The h Bar

Relativisticcucumber

01:24

my professor has written in his notes, in the context of the semiclassical model of electron dynamics that this model breaks down in the free-electron limit because the electron energy can increase without bound, but we have said that we want to forbid interband transitions. he then writes that we must have $eEa << \frac{E_{\text{gap}}^2}{E_F}$ and that this is easy to satisfy for metals but not for insulators, for which [...]

[...] we can see electric fields causing interband transitions. the thing im confused about is dont metals have no band gap, so isn't $E_{\text{gap}}=0$? then how can we satisfy the aforementioned criteria?

naturallyInconsistent

02:25

@Relativisticcucumber yeah, that's nonsense; as far as miao miao goes, we now have a mathematically rigorous theory for these things, and so we should avoid all the guesstimations that used to be the only way to get answers.

@NOTEBook You have made a reputation for yourself, routinely coming in with such an attitude, I'm not inclined to help. Also, the question that you linked to, had many correct answers on it. If you cannot recognise that the correct answers would also answer your specific question, then it will take a lot of effort on the answerer's part to dispel your question, and so there is a lack of motivation on everybody else's part.

naturallyInconsistent

02:38

@PM2Ring I know. I think I told you before that I bought Carlson's book. Don't understand it much, but it is a wonderful new way to look at functions.

NOTE Book

03:00

@naturallyInconsistent What is wrong with my behaviour? I mean i never said something bad to someone. I ask a question and if someone answers i discuss it with them and leave. Maybe my questions are too dumb. Also I didn't intended to say that everybody have to help others, I just wanted to say that if someone knows about this high school problem they should consider helping.

naturallyInconsistent

Have you not realised that there has been quite a lot of people replying to you on this topic? If you cannot see that you have done something wrong, nobody can help you.

NOTE Book

I asked what is wrong with my behaviour that nobody wants to answer like before this topic started. It all makes sense if nobody answered me after this because they don't like my attitude.

Relativisticcucumber

@naturallyInconsistent like the entire semiclassical model is a no go u mean?

@NOTEBook i think you should not self victimize. i interpreted your behavior as someone who was naive in their assumptions. now that it has been explained to you, if you realize that what you did was not a good approach, learn from it, and change, i doubt people will be negative toward you on average. we're all adults, and i assume you're a child, so it's fine. just learn from the experience and adjust your approach so you have a higher chance of getting the help you need.

qwerty

03:24

@NOTEBook "maybe my questions are too dumb". multiple people have explained why you're not getting help in chat, you don't need to make up extraneous self pitying explanations. and you clearly said much more than people should "consider" helping you, which is why you got the reactions you did. reflect with honesty.

Debanjan Biswas

03:48

I need an explanation for a simple mechanics problem. Consider a ball rolling down an inclined plane without slipping. Now consider angular momentum of the ball relative to initial point of contact. For

For that point the angular momentum generated by friction is zero. Does that mean the ball doesn't roll relative to that point?

Can you please give any suggestions about good books on rotational mechanics?

naturallyInconsistent

05:16

@Relativisticcucumber no. The issue is that if you have a constant E field over all space, then if you include this E field in V, all quantum states will break down. The only way to do this correctly, is to put this E field in A, and then the theory will give you a beautiful answer.

@DebanjanBiswas you have a few forces, e.g. Weight, Normal reaction force, friction, and maybe more. Considering just the 3 forces, as long as they do not meet at a point, then at least one of them will be providing the angular momentum.

@DebanjanBiswas there is no such book; usually a book just treats classical mechanics properly, and it would automatically include rotation problems.

Debanjan Biswas

05:49

@naturallyInconsistent but I don't see any force providing the angular momentum for rolling

@naturallyInconsistent normal and mg•cos theta create opposite torques and cancel out

naturallyInconsistent

@DebanjanBiswas if you pick the point of contact as the pivot, so that normal reaction force and friction do not provide torque, then weight will provide the torque. If you pick the intersection between weight and friction as the pivot and so they dont provide torque, then the normal reaction force will provide the torque

the point of application also matters.

