The h Bar

ZeroTheHero

00:53

@Stupidquestioninc what level?

John Rennie

04:16

@NorthLæraðr that's the distance from the Sun not the distance from the Earth.

Superfast Jellyfish

05:49

@Yashas that’s a Poisson distribution. So the maximum will be around the mean $|\lambda|^2$

@ACuriousMind oh that’s a neat trick!

Slereah

07:19

twitter.com/xkcd/status/1301182384017203201

Hm, the chat doesn't display tweets

ACuriousMind

pretty neat that it works with ordinary voltage from a socket

Slereah

07:44

@ACuriousMind I mean it's a tunneling process, IIRC

It should work at any energy mostly, just with different probabilities

John Rennie

08:14

I have a question about rotating electrons if anyone is feeling bored.

Suppose we have a beam of electrons with their spins aligned up, and we pass it through a magnetic field that rotates the spins by 360°.

How does the resulting beam differ from the original beam? That is, we've only rotated the electrons half of the 720° that spinors need to return to their original state, but the 360° rotation leaves the spin unchanged so the beam looks the same.

What physical measurement could we make to distinguish the rotated electrons from unrotated ones?

Ah ...

17

A: How do you rotate spin of an electron?

You have fallen prey to a popular simplification of spinors. The statement "you have to turn electron by 720 degrees in order to get the same spin state" does not refer to an actual rotation of an actual electron. In quantum mechanics, we describe the states of objects as elements of a Hilbert s...

So there is no observable that is different after the 360° rotation?

ACuriousMind

@JohnRennie read my comment discussion there with garyp - it depends what exactly you mean by "rotation", but if you rotate the entire system under consideration then there is nothing different, no.

John Rennie

Will do, thanks :-)

user400188

08:29

Can anyone give an example of a system with set of basis vectors that is in a mixed state but its density matrix is not diagonal? Is this possible?

John Rennie

@ACuriousMind so if you looked at the interaction between two electrons then it would change if we used a magnetic field to rotate one of the electrons by 360°?

IIUC that's what the neutron scattering expt suggests ...

ACuriousMind

@JohnRennie Yes, because you're changing the relative phase between the two electrons

John Rennie

Aha. By phase do we mean the phase of the associated de Broglie wave?

Or is that a meaningless question e.g. am I trying to compare two unrelated concepts?

ACuriousMind

No, I just mean the phase between the two states when you form a superposition between them - if you have two states $\lvert \psi\rangle$ and $\lvert \phi\rangle$, then the superposition after rotating one of them is $\lvert \psi \rangle + \mathrm{e}^{\mathrm{i}2n\pi}\lvert \phi\rangle$, where $n$ is the spin.

this is the thing you detect e.g. in neutron interferometry, see physics.stackexchange.com/a/322017/50583

John Rennie

That does sound like changing the phase of the de Broglie wave. e.g. if you start with a coherent electron beam then split it and rotate one beam by 360° then the two beams will interfere like two waves that are 180° out of phase.

ACuriousMind

08:42

sure, if the states are approximately free then it's a de Broglie wave, but it doesn't matter what sort of state we have

John Rennie

Thanks :-)

I would have posted a question, but I don't want to give anyone a platform for shouting about Mobius strips.

ACuriousMind

well, as you can see this kind of question already has been asked

but please don't feel discouraged from asking questions because you don't want certain kinds of answers - see it as a platform for such wrong answers to be downvoted :P

John Rennie

@ACuriousMind it has, though the answers had left me unclear about the specific point that you have just explained.

@ACuriousMind ah, yes, that's my exact question. Oops :-)

user400188

09:27

Regarding the question I just asked in chat, would it be ok if I just asked it again (as is) on the main site? Or would I need to modify it to satisfy site rules?

ACuriousMind

09:55

@user400188 The density matrix is Hermitian, and therefore diagonalizable just like all the observables

Jack Rod

nestexam.in/qnsans/NEST-2019-Session-1.pdf

can anyone help me on the
question? 2

physics section

user400188

10:44

@ACuriousMind I aware I can diagonalise any density matrix, but I was wondering if the density matrix for a mixed state could only be written in a diagonalised way.

ACuriousMind

11:04

@user400188 I don't understand the question

whether a matrix is diagonal or not depends on your basis, it's not an objective property of the matrix unless it's a multiple of the identity

Jack Rod

@ACuriousMind hi can you have a look at the question, Does the spring stretched due to the generation of the net electric field?

What I did is equate the spring energy+energy of inductor

ACuriousMind

@JackRod No. As usual I have no idea what you're talking about and history shows this doesn't get better when I ask you to clarify.

