@TobiasFünke i hazard a guess that almost all literature, textbooks, etc. do not use crystal clear definitions of what exactly it meant :)

@qwerty weinberg's three volumes are supposedly very thorough and logical (relative to alternatives).

Working with the Ising model I'm used to an Helmoltz energy that depends on the magnetic field $H$ and a Gibbs energy that depends on the magnetization $M$. Now, working with thermodynamics and magnetic work, I'm seeing the opposite. The Helmoltz energy depend on $M$. ($HdM$ work) and the Gibbs energy on $H$, i.e. the opposite. Why?

I mean why are the roles inverted, I know it's a Legendre transformation

@SillyGoose well, but arguably the situation is much better than in public outreach talks, podcast or w/e

and then again: if someone wants to criticize, say a new concept/definition in a specific paper, one can write an answer to that paper or a new paper etc. that's scientific debate. people have background knowledge, people know the state of the art, and can relate concepts.

...and in textbooks the situation is indeed a bit different (than, say, in journal papers) because if they are intended for students, then as I've already noted above, there is again some simplification at work, like in basically any teaching situation. That is, per se, nothing bad; it is rather necessary

@HerrFeinmann I think there are some threads on the main page about this, no?

@TobiasFünke surely/ime it would be extremely unusual to write a whole paper just to criticise a definition, and such a work would be unlikely to make it past peer review. at best, it would a be a small remark in some future paper.

@qwerty yes, it is an answer to a paper (there is a specific term for that; I've seen this alot)

and whether or not it will be a whole paper or how much response it needs depends on where the original paper was published and what it claims, for sure.

hmm. maybe condensed matter is different. i got the impression you grate on peoples' nerves to point out their small mistakes or wording, and people do not seem to see it as a big deal

no, I meant a serious flaw with implications on, say, predictive power etc.

ah. I thought we were still talking about the sort of nitpick RR was mentioning originally, like saying "QM is linear".

@qwerty no, not really. although I would bet one would not see such a statement in a paper without further context

One example I can give is e.g. the Boltzmann factor of $1/N!$ and the relation to the Gibbs Paradox. There are plenty of papers discussing the origin of this factor and the "paradox", and relate to other work, especially regarding the notion of "indistinguishable particles", and whether or not QM is really the reason for that factor (and cite e.g. books claiming so, criticizing them)

and actually I think this is a good example. IIRC, already Gibbs had the correct interpretation, but with the advances of QM it got lost, and people just wrongly used QM to introduce this factor; plenty of textbooks are full with this. So in this sense RR was correct: "experts can be wrong, too" (without a doubt), and it was not so long ago that people in the field starting to correct this

i sometimes see sloppy things in papers, or maybe just inconsequential mistakes, and sometimes it seems like the quick way to annoy people is to point it out. or there's papers with mistakes floating around, even more consequential, and it's an "open secret" that it's there - but the author just never fixed it

of course, everything I've written above was oversimplified ;), but I hope you get the point

and I can just reiterate: how much time you spend defining a concept also depends on the audience. If I write a paper on the foundations of entropy, I rather have a clear mathematical definition and conceptual interpretation (which then could be criticized); which is necessary for discussing further problems. In an educational paper for chemical engineers (random example), I don't have the same standards in "precision" as in e.g. a paper in a journal about the foundations of stat.mech/TD

some academics do not seem to care too much about fixing their published mistakes, or draw attention to them - some more than others. even on papers that are well-cited and intended for pedagogical or reference purposes. i find it academically/intellectually dishonest, but at least in the field I was working, it seemed to be somewhat accepted.

@qwerty hmmh yeah I agree. Correcting mistakes is important

Especially if these are important for reproducing the stated results

well, I guess in the cases I am thinking of, it did not seem to spark a whole field using incorrect results, as in your example. there were enough other sources with the either the right results or the right implications.

mmhm

hi

hey

well, as I just stated, I also saw a lot of small comments (from other authors) or corrections (the same authors) as responds to a paper (in a critical way) published in the same journal, but I cannot give an exact example of this. I'd say it is common practice, but maybe I am too naive there...