Debanjan Biswas

Here the torque is provided by mg•sin theta then?

Oh that's right

But as it's passing through COM, should it produce rolling?

naturallyInconsistent

it depends solely upon where you picked the pivot

Debanjan Biswas

@naturallyInconsistent then suggest the best classical mechanics books

naturallyInconsistent

if you picked the CoM as the pivot, then the friction provides the torque

Debanjan Biswas

05:57

Hmmm

PM 2Ring

06:27

I thought @Debanjan said that the friction is zero.

naturallyInconsistent

07:02

@PM2Ring how to pure roll with no friction?

Ryder Rude

07:20

GR computing could be revolutionary like quantum computing

one can, in principle, use time dilation effects to speed up computation

9

A: Relativistic Computation?

To quote a comment Scott Aaronson made on his blog: Can you perform an arbitrarily long computation with minimal effort, by leaving your computer on Earth, boarding a spaceship that accelerates to close to the speed of light, then turning around and returning to Earth, where you find civilizatio...

Aaronson talks about SR computing here. GR computing could be more feasible

antimony

@RyderRude this is the kind of insanity i can get behind :)

would it be correct that the less mass your computer has, the more difficult it would be to exploit the dilation speedup method?

Ryder Rude

In the SR method, u have to leave the computer in an inertial frame and accelerate yourself. So the mass of the computer is irrelevant. but ur own mass is relevant

antimony

oh i see

Ryder Rude

but idk about the GR method. black holes are known to freeze time at their horizon

but I think one would still need to freeze oneself and let the computer run normally

this is the naive method. maybe better techniques are possible after we understand black holes better

antimony

07:40

interesting

Ryder Rude

sciencedirect.com/science/article/abs/pii/S0096300305008398

antimony

if we're talking about parking at blackholes, can we also talk about production of gravitational waves with an anisotropic wavefront to produce a focal point in which a tiny computer could operate?

Ryder Rude

idk :P

antimony

:)

Ryder Rude

there r spacetimes in which one can perform infinite time computations. like, u want to verify the twin prime conjecture. u just let a computer run for infinite time

and then u encounter the computer and only finite time has passed for u. but u can just read the result of the infinite time process

Slereah mentioned one such spacetime here

these spacetimes could modify our understanding of computability

PM 2Ring

07:47

@naturallyInconsistent Exactly. The specification is inconsistent.

Ryder Rude

66824468 : i think this paper explores relationships between computability and GR

antimony

right

PM 2Ring

@RyderRude Greg Egan's Orthogonal trilogy is set in a universe with a ++++ metric. gregegan.net/ORTHOGONAL/00/PM.html

Ryder Rude

@Slereah what was the spacetime with infinite time paths and finite time paths between the same two points

@PM2Ring oh

@PM2Ring i haven't read his stories yet

antimony

if gravity is polarised would time flow backwards in positive gravity? or just things would repel eachother?

Ryder Rude

07:55

i think that physics determines math as much as math determines physics cuz math is part of the physical world

some people think that the largest natural number is the number that the universe can store in some sense

PM 2Ring

@RyderRude You can read the stuff on the page I just linked without spoiling the stories.

Ryder Rude

@PM2Ring thanks

@antimony time doesn't flow in GR

flow of time is an illusion of consciousness according to GR

but it is a debated topic

antimony

oh i see, thanks @RyderRude

since i read this "clocks at higher altitude tick faster than clocks on Earth's surface" (en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment)

it made me wonder if you could engineer a region of very very low gravity in a tiny space to fit a small computer chip

or if the gravity wave is more like 'rarefaction' and there's a limit on lower bound. ie. a gravity vacuum i guess you'd call it?