Jack Rod

1 hour ago, by Jack Rod

https://www.nestexam.in/qnsans/NEST-2019-Session-1.pdf

1 hour ago, by Jack Rod

can anyone help me on the
question? 2

Charlie

If someone wants to answer they will @JackRod, come on

Jack Rod

@Charlie HEY! I understand that policy but this question is jumbling inside my head for hours

Charlie

11:13

I don't know what difference you think that makes

It's always been a rule not to bug people to answer questions. Not to mention it's the middle of the work day for some people

Jack Rod

I have an exam tomorrow so even if someone answer it later it would have no use

Mayank

@JackRod You should send the image of specific question, people might find it lazy to find the question in pdf.

Jack Rod

for me

ACuriousMind

I would suggest the issue here is not other people being lazy.

Jack Rod

that's fine you have not raised any specific issue regarding my question I posted it on the wrong page sorry :(

ACuriousMind

11:19

If you want to increase to probability of people answering your questions, you should take care to formulate them in a comprehensible way. "Can anyone help me on the question?" tells other people nothing about what you want to know. And a sudden "Does the spring stretched due to the generation of the net electric field?" without any context tells people nothing about what spring you're talking about

The first "question 2" in the document you linked is a question about math that has nothing to do with physics

where is the physics section? Do you expect other people to randomly scroll through a PDF to find what you're talking about?

You expect other people to help you when you don't show the slightest effort to make it easy for them

Jake Rose

@ACuriousMind what's the best GR book you've ever read? I'm feeling the lecture notes this year are gonna be a bit lacking.

Jack Rod

@ACuriousMind I admit

ACuriousMind

@JakeRose I've never read a book on GR :P

Jack Rod

thanks for guiding me

Jake Rose

How did you learn it?

ACuriousMind

11:23

but I'm sure @Slereah would be happy to recommend his top X GR books

@JakeRose I took a pretty bad course on it and then decided I found QFT much more interesting :P

Slereah

What's his name did a pretty thorough list

Jake Rose

ahahah that's fair

Doing QFT in about a week

All online :( and David Tong took his sabbatical so he's no longer lecturing it

Quite exciting though. Likely my favourite course in the masters list

Debating taking a short course in perturbation methods too. Sounds quite interesting.

Slereah

51

A: Books for general relativity

This list is extensive, but not exhaustive. I am aware that there are more standard GR books out there such as Hartle and Schutz, but I don’t think these are worth mentioning. Books with stars are, in my opinion, “must have” books. (I) denotes introductory, (IA) denotes advanced introductory, i.e...

If you need GR books for something specific you can ask

Jake Rose

@Slereah thank you

bolbteppa

Landau does GR in a way that shows how similarly it parallels the electrodynamics and special relativity it set up earlier in the book, basically nothing like it

Jake Rose

11:25

I thought landau was a little out dated in terms of it's pedagogy

Slereah

Wald or Carroll is probably the standard these days

if that's what you want

Jake Rose

Might have to give Carrol a go. Wald is a bit intimidating

The ones we were recommended by Tong seemed good, but not sure if they'll fit the new course

user400188

Are you talking about Sean Carrols book? I own it, but its more like a dictionary than something to learn from if it's your first introduction to GR.

Slereah

Weinberg's not bad, too

Also I tend to recommend Callahan, which is where I learned GR

It's a nice introduction

Very handholdy

Although you won't get much out of it

Jack Rod

@JohnRennie sir i left the question with you

bolbteppa

11:29

Nah it's not outdated, especially in terms of pedagogy, it just wont contain stuff past the 60's which is mostly super advanced anyway or wont use bundles which shows you how avoidable these things are

Jake Rose

We're doing it from a very mathematician perspective (it's a course for masters students mathematicians) so it's probably best to have something that takes it like this

Slereah

If you want the mathematician way then Wald maybe yeah

bolbteppa

Wald is probably the safe choice

Slereah

it's not the most mathematicky but it is gentle enough

If you want the worst introduction and the most mathematical, that would be Besse

bolbteppa

I thought Wald was considered the most mathematical short of a book like Hawking or Wu

Jake Rose

11:33

This is some of the suggested books. Any comments?

Slereah

Haven't read Stewart

The rest is fine, yes

Jake Rose

Any recommendations on which one I should hunt for a pdf of

Slereah

MTW isn't good as an introduction, though

It's more of a big ressource

user400188

@ACuriousMind I thought that a mixed state required some sort of interaction for it to be produced, and if the density matrix, in whatever basis, possessed coherences beforehand then they would be removed when the state changed to a mixed one. This is why I thought it would always be diagonal.

