The h Bar

Tobias Fünke

22:01

yeah I think we will never find out

@Allie haha

Allie

their belief on determinism is indeterministic..

Tobias Fünke

mhmhm yeah

qwerty, how are you doing? have you had a nice weekend? :)

imbAF

I find it funny, that in the experiment with the coin, you had already considered all the possible variables present in the even, and then "fixed" them in such a way that you force an outcome

It's funny that you think I am arguing this lmao

Tobias Fünke

I honestly do not understand what your position is

Signor Feynman

Wait wait wait. In quantum finance, the quantum coins may be...

imbAF

22:04

@Allie What about a simple thought process, that way you might get the idea. Consider a stern-gerlach device and 10 000 silver atoms propagating one after the other

Tobias Fünke

I thought you were first saying something like: the universe is deterministic but stat. mech shows/predicts that it is indeterministic. sorry if I've misunderstood you

imbAF

can you set up the event in such a way that for every atom you can guess with 100% accuracy whether it will hit the spot A or B

simple question. And we go from here

Allie

i kinda just started studying

imbAF

Ah ok

Allie

but uhhhh now youre bringing in quantum indeterminism, and i thought you believe the universe was deterministic

imbAF

22:06

So what is your answer?

Tobias Fünke

btw, imbAF, there are so-called hidden variable models

Signor Feynman

There are two fundamental problems with that: 1. It would imply solving $\mathcal{O}(10^{23})$ EoM. Impossible technically, but let's say we can somehow solve the equation, now there is point 2.

imbAF

I know, and is another strong indicator of what I want to point out

Signor Feynman

2. Initial conditions

A system with so many degrees of freedom does not exhibit a continuous dependence on initial conditions, meaning that you'd need to have infinite precision on your initial conditions otherwise, the predictions will be fucked up

imbAF

if you are able to modify the two initial conditions , then you'd be able

Tobias Fünke

22:08

well, then the answer to your question must be: depends on what you "believe". whether or not we can, at the current state of knowledge, is a different matter.

imbAF

Well the first step is that you need to decide how many initial conditions you have

ACuriousMind

Truly impressive abilities of talking past each other are on display here. It would probably help if, instead of talking in terms of examples and leaving implications, well, implied (that then the other party misinterprets), if someone stated clearly what even the topic to be discussed is :P

Signor Feynman

And then third point: 3. Stat mech makes no sense

imbAF

It makes and it doesn't

Signor Feynman

@ACuriousMind oh, just take a seat and enjoy the mess :P

imbAF

22:09

But my question stands for Allie

Tobias Fünke

+++

Signor Feynman

At some point I thought I had been hallucinating and that I was answering a question never asked

Tobias Fünke

I guess this mess is my fault. Sorry folks

I should just shut up

Signor Feynman

Tobias, you're so Japanese

Tobias Fünke

haha

Signor Feynman

22:10

You're taking the blame even if it's not yours

Tobias Fünke

well, I could've saved us from that discussion by just not saying anything. ^^

Signor Feynman

Or anyone's I guess. It's just general chaos

Tobias Fünke

yes

but the chaos called ACM hehe like a bat signal

but OK, let us make this constructive

imbAF

Would anyone disagree if I were to say that if for an event that is characterized by X amount of initial conditions/ variable, one was able to determine all these initial conditions, than the prediction of the outcome of the event would be 100% accurate. Would that be wrong to say?

Tobias Fünke

in which theoretical framework?

imbAF

22:13

suggest one

Tobias Fünke

classical mechanics?

imbAF

ok

ACuriousMind

@imbAF The answer depends on whether you are considering classical mechanics or quantum mechanics, and what exactly you mean by the "outcome" of an "event" (in the quantum case).

imbAF

For the moment let's stick to classical mechanics

Tobias Fünke

then the answer is yes (if the EOM correctly capture the physics in order to make correct predictions)

Signor Feynman

22:14

In my mental hbar scenario, I imagined it like this: since it's Sunday, ACM left the bar to go out with some friends and he let us stay, since we're regulars. Then, he forgot his wallet and came back, so he casually called us out and walked out again

Tobias Fünke

I mean: Yes, you can predict deterministically the evolution of the system from the EOM + initial conditions.

lol

imbAF

Good. Now start to increase the amount of variables. Up to what amount of initial conditions, you'd still be able to accurately predict the result? And what is the constraint that wouldn't allow you to do so, past some point?

ACuriousMind

@TobiasFünke You also have to exclude pathological constructions like Norton's dome, but yes

Tobias Fünke

@ACuriousMind true, but let's keep it easy

Signor Feynman

I hope ACM won't try to pull a Moe on us and burn the bar to get money from the insurance policy

Tobias Fünke

22:16

@imbAF In principle any finite number would be fine. In practice it fails quite early lol

imbAF

why? and once it fails what you do?

