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12:53 AM
@Stupidquestioninc what level?
3 hours later…
4:16 AM
@NorthLæraðr that's the distance from the Sun not the distance from the Earth.
2 hours later…
5:49 AM
@Yashas that’s a Poisson distribution. So the maximum will be around the mean $|\lambda|^2$
@ACuriousMind oh that’s a neat trick!
1 hour later…
7:19 AM
Hm, the chat doesn't display tweets
pretty neat that it works with ordinary voltage from a socket
7:44 AM
@ACuriousMind I mean it's a tunneling process, IIRC
It should work at any energy mostly, just with different probabilities
8:14 AM
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 ...
A: How do you rotate spin of an electron?

ACuriousMindYou 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?
@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.
Will do, thanks :-)
8:29 AM
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?
@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 ...
@JohnRennie Yes, because you're changing the relative phase between the two electrons
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?
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
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.
8:42 AM
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
Thanks :-)
I would have posted a question, but I don't want to give anyone a platform for shouting about Mobius strips.
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
@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 :-)
9:27 AM
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?
9:55 AM
@user400188 The density matrix is Hermitian, and therefore diagonalizable just like all the observables
can anyone help me on the
question? 2
physics section
10:44 AM
@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.
11:04 AM
@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
@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
@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.
1 hour ago, by Jack Rod
1 hour ago, by Jack Rod
can anyone help me on the
question? 2
If someone wants to answer they will @JackRod, come on
@Charlie HEY! I understand that policy but this question is jumbling inside my head for hours
11:13 AM
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
I have an exam tomorrow so even if someone answer it later it would have no use
@JackRod You should send the image of specific question, people might find it lazy to find the question in pdf.
for me
I would suggest the issue here is not other people being lazy.
that's fine you have not raised any specific issue regarding my question I posted it on the wrong page sorry :(
11:19 AM
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
@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.
@ACuriousMind I admit
@JakeRose I've never read a book on GR :P
thanks for guiding me
How did you learn it?
11:23 AM
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
What's his name did a pretty thorough list
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.
A: Books for general relativity

