The h Bar

Obliv

02:39

Would rubbing an ice cube on a surface to speed up its melting process be considered frictional work? I have a tough time believing that. I think of friction as the breaking of bonds both micro/macroscopic and afaik ice is nearly frictionless. If anything, I imagine it's due to the pressure increase while pushing it as well as the natural conduction of heat.. I REST MY CASE.

this textbook is telling lies, LIES I SAY

Although I will say I stuck my tongue on a pole as a kid and there was definitely bonding to break up. In some cases with ice that happens too but not if it has already begun melting so that there is water on the surface.

Obliv

02:52

Thermo is so fascinating to me for some reason, definitely my favorite subject thus far.

John Rennie

04:30

@Obliv There would be some friction even though it was small, so there would be some work done and that would go into raising the temperature of the ice and therefore melting it. But I agree it wouldn't be a very effective way of melting the ice :-)

Slereah

06:40

Apparently the trick of the double tangent bundle $TTM$ is that it describes a family of curves $\gamma_s(t)$, and the two different bundle structures represent either $(\gamma, \frac{\partial \gamma}{\partial t}, \frac{\partial \gamma}{\partial s},\frac{\partial^2 \gamma}{\partial t \partial s} )$ or $(\gamma, \frac{\partial \gamma}{\partial s}, \frac{\partial \gamma}{\partial t},\frac{\partial^2 \gamma}{\partial t \partial s} )$

And then if you assume that the variation of your family of curves is in the same direction as the tangent vector itself, then you just have a family of curves squashed to a single curve, and the last term is the second derivative

And that's how the second jet bundle is included

And TTM itself is gonna be useful since that also allows you to describe variational calculus

Also I think this relates to Jacobi vector fields and the commutativity of derivatives for families of curves

Hence the flip

It probably also relates to the jet space for surface in some way I would guess too

Since it's essentially about doubly ruled surfaces

Slereah

06:57

Not entirely sure where the different connections enter in there yet though

Slereah

07:52

Yesss

and there already is an involution on J^2

It's all coming together baby

Silly Goose

i've heard that other interpretations (other than copenhagen I mean) of quantum mechanics are more believed these days. is there a modern quantum mechanics book that does not focus mainly on the copenhagen interpretation?

at the undergraduate level

ACuriousMind

@SillyGoose who told you that :P

Silly Goose

one of my profs said that many worlds is the most popular interpretation these days

ACuriousMind

the most widely believed interpretation is very likely still "Copenhagen" in the sense of "yeah, yeah, I believe in Copenhagen please don't bother me about this anymore" :P

Slereah

It was David Bohm wearing a fake moustache

@ACuriousMind arxiv.org/pdf/1612.00676.pdf

Although it is very much so not a random sample

ACuriousMind

08:06

honestly, textbooks saying they use the "Copenhagen interpretation" is mostly just them saying "we will not debate interpretational issues at all in so far as possible"

Silly Goose

XD

ACuriousMind

but you can't really say the latter because in order to talk about measurement you have to do something and unless you commit to a fully operationalist description that something will be a (very unsophisticated) interpretation and may involve the word "collapse", and that folklore interpretation is what "Copenhagen" often refers to

Slereah

Yeah I think most students would not enjoy very much doing actual math on Copenhagen

Doing Hilbert orthomodular lattices and non-commutative logic

or whatever people do these days

@ACuriousMind I suspect that after weeks of working on the topic, the fundamental answer I will get will be something like "The kinetic term is the one square in the speed and mass is force divided by acceleration"

but with more bundles

ACuriousMind

I mean

are you surprised? :P

Slereah

Well it's not quite that, but I guess it is reassuring

Since Coleman's approach says that the "free" acceleration terms are the ones quadratic in the velocity, and the spray approach says that geodesic sprays are the ones homogeneous of degree two

Although finding the mass from this isn't as trivial since the mass term isn't necessarily as clear as in classical mechanics

Presumably I need to split my sprays into a homogeneous and non-homogeneous part, and the non-homogeneous part is the acceleration due to force

also this is all for point particles so idk how well this generalizes to field theories

@ACuriousMind Question is, is it true for all homogeneous terms

If I have some random term in $a(x) v^2$, is it itself a kinetic term

uhoh

08:53

1

Q: Nodal precession effect on attitude?