ACuriousMind

@imbAF Non-sensical question: The uniqueness of the solutions to the equations of motion does not depend on the number of initial conditions. What is the word "accurately" doing there? There are horrible equations even in one variable where in practice you can't compute anything "accurately".

2

Signor Feynman

@ACuriousMind Incidentally, I was the one to use that example this week, and now I understand the sadistic pleasure of doing it

My friend made an interesting claim, comparing it to the runaway solutions in electrodynamics

Allie

so phonons are like the normal modes in a crystal, right?

Tobias Fünke

I understand the question as number of particles. Is that correct?

imbAF

22:18

you could say so

Signor Feynman

@Allie more properly, phonons are the quasiparticles corresponding to the quantization of each normal oscillator

Tobias Fünke

I mean the number of initial conditions needed for a sufficiently nice differential equation to have a unique solution is fixed.

Allie

im not enough of a physicist yet to understand quasiparticles

Tobias Fünke

@Allie trust me, I do not either

ACuriousMind

We're getting lost in the weeds here: No one claims that there is some magical boundary of $N$ particles/independent variables for which we suddenly lose the ability to solve the e.o.m.

imbAF

22:19

But that is precisely my point

Tobias Fünke

yeah

imbAF

Because of some reasons there's a point where we we suddenly lose the ability to solve the e.o.m.

ACuriousMind

The claim which statistical physics starts from is much weaker: That you in principle could solve the e.o.m. for all the gazillions of particles in e.g. a gas if you knew the initial conditions is a worthless statement because you can't measure all the particles in the gas.

Tobias Fünke

well, a practical limit is of course the available computational power

imbAF

Yes

limit of whatever reason, whether computation or idk is the main reason why at some point

Allie

22:21

meow

ACuriousMind

There's no claim that the e.o.m. are "unsolvable" or no longer in principle have a unique solution for fully specified initial conditions, just that that's not useful if you deal with large ("thermodynamic") system, so we try to build a theory that works without us knowing the exact initial conditions

Tobias Fünke

in principle you know how the particles evolve (at least for certain models), and thus with given initial conditions you could in principle predict deterministically the system

Signor Feynman

@TobiasFünke this was funnier than I expected

Allie

hmmm

so let's say a given normal mode in a crystal is at the zero-point vibrational energy level

Signor Feynman

@Allie ignore the "quasi", then. Think of them as the quanta associated to each oscillator

Allie

22:22

we would say there is no phonon there

imbAF

@ACuriousMind Not unsolvable. Just that with the "traditional" way of doing it, by considering all the initial conditions, you cannot do it anymore. So at some point statistical mechanics come into the picture, and so does probability

ACuriousMind

@imbAF No. The claim is not that we can't solve the equation if we had the initial conditions

The claim is much simpler: In practice, you can't collect enough information to have all the initial conditions

Allie

i could, im built diff

ACuriousMind

you can't measure all the positions and momenta of the particles in gas in any practical way

This line of reasoning leads you to the notion of a macrostate, specified by much less information than the position and momentum of each particle.

Allie

youre just not good enough

imbAF

22:24

But why not?

what limits you to do so?

ACuriousMind

@imbAF How would you do it?

Allie

lol

imbAF

@ACuriousMind I wouldn't do it because in practice that is not possible

Allie

lol

imbAF

So, statistical mechanics comes into play

right?

Tobias Fünke

22:25

...

ACuriousMind

@imbAF but that's what I'm saying!

imbAF

Yes

ACuriousMind

I don't understand why you respond as if you disagree if you agree :P

Allie

and if we're in the n-th excited state of a given normal mode in the crystal mean that there are n photons?

Tobias Fünke

this is so bizarre haha

Allie

22:25

phonons**

imbAF

So, the event, contains a probabilistic aspect to it

would that be wrong to say?

qwerty

@imbAF your practical inability to measure the state of every particle doesn't make the model indeterministic

ACuriousMind

@imbAF What are you talking about? What "event"? So far we haven't said anything about probabilities.

imbAF

@qwerty but the way to measure the state, via statistical mechanics, is probabilistic in nature

ACuriousMind

I am merely establishing that knowing the full microscopic state of a large system like a gas or a glass of water is impractical, and that it is hence desirable to try to formulate a theory that can still say something useful about it without that microscopic knowledge.