@TobiasFünke this is the kind of mistakes I was referring to

i think experts can sometimes have wrong ideas about the basics because they haven't thought about it enough

or maybe it wasn't taught to them

could be true. but this is, I'd guess, not the standard and does not happen everywhere and everytime

they r right about most things. so it is rare

but i would say everyone overlooks at least one idea. especially the ideas that r somewhat at the borders or outside their expertise

and in my example I gave, everyone agreed on the same factor; it was just that the reason for introducing this was wrong or not complete, and did not include all instances where the introduction of this factor leads to correct results (think of Milk molecules, which to some extend are all distinguishable in principle, but still one uses the corrected entropy, roughly speaking).

sure, physicists are (for now) only humans. but again: I wouldn't take public outreach as a reference.

yes, experts rarely get the facts wrong. like the factor here

but they may get broader ideas wrong, which is what ur example showed

@TobiasFünke are there? Could you link one to see if it's what I'm asking?

@TobiasFünke the reference i gave was a physicist meet-up. it is not supposed to be for an outsider audience. but they happened to upload it

@HerrFeinmann sorry, this was only my vague memory

@TobiasFünke also, many particles physicists would think that the Hilbert space of interacting theories is like that of free theories. They overlook it because it is not relevant for practical purposes and they don't expertise in mathematical physics

similarly, many physicists may think of tensors in terms of their components instead of as the abstract thing

some physicists may be unfamiliar with the PVM formalism of measurements

@HerrFeinmann I mean: What exactly are you asking? You want an interpretation for this fact, or what?

it is because they don't expertise in this stuff

@RyderRude this shifts the discussion, because in all of your last examples, I would not call them experts (in this particular subfield)

an expert would almost certainly never have incomplete knowledge in the field they expertise in, yeah

they may handwave some other ideas, which they don't expertise in

but I guess my point was about experts being able to overlook basic things in even the field they expertise in

which I would not defend too much now i guess

i think this is a more appropriate example

neither could communicate their ideas to the other

like, each expert thinking that the other expert doesn't know the basic stuff

and they had even communicated before the debate too

it is this debate youtu.be/883R3JlZHXE?si=epY1VsLkoWbVIvdE

related to this, there is also a lot of confusion in academia that Bell's theorem is somehow about free will and counterfactuals. this confusion is what showed in the debate

@TobiasFünke more like I want to understand why it's different. Different definitions of magnetic work?

for a starting point

bingweb.binghamton.edu/~suzuki/ThermoStatFIles/…

this

but the rough answer I'd give without thinking too much is just what you've said; $F$ and $G$ are related by Legendre-Fenchel transformations, and are functions of different physical quantities, so they describe different experimental situations

should be the same situation with mechanical work

@TobiasFünke I think I didn't explain well. I meant that in the context of Ising models you have $F(T,H)$ and transforming $G(T,M)$. In other cases $F(T,M)$ and $G(T,H)$. My point is that the independent variable of the Helmoltz energy is sometimes $H$, sometimes $M$

Of course the Legendre transformation will give a function of the other but that's not the point

then both links I provided should explain the reason for that

I think the reason is the division into system and field/environment

Okay, I'll read both when I get home. Thankies

(I think so too)

there is a nice book by P. Dongen (Statistische Physik), which however is in German. It has a nice appendix regarding that issue

and anyway the book contains nice things not found in too many other books about intro stat. mech... unfortunately I cannot share the joy with you haha

two references it gives: "The thermodynamics of magnetization", by E. Guggenheim and "The thermodynamics of bodies in static electromagnetic fields", by V. Heine

Physics has no language, my friend (if I read that appendix I'll bother you all :P)

haha ok. maybe AI can help by translating the PDF or so

@HerrFeinmann The real thing is that every time you bring in a new pair of conjugate variables into thermodynamics, where one of the pair is extensive and the other is intensive, you are making every pre-defined thermal state variable bifurcate into two new ones, one with each half of the pair. Even up till today, there is a war on the magnetic versions of the thermal state functions, and it is better to just be clear which one is being used. @TobiasFünke

yes

@naturallyInconsistent I like this explanation. It is very general. Thanks

@qwerty Weinberg is very good but very idiosyncratic - I recommend it but not as the first thing on QFT you read since it will make conversing with other people about it difficult if you only know "the Weinberg way". It's also got notoriously cluttered notation

