@User198 there is a variant of this view which gives absolute answers. e.g. u attribute a hierarchy of structures to reality, and these structures are what humans discover as "approximate models".

so the structures are out there. the layers of hierarchy smoothly blend into other layers (e.g. relativistic mech blends into Newtonian mech in the $c\to \infty$ limit)

to give an analogy, i would maybe think of fractals here

the structures are out there in the fractals. deeper theories describe deeper structures

@User198 my view is perhaps that the structures that humans have come up with are maybe not "out there"

as in, these structures are how humans describe their subjective experience, instead of an (approximate) description of reality

but i am also open to the other view where physics is giving an approximate description of reality itself

@RyderRude I see. Yes. You always end up with Münchhausen trilemma in the end.

@RyderRude Like of subjectivism/existentialism? But this also is like the question: "Is math invented or discovered?".

The formulation here would be:

"Does physics describe reality in it of itself or does it just help us model our subjective experiences of the world we see around us?"

@User198 yes

@User198 yes

i think classical mech gives strong vibes of (at least approximately) describing reality itself, which is why tons of physicists still cling on to that view

but some interpretations of quantum mech (like relative collapse interpretations) are explicitly about modeling ur own observations of the world instead of modeling the universe

if these interpretations are somewhat correct, then my view would be : there is the physical entity that is you, and there is the physical entity that is the rest of reality. these two interact to form ur subjective experience. and physics describes this interface between the two

@User198 This is a bizarre question - there are infinitely many pairs of commuting operators. What do you hope to gain from more examples?

@User198 I also can't quite decipher where this question comes from. What do you think the significance of the CCR is? Like, why do we care about it?

@RyderRude Ikd, it seems like some sort of solipsism. I don't know if that direction of thinking is productive.

@ACuriousMind Ah ok. I don't know. I wanted to see some nontrivial cases of where the operators commute. Maybe see some cases that are not present in CM.

I don't know what "not present in CM" means

@ACuriousMind Some situations that are exclusive to QM, because $[p,H]= 0$ is both for QM and CM systems that are translationally invariant, so its not so interesting.

@User198 Can you give an example of a situation that is "exclusive to QM"? What does that even mean?

@User198 solipsism is an attitude.... one is acknowleding an outer reality here, so the attitude is not solipsism. it is saying that physics, at the fundamental level, doesnt describe the outer reality

but it is just a speculation. and physics at an effective level does describe an outer reality

@ACuriousMind Like related to spin

@User198 And what's your question about spin? The spin operators, depending on your system, may or may not commute with the Hamiltonian.

i am open to the other idea where reality is like a fractal and different models describe different zooms of the fractical

@ACuriousMind Ok. Thanks. I see now that my question was ill posed.

in this idea, physics, including QM, describes objective reality approximately

@RyderRude Yeah

@ACuriousMind I think that it is the defining relation of quantum mechanics that differentiates it from classical mechanics.

But now SvN theorem says it only holds for infinite-dimensional Hilbert spaces.

So I was confused what about finite dimensional Hilbert spaces

@User198 "the defining characteristic of QM" is a vgaue term. but u can look at Von Neumann postulates for some sort of defining characteristic. it doesnt reference CCR

So the conclusion is that the CCR clearly cannot be "the defining relation", right? :P

but also, Von Neumann postulates r too general imo. they also cover classical theories

@ACuriousMind Yeah it seems so. xD

I don't even really know what that means - to even write it down as the commutator of operators on a Hilbert space, you have to already have built the entire mathematical formalism of QM with Hilbert spaces and operators and so on.

Can you give some system that is described in a finite dimensional Hilbert space?

The idea that observables should be linear operators on a Hilbert space instead of functions on a classical phase space is to me much more what "defines" quantum mechanics

the problem is that even hilbert spaces and operators arent the defining characteristic of QM

see Koopman Von Neumann classical mech

i have stopped trying to get the "defining characteristic of QM". there r too many characteristics

Feynman might say interference is the defining characteristic

That classical mechanics is contained in this idea of QM as a subset does not mean it's not the hallmark of what we mean by doing QM.

some other person might say it is Heisenberg uncertainty

@User198 it's any particle where you don't care about its position but only about its spin

i personally think it is useless to get a defining characteristic. different things can be called "quantum theory" in different contexts

@RyderRude Dirac-von Neumann axioms?