Silly Goose

22:27

i mean i think a stronger argument is that you don't even necessarily want all the microscopic details if you could access them

i want to know the properties of a metal, not the individual behavior of every little constituent making up the metal

Tobias Fünke

@Allie yes. and that's basically the idea of "quasi particles": You map the excitations of the system to a system of (to first order non-interacting) particles

Allie

yay i see

Tobias Fünke

good

Silly Goose

another way of putting it is that a model should capture important details with respect to the phenomena the model is trying to model

Tobias Fünke

@SillyGoose true, but only to the extent that we are practically unable to comprehend/ use the data. If we had enough computational power, this would not be a problem at all

Allie

22:30

okay i see how this fits in with stat mech now. cuz im currently reading about thermal properties of phonons

Tobias Fünke

but you are right: it turns out --lucky us-- that to capture the physics of certain phenomena, we do not need all the microscopic details

Silly Goose

@TobiasFünke true, but there is probably a fundamental limitation to the amount that we can comprehend or process using ourselves and computers and whatever technologies the future holds

Allie

so since the normal modes are independent (in the elastic model)

Tobias Fünke

yeah

imbAF

@qwerty That is what I am trying to say for like forever. Our practical inability to predict the outcome of an event with 100% accuracy, forces our hand to use statistical mechanics to make probabilistic guesses about it (outcome). This would make it seem that events, and the universe is indeterministic in nature. But my belief is that the universe is not.

Silly Goose

22:31

in any case i think no one will use the standard model to compute where a soccer ball will land upon being kicked

Allie

could your partition function be separated into partition functions for each normal mode?

where the allowed energy states are just like the energy states of the quantum harmonic oscillator

Tobias Fünke

@SillyGoose never say never hehe

Silly Goose

heh

ACuriousMind

@imbAF If you were willing to follow the line of reasoning I am presenting, my goal is exactly to show you that statistical mechanics does not necessarily imply indeterminism.

Tobias Fünke

@ACuriousMind I am not as eloquent as you are, but I tried to do that before lol

Silly Goose

22:32

equilibrium stat mech assumes determinism in the sense that equilibrium exists in the first place ~~

Tobias Fünke

@Allie good question

It depends a bit what you mean, If you have $N$ non-interacting distinguishable particles, then the partition function is $Z_N=(Z_1)^N$

However, as you might know already, phonons are bosons, so things are messier

See my question here:

9

Q: Derivation of partition function for $N$ identical quantum harmonic oscillators

What is the partition function $$\mathcal Z^{(N)}_\beta(H) : =\mathrm{Tr}\exp(-\beta H) \tag{Z} $$ $\left(\beta >0\right)$ for a system of $N$ indistinguishable and non-interacting bosons (e.g. harmonic oscillators) with Hamiltonian $H$? Why is $$\mathscr Z^{(N)}_\beta(H) := \frac{\mathcal Z_\bet...

qwerty

@imbAF I think you're just using the word indeterministic as though it's a synonym for probabilistic, but I don't think it is

imbAF

@ACuriousMind Perhaps I need to say, that to me the fact that probability as a thing (call it what you want) exist, would hint at indeterminism. Essentially probability = indeterminism. But perhaps I am wrong on this. I wouldn't disagree. Or perhaps you can tell me what you think

@qwerty I am. And perhaps that is not correct.. I just wrong ACM the same thing

qwerty

this is what we were all trying to say at the start of the conversation with coin flipping :)

ACuriousMind

That lack of full knowledge of the microscopic state is then modeled by a probability distribution (the macrostate) over several of these microscopic states - but there is no ontological need to interpret this in terms of randomness necessarily, it is merely our subjective lack of information. We already had the example of the coin: Suppose there were only 4 different initial conditions the coin could have, and two of them result in heads and the other two in tails.

Suppose further that, in some fashion, I can obtain the information that the coin is not in one of them (let's say in one of the two that result in tails). In the absense of further information, I model my lack of knowledge by a uniform distribution over the three remaining states, resulting in a prediction of 66% heads and 33% tails.

But nowhere did I need to claim that the universe is indeterministic - still one initial condition results deterministically in one final result - it's my lack of knowledge of the true initial condition that introduces the probability.

Tobias Fünke

22:37

@Allie Oh. But you probably work with the grand-canonical ensemble? Then things are easier, but this should be derived in your textbook (?)

imbAF

@ACuriousMind I 100% agree with this

Tobias Fünke

oO

ACuriousMind

@imbAF Then you agree that classical statistical mechanics does not imply indeterminism.

Silly Goose

the partition function should still factor for independent indistinguishable particles, right? $Z = \text{tr} \exp(-\beta \sum_{\vec{k}} \epsilon_\vec{k} a^\dagger_{\vec{k}} a_{\vec{k}}) = \prod_{\vec{k}} \text{tr}\exp(-\beta \epsilon_{\vec{k}} a^\dagger_{\vec{k}} a_{\vec{k}})$ (ignoring zero point energy)

Tobias Fünke

something died inside me

imbAF

22:38

is your statement, different than mine:
"That is what I am trying to say for like forever. Our practical inability to predict the outcome of an event with 100% accuracy, forces our hand to use statistical mechanics to make probabilistic guesses about it (outcome). This would make it seem that events, and the universe is indeterministic in nature. But my belief is that the universe is not."

