas at their beginning

Howard Huges's Hercules also looked like a horrible idea in the beginning

user 726941

Led Zeppelin is the iconic airship imho.

Loong

@RyderRude So helium and diesel are free now?

@RyderRude mentions a hydrogen airship that burned and crashed? Are you one of todays lucky 10 000?

user 726941

08:58

fell like a Lead ballon :P

Loong

Well, I should be glad it wasn't called "exploded" instead of "burned and crashed". 🙄

If they really hear about it for the first time, they might also be interested in watching a video that mentions a passenger liner that sank after striking an iceberg during her maiden voyage. 😂

2

user 726941

an unsinkable passenger liner

Ryder Rude

09:14

@Loong sorry. i mean that once u have Helium, u r not "using it up" and u can produce lift for as long as u want. and if u use hydrogen, then it is cheap to obtain too

Chemistry

@RyderRude morning. ^_^

have you figured out yesterday whether initial condition argument for lagrangian is solid?

So argument is this (read from "one one hand" - https://physics.stackexchange.com/a/7802/366606) and then I thought the following:

Imagine L being $\frac{1}{2}m\dot q(t)^2 - mgq(t)$ where $q(t)$ and $\dot q(t)$ are functions of t. To know L's value, let's say at $t=2$, you would plug in $t=2$ and get L. This means that behind the hood, the speed that it calculated is dependent on the position, but note that since $q(t)$ is the path which satisfies the initial conditions at $…

ACuriousMind

Oct 19, 2022 at 14:02, by ACuriousMind

see also https://physics.stackexchange.com/q/69559/50583 for a discussion why real-world systems are often usefully thought of as being in energy eigenstates

Ryder Rude

09:30

@Chemistry hello. QMechanic's second paragraph makes it clear. The Lagrangian treating its variables as independent comes from the very definition of the Lagrangian

@Chemistry but there is ofc a relation between the number of initial conditions and the highest derivative that the Lagrangian depends on. Please see this post : physics.stackexchange.com/questions/109518/…

Chemistry

@RyderRude but we wre talking about why the definition is like this and one argument for it was initial condition(he mentions it in the "on one hand")

Ryder Rude

for e.g. if ur lagrangian depends on aceleration, the the EL eqn can, at most, be of order 4. This means 4 initial conditions at most

Chemistry

most of the time, I know equation of motion is 2nd order, so 2 initial conditions needed. $q$ and $\dot q$ at some instant. have you read my argument ? chat.stackexchange.com/transcript/message/64319619#64319619

in my argument, initial conditions are still met even if we have $q(t)$ and $\dot q(t)$ - makes sense why ?

Ryder Rude

@Loong i have seen Titanic

@Chemistry oh

Chemistry

but in my argument, you can't get L's value until the path is derived.. but why would you need to even know L's value before ?

Ryder Rude

09:36

it is correct tha u cannot obtain a second order EL from a Lagrangian that, at most, only depends on position (and no higher derivatives) @Chemistry

so the presence of dot q in the Lagrangian is indeed motivated by the fact that u hav two initial conditions in the real world

Chemistry

can we not discuss 2nd order EL yet ?

Ryder Rude

okay. what r we discussing

the number of initial conditions is, at most, twice the order of the highest derivatve that the Lagrangian depends on

please see this post : physics.stackexchange.com/questions/109518/…

ACuriousMind

@Chemistry I'd like to take a step back: Why are you so bothered by this idea of $L(q,v)$ existing as a function of states and not of paths?

Like, it doesn't cost us anything to think about this function

and it's just a fact that that's how Lagrangian mechanics generally constructs its action: Take some $L(q,v)$, plug a $(q(t),\dot{q}(t))$ into that, go. We've been over this at length

so what really is the problem you're still trying to solve?