and we've also engineered a lot of other quantum systems where the system can access effectively only finitely many levels

the usual description of lasers is in terms of two-state or three-state systems

@User198 yes. the problem is that they also cover classical mech as a subset of theories

i'm a bit confused about the purpose of a community wiki post; are these supposed to be questions+answers with a likelihood of broad appeal and hence contributions/edits by a large number of people?

as is usual, one can generalise ideas beyond recognition. e.g. u can define hilbert spaces with quaternions and call that "quantum theory"

so it is useless to talk about whats the most general quantum theory

@ACuriousMind Ah ok. I see. For that system (if we don't care about position) than it is obvious that $[{\hat {x}}_{i},{\hat {p}}_{j}]=i\hbar \delta _{ij}$ doesn't hold. Because we are not even considering $x$.

@qwerty They're essentially historical baggage: Early SO introduced Community Wiki before they introduced Suggested Edits, i.e. this used to be the only way by which you could make your posts editable by other people. See this from 14 years ago :P

@ACuriousMind Ok thanks.

@RyderRude Ah ok. Thanks.

some other physicist might generalise the notion of hilbert spaces and get a "generalised quantum theory"

there already exist some of these ideas

e.g. string theory is called a quantum theory but it doesnt have time evolution so far

it only has asymptotic evolution

@ACuriousMind i searched on meta and saw something like that... I suggested a question have CW status removed as it seemed super specific to that one person, but it was declined as the OP had asked for resource recs (imo naively)

@qwerty well, we have a local policy (cf. physics.meta.stackexchange.com/a/7041/50583 and links) that recommendation questions are CW, but the reason for that is only because CW posts don't yield rep

so the breadth of appeal of the question is irrelevant in that context

the D-V postulates do not require time evolution, so string theory is admissible as a quantum theory according to D-V. what is admissible as a quantum theory depends on how general ur definition is

@ACuriousMind ah, I see. thanks

it seemed in this instance that the recommendation wasn't that relevant since it seemed the op was only asking due to misinterpreting a phrase, but I guess it's not a big deal either way

@User198 optical lattices, for example, are well-described by a finite-dimensional (single-particle) Hilbert space

or tight-binding models... and so on.

@TobiasFünke Alright thanks.

I know that integrals over Grassmann variables only share the name with real variable integrals but I wondered if there is some similar enough structure to talk about a "domain" of integration, just like for the real line the domain is $\mathbb{R}$

I know that it's not necessary, I just wondered if there a way to see these two ideas as an application of a broader, more general concept

Maybe you want to think of them as basis elements of a vector space

@Feynmate You can try checking here idk

www-users.cse.umn.edu/~shifman/Berezin/Losev/Losev.pdf

That is a nice article

math.uni-hamburg.de/home/schreiber/sin.pdf

@User198 the 2d ising model (outside the thermodynamic limit)

it is a free will debate between philosophy phds

@naturallyInconsistent I think I realized why it might not matter, right before I went to bed

Because you approximate the DOS as continuous, the result you get seems to be completely independent of what the size of your supercell is

that is, the DOS is $g(\omega) = 9N\omega^2/\omega_D^3$ has no dependence on the system size beyond a multiplicative constant

of course that approximation gets better as the size of the supercell gets bigger but we're taking the approximation anyways so it doesn't matter

Professor Garret Moddel (emeritus) from the University of Colorado Boulder claims he can harvest Zero-Point energy. colorado.edu/faculty/moddel/research/… Curiously, nobody else is verifying his claims, or denying them. At least, I found virtually nothing on a quick Google search. He just got mentioned on Space.SE. space.stackexchange.com/q/67950/38535

Apparently, he's also into psi research...

emeritus engineering professors and allegedly profound physics discoveries, name a more iconic duo

haha

@PM2Ring what is this

@PM2Ring it is strange to talk about harvesting this energy. it is just an arbitrary constant u can subtract off

is it?

hiya tobiya

only differences in energy r meaningful. if everything is infinitely large, nothing is

@RyderRude Psychic stuff.

e.g. if u added an infinity to the potential energy function in Newtonian mech, it doesnt make infinite energy extractible

@PM2Ring oh

"harvesting" zero-point energy (or "using the quantum vacuum energy" or whatever) is an extremely common crackpot claim; there is really no need to debunk every instance of it separately

hi allie :)

how are you?