I ask simply because I want to know

Tobias Fünke

@SillyGoose see my question and answer above

imbAF

how did I express myself wrong

when I wanted to transmit the same message you did

@ACuriousMind 10000000%

Allie

@TobiasFünke i was more thinking of the normal modes as the particles that have a number of different energy states

rather than the phonons being the particles

Tobias Fünke

2

Q: Partition function for independent particles

I am trying to understand Section 3.8.3, "Independent particles", of Piers Coleman's Introduction to Many-Body Physics (self-study, mathematics background). He considers "a system of independent particles with many energy levels $E_\lambda$," with Hamiltonian $$H - \mu N = \sum_{\lambda} (E_\lamb...

quantum-mechanics statistical-mechanics condensed-matter many-body partition-function

see my comments there

Allie

where the normal mode "particle" can have energy $\epsilon_0$ (zero point energy), $\epsilon_1$ (1st excited state/1phonon), etc

qwerty

22:41

@imbAF cos you said earlier

1 hour ago, by imbAF

@TobiasFünke How exactly dealing with a situation where probability is present, doesn't imply indeterminism ?

Tobias Fünke

sorry if I confused you. That's why I said: depends a bit what you mean ^^

ACuriousMind

@imbAF This statement of yours sounds like the opposite: You say "this [i.e. statistical mechanics] would make it seem that events and the universe is indeterministic", which to everyone else reads as you saying you think statistical mechanics implies indeterminism.

Allie

its okay :)

but with that clarification does what i said sound correct?

imbAF

@qwerty such a situation would make it seem as if the universe is indeterministic, but IT IS NOT INDETERMINISTIC

ACuriousMind

Following that up with "my belief is that the universe is not" then further implies you think statistical mechanics is somehow wrong

I really see no way to interpret what you wrote as agreeing with me (and everyone else).

Tobias Fünke

22:43

@Allie see the link. I have to go to sleep now, sorry. If you want, we can discuss this tomorrow or at a later point

Allie

its okay. thank you!

Tobias Fünke

@SillyGoose I've posted a link above where this was discussed.

imbAF

@ACuriousMind "my belief is that the universe is not" ....indeterministic,

But, the main thing is that

I fully agree, and has been my opinion since the beginning that

@ACuriousMind This is the case

Just because something seems to be a certain way, doesn't mean that it is

@ACuriousMind

ACuriousMind

@imbAF but...it just "seems" to imply that if you don't understand what we just discussed. If you understand that, why would you say it seems that way? What's the point of that statement?

qwerty

the problem is that no one else here thought that probabilities imply indeterminism

imbAF

22:50

@ACuriousMind :D

Signor Feynman

What have you done

imbAF

hahahaha

I used my english teacher

Signor Feynman

Get ready for the sh*tstorm

2

imbAF

Nah, linguistic shouldn't be a problem now.

ACuriousMind

I'm not debating an LLM. You can dig yourself out of being misunderstood the next time you fail to express yourself in a comprehensible manner.

qwerty

22:54

@imbAF you've taken your one statement out of the context of the rest of them :')

imbAF

what?

ACuriousMind

I invest considerable time and patience in trying to get us all on the same page and explain to you where the problem lies and what I get in response is you trying to score points by invoking a bullshit generator? I'm not wasting my time on something like this again.

2

imbAF

Oh, I think you have the wrong idea. For me, being right has no importance whatsoever. The only think that has is knowledge. I posted that to show you the difference between a correct statement and one which goes tangent to say the same thing, and that even a LLM pointed it out

And the disparities

So I don't know what the mistake here is

Tobias Fünke

that whole discussion was so pointless

holy moly

qwerty

I thought you were gonna sleep Tobias :)

@imbAF that one comment by itself might be seen as the same idea as what the rest of us or ACM was saying, but given the context of everything else that we had all discussed and other things you said, that was very much was not clear to us

imbAF

23:06

Maybe

Tobias Fünke

I will now. Have a nice day/evening everyone. See you around

qwerty

good night!

rest well

imbAF

good night

DIRAC1930

23:44

PhD is getting stressful

qwerty

what's your area?

DIRAC1930

I'm not sure how you would describe it

Maybe inbetween hep-th and cond-mat

However the deeper I go into the problem, the more problems appear lol

qwerty

those seem the most represented fields in hbar currently :)

@DIRAC1930 problems with... methodology, premise,...?

DIRAC1930

as in mathematical problems to solve

Transcript for