Ryder Rude

@antimony theoretically, one can have zero gravity

antimony

oh i see

Ryder Rude

08:02

that's what I meant earlier. one has to leave the computer in a low gravity zone, and accelerate one's own body or spend time near a black hole. then the computer will be fast relative to you

Slereah

@RyderRude malamenthogarth

Ryder Rude

Malament–Hogarth spacetime

A Malament–Hogarth (M-H) spacetime, named after David B. Malament and Mark Hogarth, is a relativistic spacetime that possesses the following property: there exists a worldline λ {\displaystyle \lambda } and an event p such that all events along λ {\displaystyle \lambda } are a finite interval in the past of p, but the proper time along λ {\displaystyle \lambda } is infinite. The event p is known as an M-H event. The boundary between events with the M-H property and...

Slereah

What's an inertial frame

Ryder Rude

i meant a free fall frame

what I'm thinking is that an accelerated frame has slower time compared to an inertial frame. In the same way, can one say that inertial frames in high gravity regions have slower time than compared to inertial frames in low gravity regions? @Slereah

in this way, one would get an asymmetry between inertial frames

Slereah

How would you compare the time between two such frames, you'd need to go through the intermediary parts, breaking the conditions of aninfinitesimal neighbourhood

Ryder Rude

08:11

yes. i think I don't have a way to compare the time. how about this : i make people sit in the high gravity and low gravity regions. and then I make the people meet at a latter time and compare who is older @Slereah

Slereah

That's just the same thing

Ryder Rude

oh

Slereah

The invariance under Lorentz transform is meant to happen in an infinitesimally small spacetime region

Ryder Rude

yes

if I start with two twins and make them free fall along different curves. but one of the twins spends time in a higher gravity region, then would that twin decidedly age less when they meet again? @Slereah

high gravity vs low gravity seems like an absolute concept

like, only one twin can claim to be in higher gravity regions, given by stress energy tensor

so it seems like an absolute notion, like accelerated frame is an absolute notion

Ryder Rude

08:55

@PM2Ring Greg doesn't explore time here

but it is interesting how matter behaves

i think time would behave just like in SR except there would be time contraction

Madder

09:15

Are the words "configuration" and "Microstate" equivalent?

Herr Feinmann

Well, it really depends on what is a configuration for you. A (classical) microstate is determined by assigning the position and momentum of each particle

Madder

Yes i understand that. But what is a configuration then? i thought it is also "assignment of positions and momenta"

Herr Feinmann

@Madder Sure, that is a microscopic configuration, which is a synonym of microstate

But you can use configuration more broadly. A macroscopic configuration is a macrostate

Madder

Btw, very funny name!
It means something like "Mister Softman" or small )

Herr Feinmann

Configuration only means that you have a set of variables and you fix the value of each. Then, the type of variables is what matters: macroscopic variables, macroscopic variables...

@Madder ACM told me that it would be the German version of Mr. Feynman D:

Madder

09:24

That would be Herr Feynman.

Fein is the word for "small" or soft . it is however read the same.

Okay so if i understand you, we can write the following.
A configuration: Is either a macro or micro configuration.
A Macroconfiguration is a macrostate, a micro is a microstate.
So the word configuration is equivalent to the word "state"

Herr Feinmann

Oh, I see. The pun was that I originally said that "Feynman--->Feynmann" (which is a common mistake) would make me German, so that's what happened

ACM told me that if I really wanted to change the name it should be so :P

Madder

Are you actually called Feynman?

Herr Feinmann

I wish :P

Madder

lol! i bet your name is beuatiful as well, i would not want to be feynman. Feynman is already taken. I am something else, and that is my own.

Herr Feinmann

That was the wittiest answer I could think of. A simple "no" would have been plain :P

Madder

09:29

:D
So do we agree on the terminology and equivalence between state and configuration

Just wait until i become the "papst" of physics. I am going to decree a unification of used terminology or immediate withdrawl of all diplomas.