Ryder Rude

i asked u the same thing, why do u want to make the Lagrangian into a functional

ACuriousMind

if you're looking for some sort of abstract compelling reason why Lagrangian mechanics has to work exactly that way and not any other, you won't find one

all you'll get are heuristics and motivations, of which you've been presented several

Chemistry

09:43

@ACuriousMind @RyderRude the reason is since I spent quite amount of time on why theere are independent variables in L, I prefer to fully get it and not just leave it here.

exactly, just want to get the initial condition motivation and I'm done

I get why $\dot q$ and $q$ are present in Lagrangian, but yesterday, we were discussing why $q$ and $\dot q$ are not functions of $t$ in the $L$. One of the reasons was if they depend on $t$, then EL won't be able to do partial derivative bcause $L$ is a function of $t$

We all undserstood this reason, but then I saw Qmechanics answer and it seems like he describes second reason/motivation why in L, $q$ and $\dot q$ can't be dependent on $t$. His reasoning is initial condition thing. https://physics.stackexchange.com/a/7802/366606 ("on one hand")

ACuriousMind

I don't understand your "counter argument" at all

as in, I don't understand what it's trying to argue

and I think you're really overthinking the "initial condition" thing

Chemistry

What Qmechanic says is that position and velocity are independent at initial condition thing which I agree

and at whatever instant, initial condition thing is given, they are independent

ACuriousMind

Qmechanic's argument is essentially just:
1. The instantaneous Lagrangian is a function of a *state*, not of a *path*
2. A state is generally an independent tuple of position and velocity since by "state" we mean the full information necessary at an instant to uniquely solve the equations of motion

I don't understand why we'd have to make it any more complicated than that

Chemistry

ok, then answer this. iF $L = \frac{1}{2}m\dot q(t)^2 - mgq(t)$, can you tell me what this breaks for initial condition motivation ?

ACuriousMind

I don't understand the question

Chemistry

09:47

imagine $q$ and $\dot q$ in L are functions of $t$

as if in the L, we directly got path and its derivative's functions

ACuriousMind

again, I think you're trying to do something that's not possible: You cannot "derive" that the way Lagrangian mechanics works is the only thing it can work

The Lagrangian is supposed to be a function of a state and not just of a path because the energy in a physical system at one point must not depend on its history or future.

that's a physical, not a mathematical argument

Chemistry

"The Lagrangian is supposed to be a function of a state and not just of a path because the energy in a physical system at one point must not depend on its history or future."

and in my case, why would it depend on its history or future ?

ACuriousMind

it's not that something "goes wrong" when you try to consider actions that are not constructed from an $L(q,t)$ and merely from something that depends on the path but that's just not useful as a physical theory (at least so far no one has shown it to be)

@Chemistry $\dot{q}(t)$ makes only sense for a path - you can't have a derivative at an instant

now, you say "but I'm only using the value and not any other information about the path"

but that claim is formally exactly equvalent to saying your $L$ has been constructed by starting from a function $L(q,v)$ and then plugging a path $q(t)$ into it

it's just confusing notation again

just because you've written your example to be "just a function of $q(t)$" it can be easily rewritten in terms of $L(q,v) = \frac{m}{2}v^2 - mgq$ and then your $L$ is just plugging in $(q(t),\dot{q}(t))$ into that

you're not really doing anything different, you're just playing notational tricks again

Chemistry

so L could be as well $\frac{1}{2}m\dot q(t)^2 - mgq(t)$

ACuriousMind

I don't know what that means

I've said like 5 times now that we should really start writing down (co)domains to be careful about what we view as a function of what

and you keep ignoring that and running into the same notational problems

Chemistry

09:55

it means that in the L, we insert path equation and it's derivative, which means to know L's value at $t=2$, you won't be able to know until you get a path function and insert into it

Ryder Rude

we can give u all the motivation for Lagrangian mechanics. imagine u already have Newton's laws. And u wonder "What if the trajectories that Newton's laws are giving me are the stationary points of a functional". Now u hypothesize the simplest functional $\int L(q(t))dt $. u see that extremising this does not give u newton's laws. so next u try, $\int L(q(t), dot q(t))dt$. u find that this gives u Newton's laws

but in ur quest so far, u hav ended up with a function L(x,y) which has independent slots for position and velocity

thats really all

Chemistry

@RyderRude yep, I get that. I'm only arguing how the initial condition is the motivation that $q$ and $\dot q$ are independent

ACuriousMind

@Chemistry again, your example is just $L(q,v) = \frac{m}{2}v^2 - mgq$ with a path plugged in. you're not doing anything different from the standard

you're just choosing to get weirdly hung up on being able to write this with $q(t)$ plugged in but this doesn't really have any significance

Chemistry

@ACuriousMind then initial condition is not the motivation why $q$ and $\dot q$ are not functions of $t$ in the L.