Ryan UngerThis 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
@Slereah thank you
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
11:25 AM
I thought landau was a little out dated in terms of it's pedagogy
Wald or Carroll is probably the standard these days
if that's what you want
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
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.
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
@JohnRennie sir i left the question with you
11:29 AM
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
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
If you want the mathematician way then Wald maybe yeah
Wald is probably the safe choice
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
I thought Wald was considered the most mathematical short of a book like Hawking or Wu
11:33 AM
This is some of the suggested books. Any comments?
Haven't read Stewart
The rest is fine, yes
Any recommendations on which one I should hunt for a pdf of
MTW isn't good as an introduction, though
It's more of a big ressource
@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.
Got it
11:35 AM
Apart from the advanced chapters, these books spend at least 5 times longer doing things Landau does in a paragraph
@bolbteppa is it best, though
Landau is, unsurprisingly, from the Landau school
They're not the biggest on pedagogy :p
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
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
@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.
Half of Wald is full of advanced stuff
11:41 AM
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
What does brass tracks mean?
The essentials
Verb: get down to brass tacks
  1. (idiomatic, chiefly US) To deal with the important details.
  2. 1863, January 21, 1863, The Tri-Weekly Telegraph, newspaper of Houston, Texas
  3. When you come down to brass tacks – if we may be allowed the expression – everybody is governed by selfishness.
  4. 1935, Clifford Odets, Waiting for Lefty...
the French and their weird slang ;P
12:12 PM
well TIL that word is tacks not tax
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"
12:49 PM
If we have a manifold with a curvature singularity at $p\in M$ does the domain of charts become $M-\{p\}$?
@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
And if this is a coordinate singularity we don't do this, we just let the coordinate blow up at that point
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
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 $x = 0$
12:55 PM
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?
I mean, it's $\mathbb{R}^n$
@Slereah ok yeah I can see that
By its very nature, it's coordinates
it's just a set of numbers
Actually I guess that's fine
I guess a minor point you can make is that $\mathbb{R}^n$ comes equipped with projection functions
1:02 PM
oh I haven't heard of that before
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 $p_i(\phi(p))$
ok I can see that
But that's a fairly low level structure here
it's not related to anything regarding vector spaces or whatever
I guess if the bottom line is that the domain of any chart is always $M-\{\text{coord. singularities}\}-\{\text{curv. singularities}\}$
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
1:05 PM
but are the of the singularities not being mapped to undefined points in $\Bbb R^n$?
Singularities may not even correspond to missing points on a manifold in some cases
oh I'm only aware of coordinate and curvature singularities
If you're still at the "defining what a manifold is" stage, don't worry too much about singularities for now
if you want to talk about singularities in a formal manner, you need something more general than "manifold" as the concept of your space
I'm pretty sure I'm happy with the definitions, just a topological space for which the open sets are homeomorphic to Rn
1:07 PM
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
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?
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
@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
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
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
1:10 PM
@ACuriousMind Not really the GR way I'm afraid :p
Usually people use the uuuuh
GHC construction?
ah the uh
Something like that
at least it's not the eh
Basically you define points by their histories
so that singularities can still be defined, since there are still curves ending at the singularity
I still see in my head the drawing of a patch of a manifold being mapped to some small circular looking region of Rn
1:13 PM
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
@ACuriousMind hey it works
well that just sounds dangerous :P
Things get dangerous when you start getting into really weird singularities
like directional singularities
it's a bold move but it pays off more often than you think :P
where the curvature blows up only if you approach it via a certain direction
1:14 PM
did not know that was a thing
they're pretty rare but they occur
Singularities are mostly fine in Riemannian spaces but in Lorentzian spaces they're a real pain
but that's all of gr ;_;
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
wait flrw has singularities?
Well, the big bang
Pretty famous singularity
1:18 PM
oh, right :P
and the big crunch, if things go bad
not sure the big crunch is worse than heat death
"things go bad" seems pretty much certain given enough time :P
@ZeroTheHero undergraduate
1:50 PM
if you want to learn more about singularities you can give what's his name a look
it's a good overview of defining singularities
2 hours later…
4:10 PM
Hello everyone! Good morning/afternoon/evening/night!

First of all: I hope you all are healthy.

So, the laws of physicas are Immutable?
@M.N.Raia if they weren't, would you not call the laws by which they can change the "laws of physics" too/instead?
Sorry, could you please say it in another way? I don't understood.
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.
@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".
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.
4:24 PM
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
But the frase of my friend was: "The physics laws are immutable, thefere they are eternal".
Almost all "laws" in physics are such approximations and idealisations, with limits to their applicability
I tend to think that they are immutable under their limits of applicability.
what would it mean for them to be mutable?
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".
4:28 PM
@ACuriousMind Just as I said: newton's Law of gravity needs to be changed close to a neutron star
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.
@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
So, we can say once and for all that exist immutable laws on physics?
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
So, my questions are pseudo-philosophy?
4:33 PM
I don't know, do you have proper definitions for what you are talking about?
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.
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.
@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
I find kind of hard to disagree with this phrase, but something seems wrong with that phrase.
On a completely unrelated note, here are two QVC hosts arguing about whether the moon is a planet or a star:
5:13 PM
@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. :)
6:24 PM
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
6:58 PM
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?
7:40 PM
@M.N.Raia : show me a law, and I will show you how to break it.
2 hours later…
9:54 PM
It had not occurred to me that $T_pM$ is the dual space of $C^\infty(M)$
mind blown
don't unblow my mind
$T_pM$ is a subset of the dual of $C^\infty(M)$
since $x\in T_pM:C^\infty(M)\rightarrow\Bbb R$
$C^\infty(M)$ is supposed to be the space of smooth real-valued functions on $M$, right?
To what number do you think some tangent vector $x$ sends a function $f\in C^\infty(M)$?
9:58 PM
the directional derivative in the direction of the tangent vector
are you applying the vector as a derivation, then evaluating at the point?
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
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
I realise now that I was less than careful with that wording :P
10:24 PM
@ZeroTheHero Tag me when you have answer ;)
Thank you all, for the answers @ACuriousMind @Secret @vzn @JMac
11:03 PM
@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.

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