Herr Feinmann

Good luck then

@Madder In this specific context, yes

I would be careful though, because for example in the context of lagrangian mechanics, a configuration is just the set of all positions, while what we are calling a state now also includes velocities/momenta

But as long as you understand it here, it's an acceptable choice of words

(Wow, the last line was so German)

ACuriousMind

09:50

@HerrFeinmann It's surprisingly hard to find a proper etymology of "Feynman", but I assumed it was a Germanic name meaning "fine man" - the modern German version of that would be "feiner Mann", hence: Feinmann. While modern "fein" can mean soft or tender, it can also mean - like the English fine - something like excellent or elegant, though it is usually not used in modern German like that a lot

Madder

I think i have some confusion about entropy.

if we consider some lattice of vector orientations at the lattice points. We say that the oriented vectors have lower entropy than randomly oriented.

But what confuses me is this: Let us look at the oriented phase.
If we assume all lattice sites take the same orientation, we still have 360 degrees. So the direction of this orientation, is infinite, it could be 24 degree 23 partial degree .. and so on.
So we have literally infinitely many states in this oriented phase, and similarly in the disoriented. Do i understand entropy then, that the diso…

Herr Feinmann

@ACuriousMind Yes, I noticed that it was hard after writing that message. I tried to look it up but I couldn't find much. Actually you made a good guess

ACuriousMind

@Madder It sounds to me as if the confusion here isn't specific to lattices: Consider simple $N$ particle mechanics, i.e. a classical phase space $X=(\mathbb{R}^6)^N$. Macrostates are probability distributions $f(x,p)$ on $X$, and the (Gibbs) entropy is $\int f \mathrm{ln}(f)$.

When $f$ is uniform, i.e. constant on some compact volume $V\subset X$ and zero outside, this becomes proportional to $\mathrm{ln}(\vert V\rvert)$ (where by $\lvert V\rvert$ I mean the Euclidean volume of $V$ in the ordinary sense). Now, every $V$ with non-zero $\lvert V\rvert$ contains infinitely many points of $X$, yet you can have bigger or smaller $V$s!

The idea that entropy is about "counting" states is only really accurate (i.e. literal counting) when the event space $X$ is discrete

PM 2Ring

10:11

@RyderRude Yes he does, but you have to explore the rabbit holes. ;) The novel involves sending a rocket ship on a high speed journey so that the rocket passengers have time to work on an important problem. See gregegan.net/ORTHOGONAL/02/Motion.html especially Time Without Timelike Directions gregegan.net/ORTHOGONAL/02/Motion.html#ACC

Tobias Fünke

you have to consider the phase space volume

PM 2Ring

In the ++++ metric, you lose the distinction between timelike, null, & spacelike intervals. So it's rather different to a Lorentzian world. OTOH, the arithmetic is simpler, since it's just plain old Pythagoras.

naturallyInconsistent

The quantities of interest tends to also converge faster. However, when we want to convert the results of those Euclidean metric back to our universe that follows the Minkowski metric, then the analytical continuation step is extremely treacherous.

ACuriousMind

10:26

@naturallyInconsistent Hm? The analytical continuation is "easy": The Osterwalder-Schrader theorem guarantees for every set of Euclidean n-point functions/every well-defined Euclidean path integral there exists a Minkowski QFT with the corresponding analytically continued n-point functions. The difficult part is well-defining the Euclidean path integral in general.

naturallyInconsistent

@ACuriousMind well, if you have ever touched numerical, you will know that the errors explode exponentially when we do that, unless we already know the correct analytical form of the Minkowski case, so that we can force the errors out. Analytical continuation is not kind when we have errors.

ACuriousMind

just don't make errors ;P

naturallyInconsistent

lol

ACuriousMind

but sure, okay, numerically it's hard

naturallyInconsistent

tears drop down uncontrollably

Ryder Rude

10:49

@PM2Ring oh

@PM2Ring i think QM also must choose a time direction, even in Euclidean theories

i don't like entropy based ideas cuz entropy is not fundamental

time is fundamental

i also think there might be a deep connection between the psychological arrow of time and the QM arrow of time and the GR time. all of these co incide

PM 2Ring

Ok. But there isn't a unique fundamental way of defining time. Years ago, I read a fascinating book with a title something like The Seven Arrows of Time. Unfortunately, I can't recall the author(s) name.

