The h Bar

01:55

@SirCumference That is actually not how things work. Even in English you can see that 4chan ppl basically speak their own language that is incomprehensible to others. Language siloes basically only speak to themselves and rarely venture out to consider what other languages are talking about.

@SirCrackpot In the most trivial case, $s$ could simply be the "starting position" along the geodesic itself, so that $x(t,s)$ actually only describes one single curve and no more.

Do you accept caustics as an example of parametrisations breaking down? Like, the phase space curve that separates pendulum swinging back and forth and pendulum always going around in circles has indetermined points that theoretically take infinite time to reach.

@Loong It is always very funny standing around these guys and hearing them make correct deductions and conclusions from complete messes in verbal reasoning that jumble these up.

Sir Cumference

03:35

@naturallyInconsistent I mean 4chan is a different breed

But in seriousness being able to easily exchange ideas and words across the entire planet is a pretty new thing (on this scale)

I feel like that'll significantly change how languages and cultures develop over time

naturallyInconsistent

05:37

@SirCumference but that is just how people are. They get trapped in their bubbles. The alt-right incels essentially speak their own language, where in their topsy turvy world, women do not have basic human rights. The far left splinters into so many tiny little cliques of their own. I can UwU with them but I am not sure what else they are thinking about. Scottish English might well not be able to communicate with Nigerian English. I think this is normal.

Sir Cumference

@naturallyInconsistent I feel like the groups you're referring to are pretty known for being close-minded though

naturallyInconsistent

@SirCumference are you sure you are not yourself closed-minded about the highly fantastical? miehehehe

Sir Cumference

that's possible lol

granted I don't think incels and some 4chan users really fit in with most of society to begin with

my thoughts were mostly considering the average joe

naturallyInconsistent

But they exist, and in large enough numbers, though just the few percent of the population that they are, to swing elections

Sir Crackpot

@ekardnam_ yeah sure, I used "" for that. I meant that it might be something full of holes, in a pathological sense so that it's not even a manifold

Sir Cumference

05:45

well, that is true

nutty people tend to be more passionate and vocal about their beliefs

so they push them more than sane people

naturallyInconsistent

@SirCumference are you insinuating that my vocal political activity to push for better teaching on physics and maths is insane? How DARE you!

Sir Crackpot

@naturallyInconsistent Caustics break down because geodesics intersect, don't they?

@SirCumference oh god, my username is not a joke anymore

naturallyInconsistent

@SirCrackpot dont ask meow meow about technical details like these. I won't even trust my own answer on that.

Sir Cumference

@SirCrackpot well it is fairly commonplace to see crackpots going on long tirades :P

anyone remember this guy?

The stackexchange SUCKS and John Rennie is an ASShole

►

I guess this highlights the downsides of increased communication, we come across nutters on a more frequent basis

naturallyInconsistent

@SirCumference I do not think that this is at all a problem. I think the problem is only that nutters get a bigger chance of seeing each other and supporting each other to go into yet more nuttery.

Sir Cumference

05:55

that is an interesting point

Sir Crackpot

06:05

@SirCumference I laughed so hard reading the title that I struggled to make a voice note here

Shashaank

Hello Guys

What exactly is entropy? The heat available to do work or the heat degraded amount of heat?

Sir Crackpot

There are several notions of entropy

Shashaank

If entropy is the degraded amount of heat ( useless form of heat ) why does the Clasius inequality hold, shouldn't dQrev/T <= dQ/T as heat gets utilised more in a reversible process?

@SirCrackpot and that is confusing :-(

In an other question author points out entropy as "heat rejected" which is quite against how Clausius defined it, Please clear this confusion

Silly Goose

that sounds like an inappropriate definition

Sir Crackpot

@SirCumference I won't watch that video but the comments alone were enough to get me enraged

Shashaank

06:11

@SillyGoose Can you correct me please

I have an exam tomorrow and I am unable to get over this entropy

Sir Crackpot

@Shashaank Regardless of who is the user helping you, you should provide these statements with a source. It sounds too generic to answer

Sir Cumference

Nov 30, 2016 at 11:55, by John Rennie

@SirCumference That's going to haunt me for the rest of my life :-)

Shashaank

A textbook of Chemical Engineering Thermodynamics - K V Narayanan

I want to know what exactly is the definition of entropy

Sir Cumference

@SirCrackpot The video's pretty entertaining lol

John Rennie

@SirCumference It still makes me laugh eight years later :-)

3

Sir Cumference

06:14

good times

Silly Goose

this is what i take to be the definition of entropy in the context of an undergraduate course in statistical mechanics

Sir Cumference

information theoretic entropy is the way to go

Silly Goose

Shashaank

But what is entropy if you don't know anything about microstates? Is the useful heat available or the useless form ?

