but we saw that we can't talk about a (1,1) tensor being symmetric using an identical notation, because we can't switch covariant and contravariant indices.
the symmetricity of a (1,1) tensor is not a basis-independent property, which is y i think it is hard to notate in index notation
to have basis independence, we have to use a generalised notion of symmetricity, which is like the Hermitian adjoint. this notion will depend on the metric
Hey y'all! I'm learning about Topological Phases of Matter + related topics and asked this question on Phys.S.E:https://physics.stackexchange.com/questions/828977/what-are-current-open-questions-and-research-directions-related-to-topological-m asking about research directions and open questions in the field
It got shut down because it's opinion based :2 but it led me to discover the h bar so all's well that ends well ig
If anyone has any input (/ generally would like to chat about this stuff), I'd love to hear it( / talk)! ty :)
> even today there are many who think one could usefully "generalize" by omitting those requirements, sometimes on grounds of dislike for the "stasis" they think they imply. However, in modern Greek "stasis" means "bus-stop"; how useless an intricate network of speeding buses would be without them, and how disembodied would be processes without states.
hm odd question, but how do you evaluate the validity or quality of a philosophical text? as someone who had no philosophical background I picked up a few well known ones and a lot of it just sounded nonsensical? but you know there have been a lot of people cleverer than me who seem to appreciate it so I don't know what's missing
i went through a Phase when I thought I could get into philosophy since great thinkers admire them blah blah , thought it could help understand this messed up human world (sadly physics has no explanation for that)...
tried a bunch of books - pop philosophy breakdowns, including Sophie's world which I detested
tried a few of the ancient Greeks, mostly the stoics which really rubbed me the wrong way
actually borrowed Kant's critique of pure reason after that
far too jargony and didn't make any sense :p
I don't remember what else I tried but I gave up after that. I ended up reading Wikipedia on political theories instead and le guin's "the dispossessed" which I liked because I found the physicist world plot relatable
> A co-Grothendieck cotopos is a locally small finitely cocomplete category with a small cogenerator, with all small products which are codisjoint and pushout-stable, and where all internal bisimulations have effective subobjects, which are also pushout-stable.
Did they just add a bunch of co's to the topos text
@kdeoskar You can check out work by Alexei Kitaev and Xie Chen (Caltech ~somewhat nearby to Berkeley~), the entire CMT faculty at University of Illinois Urbana-Champaign, and some folks at MIT (Xiao-Gang Wen). These people are all large figures in the topological phases of matter field, to my understanding.
Ah there is also Lukasz Fidkowski (UWashington), Michael Levin (UChicago), Max A. Metlitski (MIT)
Oh also like all the UCSB faculty associated with Microsoft Q
@qwerty If you wanted to get into philosophy, I'd recommend the youtube channel philotube. However, it will not be particularly helpful for understanding this messed up hooman world. Instead, you'd need economics, geopolitics, psychology, and all, for that.
good ideas are hard. i think if you have a good research programme during your PhD and you can spin off of that it's easier. if it was a dead end then it's harder
> But all this proved to be of no account in the eyes of Archimedes and in comparison with the engines of Archimedes. To these he had by no means devoted himself as work worthy of his serious effort, but most of them were mere accessories of a geometry practised for amusement, since in bygone days Hiero the king had eagerly desired and at last persuaded him to turn his art somewhat from abstract notions to material things, and by applying his philosophy somehow to the needs which make themselves felt, to render it more evident to the common mind.
@naturallyInconsistent @ACuriousMind I appreciate the responses. So I looked a little more into the addition of angular momentum and I see now how you can have different values of L but the same M_l depending on whether the angular momentum vectors are pointing in the opposite direction (L=0 if they have the same momentum) or in the same direction or somewhere in between
And i imagine that works like the rest of the measurable quantities, where each of those possible observations is an eigenstate of the “added angular momentum” operator
well...the idea of an "angular momentum vector" pointing in any particular direction is somewhat suspect in QM as its components do not commute, but yes, it's often visualized that way
I guess im just wondering, since were doing this to label atomic term symbols, is this a property of the system that like, hm, doesnt change over time? Forgive me for wording this badly, i study chemistry lol
As in the book says we label the L=0 S=0 state (the state where the momenta “cancelled out”) as the ^1 S _0
Yes, the Hamiltonian for an atom is usually spherically symmetric, so the angular momentum eigenstates are also stationary states
and I'm sorry if I was rude about "this is in intro QM" yesterday, if you're a chemist the confusion makes a bit more sense, I was assuming someone who should have done a lot of angular momentum addition already in a physics QM course :/
Its ok :) my interest is in computational quantum chemistry so I definitely plan to study QM in depth when i get the chance!
