The h Bar

Obliv

01:04

is the 2nd law of thermodynamics related to some fundamental process in physics @ACuriousMind

I'm wondering why a high pressure system wants to expand, why cold objects readily accept heat but relatively warmer ones don't. I know the description in terms of entropy/multiplicity but it's not satisfying

Is it really just probability in the end?

The reasoning is clear and satisfying, but it leads me to wonder about the nature of the interactions themselves within a system.

I basically just have to keep learning I guess

naturallyInconsistent

02:31

@Obliv yes

Obliv

03:17

@naturallyInconsistent Maybe not

Most likely macrostate might signify something deeper

Obliv

04:00

is engine efficiency ultimately limited by how closed the system is

er i guess if the engine relies on cycles, we can't really revert to a previous state if it has less multiplicity

unless we release energy into the environment

naturallyInconsistent

@Obliv No. You are the one reading an inferior introduction. If you have seen how statistical thermodynamics is given the axiomatisation treatment, or how a comically silly construction also manages to obtain almost physically sensible results, then you will not be entertaining the impossible.

Obliv

04:16

entertaining the impossible? I was simply investigating further what the 2nd law tells us but like I said, I don't have the relevant knowledge to do that digging right now @NaturallyInconsistent

for example: fundamental forces don't seem to care about increasing entropy. I was wondering if maybe increasing entropy was a consequence of something deeper. Like how inertia might

naturallyInconsistent

I am trying to trying to tell you that statistical thermodynamics is an extremely special case. There is no longer any doubt as to how it works. We have reduced, for the one and only case of this happening, a physical theory to purely mathematics. There is nothing left to speculate about the nature of entropy. It is probability and statistics, nothing more. There is nothing deeper for it to be a consequence of.

Obliv

So that's it? Just gonna close that book and never think about it again? What's the point of doing physics if you aren't curious about connecting ideas

naturallyInconsistent

It is not that we are not curious. It is that it is reduced to mathematics. There is no leeway left.

And it is also a fool's errand. Unless we have better experimental evidence to lead the way, it is impossible to know, even if you guessed correctly, if the next leap in improvement in guessing would even be correct, because, as I just told you, a comically silly guess also gets qualitatively correct results. That means that the framework is particularly tolerant of bad guesses, and so it is extremely difficult to know how to improve at all

Obliv

Maybe it's just because of our gap in experience and knowledge. I'm still learning things for the first time and connecting ideas in my worldview so I don't really understand what your argument is.

I understand, experiment precedes theory always.

naturallyInconsistent

And the existing framework is full of connecting ideas. If you had a good understanding of statistical thermodynamics, you should see that it is itself a wonderful summary of a tremendously wide variety of phenomena. It is a topic that forms a tremendously strong backbone from which the rest of physics is organised.

Obliv

04:27

I'm not at the forefront of either so it's just me thinking out loud in the room. I don't expect serious answers most of the time.

@naturallyInconsistent I figured as much, the answers will come as long as I keep at it.

naturallyInconsistent

What I am trying to tell you, is that your position is coming from ignorance of what is actually already explored to death, and how to see the subject as a cohesive whole. I am not saying that a wonderful treatment of the subject is common, but they do exist, and Schroeder is just nowhere near one of them. Your current conjecturing is coming precisely because Schroeder left you with so many gaps in your knowledge that you have all these doubts.

Obliv

Oh here we go again LOL just had to bring Schroeder into it. I know you think I'm being too charitable, but I honestly think regardless of the textbook and introduction I have to the subject, I'll conjecture weird things that don't make sense.

naturallyInconsistent

Well, I am aware of your tendencies to do that.

But if you had a textbook that starts by axiomatising everything, you would have little chance of doing this.

Or if you had a textbook that defined a comically silly "entropy-like" function, and yet it gets the predictions qualitatively correct, then your current conjecture is impossible to raise.

Obliv

But we did define an entropy function $S = k\log\Omega$ where $\Omega$ is specific to the system

we got sackur-tetrode eq. for monatomic ideal gas, einstein solid, 2 state paramagnet

naturallyInconsistent

Yes, but then you will be confused as to why that particular choice of entropy function. That lets you conjecture different choices for the entropy function.