I don't think Egan is trying to claim that the entropy arrow is the ultimate fundamental basis of time. It's just a practical, useful arrow.

Ryder Rude

@PM2Ring i think, in QM, the wavefunction collapses in a single direction of time, which does pick time asymmetry

entropy should be less fundamental

like, the wavefunction can't collapse bidirectionally without contradictions

also, in practical experiments, the wavefunction collapse is always modelled past to future

where past refers to psychological past and future is psychological future

naturallyInconsistent

11:05

@PM2Ring Penrose? Ne'eman?

PM 2Ring

@naturallyInconsistent I'm pretty sure I'd remember if it had been Penrose.

The book wasn't heavily mathematical, but the author knew his physics, and IIRC, was fairly well-educated in philosophy, too.

Ryder Rude

Carroll proposes a model in which the entropic arrow changes direction mid-way

William Lane Craig and Sean Carroll | "God and Cosmology" | 2014 Greer Heard Forum

►

Carroll mentions it here

PM 2Ring

You kinda need something like that if you want an eternal cyclic cosmos. But it's always seemed a bit contrived to me. And the reversal mechanism is no less mysterious than whatever "caused" the initial conditions at the Big Bang.

Of course, causality isn't well-defined "before" time itself exists. ;)

Ryder Rude

yeah...

@PM2Ring in this model, causality exists before the big bang

the time of the spacetime manifold is taken as more fundamental than entropy time which can reverse direction

PM 2Ring

Whenever you try to talk about the cause of the Big Bang you have to do something dodgy with time ordering & causality. Invoking some kind of meta-time is a common technique.

Ryder Rude

11:22

@PM2Ring i would say it is not dodgy. at the fundamental level, there is nothing fishy. It is just the GR equations. but at he emergent level, entropy changes direction

PM 2Ring

I like the idea that the "precursor" to the spacetime manifold was in some symmetrical state. But the symmetry was broken, thereby putting the manifold into a -+++ state.

Ryder Rude

i like the idea of explaining the initial conditions using some beauty argument about symmetry..but it cud also be that the initial conditions have no explanation

if physics is able to explain initial conditions, that wud be a huge achievement

PM 2Ring

Which reminds me of Mirror Universe theory physics.stackexchange.com/a/487304/123208

Ryder Rude

@PM2Ring yes

if we assume psychological arrow is reduced to entropic arrow, then the people in the mirror universe and our universe have mirrored time

PM 2Ring

Yes. That restores the symmetry.

And explains where all the antimatter went.

Ryder Rude

11:28

I think psychological arrow may be related to QM time and may require deep understanding of consciousness and quantum gravity

@PM2Ring lol

@PM2Ring there is a movie called Tenet where they reverse their psychological arrow by converting their body to anti particles

PM 2Ring

I've heard of that movie, but I haven't seen it. But we get questions about it from time to time on the Scifi stack.

Ryder Rude

oh

PM 2Ring

It appears to be a bit paradoxical, with numerous plot holes.

Ryder Rude

how do we answer the question "why can we choose to move forward and backward in space but not in time"?

@PM2Ring i think it says in the movie to not think about it too much

@PM2Ring i recommend it 7/10

it doesn't have plot holes. just unexplained things

PM 2Ring

It's pretty hard to do any kind of time travel story without creating paradoxes. But Tenet sails full steam ahead into paradoxical territory. ;)

scifi.stackexchange.com/questions/tagged/tenet

Ryder Rude

11:36

lol

it has unexplained stuff

PM 2Ring

The psychological arrow of time seems pretty fundamental to us, because it's ultimately how we experience time. OTOH, it's just what our mind/brain has managed to cobble together in its attempt to model time.

naturallyInconsistent

@PM2Ring miao miao cant know; just suggesting

Madder

12:04

@ACuriousMind Thanks for you reply. So in the case of continous event space, what would be the proper interpretation?

