Ten bosons you can probably do numerically :p

@Slereah okay maybe order of hundreds

I would not universally claim that "50 bosons" are well-described by thermodynamics, it's depends on what you're doing with them and what quantities you're interested in

or like small thousands

Well as I said, there will be an error between the two descriptions

And that error will depend on the size of the system

I'm sure you can find some explicit comptuation somewhere

yeah, it's just an approximation like every other physical model

I'm not sure why this is the one idealization you find inappropriate :P

When you do an actual macroscopic system, since $N \approx 10^{26}$, that error will always be nigh zero

i mean it is a very blatant contradiction compared to other idealizations

@ACuriousMind Oks thanks

Is it

Every idealization is like that

If you try to do physics in the real world with no idealization you'll just go insane :p

i mean say i want to study a system of 10,000 particles and its phase transitions. then what? the conventional theory can't say anything about it. I need to come up with a more general definition of phase transition?

All this arguing is quite pointless. Whenever thermodynamics does not work, there would be at least one appropriate quantum theoretical model of the system that will work well in describing said system.

@bolbteppa this youtube.com/shorts/Jn4SQMHAHO8?si=BRCiRoYTxfgbDpNm

Kaku is saying that the multiverse in MWI is a fact

i mean i think it just seems quite silly that the usual notion of phase transition is so narrow

It works :p

i mean it works when its constructed to work

yeah but that's true of all models

people almost never use fundamental laws to do actual computations on a real system

i mean also i was reading cardy's book on RG and it said one of Wilson's motivations for RG was to see singularities in the TD free energy without actually taking the TD limit

@bolbteppa also see this youtu.be/W39kfrxOSHg?si=9KIPSF3ptqZ3gVGU at around 2:13 when Kaku begins speaking

@RyderRude He should have said: 'QM in turn is POTENTIALLY based on the multiverse (if we buy into MWI)'

The real secret is that the proper procedure is to just do it with the knowledge that maybe the approximation will be wrong :p

Just gotta suck it up

And if it doesn't work, try something less approximated

@SillyGoose Do you really? I would just view is like this: Only in the thermodynamic limit we have sharp phrase boundaries and transitions, as you go to finite/real systems, those boundaries simply become fuzzy and the singularities merely sharp peaks (or whether else would give the singularity in the limit). You can still usefully identify the "core" of the phases by looking at the limit, you just need to let go of the idea that their boundaries are quite as sharply defined as in the limit

i mean i have become at peace with guessing the answer and checking because that's all we as people can do.

@ACuriousMind right this is okay but why not take the latter as the more fundamental notion of phase transition then

@bolbteppa yes, he shouldve said that. but Kaku def thinks MWI is fact, especially based on the second video

@SillyGoose Historical reasons, probably?

because you can't write down a sharp definition outside of the limit :P

it seems that it's just out of convenience, so that we can have a sharp definition

right but then it's not for physical reasons. it's out of convenience

yeah but that's true of many things

See "suck it up"

I don't understand the distinction you're making - all definitions are convenient in some sense or another

but that seems like a strange way to do physics :P. i mean yes if it works that's fine, but there is a clear contradiction with reality, which should be resolved.

@SillyGoose If you want to do dialectics you should move to the philosophy SE :p

That's neither strange nor a contradiction with reality

he doesnt say "potentially" in any of these. he thinks QM is synonymous with MWI. he doesnt even bother to name MWI. he just thinks QM is MWI @bolbteppa

We must do the synthesis of the contradiction!!!

We must sublate the phase transition

the romantic era of physics begins now

@RyderRude None of his textbooks explain what MWI is, his QFT book introduces normal QM, and then he 're-does it' assuming a Feynman path integral starting point, this is not MWI, it's possible he has just convinced himself that MWI makes sense but he's never explained it mathematically or where it comes from

As I said, if you start going down that route, you'll just go insane

You can't talk about a "ball" in a physics problem of a falling ball because what is a ball

There's no sharp boundary of that object!!!