Obliv

04:36

Yea he explains that in chapter 6+ we do more stat mech that's more concerned with devising entropy functions

So until then that's what I got lol

Andy

ok let`s tall about blackholes

talk

naturallyInconsistent

The issue is, what is there to talk about it that would make for a good conversation?

Andy

yeah its blackholes

Obliv

black hole thermodynamics is in the later chapters of Schroeder I believe

ducks under the cats inevitable rage

Andy

?

i`ve never read that book

Obliv

04:42

It was a joke, it's an intro thermal physics book but @NaturallyInconsistent hates it. If he actually did do blackhole thermo in it somehow I'm sure they would have a heart attack :P

Andy

lol

can u tell me the name of th book

Obliv

just google "An introduction to thermal physics" by dan schroeder it should come up. It's not at all rigorous so if you're looking for that then I'd stay away

Andy

thx

:)

Obliv

@NaturallyInconsistent what do you recommend for optics? I might review pedrotti/hecht over the spring break or summer I don't want to forget everything

naturallyInconsistent

05:01

@Obliv IIRC, he did have bits of it. Kinda difficult to avoid, since they are all trying to be impressive.

Obliv

Are you teaching any classes right now btw?

naturallyInconsistent

@Obliv Optics was not considered fundamentally important and so we only got the barest minimum of geometrical optics, and then the rest is treating things with waves. Too short a coverage to require a textbook.

@Obliv Right now? I'm preparing for some small one-off lectures for really old people so I'm dumbing things down as required.

Obliv

That sounds chill, I would attend if I was a dumb old person living around your area (I already forgot where that was)

What are the lectures on?

naturallyInconsistent

Nookooliar fooshun

Obliv

I don't know anything about fusion, let alone nuclear physics... man.

naturallyInconsistent

05:06

Actually, apparently the non-plasma physics part of it is pretty understandable if you do not care for the minute details.

Obliv

Lol, something I would ask

naturallyInconsistent

Quite a lot of it can be treated with basic quantum theory + perturbations

Obliv

good to know

naturallyInconsistent

@Obliv It took some effort to not just vote to close that. Or downvote it

Obliv

Hah, I think it's a good learning moment for a student to recognize the limits of a theory

sometimes students don't understand the scope of what they're learning. They see F=ma and try to apply it to their love life for example

or the 3rd law. "ah Romeo, my love for you is met with equal and opposite force, like Mr. Newton described." - shakespeare's Romeo and Juliet circa <1800

Ok time to sleep I am getting silly

but Cort's answer is pretty cool

naturallyInconsistent

05:18

Yes, it is.

@Obliv It is fun to see that forces were the first to die in the quantum revolution

Obliv

are the analogues to forces in more advanced physics still inherently $\mathrm{mass}\times\frac{\mathrm{space}}{\mathrm{time}^2}$

It seems like a pretty fundamental definition of an observable

naturallyInconsistent

no; mass is not well-defined, along with forces, except as the rest mass term that is in its wave equation. It is also not clear what it means to define the space / time^2 terms.

in particular, parts of a wave do not have masses. The whole wavefunction, or better, the field's equation of motion itself, has a well-defined rest mass term.

Andy

06:04

what about higgs

doesn`t that describe mass

or will describe mass

Silly Goose

what is the higgs to you

John Rennie

06:33

@Andy The interaction of the Higgs field with a quantum field adds a term to the equation of motion for the field that looks like a mass, and that's how masses of the fermions in the Standard Model are created. But this mass is still a property of the field in the sense that it appears in the equation of motion for the field.

nickbros123

@naturallyInconsistent i thought forces died before quantum

@Obliv I'm telling you friend, Griffiths 9th chapter. From there the rest of optics can be derived

That was a gross overstatement btw

Ryder Rude

07:16

@nickbros123 theyre still talked about in Lagrangian mechanics and SR, but theyre never talked about in QM

Silly Goose

07:35

have any of you guys read "Gödel, Escher, Bach"