Silly Goose

and then here is my definition of macrostate

Shashaank

06:16

Yeah..

Sir Cumference

entropy is basically a concept that originated in physics and later on we gradually got a better idea of what it's all about

which leads to the information theory definition

Shashaank

So entropy doesn't have a precise definition without information theory?

Silly Goose

@Shashaank i see entropy as a function which gives you all thermodynamic quantities of interest in the microcanonical ensemble

Sir Cumference

@Shashaank well, information theory is pretty much just a branch of probability theory

Silly Goose

all of this doesn't sound very helpful for your circumstance, though

Sir Cumference

06:17

entropy there kind of characterizes how uncertain you are about a set of outcomes

in the scope of thermodynamics, it roughly describes how uncertain you are on what the exact microstate is

Shashaank

Yeah, But how exactly did entropy originate is my question, how was it formulated?

Silly Goose

i think the original purpose of introducing entropy was to do computations for heat engines

Sir Cumference

something like that

Silly Goose

perhaps along the lines of what you started off with saying

Sir Cumference

I'm not too familiar with the history behind it, but it originated in thermodynamics and was later explored more generally in probability theory

Shashaank

06:19

but for Clausius inequality entropy was taken as the useful heat and for some other question as the useless form of heat? what is dQ rev?

Sir Cumference

you may hear people describe e.g. the entropy of website passwords

it's generally just applicable whenever you're talking about a set of possible outcomes

information theory became very important to probability, but a lot of the concepts in it are comparatively recent

so unfortunately it's not something a lot of undergrad probability classes go over yet

Shashaank

yeah

Silly Goose

stat mech really racks my brain

Sir Cumference

a bit off topic, but if you've ever used Occam's razor, that's just actually just an application of a principle regarding information theoretic entropy

Principle of maximum entropy

The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information). Another way of stating this: Take precisely stated prior data or testable information about a probability distribution function. Consider the set of all trial probability distributions that would encode the prior data. According to this principle, the distribution with maximal information entropy is the best choice....

anyway i gotta head off, but for now just think of it as describing the unpredictability in what your microstate is

Shashaank

Yeah I will look onto it

I wonder how people come with such intriguing topics!

Sir Crackpot

06:29

@SirCumference I can't laugh about conspiracy theories especially if they involve science

Sir Cumference

@SirCrackpot well his reactions are pretty funny :P

Sir Crackpot

I don't doubt that, it's more a problem of mine

Let's just say I get bloodlusted

Sir Cumference

well, if you say so

though in that case i'm surprised you went with that name

Sir Crackpot

I don't laugh when people go against science, I do laugh when people laugh at them :P

Sir Cumference

fair lol

naturallyInconsistent

06:46

@Shashaank It cannot even be anywhere near what you are suggesting. Heat is a transfer of energy, i.e. it is measured in units of energy, i.e. Joules, whereas entropy, if you want to understand it, should be dimensionless just like probability and statistics need them to be pure numbers. But for continuity with how we ran into this concept from thermodynamics, entropy is defined, due to appearance of Boltzmann constant $k_B$, with units of $\frac{\text{Energy}}{\text{Temperature}}$

i.e. it literally cannot be identified with heat, just by having different units.

Shashaank

change in Entropy is defined as dQ(rev)/T ?

naturallyInconsistent

If you have a textbook that even vaguely suggests that entropy is heat, then the appropriate reaction is to throw that entire book in the bin.

@Shashaank If that is the case, then if the transfer is irreversible, there would not be a change of entropy, which is thus also wrong.

Shashaank

entropy is defined to set a limit on the amount of heat that can be used to do useful work

for any process whether reversible or irreversible it is dQ(rev)/T

naturallyInconsistent

Again, that definition seems insane. Maybe it is possible to get that definition to function properly, but it is not obvious to meow that it is correct, nor that it could handle irreversible processes correctly.