It is merely falling off quantum fields

@bolbteppa it is because no one knows what MWI is mathematically. it is all fluff :P

how do u define a world or the world duplication

i mean but it begins hard to disentangle "idealization" from "making a wrong assumption so as to close yourself off from what is really going on"

There is also no sharp boundary if you want to define the image charge distribution on a metallic surface that is trying to do classical electrodynamics

@SillyGoose What's the difference

@bolbteppa but Kaku surely believes MWI, however vague MWI is

if one makes an idealization one should understand the consequences of that idealization: what it closes you off from.

so the presence of knowledge of what you are doing is the difference i guess.

Sure but there are thousands of approximations you do in physics all the time :p

And what does the idealisation of phase transition being mathematically defined this way closes us off from whatever physics is involved?

Maybe I will use gpt to think about the Everett paper a bit more and see if it can make sense of my serious issues with it which I doubt

I mean you should be aware of it, sure, but no need to get worried about it

@naturallyInconsistent i mean i just wouldn't expect it to adequately model phase transitions in a mesoscopic system

> It's a very difficult challenge to avoid all the ingredients we’ve already mentioned.

where mesoscopic is suitably defined so as to evade being microscopically tractable and being in the regime of modelable by TD limit

@SillyGoose do you have an example of a system where you see something that is a "phase transition" but where the thermodynamics approach does not work?

@bolbteppa i think ur love for Kaku is outweighing ur love for the Copenhagen interpretation :P

@ACuriousMind I mean I would say a BEC, but I think BEC is not considered a "phase" but I think it's not considered a phase because of the usual definitions being defined how they are.

i never thought u would consider any other interpretation

I would love to see him actually try to justify this mwi stuff, maybe he has done it somewhere but I really doubt it

Relevant :

@bolbteppa it is just the usual justification. if the cat goes into a superposition, the superposition must mean two cats exist

@SillyGoose I dont even know what you mean by "phase transitions in a mesoscopic system"

MWI has never been precise

@SillyGoose see e.g. physics.stackexchange.com/q/512457/50583

@bolbteppa in the second video, Kaku says exactly that about electrons being in two places at once

To me it sounds just as if you're complaining that the theroetical definition of "phase transition" does not match your intuitive/colloquial idea of what a "phase transition" should be

that's unfortunate, but it's not really a problem with the physical model or a case of people making "wrong assumptions" or anything like that, it's just that the terminology is different from how you want to use it

i mean it doesn't make sense, especially in the context of physics :P

what doesn't make sense?

> The defining feature of a phase transition is behaviour that jumps discontinuously as we vary β or B. Mathematically, the functions must be non-analytic. Yet all properties of the theory can be extracted from the partition function Z which is a sum of smooth, analytic functions (5.193). How can we get a phase transition? The loophole is that Z is only necessarily analytic if the sum is finite. But there is no such guarantee when the number of lattice sites N→∞.

> We reach a similar conclusion to that of Bose-Einstein condensation: phase transitions only strictly happen in the thermodynamic limit. There are no phase transitions in finite systems.

From Tong's notes

so tong would say that Cornell, Weimann, and Ketterle did not produce a BEC?

No, that is not the correct implication to take of that quotation.

He understands when experimenters claim that they have made a BEC, that it is sensible and true.

Whatever does not make sense, lies only in your head.

@SillyGoose Again, no one claims ice isn't different from water just because you don't have infinitely much water and hence no phase transition could have happened

@naturallyInconsistent I mean then it just points out the stupidity of the definition.

we've already been over this:

even in the continuous limit you can have a continuous path between the two via the super critical phase :p

i mean so you are claiming that you can produce a BEC without going through a BEC phase transition? when a BEC phase transition is the defined transition you go through from being a non BEC to being a BEC?

also really, as a general principle

obviously we extend the definition of these phase in terms of state variables then down to the finite systems, and when the system is in a region of state space where, in the thermodynamic limit, it would be in a certain phase, then we name that region of the finite state space the same

yes for water you actually can just go through the super critical phase

Discontinuous transitions are always fake in physics

It's always just a very steep curve

But if you treated every curve as a continuous function in physics you'd just be solving nasty PDEs all day

So sometimes you have to pretend they're just tophat functions or whatever

@SillyGoose I am claiming that you can produce a state of a finite system that, to a very good approximation and for all practical purposes, exhibits the properties we would attribute to the BEC phase of the corresponding infinite thermodynamic system. By abuse of notation/terminology, we also call that real-world finite state BEC

yes it's an abuse of terminology either way is all I am saying

but you always do this kind of approximation in thermodynamics, otherwise you couldn't even attribute temperatures to finite systems

the terminology if interpreted literally is just flat out contradictory

There is no contradiction

It is purely you being unhappy irrationally so of the definitions

The definitions are perfectly fine and workable

That's why they are universally agreed upon to be good definitions that all textbooks take