When a satellites orbit experiences nodal precession, does this have any effect on the actual attitude or orientation of the satellite? For example, if the satellite is pointing at a particular star, will it remain pointed at that star?

orbital-mechanics

ACuriousMind

09:33

@Feynman_00 Bird invasion update: A sparrow just flew into my flat, and extremely politely just left again when I greeted it.

fqq

10:43

@SillyGoose I suspect it might be "the most popular" among your professor and their friends, but overall it's highly unlikely

I don't know if there's good data about it but it does not seem to be very popular among people who are at all connected to experiments

Slereah

Interpretations as they relate to experiments tend to go for the old shut up and calculate kind I think

Me I don't even believe in interpretations, I think you should just leave such things unmeasured

How uncouth to have prequantum bundle and then try to extract informations from them

That is where problems begin

Problems arise because of André Weil and Hermann Weyl

It's Lorenz-Lorentz all over again

Can't we merge them into a weẏl

Feynman_00

11:21

Question: is there a rigorous version of the stuff we do in QM with the eigenstates of position and momentum? More specifically, is there a rigorous explanation on why completeness relations hold in the case of continuous spectrum?

ACuriousMind

13 hours ago, by ACuriousMind

behind that is even more terrible math about generalized eigenvectors and rigged Hilbert spaces :P

Feynman_00

@ACuriousMind I guess sparrows are gentlebirds in contrast to bats

which aren't even birds

@ACuriousMind So everything is actually explained rigorously unlike e.g. path integrals

ACuriousMind

path integrals are also rigorous for ordinary QM

Feynman_00

Oh

ACuriousMind

see Wiener integral, Feynman-Kac formula

Feynman_00

11:26

I thought there was a problem with the normalization factor as Feynman and Hibbs mention

ACuriousMind

@Feynman_00 yeah, and they're extremely skittish - there are often sparrows on my balcony but they fly away whenever they see me moving

@Feynman_00 I'm not aware of that

Feynman_00

I mean this

Regarding birds, I also have some magpies hanging out in my place

ACuriousMind

@Feynman_00 ah, but that's just if you want to see this as some sort of Riemann sum limit

Slereah

@Feynman_00 path integrals have like three different kinds of divergences going on

but it can be shown that they all compensate each other

ACuriousMind

the rigorous approach I mean just directly defines a measure like $\mathrm{e}^{-S[x(t)]}\mathrm{d}x(t)$ on the space of paths, no limits involved

Feynman_00

11:31

@Slereah This reminds me of Mr. Burns diseases that compensate each other in one episode of The Simpsons :P

Slereah

that's physics for you :p

Gotta manage your pathologies

Feynman_00

Oh, I see. So things can be made rigorous but what is not rigorous is the definition using that fake Riemann sum

ACuriousMind

yes

@Feynman_00 neat - the only corvids I get here are rooks, they like to sit on the guardrail and stare at me :P

Feynman_00

An interesting fact, which I have to understand, about the birds I watch is that they don't "walk" but prefer to make little (cute) jumps

I think hop is the right word

If I had to choose a bird as a pet I think I would go for an owl, though

Slereah

11:57

I've had the occasion where some pigeons just went in for a look

ACuriousMind

@Feynman_00 apparently, hopping is easier for those that do because they are much lighter in comparison to their size than we are (and because of the general structure of bird bodies)

Slereah

ACuriousMind

@Feynman_00 unfortunately, owls are rather stupid birds :P

Slereah

@ACuriousMind Owls are renowned for their skills in astronomy

As can be seen in the Major Keys of Solomon

This guy can help you with astronomy

ACuriousMind

is that the king of astronomy

or what's the crown for?

Slereah

12:18

Only a prince I'm afraid

Stolas[5] (also known as Stolos, Stoppas and Solas) is "a Great Prince of Hell, commands twenty-six legions of demons. He teaches astronomy and is knowledgeable about herbs, plants, and precious stones. He is often depicted as a raven or a crowned owl with long legs."

Sometimes if I get no answers on GR questions I will turn to the dark lord

More Anonymous

Can GR be thought of as the relation between the tangent and geodesic deviation vectors?