Shashaank

oh

Silly Goose

06:58

consider a tensor product of same dimension hilbert spaces. for concreteness, $\mathcal{H} = otimes_{i=1}^k \mathcal{C}^2$. A local unitary operator on this Hilbert space acts tensor factor wise. I.e. $U$ is local iff $U = U_1 \otimes U_2 \otimes ...$, where $U_i \in SU(2)$.

Why is a transposition of tensor factors on a unitary $U$, i.e., $U' = \Pi_{12} U \Pi_{12} = U_2 \otimes U_1 \otimes U_3 \otimes ...$ considered distinct from a local unitary transformation?

I can just as easily describe $U'$ by conjugation by a local unitary operator, no?

Namely, the local unitary $L = L_1 \otimes L_2 \otimes \mathbb{I} \otimes ...$ such that $L_1 U_1 L_1^{\dagger} = U_2$, etc.?

i mean this definition of a "transposition operator" will be dependent on the particular unitary, but still

Slereah

08:39

Reading some 19th century book on Indian astronomy

The language is a lil bit dated

naturallyInconsistent

09:11

English as she is spoken in India is still rather dated right now. They will say "very less" where we will usually say "very little"

Slereah

I mean more in the ideas :p

Apparently the Mughals were defeated due to the indolence provoked by the warm climate

John Rennie

@naturallyInconsistent "rather dated" is a little tendentious. Indian English is a dialect that is just as valid as UK or US English.

ekardnam_

@naturallyInconsistent that's the usual definition of entropy used in thermodynamics. It works because of Clausius theorem

You just connect the two states you want to compute the entropy difference of through a reversible transformation and compute the integral of the differential. It doesn't depend on which reversible path you pick because of Clausius theorem

Jason Harwell

Hi John, thanks for your clarification earlier; if convenient would you be able to explain to me if my terms are correct and if there is considered to be any difference between Zero-Point fluctuations, Vacuum "Fluctuations," and Virtual Particles? My current best understanding summarized is:

"Vacuum Fluctuations: the temporary changes in the energy content of empty space, or the vacuum, as described by quantum field theory. Even in a vacuum devoid of particles, there are still fluctuations in the fields that permeate space. These fluctuations can lead to transient changes in the energy den…

naturallyInconsistent

@JohnRennie Yes, but the reason why they are using English that way is because it is a version of English that kept the characteristics from >200 years ago.

John Rennie

09:26

You could say the same about US English. It preserves archaisms that have disappeared in UK English.

And probably vice versa.

naturallyInconsistent

That's true.

naturallyInconsistent

09:41

@ekardnam_ that assumes that the initial and final states are equilibrium states, in which case then yes, reversible paths exist to connect any two equilibrium states. However, consider the scenario whereby irreversible spontaneous entropy is generated. Then it is not obvious whether the notation being used covers the case properly or not.

Ryder Rude

10:28

do u think we should.be grateful for little things? and can this be done in practice?

Sir Crackpot

10:44

Ryder, please don't read my message with a harsh tone as it's really not intended that way (I'm actually chuckling)

Why do you keep asking questions that are so random?

I mean, they are not meaningless but I expect to log some day and find a question going like "what do you think about urban development projects during the Sacred Roman Empire?"

naturallyInconsistent

@SirCrackpot Holy Roman Empire. Which should always be noted that it was none of the 3 words that made up the name.

Sir Crackpot

11:01

Uhm sorry, I translated directly from Italian "Sacro Romano Impero"

There was gauge freedom with "holy" and "sacred"...

naturallyInconsistent

@SirCrackpot don't you know other people of that ilk in your life? There are actually pretty many people who are similarly broken, and they fit a particular standard stereotype. After some back-and-forth, one will generally give up and accept that they will never be able to get out of that kind of mindset, and simply move on with our lives instead.

@SirCrackpot miahahaha. Now, there is nothing at all to be sorry there. It was not a scolding, and much more a reason to bring in the joke.

Sir Crackpot

Purrfect

@naturallyInconsistent Mhhh not quite I guess

naturallyInconsistent

Maybe we should refer to it as Heiliges Römisches Reich

Ryder Rude

@SirCrackpot i sometimes want more casual discussions than physics :)

naturallyInconsistent

@SirCrackpot Not too long ago PhiloTube made a video about anti-vaxxers. They actually went out there and surveyed people who had anti-vax sympathies, whether or not they are fully anti-vax, and treated the actual ground situation without dismissing them out of hand as anti-science. The point is to figure out what is actually their belief systems. One group that is simultaneously obvious upon hindsight and yet fascinating to observe the link, is the gym-bro stereotype.