It is a perfectly sensible physics manner to deal with a physical situation

and now imma let it go; it is time to sneeppuu

@ACuriousMind in some sense, the fact that it's not ideal is what makes real BEC special. For example, superfluid properties only arise because of that :P

@Feynmate No, the idealisation is only helpful in giving concrete definitions of physical phenomena that we all recognise. It doesn't make any real phenomena any special just because they aren't the idealisation

@naturallyInconsistent an ideal BEC has zero critical velocity, in constrast to a real one (because the dispersion relation is not free). Zero critical velocity means no superfluidity

there we go

@SillyGoose it's the only way to do physics. Taking a step back, you are arguing against the idea of using idealised models and limits to capture the essential features of physical phenomena

@fqq i am only arguing for this particular case. i don't mean to generally attack all idealizations.

exactly, it's not clear why you are so hung up on this particular case, when it's just how all of physics works

@fqq last year we joke about Amadeus but no jokes about Carlo Conti this time?

everything you say applies to the unitary evolution of isolated systems, to point particles in classical mech etc

Imagine if Carlo Conti handled the chats of the hbar

i mean in those cases it is always clear that you are approximating and in what regimes the approximations are valid.

I hate the path integral formalism

I think I've posted this some time ago already, but nvm:

how can you "approximately have a singularity in the free energy"

it literally is not possible

a singularity is there or not, it is a very discrete thing

@Feynmate I managed to avoid exposure to sanremo almost entirely this year, except for some second hand memes. Until last night, I was at a party with mostly italian people and they started talking about it and putting songs on

from what I gathered there's less "interesting" stuff to talk about with Conti compared to Amadeus

i mean also it's more reasonable to talk about the "idealized X" versus the "real X", not just define the "idealized X" as "X"

which is actually what is done in other cases

@fqq me too, but Carlo's memes are so funny, even though the joke is always the same

i mean the problem is that people want a nice short and sweet definition that is catchy for a phase transition. real life is more complicated than that. i don't see why the situation is not accurately summarized as this.

???

what do you mean. it is clear that e.g. the thermodynamic is a mathematical idealization

and so is (often) assumed periodicity of solids and so on

i mean i'm not sure if my point is really being communicated

philsci-archive.pitt.edu/8340/1/…

@SillyGoose it seems not. would you want to try one more time?

the point is that the TD limit is a mathematical idealization. the phrase "phase transition" by definition is a mathematical idealization. hence, the phrase "phase transition" cannot ever be applied to a real system. this points out the fact that the definition of "phase transition" should be appropriately extended from its mathematical definition, so as to actually refer to real life examples that are unanimously agreed to be "phase transitions".

what you say can be transferred to any other technical term, no?

now replace "phase transition" by "point particle"

exactly

other people in the chat are claiming, yes! indeed you do extend the notion of phase transition. but then the claim "phase transitions only occur in the TD limit" is false.

i mean the correct definition should be the more general one (as it actually applies to real life!). it seems misleading to actually claim that phase transitions only occur in TD limit.

ah yes let me go in my lab and take the TD limit of my system...I mean that is ridiculous

but point particles are not real. people use phase transition to actually refer to real things happening in the real world

you are clearly mixing up two aspects

@SillyGoose yes. and solids are real too

but they are not periodic either

and finite

in intro solid courses you still assume perfect periodicity

and this describes quite well certain aspects

or even more so, you describe the electrons as non-interacting

i mean then ACM's response is invalid. they are not equivalent situations. there is something in the real world that people refer to by the name phase transition. there is not the same idea for point particles.

real-life electrons are interacting, though (if you believe in electrons ;))

@SillyGoose There are two senses in which the word "phase transition" is used - as a mathematical definition that makes only sense in for infinite systems, and as an operational description of a real-world process that has approximately the same properties as the mathematical definition. Similarly, the word "particle" can refer to the mathematical idealization of a point in mechanics or to a real-world object that is approximately described by the properties of the point particle model.