Feynman_00

@ACuriousMind For real? I thought owl were quite smart compared to other birds :(

Slereah

@MoreAnonymous that is sort of what a spray is I guess

ACuriousMind

@Feynman_00 They're not especially smart

the smart birds are parrots and corvids

Feynman_00

Well, now I feel a stronger need to protect owls

Also co(r)vid is smart. I'm still positive after a week (I feel normal though)...

ACuriousMind

12:26

we had a bunch of nut trees in the street where I grew up and the rooks and crows would position the nuts on the street so that cars passing by drove over them and cracked them

pretty clever

More Anonymous

@Slereah jokes apart?

Slereah

What do you mean "jokes"

More Anonymous

Also I knew it! the bishop is better than a rook: lichess.org/MNm32AzF9qap

Slereah

Spray (mathematics)

In differential geometry, a spray is a vector field H on the tangent bundle TM that encodes a quasilinear second order system of ordinary differential equations on the base manifold M. Usually a spray is required to be homogeneous in the sense that its integral curves t→ΦHt(ξ)∈TM obey the rule ΦHt(λξ)=ΦHλt(ξ) in positive reparameterizations. If this requirement is dropped, H is called a semispray. Sprays arise naturally in Riemannian and Finsler geometry as the geodesic sprays whose integral curves are precisely the tangent curves of locally length minimizing curves. Semisprays arise naturally...

More Anonymous

:P

Slereah

12:38

You can define the GR connection in terms of spray

More Anonymous

@Slereah Recommended book?

Slereah

Not sure I have one

More Anonymous

@Slereah thanks :)

Slereah

Usually spray is more of a hamiltonian mechanics thing

Particles in GR follow what's called a geodesic spray, which is a special kind of spray

And the spray sort of defines how families of particles act

their deviation

More Anonymous

Thanks ... I was looking for this

I think I'll ask on PSE for references?

or lecture notes?

Slereah

12:40

you can look it up on google

The spray is basically a vector field with integral lines that minimize some quantity

for geodesics that's length

More Anonymous

how does the geodesic deviation enter the story?

Slereah

You can analyze the behaviour of families of geodesics $\gamma_s(t)$ in terms of spray

this gives you some relation between the acceleration of curves and their separations

More Anonymous

yea this was the kind of stuff I was thinking of

Slereah

elib.mi.sanu.ac.rs/files/journals/nsjom/47/nsjomn47p69-78.pdf

idk try this maybe

Feynman_00

12:58

@ACuriousMind Those crows are smarter than me fr

More Anonymous

thanks

Slereah

But more generally just look into the Jacobi equations

More Anonymous

ah okay

Slereah

and the raychaudhuri equation

Slereah

13:18

"given the symplectic form ω, it is natural to ask if it is the curvature 2-form of a 7U(1)-principal connection ∇ on complex line bundle L over X"

I think Schreiber may be projecting a little

Feynman_00

13:53

@ACuriousMind It seems some birds are acquainted with the concept of volume of water since they throw stones inside bottles to raise the level of water and drink

I think that's some pretty advanced knowledge of Physics for a bird :P

Here

ACuriousMind

15:24

broke apocalypse plot: Mad computer scientist releases intelligent machines and they destroy the world.
woke apocalypse plot: Mad biologist creates generically-modified corvids with hands and they destroy the world.

Emilio Pisanty

0

A: Moments of coordinates of uniform distribution on unit sphere

Here is a seat of the pants partial demonstration, but I just know there are elegant proofs in MSE, and I have no gumption to translate them. (Confirming the formulas for the 1-sphere, $S^1$, the circle, already nets you a normalization problem: try it.) Take coordinates x,y,z,...,s on your $S^...

whoa

@CosmasZachos studied with Bargmann x.x

:-O

Slereah

16:18

Ugh

I feel like if I want to talk about length scales with mass, I'm gonna need to figure out how the Weyl weight thing works

It is hard to advance because I have all the papers in the world open on my browser

It makes searching a bit hard

Slereah

17:10

currently have about 1500 tabs open

Feynman_00

There is nothing I hate more than twisted notations

Any time I run into some bad notation my OCD triggers and I start writing wall of texts in my notes which are both a harsh criticism and an explanation of the mess that has been done