Jake Rose

Got it

bolbteppa

11:35

Apart from the advanced chapters, these books spend at least 5 times longer doing things Landau does in a paragraph

Slereah

@bolbteppa is it best, though

Landau is, unsurprisingly, from the Landau school

They're not the biggest on pedagogy :p

bolbteppa

The very few times it's not better are e.g. when L&L just state the components of a curvature tensor that takes pages to work out and other books will be friendlier on

Slereah

It's generally a good idea to check out a few different books for a given subject I would say

But then again it depends on the time you have for it

user400188

@ACuriousMind Thank you for answering the question. I might still ask it on S.E. however for an example of a mixed state density matrix with an off diagonal. I'm curious as to how it could come about.

bolbteppa

Half of Wald is full of advanced stuff

Slereah

11:41

yeah

you problably only need to read the first half for an intro

If you want a very brass tacks approach Weinberg's a good choice

it's very application oriented

Jake Rose

What does brass tracks mean?

Slereah

The essentials

get down to brass tacks

Verb: get down to brass tacks

(idiomatic, chiefly US) To deal with the important details.
1863, January 21, 1863, The Tri-Weekly Telegraph, newspaper of Houston, Texas
When you come down to brass tacks – if we may be allowed the expression – everybody is governed by selfishness.
1935, Clifford Odets, Waiting for Lefty...

ACuriousMind

the French and their weird slang ;P

Charlie

12:12

well TIL that word is tacks not tax

Slereah

Strangely enough people rarely recommend actual experimental GR books

I don't know that many of them that are like all experimental focused

probably the only one I can think of is "Clocks and Drag-Free Control : Exploration of Relativistic Gravity in Space"

Charlie

12:49

If we have a manifold with a curvature singularity at $p\in M$ does the domain of charts become $M-\{p\}$?

Slereah

@Charlie Yes.

you can still use $M$ as the spacetime, but then you would lose the metric character of the manifold

but it's still fine to use $M$ for say, the topology or whatever else

Charlie

And if this is a coordinate singularity we don't do this, we just let the coordinate blow up at that point

Slereah

In which case $p$ becomes a boundary point

Well if $p$ is a coordinate singularity, then it just means that the current patch you're considering doesn't contain $p$

But another patch will

Charlie

oh

Slereah

If you want a simple case to consider, take the spacetime defined by doing a dumb coordinate transform on Minkowski space

say $x' = x^{-1}$

Defined on $x > 0$

You will see easily enough that this has a coordinate singularity at $x = 0$

Charlie

12:55

I've definitely asked a variant of this question before here so I apologize, but the coordinates in the target space of the charts come with the chart, right? We can't have a map $\phi:M\rightarrow U\subseteq \Bbb R^n$ in which $\Bbb R^n$ is not equipped with coordinate functions right?

Slereah

I mean, it's $\mathbb{R}^n$

Charlie

@Slereah ok yeah I can see that

Slereah

By its very nature, it's coordinates

it's just a set of numbers

Charlie

hmm

Actually I guess that's fine

Slereah

I guess a minor point you can make is that $\mathbb{R}^n$ comes equipped with projection functions

Charlie

13:02

oh I haven't heard of that before

Slereah

that is, $$p_i(x_1, x_2, \ldots, x_i, \ldots, x_n) = x_i$$

When we talk about the coordinates $x_i$ of a point, we basically mean $p_i(\phi(p))$

Charlie

ok I can see that

Slereah

But that's a fairly low level structure here

it's not related to anything regarding vector spaces or whatever

Charlie

I guess if the bottom line is that the domain of any chart is always $M-\{\text{coord. singularities}\}-\{\text{curv. singularities}\}$

Slereah

Well no

A chart can have any domain, as long as it's an open set

and most manifolds can't be covered by a single chart

and manifolds covered by multiple charts don't necessarily end at coordinate singularities

Charlie

13:05

but are the of the singularities not being mapped to undefined points in $\Bbb R^n$?

Slereah

Singularities may not even correspond to missing points on a manifold in some cases

Charlie

oh I'm only aware of coordinate and curvature singularities

Slereah

If you're still at the "defining what a manifold is" stage, don't worry too much about singularities for now

ACuriousMind

if you want to talk about singularities in a formal manner, you need something more general than "manifold" as the concept of your space

Charlie

I'm pretty sure I'm happy with the definitions, just a topological space for which the open sets are homeomorphic to Rn

Slereah

13:07

A simple example you can take is that you can define the charts of a circle with just two intervals

There's no singularities involved at all here

there's just dumb mappings with slightly non-trivial transition maps

Charlie

as it happens I've just looked at the circle example so I can see that yeah

@ACuriousMind how can we generalise the idea of a manifold?