That is one mindset that is pretty similar to this one.

Ryder Rude

11:06

@SirCumference i wud say the gradient of language mixing due to the internet is not as steep as due to conquests in the older times

so i think language mixing has more slowed down. there used to be fierce language mixing due to conquests @SirCumference

but language mixing is more globalised due to the internet

naturallyInconsistent

Actually, this is generally considered good and is somewhat doable in practice. Now, of course, conservatives in particular would always want to venerate gratitude on a pedestal, because they want the status quo to never change (since they are already the winners in society, so they never want their privileges to diminish). They want people to stay in their lane and be grateful for what they have in life.

However, it is also known that gratitude increases happiness. Just for our own mental health, we should do that, as long as we do not go into the wrong political bent for it.

Relativisticcucumber

@SillyGoose i dont think this paper is ab stirap XD

ekardnam_

@naturallyInconsistent i think with that definition, he is definitely doing equilibrium thermodynamics

naturallyInconsistent

H O N K

B A H

Ryder Rude

@naturallyInconsistent do u do it as a habit? i dont know anyone who has been able to make this a habit, so i dont think if it's even possible

naturallyInconsistent

11:14

@ekardnam_ Which is why I am wary of just accepting that definition as true. It is way too easy for the students to have a misunderstanding of that definition and not know how to handle the irreversible stuff. It is a pretty delicate thing. It is far better to have something is obviously going to work in all situations.

Ryder Rude

or maybe it's extremely hard to get over the wall

naturallyInconsistent

@RyderRude Yes, I do it as a habit. I am generally pretty happy and grateful of my life, especially in my current status. I am loved, I have a wonderful job that is considered well-paying for science (despite annoyances here and there all the time), people are caring for meow at work and appreciate my work output, I get to shakies ass all the time, etc. So I can just be grateful for the nicely kept bush on the way to work, for the nice weather when it happens, etc.

ekardnam_

@naturallyInconsistent usually people in first year's college do axiomatic thermodynamics. they dont start off directly with the statistical interpretation. which way is better pedagogically idk but i dont think it will be of any help to their exam to know the statistical interpretation. there is still some sense with the clausius definition of entropy and its worth understanding it in my opinion

naturallyInconsistent

It is, of course, difficult to acquire such a habit, but it is possible.

ekardnam_

@RyderRude grateful to whom, though?

Ryder Rude

11:18

@ekardnam_ just grateful that u hav little things

@naturallyInconsistent then maybe it's possible. thanks

@ekardnam_ grateful to life

ekardnam_

i mean i think it is important to be aware of the good stuff that happens to oneself everyday

naturallyInconsistent

@ekardnam_ You are absolutely wrong. There is no possibility that people do axiomatic thermodynamics in first year of college. It is definitely rare even for grad sch. Most people just get a hodge-podge of random experimental facts and not even sure that it builds up to entropy. If anything, the axiomatic version of thermodynamics is so rare and difficult that it is so fulfilling to understand what that is saying.

Ryder Rude

@ekardnam_ yeah but this philosophy is also about classifying the neutral things as good. like merely being able to breathe should make you grateful

so u take advantage of both the good and the netural things

ekardnam_

@naturallyInconsistent thats what i did in my first year

we started from the principles and found definitions of thermodynamical quantities such temperature and such

naturallyInconsistent

@ekardnam_ Well, I would not put it as being done every day. I mean, if one is being bullied or some such, it is totally normal to just get depressed for the entire period, even if it takes months or years.

Relativisticcucumber

11:22

@naturallyInconsistent honk bah honk bah

ekardnam_

i guess european programs are very different from us though

in uni

naturallyInconsistent

@ekardnam_ You had an extremely good introduction and it is vastly out of the norm. I was not taught by axiomatic version, (the first year was horrible) but 2nd year intro to stat therm for meow was also an extremely good introduction, albeit of a totally different type. I self-learnt the axiomatic version from Callen simultaneously while reading also Kittel and Kroemer, Pippard, and more.