ACuriousMind

at this point I'm fine with you thinking that :P

Chemistry

10:00

haha, then I don't get what Qmechanics point is about initial condition :D

ACuriousMind

I don't know how else to explain the point about states being initial conditions and the Lagrangian being a function of it

I've tried to phrase it every which way I know, if you don't get it you'll have to find someone else

Chemistry

I think I have to stop this and let it go

Ryder Rude

10:14

im.not sure what it would even mean for the Lagrangian to treat x and dot x as dependent variables, as it is in the very definition of the Lagrangian to not do that

Chemistry

@ACuriousMind @RyderRude kudos to you for bearing with me. Thanks so much <3

Ryder Rude

@Chemistry hello. i can help u with this. i challenege that u cannot write any action such that its Lagrangian treats x and dot x as dependent variables (this will follow from the definition of the Lagrangian)

Chemistry

@RyderRude not sure why I can't and why it wouldn't be the same thing

Ryder Rude

as soon we u write any weird formula of the action, let's say, S[q(t)]=\int q^2(t) e^{dot q(t)} dt, the Lagrangian is defined as the two variable function L(x,y) that u would get by taking the integrand, and replacing q(t) with x and dot q(t) with y

so the only thing that u can ask this "why do we care about this function L(x,y)"

it treating the x and dot x as independent is just by our definition of it

u can write any weird action formula, and the Lagrangian will, by definition, have x and dot x as independent variables

as for "why do we care about this function we have defined", it's because when we get the eqn for the stationary path, this function shows up there

Chemistry

yeah, best motivation I found why L can't be written as $q(t), \dot q(t)$ is the partial derivative can't be applied in the end

and if $L$ can't be written like that, they $q$ and $\dot q$ definitely are independent

Ryder Rude

10:25

yes, but remember that our starting point here has pretty much no restrictions. we didnt start with the Lagrangian. i just told u to write any weird action expression

it still cant be too weird

u can write any action. the lagrangian will just later show up as a useful function in the extremisation problem

there r some restrictions on how u can write the action tho. it must b an integral of a function of t, etc

Chemistry

in your example, you already use the definition of Lagrangian

and if you do that, ofc, you end up with 2 independent variables, but that's not quite the solid proof

Ryder Rude

yes. becuz we r not proving anything! we r just defining the lagrangian

the only question u can ask is "why is this function useful"

Chemistry

yeap, it makes sense

btw, have you read Landau's book ?

Ryder Rude

no

Chemistry

He has got some interesting proving method about why L = K - U

but in the end, he just fails in my opinino

Ryder Rude

10:30

oh

L=K-U is just justified by experiments, I think

Chemistry

not quite

Ryder Rude

why

Chemistry

he spends 5 pages on explaining why L must be consisting of K

he uses inertial frame logic

Ryder Rude

thats all experiments

he is giving u physical motivations

Chemistry

yeah true

Ryder Rude

10:31

u cant mathematically prove L=K-U

Chemistry

you know in the end what he does ?

Ryder Rude

what

Chemistry

he arrives at $L = cv^2$ ($c$ some constant) and he out of nowheere says that $c$ must be $\frac{1}{2}m$, because when you take euler lagrange on it, you should get the same thing as newton does.

this logic is not solid in my opinion, why spending 5 pages on inertial frames, if in the end, you look for function whose erivative matches newton's ($m\ddot x$)

you could have just thought: hm, what shoud my L be, such as EL gives $m\ddot x$

then he out of nowhere decides that L = K - U (with minus sign)

the long story short, he spends 10 pages of explaining why L = K - U and fails in it because he still uses newton heavily.