Slereah

there's a few ways to deal with singularities in your space and mostly you have to define something that can be used to define both points of the manifold and "missing points"

singularities, infinities, whatever

ACuriousMind

@Charlie E.g. a common way in which mathematicians talk about spaces with singularities is via stratified spaces - the top-dimensional stratum is the usual manifold, and the other strata are the singularities

Charlie

I'm not sure at what point I stop asking useful questions here. I'm never really sure when I'm flogging the absolute life out of a dead horse vs when I'm getting at something more instructive :P

ACuriousMind

but I guarantee you that you will not need to think about this notion as a physicist unless you dedicate your life to the rigorous research of various singularities :P

Slereah

13:10

@ACuriousMind Not really the GR way I'm afraid :p

Usually people use the uuuuh

GHC construction?

GPK?

ACuriousMind

ah the uh

Slereah

Something like that

ACuriousMind

at least it's not the eh

Slereah

Basically you define points by their histories

so that singularities can still be defined, since there are still curves ending at the singularity

Charlie

I still see in my head the drawing of a patch of a manifold being mapped to some small circular looking region of Rn

ACuriousMind

13:13

but really the most common treatment of singularities in physics is "pretend everything is not singular except sometimes we get $\infty$ as a result" :P

Slereah

@ACuriousMind hey it works

Charlie

well that just sounds dangerous :P

Slereah

Things get dangerous when you start getting into really weird singularities

like directional singularities

ACuriousMind

it's a bold move but it pays off more often than you think :P

Slereah

where the curvature blows up only if you approach it via a certain direction

Charlie

13:14

did not know that was a thing

Slereah

they're pretty rare but they occur

Singularities are mostly fine in Riemannian spaces but in Lorentzian spaces they're a real pain

Charlie

but that's all of gr ;_;

Slereah

it's mostly fine, rly

Basic GR doesn't have a ton of singularities

Just Schwarzschild, Kerr and FRLW

and (A)dS I guess

and they're mostly well-behaved singularities

Charlie

wait flrw has singularities?

Slereah

Well, the big bang

Pretty famous singularity

Charlie

13:18

oh, right :P

Slereah

and the big crunch, if things go bad

ACuriousMind

not sure the big crunch is worse than heat death

"things go bad" seems pretty much certain given enough time :P

Stupid question inc

@ZeroTheHero undergraduate

Slereah

13:50

if you want to learn more about singularities you can give what's his name a look

sciencedirect.com/science/article/abs/pii/0003491668901449

it's a good overview of defining singularities

M.N.Raia

16:10

Hello everyone! Good morning/afternoon/evening/night!

First of all: I hope you all are healthy.

So, the laws of physicas are Immutable?

ACuriousMind

@M.N.Raia if they weren't, would you not call the laws by which they can change the "laws of physics" too/instead?

M.N.Raia

Sorry, could you please say it in another way? I don't understood.

JMac

Then there's the whole problem of all our laws being based only on what we can observe, so we can't really completely rule out that things can change and we just haven't seen it yet. But that kinda starts to get into meta-physics territory instead of focusing on practical use of science.

ACuriousMind

@M.N.Raia I'm trying to say it depends highly on what you think "the laws of physics" or "immutable" mean. If the "laws of physics" could change, they would do so according to other laws. Either these are unchanging, and deserve to be called "laws of physics", too, or there are again laws by which these change, either ad infinitum, or until you have a set of unchanging laws that you can call "the laws of physics".

M.N.Raia

That's the point JMac, I was in a discussion with a non-physicist friend, and the thing become messy.

I based my comments on "domains of validity of a theory", like: "the newton's law of gravitation" isn't immutable close to a neutron star.

ACuriousMind

16:24

Most people would say that Newton's law of gravitation is immutable, it just doesn't apply everywhere, or rather, it's merely an approximation to another underlying theory - that of general relativity

M.N.Raia

But the frase of my friend was: "The physics laws are immutable, thefere they are eternal".

ACuriousMind

Almost all "laws" in physics are such approximations and idealisations, with limits to their applicability

M.N.Raia

I tend to think that they are immutable under their limits of applicability.

ACuriousMind

what would it mean for them to be mutable?