Since I actually did read many books, skimming even more, I can safely say that axiomatic treatments of thermodynamics is extremely rare.

ekardnam_

what we used was some italian book. but also Zemansky was a reccomended read

naturallyInconsistent

Still, if it had been axiomatic, then it ought to be amazing. Otherwise, there would be no point in doing it axiomatically.

ekardnam_

i enjoyed the course quite a bit

naturallyInconsistent

11:27

However, it is a tremendous burden on the student if we do it that way. The concepts being discussed is really difficult.

ekardnam_

id say one of my favourite courses in first year

@naturallyInconsistent i think in italy courses tend to be like that, rather then simplified for the students

naturallyInconsistent

I think that is very unkind to students.

ekardnam_

the high school program though includes more physics

naturallyInconsistent

And also very anti-research. Research, by definition, are things that we do not yet fully understand. We cannot go by axiomatisation on research.

ekardnam_

for example a good high school student at scientific high school could do american colleges introductory physics basically

naturallyInconsistent

11:29

Of course, we can try to do axiomatisation on research, and sometimes it will be fruitful, but it is not always the correct thing to try.

@ekardnam_ That is mostly because USA is in a pretty sad place in terms of pre-uni education. The specific constraints that they are working with, is just beyond woeful.

ekardnam_

@naturallyInconsistent yeah

all im saying is that you can afford more involved courses in the first year given the high school education was better

though it is hard on people who didnt do scientific oriented high schools

but the education system here is very different. I feel like italy is different compared even to the rest of EU, let alone US

naturallyInconsistent

Yes, and that is actually very helpful. I had soooo much free time in my first year that I could crash into law lectures, economics lectures, maths lectures, computer science lectures, etc and also have time for fun at societies and yet still have good grades. Fun times.

@ekardnam_ I would not think so. EU is quite full of weirdness. French, German, UK, Italy, Scandinavian, etc, all have their quirks. It is fine this way.

ekardnam_

@naturallyInconsistent there are many things that are common to most european countries but italy. For example we are basically the only country which does one year more of pre-uni education

naturallyInconsistent

The crucial point is "what is being especially taught in that one year that is not being taught elsewhere?"

ekardnam_

@naturallyInconsistent the high schools program include more stuff. Also stuff is really tought from a different perspective

i took GCSE exams for international students (IGCSE) which are the exams you take in england after high school

it was way easier than anything i did in italian high school

it wasnt the level you are supposed to reach at the end of highschool, but i could take them when i still had two or three years of high school left ahead

Sir Crackpot

11:42

@naturallyInconsistent I don't know if I see it that way, though

I see it more as an untenable curiosity concerning the opinions of the users of the chat about everything

ekardnam_

generally mathematics is tought in a very different way. You do prove most theorems. The english way was mostly "hey this is how its done, you dont need to know why. Take this thirty exercises and do the same thing over and over"

i even had teachers who thought in US tell us the same thing in uni

naturallyInconsistent

@ekardnam_ That is a quirk of the British school system. They are sad. Ex-colonies of the Brits can have far more difficult exams.

ekardnam_

there is really an approach bases more on doing things rather than understanding them in US

or UK

naturallyInconsistent

@ekardnam_ Again, unlike the rest of the developed world, in USA, this is forced upon them from below. If they tried to make it difficult, they would graduate only the elites.

ekardnam_

also at uni there is no homework like in most other countries

you just book the final exam on one day and take it. You can either accept it or take the exam again if you arent happy with the result

naturallyInconsistent

11:48

@SirCrackpot Oh, that is very much never the case. If you read their responses and so forth, you will realise that it is an illusion. People like that will put up the façade of being open-minded, act like they are Joe Rogan, and then be as fixated on their worldview as Joe Rogan also is. It is particularly the case if you try to get them to see that their behaviour is unwelcome.

@ekardnam_ which? is happening where? this is too vague to deduce what you actually mean

ekardnam_

@naturallyInconsistent usually people in other countries during their courses have to hand in every week some homework or something

here there is nothing like that

naturallyInconsistent

Yes. However, in UK it is some small percentage to the total. Essentially I can hand in nothing and yet get my 1st class honours.

Unless, of course, the module does not have examination, and then of course it would need some other way of assessment. e.g. QFT should probably be graded on the 2-loop correction to renormalisation.