ACuriousMind

@Madder well, it's still "counting", but in the figurative sense that computing a Euclidean volume is "counting how many points are inside the volume"

more or less exactly like an integral is "like a sum" except it's not :P

GroveRover

Do you guys know any long, detailed videos on the interpretations of QM? Something on the level of the classical papers. I want to listen to it in my dead time

Talks at conferences et similar are good as long as they have decent audio

Madder

@ACuriousMind Oh i see.

Ryder Rude

@GroveRover hi. if ur goal is to learn interpretations, i think best way to learn interpretations would be to read books/papers about them

some interpretations have their math equations and stuff, e.g. Pilot wave theory and Many worlds. so listening to videos wouldn't be ideal

CU-Prime's 1st Annual Physics Debate: Many-worlds (Dr. Graeme Smith) vs QBism (Dr. Chris Fuchs)

►

this is a debate between QBism and Many Worlds

GroveRover

13:31

@RyderRude I'd like to watch while eating and stuff like that so papers are not suitable (I agree they would be better)

Equations can be shown on video

Herr Feinmann

What about printing papers and eating those?

These younglings...

GroveRover

@HerrFeinmann 💀

Herr Feinmann

Now guys it's about time I prepare the dreaded superconductivity exam

Tobias Fünke

oha

good luck

Ryder Rude

13:48

@HerrFeinmann gl

@GroveRover oh

i found a lecture presentation on many worlds youtu.be/Rtaq1DJPhBI?si=LkVc9xSLAJvlrRNV

Herr Feinmann

I will need something stronger than luck: interest :P

Ryder Rude

this is on transactional interpretation youtu.be/-Gj_sY7hDk0?si=UfeAewc2ScU9Bscc

this is on QBism youtu.be/I2w-BtI01sA?si=1NtUADxLTo-34jsU

Tobias Fünke

cmon, superconductivity is quite interesting, no?

Ryder Rude

@TobiasFünke is it a kind of qft

Herr Feinmann

@TobiasFünke Oh sure it is, that's why I chose the class. The bad thing is that the class turned out to be one of the worst experiences I've ever had with physics. Total scam :P

Tobias Fünke

14:02

whut :( oh no

naturallyInconsistent

@HerrFeinmann magnetise the exam paper

Herr Feinmann

No written exams anymore

Most of Master's degree exams are oral here

Ryder Rude

this is another QM interpretation but not a big one. youtu.be/sshJyD0aWXg?si=zlKkNW_ck_rCpRWF .

Tobias Fünke

@HerrFeinmann do you like this more?

Herr Feinmann

@TobiasFünke Complex question. I have less performance anxiety than for written exams, because I have more control over the situation. On the other hand, the kind of questions is different and I have the impression that acing an oral exam is not nearly as impressive as getting a perfect score on a written exam, which surely doesn't help with the impostor syndrome :P

Tobias Fünke

14:11

I see

Herr Feinmann

An oral exam is more about acting than knowledge :P

Tobias Fünke

well, yes, oral exams are more "forgiving" in the sense that the lecturer can immediately correct you or help you to notice you did something wrong/have a misunderstanding. On the other hand, I think in oral exams you can better see if a student really understood the subject (to a certain extent)

@HerrFeinmann nah, I would disagree

Herr Feinmann

You know, dramatic pauses, delivering lines at the right moment, using the right amount of pathos

much like a TED talk :P

Tobias Fünke

At my uni we had for all "big" subjects (which were 2 semesters long) written + oral exams in fact. You needed at least 50% of the exercises to be correct to be allowed to write the exam (each semester), but there was no grade. The oral exam was then over the two semesters and was graded.