Is this a normal thing to do? $$\frac{d}{d \lambda} d x_\mu = \frac{d^2 x_\mu}{d \lambda^2}d\lambda$$

$\frac{d}{d\lambda} \left( \frac{d x_\mu}{d \lambda} d\lambda\right) = \frac{d^2 x_\mu}{d \lambda^2} d\lambda + \frac{d x_\mu}{d \lambda}$

What happens to the last term

oO where did you encounter this?

that is extremely cursed notation (starting with having the coordinate index on the coordinate be lower) and without context it's impossible to tell if it's doing something that's correct weirdly or whether it's nonsense

Page 79 of the pdf but page 54 of the book strangebeautiful.com/other-texts/schrodinger-st-struc.pdf

The RHS of the first equation

oh, it's supposed to be the geodesic equation but "times $\mathrm{d}s$"

I guess it's par for the course for physics math :P

Pg 75/76 of this book does something weird as well profmcruz.wordpress.com/wp-content/uploads/2018/02/…

Oh I think it's just a Taylor expansion

the subjective experience of animals also behaves according to physics rules, but animals lack the ability to actually come up with physics

this means that physics is there regardless of whether or not anyone chooses to or is able to write it down

so physics is more fundamental than the ability to describe physics

or the ability to describe anything. most animals lack anything resembling a language

consider this : an animal (e.g. a bat) fundamentally lacks the ability to comprehend the notion of operators or differential equations or Hilbert spaces

but the subjective experience of the animal nevertheless behaves according to rules that are given by these mathematical objects

this also means that humans not only have the ability to experience physics but also to describe physics

and it is mindblowing that humans are able to get a pretty much bijective map between between the description and the experience

we haven't encountered a phenomenon that seems to be outside the limits of description

while there are open problems, it is generally considered that they are solvable via the usual process of modeling

this means that humans have just the right amount of ability (if not more) to be able to describe their experience

if the bohr and van leeuwen theorem exists, how does it make sense to study classical e&m?

@Relativisticcucumber If Bell's theorem exists, how does it make any sense to study classical mechanics?

so is electromagnetism in media non-relativistic?

In my EM course, we used a simple model of a dielectric, which gave rise to a non-local in time electric displacement field. As Slereah stated yesterday and De Witt also, this field is then not possibly relativistic?

@ACuriousMind Bell's theorem says no hidden variables, right? so this just helps narrow our idea of what quantum mechanics can actually be? but it doesn't negate a field that we actively study, no?

:66860724 my statement is unrelated to the cucumber

@Relativisticcucumber Bell's theorem states that classical mechanics cannot explain the results of Bell-type experiments, just like the Bohr-van Leeuwen theorem states that classical statistics + classical EM cannot explain non-zero magnetization of materials. I think it is obvious no one thinks this invalidates classical mechanics generally as a field of study, so I wonder why you seem to think the BvL theorem would generally invalidate classical EM as a field of study.

@ACuriousMind maybe im making an inaccurate jump. A&M says that "a theorem of Bohr and van Leeuwen asserts that no properties of a classical system in thermal equilibrium can depend in any way on the magnetic fields" so my two jumps are 1) tmu we always assume systems are in thermal eq and 2) classical e&m studies magnetic fields and how things respond to them (also electric but that's irrelevant to this) so e&m seems to be precisely [...]

[...] the study of how classical systems depend on magnetic fields so this seems to be in contradiction

@SillyGoose To me all this seems to say is that your simple model is not relativistic.

That's a very different statement from "electromagnetism in media" not being relativistic

but I think we usually don't shoot dielectrics across the room with high velocity so it's okay :P

@Relativisticcucumber all the systems you normal study in EM are not "in thermal equilibrium", they are just not statistical systems

the antenna that radiates an EM wave or the current in a solenoid are not systems "in equilibrium", the concept doesn't really apply to them and even if it would plenty of them - like the radiating antenna - are obviously variant in time and so not equilibrated

hm ok so the theorem just doesnt really apply here?

@ACuriousMind hm but at the least is poincaré symmetry generically broken in media?

@SillyGoose Sure - a lattice is not Poincaré invariant under any transformations that put a lattice point where there wasn't a point before, the symmetry groups of lattices are discrete

so the punch line of this theorem is that classical physics cant model magnetism, right?

@Relativisticcucumber classical physics + stat mech cannot.