Ryder Rude

lol

Chemistry

his book is so complex btw, maybe it's me who doesn't get him

Ryder Rude

10:36

the constant need not be 1/2m anyway becuz the Lagrangian can be multiplied by any constant

but ud hav to multiply U too

Chemistry

yeah, i know, he just discusses it for free particle (even easier :D)

Ryder Rude

even for a free particle, he couldve left the Lagrangian at cv^2 instead of involving Newton in an ad-hoc way

if he got to cv^2 using inertial frame arguments, he really did something

Chemistry

yep. thats my point. if you anyways involve newton, you could say: what my L should be in order to get to newton ?

well, he did something but then he should have stopped

involving newton made things worse

Ryder Rude

yes

A ZEE's GR book also had similar arguments for justifying the free particle action

Chemistry

but i don't know. maybe in his head, something else was going. he was a genius and who am I to say that his logic is horrible

Ryder Rude

10:41

at least he derived v^2. i wud say his argument must be good

Chemistry

yeah, it is. it's mind blowing how he arrives at that

it's his own logic that you will not meet in any other book

Ryder Rude

v^2 is rotationally invariant but so is v^4

Chemistry

he proves why it can't be v^4

Ryder Rude

ooh v^2 has Galilean symmetry

Chemistry

yep

Ryder Rude

10:44

yes, becuz he uses the concept of inertial frames

Chemistry

100%

Ryder Rude

to motivate U(x), u probably need to ad hoc involve Newton

ACuriousMind

@Chemistry The Landau books are notorious for being different from most other texts dealing with the same subjects, people either love or hate them - I've rarely met anyone who didn't feel one way or the other about them

Chemistry

yep, exactly. it's super hard to read his book, but once you understand what he means, no way you won't be mind blown

Sir Cumference

@RyderRude yeah that was the hindenburg

but that was a zeppelin, i.e. a rigid frame airship

blimps (soft body airships) stuck around for a lot longer but seem to be dying out nowadays

user 726941

10:53

the band's music will never die :P

Sir Cumference

supposedly led zeppelin got its name because they were rejected by a record label who said they'd sink "faster than a lead balloon"

or something like that

user 726941

2 hours ago, by user 726941

fell like a Lead ballon :P

yup

Ryder Rude

crazy that around half the people survived

Sir Cumference

two thirds even

surprising

i remember taking a class on aviation, there was a lot of interesting stuff about airships

apparently zeppelins were advertised to be cruise ships in the sky

Loong

@SirCumference Keith Moon said that.

Sir Cumference

10:58

with their own piano rooms, bunk beds, etc.

and supposedly the empire state building's peak has a ladder that was meant for people to climb off zeppelins from, so they'd exit in the "center of the city"

problem is the zeppelins kept bursting into flames

Ryder Rude

those people exit all over the city then

user 726941

in the middle of NYC :O

Ryder Rude

if u dive into Titanic's corpse, the piano rooms, etc are stil there

it is tragic really

Sir Cumference

untappedcities.com/2013/05/28/…

Apparently what I said about the empire state building was part of the plans, but didn't get built into fruition

oh well, would've been cool

Mr. Feynman

@ACuriousMind in which category would you put @bolbteppa? :P

ACuriousMind

11:07

uh, obviously in love with it?

user 726941

@SirCumference thanks for the fact check

ACuriousMind

not sure how that's even a question :P

Mr. Feynman

Let's just say I love restating facts

Ryder Rude

airships are making a comeback now

they can supply food too. transportion is a big problem with world hunger

Loong

unlikely

Sir Cumference

11:08

well to some extent

but it'll be a good while till they really become prevalent

user 726941

@Loong TIL, thanks

Ryder Rude

@SirCumference yes. the company owners said they dont yet know if it is feasible

Loong

Cargolifter tried and failed.

Ryder Rude

veritasium also said that analog may be making a comeback over digital. i forgot his reasoning

ACuriousMind

you really shouldn't believe every silly tech start-up's ridiculous claims

Ryder Rude

11:11

there r some new innovations in analog these days

Sir Cumference

@ACuriousMind well everyone likes to dream of the future lol

but yeah plenty of things get hyped up without going anywhere

Ryder Rude

analog is futuristic as hell from the looks and functioning perspective

but it is now a thing of the past

user 726941

veritasium is venom for high school students

Ryder Rude

Future Computers Will Be Radically Different (Analog Computing)

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ACuriousMind

@SirCumference It's not the dreaming that bothers me if that's what it was, but most of this hype is selling products that don't actually benefit anyone but the ones selling them, poisoning "normal" people's ability to separate the likely from the improbable in the process

Sir Cumference

11:14

honestly you do have to remain skeptical whenever someone tells you what the future will be like