@ACuriousMind Sure. It's a bit disturbing seeing it on a university site, though. And coming from a guy who's been working on engineering devices using QM all through his career.

You can harvest vacuum energy, but then you're not gonna get much out of it :p

You approach the plates, they work against the vacuum pressure

Then you let them go, and that energy is gotten back

It's basically just a spring

I hear it has some possible applications in nanotech, but it's not free infinite energy

why are people so invested in the idea that the science establishment is hiding stuff and doesnt want these big discoveries to come out

@TobiasFünke im eh, gonna get my nails done and try to do some studying today i think

hbu?

i have started meditation, etc

you must be enlightened now

@Slereah Agreed.

@Allie maybe in a few years ...

@Allie Maybe they never fully recovered from learning that Santa Claus isn't real. ;)

@Allie probably the period since WWII when governments started doing Secret Research for the military

for infinite energy to be extractible, one needs a system such that the difference of energy between two of its states is infinite

then one needs to perform that state transition

i hate militaries

or one can speculate a weaker hypothesis : an arbitrary amount of energy extraction. this may be achieved, e.g., if a system has no vacuum. because it means there are states that are arbitrarily far below in terms of energy

@PM2Ring they may like the idea of conquering other worlds using MWI

lol

One cute plan for cheap energy I read in a scifi story decades ago used a device that rotates particles through the 4th dimension. Rotation shouldn't take much energy. But you end up with antimatter, which you can annihilate with regular matter to liberate a lot of energy.

Quantum foundation is cool again now because of quantum computing

To beat the chinese

Quantum computing companies just care about decoherence stuff. do they care about the measurement problem?

@PM2Ring cool

@PM2Ring is it because of CPT stuff

The latest entry on Scott Aaronson's blog is quite good. FAQ on Microsoft’s topological qubit thing

@RyderRude Yes

The important part isn't whether or not it's useful, it's whether or not some CIA spook can be convinced that it is

@PM2Ring Aaronson does good reviews

@Allie well, I wouldn't call it science establishment, but for sure governments have more or less secret research projects going on

@Allie nice. I just made some Hotteoks

is there any chance QFT computing could be a thing

like, using high energy scattering to solve complex problems

@RyderRude Practically speaking, the measurement problem isn't relevant. A quantum computer doesn't care which interpretation of QM you believe in. OTOH, David Deutsch was inspired to "invent" quantum computing because of his hard-core belief in MWI. And a lot of quantum computing people are fans of MWI.

hello party people

@PM2Ring yes. Deutsch is going around saying that not believing in MWI based on not having seen multiverses is like not believing in dinosaurs based on not having seen dinosaurs

@SillyGoose hello

@PM2Ring i think it is the influence of Deutsche. people r taking QC as the evidence for multiple universes

the very fact that quantum computing works is supposed to be evidence, when in fact it is no more an evidence than any other experiment we've had since the beginning of QM

when do people learn about renormalization group :P

i feel like i am swamped with things to learn in the next year...

hi

Right. At best, all you can claim is that it's easier to think about qubits in MWI than in some other interpretations.

@User198 PDEs are just PDEs.

@PM2Ring im not familiar with this. what is the visualisation of qubit processes according to MWI

they were saying some stuff like how the computations are being done in parallel universes. is this it

Many Worlders wouldnt agree with the above. many worlders think that parallel universes r created upon measurement

generically, random variables do not have PDFs. is there an instance in physics where we work with random variables that do not have PDFs?

@RyderRude In Deutsch's flavour of MWI, the branches already exist. See my answer: physics.stackexchange.com/a/536580/123208

@PM2Ring oh. i remember this version of MWI.

it is like stacked cards of universes that just diverge

this means that Deutsche would think of the computation as taking place on stacked card universes that havent diverged yet

do you guys know of a good reference/paper on BECs?

@RyderRude Yes

I am just curious what it means to have a BEC in real life and what people practically do to predict existence of BEC and diagnose the presence of BEC in their experimental system.

"If you take nothing else from this blog: quantum computers won't solve hard problems instantly by just trying all solutions in parallel" - Scott Aaronson

> Reasoned for 47 seconds: "The user seems really frustrated with my previous attempts. I get it — it’s important to clarify things clearly..."