I guess this was the first time in this book where ive felt like it didnt explain it very well. Everything up to here has been awesome. It’s mcquarries pchem
> I am convinced that quantum mechanics is not a final theory. I believe this because I have never encountered an interpretation of the present formulation of quantum mechanics that makes sense to me. I have studied most of them in depth and thought hard about them, and in the end I still can't make real sense of quantum theory as it stands.
@Slereah It sounds like "La Trahison des Clercs" -- the treason of the intellectuals (actually of the clerks, which I suppose used to be taken as the anointed intellectuals back when the book by this title was written). This phrase however sometimes means they are too concerned with worldly affairs, and at other times that they're lost in their abstract matters. At every age they are a very comfortable bunch of people to scapegoat it seems
@nickbros123 oh, this is not even yet the kind of maths that requires functional analysis to understand. It is sufficient with differential forms' upgrade of contour integration trickery
> Currently, there is no proof that the Wightman axioms can be satisfied for interacting theories in dimension 4. In particular, the Standard Model of particle physics has no mathematically rigorous foundations. There is a million-dollar prize for a proof that the Wightman axioms can be satisfied for gauge theories, with the additional requirement of a mass gap.
this is a mathematical foundations problem
> Under certain technical assumptions, it has been shown that a Euclidean QFT can be Wick-rotated into a Wightman QFT, see Osterwalder–Schrader theorem. This theorem is the key tool for the constructions of interacting theories in dimension 2 and 3 that satisfy the Wightman axioms
but u also need to know Newton's laws. I feel Goldstein is comprehensive classical mech. Read this if u r interested in classical mech for the sake of classical mech, instead of for getting into qm
i think Shankar's Chapter 2 has all the required classical mech for QM
a lot of QM stuff is understood from a classical motivation.. like angular momentum, what does it even mean classically. Then there's relativistic QM that requires relativity, and you really can't understand relativity without a good CM basis I think
@DannyuNDos While many people tend to try to learn QM without a firm grounding in classical mechanics, I think the more classical mechanics you know (especially Hamiltonian mechanics), the better. Classical EM is not really helpful for QM, though.
@DannyuNDos If you mean that Linear Algebra of them all is the one that unlocks the most doors, I kind of see that. Though Idk the context you responded to
@RyderRude math majors can jump into a lot of physics "cold", in general. the question is how to prepare them to understand the physics that motivates the stuff and not just the formalism
Still, I wonder they should really lack relativity courses, considering that some heavy elements, such as Au, Hg, and Pb, express phenomena caused by relativities.
@bolbteppa I mean you've linked a video by a channel whose description states they are "Exploring theoretical physics, consciousness, Ai, and God in a technically rigorous manner.", what did you expect to find here?
I clicked on this timestamp and he is now admitting the Distler criticism is correct and admitting he wasted everybody's time with basic well-known representation theory mistakes
@RyderRude try to imagine the state of mind of a person uploading a video with the title "Retired Off Apple Stock Then Revolutionized Physics Living in Hawaii". Now, does this state of mind rings more like "scientific integrity" to you, or more like "GET THOSE CLICKS" lol
Of course he brushes under the rug the massive controversy all this caused and pretends him spending a lot of time trying to get something to work was a valiant effort, when he was ignoring textbook level info
ok... so that's why it's hard to take seriously that's all. of course that's before making any technical and deep critique. the point is that this kind of stuff makes one not feel it's worth a deep critique
Lisi spends most of his time talking about things like quaternions etc, the guy cannot give a straightforward expert level talk about his theory because it is crank nonsense
Anybody who goes on there with big claims then spends most of their time talking about spinors and triality will dazzle a low-math audience into thinking he's a genius, that's the whole schtick
@ACuriousMind it took me too long to figure out course content at higher levels are mostly dictated by who is employed at a university and what they know
I'm not watching any more of this garbage, "he platforms grifters and crackpots but at least they're sometimes precise about their unscientific ideas" is not a selling point
Even in this you can see the host's prediliction towards absolute bs
I see I've started a firestorm of crank stuff now :p
This is why Motl shouldn't have thrown away his blog, unfortunately he gave in to the lunacy instead of just focusing on calling out this kind of nonsense
@Amit sometimes it does though. I mean you and I and others on stackexchange are fine but to a layperson they don't understand what's handwaving and what's not
@qwerty because the fringe people tell you they've got an understanding of everything that only requires you to understand their stuff, instead of having to put in the hard work of actually learning the actual science; it's tempting because it pretends to offer a short cut to knowledge, it's the same mechanism as the grifters who promise you get-rich-quick schemes - short cut to money without putting in the work.