Feynman_00

17:36

@Slereah Lol I had ~10 and I felt guilty

ACuriousMind

I've never understood how people live with that many tabs

Feynman_00

18:00

The ideal number is 5ish

At most 9, so you can use ctrl+number to change tab

Slereah

@ACuriousMind I don't

I am dying

🪦

Feynman_00

Lmao

Slereah

18:32

why must everything relate to everything in physics

it makes for a pretty big task

Obliv

19:13

If it isn't stated that two rods connected end to end are in a steady state condition, the rate of heat conduction isn't necessarily equal for both rods right

Feynman_00

@Slereah You started this for black holes and all you got is a rabbit hole

Slereah

Hell I'm not even investigating specific spacetimes

Just the general concept of a spacetime

Worst part is a lot of what I want to do is already done by Coleman, but it's spread over a bunch of papers and being pretty vague?

I think some of it may be references to epistemology papers I am not aware of

They kind of form their own little communities outside of physicist circles

wish the dude just wrote a big book on the topic

Feynman_00

Now that you mention it, I've never asked you if you're doing this on your own or like as a PhD student or anything like that

Slereah

I am doing it on my own I'm afraid

Feynman_00

Why would you be afraid, just asking out of curiosity

:P

Slereah

19:24

I'd rather get paid for it

get that big differential geometry money

Obliv

does a thermal conductivity question make sense if T = 0 celsius

or do i have to convert to kelvin so it doesn't just multiply the terms with 0

ya i guess i do

Slereah

19:44

Maybe I should figure out where the epistemologists are hanging out*

Reading some wild post on philosophy SE, and I'm thinking "Who is that guy?"

I look at the poster, and it's Ron Maimon

"Physicists are not immune to philosophical fasion, and between the years of 1974 and 1984, string theory was rejected essentially for the same reasons logical positivism was dying in other fields--- marijuana and New-Age thinking, plus a desire to revive the nice classical questions of philosophy about an objective world."

imbAF

21:18

If a quantum system is characterized by spin. Is it correct to say that the spin can have any possible direction, before a measurement ?

fqq

22:52

quantum spin states in general don't have a direction

imbAF

23:06

I mean when you make a measurement using a SG machine, the z spin component might be up or down, before the measurement no?

Meaning a physical quantity of the system, before the measurement, has every value, from the possible range of values that it can take

ACuriousMind

@imbAF the notion that the values of physical quantities exist before measurement is called realism

imbAF

well since the physical quantity before the measurement can have any possible value, from "pool" of values that it can take, doesn't that make the realism part not true?

Since physical quantities aren't pre determined

ACuriousMind

it's not "can have any possible value"

it's "it is not meaningful to talk about its value prior to measurement"

imbAF

I don't know what the correct way of expressing myself is

But you get the idea

@ACuriousMind if this is the correct way of saying it, and it's the case so, then the realism claim is not true, right?

ACuriousMind

well

not everyone believes that is the correct interpretation

imbAF

23:13

but one of the first things we are taught in QM, is that the measurement can influence the system

and that the measured value, it's a probabilistic one

ACuriousMind

that's because your textbook/lecture started somewhere with a disclaimer that it's going to "use the Copenhagen interpretation"

imbAF

What I am trying to find out, is how the claim of the nobel prize winner about the local universe not being true, is something new?

Since probabilistic measurement of values of physical quantities

ACuriousMind

...do you know what Bell's theorem is?

imbAF

have been a known thing in QM

Bell's inequality about the hidden variables or smth?

ACuriousMind

sure

imbAF

23:16

Kind of

very superficially

ACuriousMind

if you know what the idea of "hidden variables" is about, you should understand that it is precisely about the nature of probabilism in QM

if you don't know, go read up on it :P

imbAF

I will do then so

One more thing

ACuriousMind

(I don't know what "claim of the nobel prize winner" you're talking about but you'll have no chance to understand advanced discourse in quantum interpretation if you don't understand a) what Bell's theorem says and b) what the measurement problem is really about)

imbAF

If this holds true : it is not meaningful to talk about its value prior to measurement

Look, cuz I can't formulate the sentence, the proper way

If the measurement influences the system, and if the result of the measurement, can be

a value, from the possible values that the physical quantity can take, with a certain probability