Also, I don't understand the claim "phase transitions only exist in TD limit". I know the usual (mathematical) argument for this claim. But, shouldn't we (as physicists) really interpret the conclusion of the argument as phase transitions obviously exist in finite systems. taking the thermodynamic limit in theoretical analyses is purely a convenient theoretical device to emphasize the nature of the phase transition?

Or does this confusion reflect an absence of a precise definition of "phase transition" in physics?

@SillyGoose What do you mean "phase transitions obviously exist in finite systems"? Be careful not to confuse the theoretical definition of a phase (transition) with experimental statements like "a finite amount of water can become ice". Your claim is only true if from the latter observation you could somehow deduce the theoretical definition of a phase transition must have happened

Or, are we making some stronger claim that conventional statistical mechanics is only an accurate predictor in the TD limit.

@ACuriousMind Well I am more confused about the theoretical definition in the first place.

I should clarify that I am referring to the "conventional" notion of phase transition <-> singularity in free energy or its derivatives.

@PM2Ring Aaronson also believes in MWI

or at least he thinks it is the simplest thing to believe

@RyderRude Ok. But he doesn't claim it's the "true" interpretation. Or that people who prefer other interpretations are misguided.

@SillyGoose that you're confused is clear, but I'm not sure what exactly the confusion is: The definition of phase transitions in terms of singularities is only possible in infinite systems, as you've said. What is the question?

If you don't take the TD, you are just doing QM, what is a phase transition in a finite QM system? The partition function will be a finite sum of exponentials, it is analytic, only if its an infinite sum can it be non-analytic

There is empirical evidence that this is an inappropriate model of the world. Namely, I can make my system (in the real world) occupy a superconducting phase. Are you arguing that a system in the laboratory is composed of an infinite number of particles?

@RyderRude There isn't a word about MWI in any of Kaku's textbooks as far as I know, even if his popular books seem to wax lyrical about it (if he really is arguing for it)

I mean is it not a clear contradiction? TD limit = $N, V \to \infty \text{ s.t. } N/V = \text{const}$. No real world system obeys this.

@SillyGoose No, see my statement about water/ice above: The claim "I can make my system occupy a superconducting phase" is clearly false for any finite system with the theoretical definitions of "phase" and "phase transition"

How do you know that it is a phase transition instead of a very steep curve

what you observe in your laboratory is not "this thing just changed its phase"

But then why come up with a theoretical label that will never apply to any system?

To simplify things

@SillyGoose as with every model: because it can be useful

the point particles of classical mechanics don't exist either :P

Hell if you don't want to simplify the continuous into the discontinuous, you can't even assume the existence of objects

There's no sharp boundaries for matter!

@PM2Ring oh

When you have so many identical particles in a finite volume that the total energy spectrum is for all intents and purposes continuous and always will be continuous compared to the accuracy of your measuring device, you are working with a quantum mechanical system with a continuous spectrum in a finite volume, but every finite volume QM system has a discrete spectrum

Aaronson seems reasonable for the most part

@ACuriousMind Yes but we actually treat objects like point particles and call them such in the context of analyzing the world using classical mechanics.

there is no limiting procedure that we are taking. we are taking a ball as definition to be a point particle (its center of mass or what not)

@SillyGoose sure, and similarly you apply thermodynamics to systems that are "large enough" to be effectively infinite :P

but my point is that real systems are not always even large enough

I dunno, thermodynamics seems to work well enough for them :P

Go touch your stove, you will find it is for all intents and purposes continuous and the burn you get from it will be described by thermodynamics :p

i mean you expect thermodynamics to apply to mesoscopic systems?

say i have 50 bosons, i should be able to study this by taking the TD limit of the theoretical model?

depends on your definition of "mesoscopic" and what system we're talking about

I mean if you want to be fancy you can look at the process of computing the error between a discrete system of many degrees of freedom versus the equivalent system and then notice the size of the error is very smol

i mean in some sense also thermodynamics was phenomenological at first, so i would expect it to model a stove. but a system of tens of bosons idk.

@bolbteppa i saw him in a video saying that MWI was pretty much a fact

@SillyGoose there is a deep contradiction buried in what I just said about continuous spectrums above, if your measuring device can't distinguish that the spectrum is not continuous (like your eyes can't tell that the stove is not continuous) then you have to treat the system like it has a continuous energy spectrum, but this contradicts basic QM - the spectrum of a finite system should be discrete

i will link it

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".