@Relativisticcucumber It can't model magnetization in systems in thermal equlibrium. Magnetism from currents still exists classically.

the theorem is a statement about statistical, classical mechanical systems.

Instead of being the wide-ranging blow you seem to think it is, it's rather a very specific statement that affects mostly stuff like us being classically not able to explain how permanent magnets stay magnetized "forever", i.e. in equilibrium

but since we can't model what's going on in a material classically anyway (all these little electron loops acting as currents should just fall into the nuclei with time...) I don't see this as particularly worrisome, it's one of the many things that goes wrong if you try to model the microscopic world classically :P

hm i guess the symmetry group of a system is a separate thing from whether the framework being used to study the system is relativistic or not

Of course - almost all classical systems lack rotational symmetry (and hence full Galilean symmetry) yet they happen in Galilean spacetime :P

@ACuriousMind ah darn i think i see now

hm so i guess wigner's classification is just physically abstracting out of everything and considering what the possibilities are in vacuum as constrained by relativity

@SillyGoose The idea of Wigner's classification is that different inertial observers should not disagree about the number and kinds of particles that exist. Hence any one-particle space must be an irreducible representation of the Poincaré group. It doesn't say anything about vacuum or not or whether the Poincaré group is a symmetry or not.

It really is completely orthogonal to any interactions or systems those particles might find themselves in

@ACuriousMind what justifies the first statement that you made?

@SillyGoose It would be pretty strange if we lived in a world where I could put an electron into a box and some other inertial observer saw me putting a muon into the box instead

@ACuriousMind Sure, but to me the more dubious of the two is that the number of particles that exist must be the same.

It is also a statement that seemingly cannot ever be experimentally proved

@SillyGoose It would be similarly strange to me if they saw me putting 2 electrons into the box instead

Is there a way to abstract this away from human observers?

or, more viscerally perhaps, if I could trap an electron in a trap and just by sending with a rocket somewhere suddenly there would be two electrons in the trap

without anything happening to the trap except that it is now in a different inertial frame?

Sure, but isn't the entire point of relativity that things once held dearly as being "constants" are now frame-dependent?

I would much rather consider the whole point that there are certain things - the "proper" quantities - that can be talked about frame-independently

the physical idea of Wigner's classification is that it is a good guess that the number and species of particles is such a frame-independent thing

and given that the irreps are precisely classified by the properties we associate to a single particle, namely mass and spin, I would say that guess was indeed pretty good

Funnily enough even so QFT - slightly extended beyond inertial observers - still predicts that non-inertial observers will see Unruh radiation emanating from the Rindler horizon, i.e. we do get that different observers will see different particle numbers if we drop the condition of being inertial.

But if inertial frames differed in the number of particles they saw, then this would give us a way to choose a preferred inertial frame (or at least some preferred frames, e.g. those in which the number seen is lowest)

Hm I would like to learn about the Unruh effect.

Separately, is it a true statement that photons can never have longitudinal polarization?

In classical EM, electric waves can have longitudinal polarization in media. So, I was wondering if photons in media can also have (or at least effectively have) longitudinal polariation?

@SillyGoose There are quasi-particle states corresponding to a longitudinal EM wave in media. Those are not the "photons" the statement is about. The more unambiguous way to say it is to say that massless spin-1 fields/particles cannot have longitudinal polarizations. The quasi-particle states associated with the longitudinal EM waves in media have mass.

One way to see it is Wigner's classification, see this answer of mine

(and if you press me for a demonstration of the mass of the quasi-particle, I would have to admit I don't have any - this is beyond my rather superficial CMT knowledge, my assertion is purely born from my trust in the very general absense of longitudinal polarizations from massless vector fields)

Slightly annoying that all the nlab nomenclature for cohesive topos is based on extremely obscure cohomology stuff

From the names you'd think that "sharp" and "flat" mean the opposite of what they mean

But they're about flat cohomology and sharply varying principal bundles

when has one destroyed too much

In 5.2 it is implied that $\frac{\partial L}{\partial q_i}\dot q_i = \frac{d}{dt}(\frac{\partial L}{\partial \dot q_i}\dot q_i)$?

Is it perhaps wrong?

And finally, how is equation 5.7 derived, when we consider the variation of the Hamiltonian?