Considering the case that humans are smarter then what they are now

couldn't we make experiments and measurements, which would measure, the exact value that we would want, which would imply, that the system would be in a state that we would want

fqq

if the measurement is certain, the system is already in the state you want (before the measurement)

imbAF

23:22

The measurement influences the ssytem

so it's certain

ACuriousMind

I'm afraid I have no idea what the question is. The result of a quantum measurement is random in common interpretations. What does humans being smarter than now (???) have to do with anything?

imbAF

If we would be able to tell how it would influence it

then we would be able to know the value that we would receive before receiving it

ACuriousMind

then the result wouldn't be random if we could predict it, would it?

imbAF

correct

ACuriousMind

that's exactly what "there are no hidden variable theories" is about!"

if you can predict the result, there's a hidden variable

imbAF

23:24

because the randomization is a result of us not being able to tell or explain how the experiment would affect the system, prior to actually doing the experiment.

@ACuriousMind is this related to Bells inequality ?

ACuriousMind

yeah, go read about Bell's theorem :P

this isn't "one more thing"

it's just the same thing as before, i.e. the measurement problem

imbAF

This is fascinating

@ACuriousMind a problem which exist, because we cannot tell how the experiment would affect the system, prior of this experiment taking place, I guess

ACuriousMind

I just today answered a question about superdeterminism, which is the notion that it's not the measurement that influences the system, it's that both the measurement and the system are completely deterministically produced from the initial conditions of the universe, no "interaction" required

imbAF

And then the experiment takes place, we get a value that we cannot predict, and we call this probabilistic behavior or something

ACuriousMind

yes, that's just the measurement problem

this notion/puzzle has been literally debated for over 100 years

imbAF

23:28

completely deterministically produced = realism?

Or am I mistaken?

ACuriousMind

it's, uh, supercharged realism?

imbAF

so realism on steroids?

xD

ACuriousMind

there's a lot of subtle differences between there interpretations that are really more about epistemology than they are about physics

fqq

@imbAF what claim and what nobel prize winner are you talking about?

imbAF

And if I believe that the probabilistic nature of the result of the measurement, is our incapability of knowing how the experiment will affect the system, prior to this experiment taking place, where would that put me? With the group that believes in realism or in the one that doesnt?

@fqq reddit.com/r/askscience/comments/xxyqgx/…

ACuriousMind

23:31

@imbAF It would put you in the group that hasn't understood the problem

imbAF

That the universe is locally not real

fqq

if you mean in general the work that lead to this year's nobel prize, it's not new at all

one of the winners was awarded for work he did in the 60s/70s

imbAF

@fqq Exactly, that is what I am trying to say.

ACuriousMind

@imbAF That's literally a butchered statement of Bell's theorem that no local and realist theory can explain the results of QM

imbAF

I fail to understand how the probabilistic nature of a measurement is something new

ACuriousMind

23:32

it doesn't really have much to do with the nobel prize winners

imbAF

@ACuriousMind scientificamerican.com/article/…

I read this article today

Hence why I am asking

fqq

the point is that your courses and textbooks were written after their work

8 mins ago, by ACuriousMind

yeah, go read about Bell's theorem :P

ACuriousMind

@imbAF Aspect and the others got their prize for groundbreaking experimental realizations of tests of Bell's theorem

imbAF

@fqq Most definitely. I doubt I have the knowledge to understand it, but I'll give it a try

ACuriousMind

(and related "non-classical" demonstrations like Wheeler's delayed choice)

"the universe is not locally real" is just a silly pop-sci attempt to sound provocative (fishing for the reaction "What do you mean the universe isn't real?!")

imbAF

23:36

Yeah, I thought so much

ACuriousMind

when in reality the terms of locality and realism don't apply to the universe but to specific quantum interpretations

imbAF

but locality and realism are 2 characteristics of the universe?

ACuriousMind

"the universe" is neither local or realist, these terms make no sense to apply to the universe

imbAF

Ah, ok

you just answered my question

ACuriousMind

our theories about it are local or realist, not the universe itself

imbAF

23:37

local is what? Study over a confined region ?

ACuriousMind

again, just learn about Bell's theorem

imbAF

Ok

But thanks for the info

Goodnight

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