Ryder Rude

Veritasium mostly just wants to teach analog, I think

he partners with startups to make the teaching interesting

he just uses history and start ups as a way of teaching

ACuriousMind

counterpoint: he partners with startups because he likes money

Sir Cumference

@ACuriousMind i do think this is kind of a cynical way to look at it

Ryder Rude

he makes extremely interesting videos while being educational, so it is all good

ACuriousMind

@SirCumference It is. I'm a cynic. :P

Sir Cumference

11:16

oh lol

user 726941

LoL

Ryder Rude

his use of history while teaching is a work of art

Sir Cumference

i guess i like looking from a more optimistic perspective

Ryder Rude

he just constructs a well structured story

Sir Cumference

makes the world seem like a less crappy place to live

user 726941

11:17

me too

Ryder Rude

for e.g. he made a video about quantum computers breaking the primer number algorithm but started storytelling about how the past cryptography was created

it makes for very engaging content

Sir Cumference

i think his videos are pretty good

Ryder Rude

yes. he has really mastered storytelling by now

even better than Vsauce

Sir Cumference

he makes some clickbait titles (especially the "This is Math's Fatal Flaw" video about Godel's incompleteness theorems), but he also openly admits why he has to make clickbait

Ryder Rude

yes

Sir Cumference

11:19

i think he's made like 2 videos explaining how much of a difference it makes

ACuriousMind

so many of these technology-optimist programs (often with more or less subtle libertarian bend) - be they Youtube channels like Veritasium or Kurzgesagt or other forms of media - suggest to their audience, either explicitly or by omission, that the problems in the world will be solved by advancing technology. That not only new tech is cool, but the most important thing to focus on.

I think this is a pernicious ideology even when the raw facts presented are largely correct. All media is political, and this kind of media represents politics I do not share.

2

user 726941

Interesting perspective.

Ryder Rude

i dont find them very political. you r overthinking/overanalysing their videos. they r educational first and foremost

Sir Cumference

@ACuriousMind I mean advancing technology is part of it. But yeah, whenever you receive information from someone else you gotta consider what message they're trying to give you

Which is why it's important to hear from a lot of different sources

Ryder Rude

Kurzesagt sometimes post about political topics tho

user 726941

11:26

I think this political ideology is aimed at young STEM students hooked on social media

Ryder Rude

kurzesagt made a video about fighting climate change. at least they said that they had researched it from a variety of papers

in their defense, they hav to condense a lot of research in a 20 min video. this may seem like they r oversimplifying things

user 726941

Why else would he change a tweeting bird to the common variable X

nickbros123

Plasma physics seems like (as slereah said) it deals with charged particles behaving like fluids (applying fluid dynamics laws?). I don't know head or tail of this now, but I have a feeling this is then the most general study of moving charges. In this case, is there a derivation for $\frac{1}{2\mu_{0}} \iiint B^2 d\tau $, the work it takes to set up a current configuration?

user 726941

11:58

Is it the subtle libertarian bend that you do not share @ACuriousMind

@SirCumference how humble of him :P

Sir Cumference

@user726941 well they are interesting lol

Clickbait is Unreasonably Effective

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user 726941

The unreasonable effectiveness of bait to catch fish.

To me he sound too much like an advertising agent, rather than a teacher.

The old "chocolate covered broccoli" speech.

Ryder Rude

12:18

who is your favorite singer who is currently alive

user 726941

Trying To Find Fitness Advice Online

►

Sir Cumference

@user726941 I guess it's a difference in how you feel about him. If you like his videos, then you hear "I know clickbait sucks, but it lets my educational videos reach a lot more people". If you don't care for him, then you hear "this is why clickbait is great"

user 726941

12:43

Sure, mindset matters; but, I would rather see him use the educational psychology recently developed in learning science.

Ryder Rude

anyone wanna play this? : lichess.org/U9O6Jerf

user 726941

Learning sciences

Learning sciences (LS) is an interdisciplinary field that works to further scientific, humanistic, and critical theoretical understanding of learning as well as to engage in the design and implementation of learning innovations, and the improvement of instructional methodologies. LS research traditionally focuses on cognitive-psychological, social-psychological, cultural-psychological and critical theoretical foundations of human learning, as well as practical design of learning environments. Major contributing fields include cognitive science, computer science, educational psychology, anthropology...