@ACuriousMind yes i agree with this exactly

That is, yes, there is a tacit confusion of terms here, but it's exactly the same confusion of terms as with every other idealization

i mean would you agree that operational phase transitions happen in real world systems

they happen in the same sense as there are point particles in the real world

that's just how the terminology is set up

you could have chosen to call the real-world process "phase transition" by definition (though it is hard to imagine what kind of definition that would be) and then the mathematical thing in the infinite limit something like "ideal phase transition"

it seems this is the definition you would prefer, but it's not how the evolution of the subject has happened

it's just words, you're not disagreeing with anyone about anything in the actual physics

i mean i am disagreeing with the claim that "phase transitions only happen in the TD limit". i would qualify it by saying that "perfect phase transitions only happen in the TD limit" and the statement becomes a useless triviality.

@SillyGoose yes, but that's only because you insist on using the term "phase transition" differently from how the established jargon works

you're not disagreeing with what that sentence is supposed to mean

yes but why would anyone ever say that? it carries very little if any at all physical content

otherwise you get students computing things for finite systems and complaining they don't see the free energy diverge or whatever

I don't really get why you hate that statement so much :P

because it is incredibly misleading :P

no it is not

maybe for you, because for some reason you have some sort of "expectation" what phase transition means.

and don't get me wrong: I guess it is natural and everyone has such a thing with possible other terms

i mean such a physical concept should be rooted in reality. everyone should come in with an expectation with what phase transition should refer to, by observing phenomena in real systems, no? this is not some crazy idea like quantum mechanics. it is something that you can literally (in some cases) observe with your eyes.

what do you mean? I can also talk about the mathematical structure of Newton's equations, where I can also observe the consequences, but this is "high-level" mathematics, where complicated definitions and concepts enter.

the success of math/theoretical physics comes from abstracting things

and making things precise

but this isn't making things precise. it is trading off accuracy for tractability, which is what I see physics as doing.

in abstracting a physical concept, you necessarily lose information.

you just have to ask if the tractability you gain from the abstraction is worth it.

OK. Let me ask you: How do you define phase transition?

Without vague terms

in the framework of stat. mech

It would necessarily be vague

and imprecise

but that is the nature of the physical world. I never claimed that defining phase transition is easy.

> "Every mathematician knows it is impossible to understand an elementary course in thermodynamics." - V. I. Arnold

@Slereah i think physicists might say the same ;)

OK

But don't you agree that it can be helpful to have precise definitions?

I mean i think I will hopefully be reading more about phase transitions in mesoscopic systems this summer...so maybe I'll have more formed thoughts then

I agree it is necessary to abstract. It is also useful to re-examine the abstractions and see where they would break down.

When doing thermodynamics/stat. mech, there are a lots of (more or less implicit) assumptions going on, and no real system will (most probably) satisfy all of them...

and as I've pointed out, this is basically always the case also in other or related fields

when you do QM and say "time-evolution is governed by the TDSE" then you could also claim: "No, wrong, a real system is not in isolation" and so on...

we make models, perhaps highly idealized, and then hope that they capture enough "physics" to be useful

Students will tend to drift off if you start telling them the most general theory possible :p

@TobiasFünke i mean but people acknowledge this and then take appropriate measures (e.g., accounting for decoherence and etc.)

take the appropriate measures that they can take (as in using the available resources, e.g. physical theories, available)

yes. but where is the difference to the phase transition case? people know that real systems of interest in stat. mech are finite and so on

as I've mentioned: in thermodynamics you abstract away sooo many things of real system; still it is applicable and useful in many cases (and part of its success and universality is in particular due to the fact that you do not care for the microscopic particularities)

I think that physics has fried my brain. I was studying Japanese grammar and I found myself writing "the action of i adjectives on nouns..."

I turned grammar into rep theory smh

hehe

Does anyone watch Stand-Up Maths on Youtube?

meow

@Feynmate I have been recommended a number of YouTube videos by a woman who teaches Japanese in Italy and it always reminds me of you :p

@qwerty I'm flattered but I assure you that I don't look like a Japanese woman :P

The real question is: why do you have her in your feed?!

@Feynmate haha I don't know! the algorithm is random sometimes. maybe because the first one was a cooking video