Ryder Rude

07:54

i will read it

nickbros123

I would read it if I didn't have ADHD

Ryder Rude

do u hav diagnosed adhd

nickbros123

No, but the symptoms all add up

I'm just kidding, but I do have an abnormal disliking towards books with a lot of words (the usual 'books' kind of books, not technical ones)

Ryder Rude

i have a simultaneous like and dislike for all books

John Rennie

@SillyGoose 800 pages? Good grief!

nickbros123

08:00

@JohnRennie average math methods for physicist book

Ryder Rude

is thinking hard supposed to feel good or bad

John Rennie

@nickbros123 Yes, but those books are generally used like reference books i.e. you read selected sections to learn specific techniques. You wouldn't read them cover to cover.

nickbros123

@RyderRude for me it feels bad when no idea penetrates a problem. But when the solution finally comes it feels great, for a few mins. Then it goes back

3

Ryder Rude

lol

John Rennie

That's how my students react when I point out they can approximate a problem using a binomial expansion :-)

Ryder Rude

08:06

@nickbros123 this feeling can sometimes last long, but it always goes away

maybe can last for 2 days if u understood something conceptual

Sir Crackpot

08:41

I don't want to start this day, I'm feeling lazy

As usual, more than usual

Slereah

> Roger Bacon (1214? - 1294), Opus Majus, by order of Pope Clement, delivered to him in 1267 as a seven-part handwritten manuscript series; resided in the Vatican Library, remained unpublished for more than 500 years.

Worst bibliography

bolbteppa

That graphic vaguely describes my weekend

Swan

09:56

I was taught that the torque of internal forces is always zero because they act along the line joining joining the two particles. I'm not able to intuitively see this in the case of frictional force. Let's say we take eart and a horse cart as our system so when the horse pushes on the ground, isn't he applying a force perpendicular to the surface of earth?

*earth

Am I even making sense or I've got this all wrong?

ekardnam_

this is a stupid terminology question

in $$\int_a^b f(x)dx$$ $a$ and $b$ are called integration limits?

John Rennie

Yes, though more commonly I see them called "Limits of integration":

Limits of integration

In calculus and mathematical analysis the limits of integration (or bounds of integration) of the integral of a Riemann integrable function f {\displaystyle f} defined on a closed and bounded interval are the real numbers a {\displaystyle a} and b {\displaystyle b} , in which a {\displaystyle a} is called the lower limit and b {\displaystyle b} the upper limit. The region that is bounded...

ekardnam_

great thanks

Relativisticcucumber

what is $\hat{h}$ in 3.1 here?

Swan

@JohnRennie Can you take a look at my question also? It's just above ekardnam's message. Although, I'm not sure I'm phrasing it clearly enough. It's the best I could articulate

naturallyInconsistent

10:09

@Swan You have chosen a case whereby it is true. Contact forces tend to obey this, because contact forces act through a point. If you have seen the concept of couples, it should be obvious that it is the perpendicular separation of a pair of forces that will generate torques. That is, what you are taught is wrong, but you have chosen a wrong thing to check it. Try 3 bodies interacting both electrically and magnetically at a distance

John Rennie

@Swan You are quite correct that in this case the force doesn't act along the line joining the centres of masses, but it's still obvious the net torque has to be zero.

naturallyInconsistent

@Relativisticcucumber Those are some operators, written in a way to evoke the memory in the reader of creation and annihilation operators.

John Rennie

The force on the Earth and the force on the card act at the same point, and the 3rd law tells us they are equal and opposite. So regardless of where we take the reference point they have equal and opposite torques and sum to zero.

Swan

>contact forces act through a point. If you have seen the concept of couples, it should be obvious that it is the perpendicular separation of a pair of forces that will generate torques.

Relativisticcucumber

@naturallyInconsistent oh

Swan

10:12

This part clears it.