Ryder Rude

I have no problem with click bait, personally...especially because the videos are contentful

Olivia Newton-John - Blue Eyes Crying In The Rain

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it is very good

user 726941

13:23

From N. David Mermin who coined the phrase "shut up and calculate!"

Wrote in his book:

> Henceforth, by 1 foot we shall mean the distance light travels in a nanosecond. A foot, if you will, is a light nanosecond (and a nanosecond, even more nicely, can be viewed as a light foot). ... If it offends you to redefine the foot ... then you may define 0.299792458 meters to be 1 phoot, and think "phoot" (conveniently evocative of the Greek φωτος, "light") whenever you read "foot".

source

Ryder Rude

14:05

Michio Kaku is saying u need quantum computers to study wormholes : youtube.com/shorts/pioXo0VtZSc?si=V8X-f7EqoTDDJLNF

i dont think this is correct. do wormhole calculations require quantum computing?

he also says that wormholes allow u to break the "Einstein barrier" and travel faster than light, which is not correct technically

imbAF

14:37

ACM I have a question. If we consider the many times discussed case of two frames F and F', but now Instead of considering how the four position changes accourding to the LT, and it's meaning, I am now considering the Dirac equation and the Dirac spinor

I believe both observers can, in their respective frames use the Dirac equation

If they solve it they will calculate the corresponding $\psi$ and $\psi'$

Now, at what point does the LT of the dirac equation in one frame

into the other

comes into play?

bolbteppa

16:57

@imbAF when you have it in one frame, you can determine it in another frame via the LT, if you independently calculate the solution in two different frames, the way to pass between them is a LT, and the correct representation of the LT which lets you pass from one spinor to the other can be determined by studying the invariance of the Dirac equation

@RyderRude Kaku is probably right, if you've ever looked in the mans textbooks you'll realize he is all-knowing, don't let the polite demeanor and crazy things about teleportation fool you

Silly Goose

19:29

@ACuriousMind this answer by shor seems to assume that the only possibly occuable states are the energy eigenstates; does it not?

imbAF

If U(p) is a spinor (dependent from 3D momentum), why when investigating the orthonormality of such elements, we consider $\bar U U$ instead of $U^\dagger U$ ?

Relativisticcucumber

@SillyGoose also wondering about this

ACuriousMind

@SillyGoose no?

but indeed if you read these answers carefully you'll indeed note that the reasoning applied there would apply to most eigenstates of other operators, too - we can pick any basis we want for our states, after all

there isn't really an argument here that things "are" in energy eigenstates

because most things in the real world are so horribly messy we have to describe them by statistical mechanics, anyway

Relativisticcucumber

@ACuriousMind i dont understand how shor's answer "Even if we know everything about the collision except how long ago it collided, we can't determine the phase of this superposition, so we might as well think about it as being in a probabilistic mixture of energy eigenstates." answers the question "Why should we expect to find the electrons only in such energy eigenstates, as opposed to say, some arbitrary superposition?"

ACuriousMind

@Relativisticcucumber oh, for the electrons in an atom there's a much more specific explanation: When the electrons are not in energy eigenstates they can decay by emitting photons

that's not some general mysterious principle of quantum mechanics, it's just very specifically that the only stable states of atoms are those where all the electrons are in as low energy levels as they can get

Silly Goose

19:40

quoting from shor's answer: "If we take a system, and let it evolve for some indefinite amount of time, it will be in an incoherent mixture of energy eigenstates. Many systems we encounter in nature have been sitting for some time, and not interacting with the environment (much). These can be considered to be in energy eigenstates."

it is stated as fact (not supported by explaination) that the system will be in an incoherent mixture (not superposition) of energy eigenstates

i.e. if we had no lack of information about the system, we would know it was in energy eigenstate $\lvert E \rangle$

i thought one explaination for the system certainly being in an energy eigenstate (or mixture of) is due to decoherence; i.e. atoms are generally considered to be in an environment such that the selected pointer states are energy eigenstates

ACuriousMind

@SillyGoose I wouldn't read this isolated from the second paragraph, where he explains this is very much a "we might just assume as well" and not a claim about the "actual state" of the system

Silly Goose

hm but then i dont get the logic to go from "huh well we can't tell what the relative phases are if it is in a superposition, so let's just consider statistical mixtures of the eigenstates"

why not statistical mixtures of various superpositions of energy eigenstates with various relative phase relations

imbAF

The solutions to the DE, the dirac spinors, can be considered as spanning a basis?