Which is not something you can set an examination on in a seated setting.

Sir Crackpot

@naturallyInconsistent I acknowledge this view although I only know Joe Rogan by name

naturallyInconsistent

12:03

@SirCrackpot Oh, you are so lucky to not have many bros of that sort in your life.

Sir Crackpot

I just don't have many because I'm weird too :P

Swan

12:21

A humble question amidst the QFT discussions. I've calculated the $/mu$ but I still have a slight doubt about why would there even be a minimum angle?

Mathematically, I could only show this. Is this a good enough explanation for why there would be a minimum angle. The requirement for $/mu$ increases as the angle decreases.

Is there some better way to prove the existence of this minimum angle?

@naturallyInconsistent

*Negative in (0, pi/2)

Slereah

Apparently the whole "QM is linear logic" thing that nlab keeps talking about is the cooler more recent version of the old quantum logic

naturallyInconsistent

12:43

@Swan Why are you even calculating its derivative? The minimum angle exists because the way static friction works is up to a maximum force it can provide given a certain normal force. Any smaller angle, it slides. You are supposed to work that out with all the inequalities. I have no idea what your derivative could mean. Also, you are not supposed to ping somebody in the chat to solve your problem for you. Just wait for someone to have the time.

@SirCrackpot miao miao iz too weird for friends and colleagues to forget meow

Swan

12:59

>The minimum angle exists because the way static friction works is up to a maximum force it can provide given a certain normal force.

Yeah but how do I even know that the force along x-axis increases as the angle decreases. In the 2nd law equation, the theta, the two normals (one from the roller and one from the ground) all would change as the ladder would slip down. I can somewhat relate it to the real life but can't really see it mathematically.
The derivative wasn't well though out, yup.

Sorry about the ping. Didn't mean to disturb you. Would be more careful next time.

Sir Crackpot

@naturallyInconsistent Uh regarding cats, I forgot to mention I found some cats living by the seaside

Kittens, actually

And so I dubbed them "Umi neko"

nickbros123

omg omg omg

Callen was the text I have been looking for all along

Sir Crackpot

It's intended to be a pun because "umi"="sea" and "neko"="cat" in Japanese (romaji)

But "umineko" is a type of seagull

2

Found the pic :P

naturallyInconsistent

13:21

@nickbros123 told ya

@SirCrackpot awwww

nickbros123

@JohnRennie unfortunately, at least from my personal experience, the new gen people from the big cities want to be like US, and this is rather clear in the way the modern science education system is laid out, and the new slang words they use, the food they eat and so on. Earlier they wanted to be like the British diplomats, now its come to trying to replicate the US. The villages are still culturally intact though, which I like. Just speaking from my experience though, others' may vary

naturallyInconsistent

brb

nickbros123

@naturallyInconsistent shouldve listened :) In my own defense though, before callen gets interesting you have to go through a truck load of words thats sort of like an advertisement to thermodynamics

naturallyInconsistent

15:29

@nickbros123 true that. But as mentioned, it is worth it to read a properly axiomatised treatment. However, it is not the end-all and be-all. You should also read other treatments to see a different viewpoint. Axiomatisation makes it difficult to talk about what-ifs.

Mad

16:22

In My lecturenotes, its talked about Statistical statefunctions X_i and that can they be represented by generalized displacements x_i and their conjguate forgces J_i.
after i checked some articles, my understandig is, basically the coordinates span some space similiar to the eucledian, and the generalized displacments is like the basevectors for this base, and that "conjugate" is like dual to these vectors in sense that they fullfill the poisson bracket realtionship.

Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details. As Hamiltonian mechanics are generalized by symplectic geometry and canonical transformations are generalized by contact transformations, so the 19th century definition of canonical coordinates...

My question: is this good explanation,
2) what is the poisson bracket in statistical mechanics?

ACuriousMind

17:08

@Mad The bracket is defined by declaring that the $J_i$ are conjugate to the $X_i$ to be $\{X_i, J_j\} = \delta_{ij}$

Mad

@ACuriousMind Okay, so is the analogy draw actually correct.