Herr Feinmann

it was like that during the undegrad

or bachelor's, whatever

Tobias Fünke

14:16

ah yes, I meant Bachelor

Herr Feinmann

I'm completing my Master's

Tobias Fünke

In masters this was different. but except the defense of the thesis (of course) and one big and one small oral exam, everything was a written exam, if I remember well

I guess it is quite normal

Also because the classes are, usually, and in my experience, much smaller. But this may also depend on how large the faculty is

Herr Feinmann

Small faculty in my case

Tobias Fünke

yeah... so oral exams can be much less work for the lecturer lol

Herr Feinmann

I think that some lecturers wouldn't be able to solve an exercise :P

Tobias Fünke

14:19

or you use the exact same written exam over and over. this might be the most economically procedure

haha

Herr Feinmann

There was my analytical mechanics professor that would prepare like 5/6 written exams per year. The fact is that he has been doing that for decades and those exams are all the same but different

He's been exploring every possible combination of rods/disks attached to springs on rotating planes

Tobias Fünke

xd

Herr Feinmann

Or rods attached to other rods

and disks rotatings inside circles lol

Connected to the origin by a spring

Tobias Fünke

xD

what the...

Herr Feinmann

Typically the computations are standard (although stability typically requires a lot of algebra for the secular equation) but sometimes you get a kinetic energy with 14 terms (guess who was the lucky guy?)

Tobias Fünke

14:24

xD

I mean...the last time I did such a computation (perhaps not that complicated anyway), was like several years ago

but yeah, I guess with a bit of practice it is manageable (?)

Slereah

@ACuriousMind Apparenly Lawvere typically asked that a topos would be sufficiently cohesive, which is like that every space can be embedded into a contractible space [which fine] but also every function space on that larger space is contractible?

Any idea why that requirement

Basic example being that Set is cohesive but not sufficiently cohesive since only the terminal set is contractible

bolbteppa

14:52

The usual caliber of the 'alternatives' to string theory

ACuriousMind

@Slereah What do you mean by "function spaces"? The "standard" definition (cf. nLab) would just be that the subobject classifier is contractible. This implies the embedding of all objects into contractible objects, but nothing about "function spaces".

Slereah

Well what nlab says comes from the original paper, but Lawvere's original definition is that one, ie tac.mta.ca/tac/volumes/19/3/19-03abs.html

apparently an equivalent statement to the contractibility of the etc

ACuriousMind

@Slereah but where is there a statement about contractibility of function spaces here?

(d) just defines in one line 1. what contractibility means and 2. that all objects should embed into contractible objects

Slereah

$p_!(Y^A) = 1$

ACuriousMind

@Slereah That's just the definition of $Y$ being contractible

Slereah

15:03

Wouldn't that just be $p_!(Y) = 1$

ACuriousMind

no, that's $Y$ being connected

a space is contractible if all mapping spaces into it are connected (which normal topology would express as "all maps into $Y$ are null-homotopic")

Slereah

Hm

Ah I guess in more normal circumstances it would be with $A = S$

But for everyone

or $S^n$

So it's the existence of a boring space that can contain the other spaces

ACuriousMind

@Slereah no, it's a normal theorem of topology that $X$ is contractible iff for every other space $A$ you have that every function $f: A\to X$ is null-homotopic

that's what $p_!(X^A) = 1$ means

Slereah

alright thx

had to look into that because technically Set is a cohesive category but it feels weird to claim such a thing :p

The codiscrete functor is just the identity and they don't feel very codiscrete

btw one thing that I have not seen so far is, are codiscrete objects typically contractible?

Feels like they should be but I haven't seen any property for the interaction of $\int$ and $\sharp$ so far

It is true of the trivial topology and the coarse diffeology [I think?]