Thanks both of you guys 🙏

Relativisticcucumber

that actually cleared it up thanks @naturallyInconsistent i was not realizing that my system has a harmonic "perturbation"

naturallyInconsistent

oh lol I wasnt expecting that to be the solution to your problem

Mad

14:37

core.ac.uk/download/pdf/81117368.pdf

"Urysohn metrization lemma.
Temperature is usually defined for thermodynamic systems in equilibrium.
As is well known, each possible state of any such system can be completely
specified by an n-tuple (li, 5,) *em, .&) of real state variables"
Why is it finite n and not infinite?

i am guessing this refers to the state of a quantum mechanical system?

Sir Crackpot

15:00

Thermodynamic systems admit a "simple" description (compared to their description in terms of microscopic variables)

For example you may have $n=3$ and $x=(p,V, T)$

Mad

15:12

Ah okay.

Sir Crackpot

16:08

Question: suppose you have a one-parameter-family of geodesics $x(t,s)$ in a manifold, where $t$ moves along the geodesics and $s$ parametrizes the deviation i.e. which geodesic. Although it's intuitive that this family determines a surface, is it really obvious?

If we were just deforming arbitrary curves I wouldn't have many doubts about it but since there is the constraint that they are geodesics, is obvious that $x(t,s)$ parametrizes a surface?

Slereah

16:53

You could have it be one dimensional

Whether it is at least of constant dimension depends on the rank of the differential map

Sir Crackpot

Oh the rank theorem

So that's the same thing one would require for arbitrary curves

My doubt was that the constraint of being geodesics may not span a surface and leave "holes"

Silly Goose

17:27

These notes on conformal field theory and representation theory seem cool: sporadic.stanford.edu/conformal

@Relativisticcucumber wow stirap

Obliv

18:12

is part b) impossible? How would I know how much electricity this plant produces per second to convert to kilowatt hour

I have the abundant energy at $69,000$ extra kilowatt but idk what to do

what if the plant produces $1$GW per year? per second? like come on

Nice, the next question does the same thing. Am I just supposed to assume it's not actually watts but Joules?

nvm ur supposed to assume it's watt-hours for plants I think

Loong

18:34

@Obliv Your question doesn't make sense.

GW is a unit of power.

The plant produces 1 GW.

So it's something like a big coal-fired unit. Obviously, it cannot be nuclear.

With a typical availability factor for such a unit, it will produce about 4000 GWh per year.

Obliv

Oh, I thought GW was a measure of energy not power, my bad.

So it's 1E9 J/s

kilowatt-hours are just joules*3600/hour

Loong

@Obliv No problem, all Green politicians make this mistake when they babble about so-called renewable energies. 😄

bolbteppa

19:14

String ******* theory

@SillyGoose Those Osborne videos are probably worth watching

Sir Cumference

Weird question but as more people communicate across the world via the internet, do you think differences in dialect will gradually smooth out over time?

Like Americans will come across enough British English terms that it'll eventually become part of their everyday vocabulary, and vice versa

and centuries from now differences in separate languages might even smooth out

idk why this randomly popped into my head

WaveInPlace

19:35

It depends on how much online communities mix. Widespread mixing would definitely standardize language, but small communities tend to balkanize pretty fast.

Think memes. Rapidly emerging and evolving, often localized to particular subcultures.

Common tools are the more likely standardizing force, in my view. Word's spellchecker constantly emphasizes American spelling over British, and consistently adds commas to text that don't need them. If someone is learning, they're far more likely to accept/internalize the spellchecker's rules.

Sir Cumference

That's an interesting point, there could still be localized communities. I do wonder if it's a different situation from the pre-internet era though. With fewer geographic restrictions, it's a lot easier for ideas to be exchanged

WaveInPlace

Ugh, my last comma wasn't strictly necessary. Stupid spellchecker.

Sir Cumference

So it'd be a lot easier for a small online community to grow than e.g. a smaller culture before the advent of the internet

WaveInPlace

It's an interesting change, for sure. Communities based on interests weren't anywhere near as common 40+ years ago.

Heh, there's a legal news site named "Above the Law."

We need a "Beyond Physics" site/blog.

ekardnam_

22:27

@SirCrackpot idk if it is the case or not for geodesics in general, but a surface could as well have holes in it no?

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