So why not say Dual.

seems more reasonable

ACuriousMind

the, well, canonical term is "canonical conjugate"

they're not exactly the dual of displacement vectors

Mad

Just note for your comment, they are saying J_i is conjugate to small x_i not big X_i

Honestly, not really clarifying any of this jargon, probably due to none existent easy clarifications

ACuriousMind

think about ordinary Hamiltonian mechanics - the canonical momenta $p_i$ are not the duals of the tangent vectors $\partial_i$ (or "$\dot{x}^i$"), but if you want to express the $p_i$ in terms of the coordinates $x^i$, you have $p_i = \partial_{\dot{x}^i} L$

but to be honest I haven't seen a lot of a Hamiltonian formulation of statistical mechanics like you're talking about

Mad

web.mit.edu/8.333/www/lectures/lec1.pdf

MIT lectures

scroll to end of Page 4

According to your comment, this is then a matter of choice. And then one asks directly, why make this choice, rather any arbitary other!

ACuriousMind

17:13

ah, it's saying that if you write $\mathrm{d}W$ in this way, then it is the tautological one-form on the space of $(x,J)$

Mad

Can you provide an explanation, i dont think i am willing right now to dive deep into differential theory for this, i had forms and what not, but like two years ago.

ACuriousMind

since the text doesn't go into any more detail, I don't think there's any deep significance to this at this stage

it's just saying that formally the $x$ and $J$ are analogous to the $x$ and $p$ in usual Hamiltonian mechanics

and the $W$ functional that assigns to paths the work along them is analogous to the action

Mad

Alright, so in some sense postulating this, since no proof is provided.

Mad

18:19

Oh no i feel i am going to suffer greatly in this course

why change to partial for deriving the inner energy? literally two lines above it, they mention E is a function of T alone

And at that point, does it matter to keep mentioning the Ps and Vs ? its not functions of those anyway.

naturallyInconsistent

18:43

@Mad You are suffering from the 2nd fundamental confusion of multivariable calculus. When using partial derivatives, the thing that you are considering as constant actually defines the direction at which you are taking the derivative (the thing you are differentiating only determines, of this last single dimension, which is positive and which is negative). So, if you do not mention which thing it is you are keeping constant, then you have not understood the multivariable calculus at all.

Mad

Look if your function E depends only on T then $dE/dT= \partial E / \partial T $ right?

ACuriousMind

you are probably misunderstanding what the text means when it said "it's a function of $T$ alone" - you need to define in what sense all these things are functions "of $T$ alone" (e.g. alone a path in state space parametrized by $T$) in order for the total derivative to even make sense, but generally $E$ is a function on state space and hence depends on all state variables

in this particular context, you are probably considering certain paths in the space that are defined by constant $P$ or constant $V$, making the other a direct function of $T$: At constant $P$, you have some $V_P(T)$ and this makes the state space function $E(T,P,V)$ into a function "of $T$ alone" $E(T,V_P(T),P)$, where $P$ is a constant and everything that varies varies with $T$ along the isobar

Mad

18:59

Ok i think i was confused, the notation dE/dT is used if the space is spanned by T only, ie one dimensional derivative.

Other than that, its either dE or partials.

just because f: R^n to R is given by f(x)= x_1 doesnt mean to write df/dx1 .

nickbros123

how does one go from $PV=RT(1+A_1 P+A_2 P^2 \dots)$, where $A_i$ are only temperature dependent, to $PV=RT(1+B_1\frac{1}{V}+B_2\frac{1}{V^2} \dots $ where again $B_2$ are tepmerature dependent only

naturallyInconsistent

@nickbros123 do you?

nickbros123

I dont know. this zemansky book asks me to. Ideally I would individually taylor expand whatever equation of state we have (basically expansion of $\frac{PV}{RT}$), for either case and leave it at that

naturallyInconsistent

Hmm, that seems really crazy to even attempt. There is a inverse function algorithm that you can use to iteratively get the terms, but it gets tedious and hairy very quickly

Sir Cumference

19:26

@SirCrackpot Do they cry?

Silly Goose

@SirCrackpot ohmygooood @Relativisticcucumber look at this

naturallyInconsistent

H O N K

Silly Goose

hooonk

what is the most modern formulation of quantum mechanics? C* algebra formulation?

naturallyInconsistent

what does "most modern" even mean?

Silly Goose

the most valuable formulation for making contact with the most advanced theories of physics today

ACuriousMind

19:40

what does "advanced" even mean there

Silly Goose

like contemporary

i mean to convey "developed today"

or in the past 10 years

or etc.