ACuriousMind

@Slereah no idea, this isn't the kind of category theory I like :P

Slereah

15:12

what's your favorite category

ACuriousMind

rings are nice I guess

Slereah

answer is probably in Schreiber's monstrous book somewhere

but it is all entirely for $\infty$-categories so it's a tough read

$\infty$-categories seem to have more fun discrete and codiscrete objects since apparently they correspond to types of connections in some categories?

instead of being "points" and "blobs"

the least fun objects

Parmenides would have loved codiscrete objects

think_meaning_buildß

15:39

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Relativisticcucumber

17:03

in lecture notes talking about landau levels where the levels are described by quantum number $\nu$, my professor has stated that electrons near the fermi surface have very high quantum numbers. why is this so? i thought $\nu$ is just an index in the same way that $n$ is in standard qm

ACuriousMind

@Relativisticcucumber well, the surface is the "top" of the part of the states that are occupied, so it has higher quantum numbers than all the completely filled states below it, no?

Relativisticcucumber

oh i think i see

hm

but he goes on to say that for this reason we can use the correspondence principle to treat this as a case where orbits reproduce classical mechanics

i am just uneasy about this statement

i mean i guess that is just what the principle says :P ok i accept

Silly Goose

17:19

Echoing Arjun, is there a standard reference for tensor calculus? At a mathematical level that is consistent with how practicing physicists use it?

I think someone has suggested the beginning of Wald before for this purpose.

ACuriousMind

@SillyGoose What kind of questions would you expect such a reference to deal with?

"tensor calculus", from where I'm at, is just a silly name for the rules of index notation, nothing you'd write a book on

Silly Goose

@ACuriousMind Sorry, what do you mean by this?

ACuriousMind

@SillyGoose As I said right after - I don't understand what content you expect this supposed reference to have

what is "tensor calculus" other than knowing how the index notation works?

or, somewhat more generally, doing differential geometry in index notation

Silly Goose

I think that is the question I'd want such a reference to deal with: precisely what is index notation, including 1) the definition of the objects it manipulates and 2) the rules of manipulation and possibly 3) its shortcomings and 4) alternatives and 5) its various forms (e.g. different people using slightly different conventions).

ACuriousMind

you just want a differential geometry text :P

Silly Goose

17:27

do diffeg texts go into index notation? I guess I didn't know that.

ACuriousMind

I mean, some of them may not (just like some physics texts like Straumann conversely generally don't use index notation)

Silly Goose

Do you have a favorite diffeg book?

I have Lee smooth manifolds open and I think I see that chapter 12 has some index notation.

I guess maybe it is time to sit down and learn diffeg.

ACuriousMind

@SillyGoose nope (because I haven't really read any so much that could judge it)

Silly Goose

do you have any diffeg resource recommendations?

ACuriousMind

but really I think focusing on "tensor calculus" as this obscure separate thing that manipulates objects with indices or whatever is misleading, it's really just doing differential geometry in coordinates where you declare some summation signs to be implicit

There are really only two golden rules: 1. No index may occur more than twice, once upper and once lower. 2. Both sides of an equation must have the same free indices (i.e. indices that occur only once). If you break them, you know you did something wrong, but apart from that I struggle to think of many things to say about it.

But I guess Wald is a good recommendation if you want someone to talk about the indices at a little more length since he does that "abstract" index notation where he doesn't want to "work in coordinates" but wants to have the same kind of index expressions

Silly Goose

17:48

@ACuriousMind Stuff like writing the "transpose" of a tensor or etc. continues to trip me up.

ACuriousMind

@SillyGoose well it depends on what you mean by "transpose" - are you not just being "tripped up" because some text uses the word without defining it properly?

Silly Goose

Now that is another possibility that I was hoping to solve by finding a good resource.

ACuriousMind

@SillyGoose but "transpose of a tensor" is not really some general concept that's being hidden from you here

it's just some text being imprecise :P

I can see an obvious way to define the transposes of tensors with 2 inputs/indices, but not in general

Slereah

I guess you could do it with 2n indices too, treating it as an operator on $V^n$?

Ryder Rude

@SillyGoose i think it is because the transpose of a tensor is a basis dependent operation in general

one should replace it with a notion like the adjoint

the adjoint involves a metric and it is a well defined notion in the abstract

ACuriousMind

17:59

@Slereah I had an entirely different generalization via the symmetric group in mind briefly, but I guess that just shows it's not a common notion with an established definition :P

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