Silly Goose

and i guess i don't get why decoherence does not get a mention in the discussion in general (i.e. none of the answers mention it). so it makes me feel like im misunderstanding decoherence's place in this sort of physical situation

ACuriousMind

@SillyGoose you are absolutely correct that if the claim was that, in nature, systems actually occur in specific decohered energy states, then some sort of decoherence argument would have to be made

Silly Goose

19:46

okay i see

ACuriousMind

but I submit that that's not actually the case: No one really claims that systems in nature are "always in energy eigenstates"

either they're claiming this for specific systems, like electrons in atoms where you can argue this much more specifically, or they're just making a handwaving argument for why it's generally fine to model stuff like that

I mean, it's very easy to show that the strong version of this claim is nonsense: If you start an isolated system in something that's not an energy eigenstate, it will never reach an energy eigenstate due to unitarity of time evolution

Silly Goose

how does the argument go for electrons in atoms (if we ignore interactions between system and environment, which leads to decoherence arguments)

ACuriousMind

in the end this is much like the thermodynamic fiction of equilibrium: No real world system ever reaches true equilibrium, but a large range of cases is very well modeled by just assuming it does

Relativisticcucumber

@ACuriousMind wait so you mean the statement "systems in nature are "always in energy eigenstates"" is false? to what extent is this a reasonable statement?

Silly Goose

wouldnt this just be an isolated system?

and then what you just said applies

ACuriousMind

19:49

@SillyGoose no, you can't uncouple the atom from the EM field

Silly Goose

the atom from what EM field?

ACuriousMind

so the excited parts of the energy superpositions have a chance to decay by photon emission and you always end up with the lowest lying energy states (or an electron trapped in some higher state where decay rules block it from dropping down)

@SillyGoose you know that when you have an electron in an excited state, it can drop down to a lower state and emit a photon, right?

spectral lines

that's the interaction with the EM field

@Relativisticcucumber well, for starters, any "big" systems we usually model via statistical mechanics and not even a single pure state

it really depends on why you're asking this question

Silly Goose

@ACuriousMind do you mean like the ambient EM field spread in all space?

ACuriousMind

@SillyGoose Sure, "the EM field" of quantum field theory, just like "the Higgs field" or "the electron field"

Silly Goose

but i am more asking about how the atom gets into an energy eigenstate in teh first place. since we either assume it starts there (unsatisfactory) or it some how evolves in time into it by some mechanism

ACuriousMind

19:53

the reason electrons can emit photons is because there's an interaction term with the EM field

@SillyGoose I just told you the mechanism: If you start with a state that's a superposition of different energy eigenstates, the excited ones in that superposition will decay by photon emission

Silly Goose

oh

hm so QFT explains why say hydrogen atoms would gravitate towards occupying their ground state--is that a correct understanding of this discussion?

ACuriousMind

yes

Silly Goose

but it wouldn't explain why atoms generally occupy energy eigenstates (if this is the claim we are trying to make)

in that case we need another mechanism (e.g. decoherence)

ACuriousMind

@SillyGoose I'm not sure what you mean here

the ground state is an energy eigenstate

we have an argument for why atoms go into ground states, so that's an argument for them occupying energy eigenstates

Silly Goose

right right, but let's say the claim i am making is that we can only ever observe a hydrogen atom in a mixture of energy eigenstates including but not limited to the ground state

especially including non-ground states

ACuriousMind

19:57

again, if you let time pass the excited ones in that mixture will decay

Silly Goose

but it doesn't explain how the atoms found their way into an excited state i feel like

ACuriousMind

not sure why that's relevant

if you don't see how the atom could ever get into excited states, that's even better - it's always in its ground state :P

Silly Goose

well i think i am just saying i dont see how the mechanism you described explains how the atom can only be found in non-superpositions of energy states, ignoring the ground state. because the ground state situation makes sense

and keeping say temperature and so on constant

ACuriousMind

what temperature???

this is a single atom, not a statistical system

Silly Goose

it seems unlikely that all the decays conspire together to never allow mr hydrogen to occupy a superposition

oh

but in any case

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