JMac

It also kinda depends on the context. In the context of physics, laws are generally considered immutable, and that basically allows us to actually progress. In the context of like looking at a specific physics law and saying "Is it impossible for this to change?" I think the only answer is "We can't say it's completely impossible but we have no evidence or reason to believe it would happen".

M.N.Raia

16:28

@ACuriousMind Just as I said: newton's Law of gravity needs to be changed close to a neutron star

JMac

Like you can't really prove the negative that it cannot change; but science focuses on what we can repeatedly observe, so pedantic arguments like that generally aren't worth much in science.

ACuriousMind

@M.N.Raia But why are you talking about "mutability" rather than the domain where the law applies?

mutability implies a change in time, not a limit to validity

M.N.Raia

So, we can say once and for all that exist immutable laws on physics?

ACuriousMind

I know neither what "immutable" nor what "laws on physics" means in that sentence :P

This is the danger of much pseudo-philosophizing: If you don't define your terms carefully, all statements can be true or false depending on how you interpret them!

And giving an example is not a definition, it is at best something that can guide you to one

M.N.Raia

So, my questions are pseudo-philosophy?

ACuriousMind

16:33

I don't know, do you have proper definitions for what you are talking about?

M.N.Raia

Acctually not kkkkk my friend just said "The physics laws are immutable, thefore they are eternal". and then I throw arguments based on limits of validity on he.

JMac

TBH in a totally general sense I find it hard to say that statement could ever be considered true from a human perspective. We in no way have the ability to determine if things are completely immutable at some fundamental level, or if everything is ultimately guided by a total lack of structure that might sporadically change at some point. But from a science point of view that's really just impractical.

ACuriousMind

@JMac The idea that all knowledge is preliminary collides with a lot of people's half-formed intuitions about how the world works and what physics/science is. Which is why I always try to bring them to pin down what they actually mean when making such statements or asking such questions, because many of them (the questions, not the people, though that also happens :P) just go away when you're trying to be precise about them

M.N.Raia

I find kind of hard to disagree with this phrase, but something seems wrong with that phrase.

JMac

On a completely unrelated note, here are two QVC hosts arguing about whether the moon is a planet or a star:

Is the Moon a planet or a star?

►

vzn

17:13

@M.N.Raia a kind of zen question at heart eh? but will say, anyone who thinks they are immutable should study kuhn, an (at times) esteemed colleague. :)

vzn

17:48

in theory salon, 58 secs ago, by vzn

DATA SCIENCE-- Artificial Intelligence Enhances Speed of Discoveries For Particle Physics / unite.ai

Secret

18:24

So random thought

I wonder if the maximum action principle in path integrals can be modelled as a busy beaver with uncountably many cards (that is, a transfinite busy beaver function)

The inspiration came from reading how the Busy beaver works, and how it tries to find the program that halts and print the most ones, sounds almost like the idea of computing all paths between state A and state B, and then extremises it

Marco

18:58

Can anyone recommend me some good material(s) about the numerical methods/schemes for the solution in 1, 2 and 3 spatial dimensions wrt Boltzman Transport and Ginzburg-Landau (Real and Complex) equations?

John Duffield

19:40

@M.N.Raia : show me a law, and I will show you how to break it.

Charlie

21:54

It had not occurred to me that $T_pM$ is the dual space of $C^\infty(M)$

mind blown

ACuriousMind

what

Charlie

don't unblow my mind

$T_pM$ is a subset of the dual of $C^\infty(M)$

since $x\in T_pM:C^\infty(M)\rightarrow\Bbb R$

ACuriousMind

$C^\infty(M)$ is supposed to be the space of smooth real-valued functions on $M$, right?

Charlie

yeah

ACuriousMind

To what number do you think some tangent vector $x$ sends a function $f\in C^\infty(M)$?

Charlie

21:58

the directional derivative in the direction of the tangent vector

ACuriousMind

are you applying the vector as a derivation, then evaluating at the point?

Charlie

ah yes, that's what I'm doing

don't tell me I've been lied to, I can't handle the rejection this late in the night

ACuriousMind

well, you're right about the "subset" thing, it's just a very different thing from the two spaces being duals of each other you said first

Charlie

I realise now that I was less than careful with that wording :P

Stupid question inc

22:24

@ZeroTheHero Tag me when you have answer ;)

M.N.Raia

Thank you all, for the answers @ACuriousMind @Secret @vzn @JMac

ZeroTheHero

23:03

@Stupidquestioninc for something basic (junior undergraduate 1st courses) that oozes with physics physics.pomona.edu/sixideas . Maybe you want something at a higher level but this guysimpressive in the way he explains things.

@JohnRennie I personally prefer the management citation for this year.

Transcript for