ACuriousMind

there's a lot of branches of modern theory

Slereah

There's always new formulations of QM being made

Physicists do them when they get bored

ACuriousMind

some people do algebraic quantum theory (i.e. indeed based of C*- and von Neumann algebras), some do functional (i.e. path integral methods), some do more unusual stuff, some talk about the projective Hilbert space and its FS metric, etc... and most just have operators on a Hilbert space and never need anything else

Slereah

"modern" tends to be relative because most modern theories tend to be at least 30 years old

Or be so niche that you'd never hear of it

Silly Goose

19:43

@Slereah hm i guess if this is the case this would answer my question

ACuriousMind

but this kind of theory is much more like a many-branched tree rather than a linear progression of ever more "advanced" theories

Silly Goose

i am wondering what is the point of all these different formulations, I guess

Slereah

Currently reading about linear dependent logic, which is apparently touted as a formalism for QM?

At least in some cases

ACuriousMind

@SillyGoose the people working on them think they're neat :P

Silly Goose

like it seems like the C*, path integral, and textbook Hilbert space formulations are more amenable to different computations or tasks

even though provable equivalent (?)

Slereah

19:44

It's pretty recent

ACuriousMind

they're like different lenses to view things through, some things that are trivial to see in one approach are difficult to derive in another and vice versa

Sir Crackpot

@SirCumference Sir, your culture is non-compact

Sir Cumference

lol

Silly Goose

hm well I guess maybe I should know a bit about the main ones at least :P

Sir Crackpot

@Slereah QM sucks in every form

ACuriousMind

19:45

and also there's always the idea of generalization/restriction - you can always ask "what happens if I relax this axiom? how much can we still prove?" or "what happens if we add that one? is it still consistent?"

Slereah

Oh yeah QM is fake and boring

Read GR instead

Sir Crackpot

Being a crackpot I'm entitled to think so

@Slereah yeah, GR is the love of my life

Until I get back to QFT

Silly Goose

why not do geometric quantum ;)

Slereah

Recently I learned that the whole "QM has tensor products while classical mech has cartesian products" is actually fake???

Sir Crackpot

Isn't that too generic?

Slereah

19:47

Classical mech also has tensor products, but in the category of Poisson manifolds

But as pure manifolds, it's Cartesian

Which leads to weird things

Sir Crackpot

Is that about entanglement?

Slereah

The no cloning theorem dors apply classically???

Sort of

Yeah

Silly Goose

j'aime le poisson yum

that is the extent of my french

Sir Crackpot

@SillyGoose Eric Poisson

A GRist

ACuriousMind

@Slereah I asked about this 8 years ago :P

Slereah

19:49

I'm a bit slow

Silly Goose

Lol Craig's response the "probability cloning challenge" sounds like a modern trend

can YOU complete the probability cloning challege!?

Slereah

Shit like this makes me despair I'll never get QM

Silly Goose

it's okay no one will ever get anything :D

Slereah

It's pretty hard to know what's even a properly QM behaviour

Sir Cumference

@SirCrackpot ugh I want to forget about that guy's GR book

That shit sucked

bolbteppa

19:53

@SirCrackpot are you calling Feynman a crackpot

Silly Goose

how did a crackpot smoker become synonymous with the crackpot itself

or maybe a crackpot is not a thing

bolbteppa

Don't worry there are a lot of them out there, it is a thing

Slereah

@ACuriousMind why is there no classical entanglement anyway

ACuriousMind

@SillyGoose you can smoke crack or pot, not crackpot :P

crackpot is likely from cracked pot (=head)

Slereah

What's the extra ingredient for a tensor product of spaces to admit entanglement

Silly Goose

19:57

oh

i was thinking like a pot for smoking crack in

bolbteppa

@Slereah unclear thinking

Silly Goose

i guess i don't know why someone would use a pot for smoking crack

Lol

this is tangentially related, but the title of this paper sounded interesting symplectic geometry of entanglement

ACuriousMind

@Slereah The Cartesian product of the state space (as a manifold) must not embed bijectively into the actual product of the state spaces in their category

you can call the classical product of the Poisson manifold a "tensor product" all you want, that doesn't change it's a Cartesian product on the manifolds and so for every state of the combined system there's a unique pair of states of the subsystems

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