I will try it out as an exercise later as I need the geodesics to investigate and to do so I need the first compute the christoffel symbols which I cannot do it within 5 mins
The gaussian should make this computation not very difficult as I knew gaussians tend to have nice properties when integrated
@ACuriousMind A bit sanity check question for me: How is spin differ from (ordinary) angular momentum. I noticed they had more or less the same form of commutation relation, that they are both involved in magnetic moments and they can add like vectors, so how are they different other than spin only has 2s+1 values?
@Secret Ordinary angular momentum is $L_i = \epsilon_{ijk} x_j p_k$. Spin is not, the spin d.o.f. is unrelated to actual spatial rotations (but contributes to the Noether charge under global $\mathrm{SO}(3)$ all the same)
@0celo7 You have arrows in all major directions that you can use as the content of a cell. It's a hassle, and it doesn't look very pretty
@ACuriousMind Am I insane? Suppose we have a pendulum that hits a peg and deforms around the peg. We raise the pendulum a height $h$ above the lowest point of the swing on the side that doesn't hit the peg. When we let it go, it will rise to the same height $h$ after hitting the peg, due to conservation of energy.
The string of the pendulum is massless, so no energy should be lost in the deformation.
@Danu Even if you have all "matrix elements" (in math terms it is called the associated quadratic form), it has to be justified that this is enough to say the operators are equal. There is a theorem that says that to a semibounded (or positive if you want) closed quadratic form corresponds a unique operator, but that is a non-trivial result
and then you also have to split operators in a positive and negative part and finish the proof.
And here I am just restricting to bounded operators, with unbounded ones it's not true (probably you can't even do the splitting on positive and negative part, and there are a lot of domain problems as usual).
@ACuriousMind Are you familiar with the material contained in Bott & Tu, Differential Forms in Algebraic Topology? (Springer, GTM.)
It looks like the summer schedule won't work out for me to take physics, so I'll do a reading course with my adviser. That book is also on the list he gave me.
In most introductory quantum mechanics classes, we are introduced to the Dirac notation, concept of the 'state' of the system being represented as an abstract vector in the Hilbert space associated with it, and we are told that measurements of physical quantities involve the action of a Hermitian...
@JohnRennie No, all I can see is that you wrote: "However if you want to make large changes, e.g. completely rewrite a section, please post the revised text as a separate answer and I will review and edit it in." and that's not what he claims you said. In particular, it doesn't ask for comments, but for suggestions for additional/replacement section
@Secret : see the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics".
The possibility of randomness in physics doesnt particularly bother me, but contemplating the possibility that quarks might be made up of something even smaller, just in general, leads me to think there are likely (or perhaps certainly?) thousands of particles and forces, perhaps layers and sub l...
@DanielSank They have this interesting idea that wrong stuff will be pushed down because it gathers more downvotes than upvotes. Unfortunately, that presupposes that the expert population able to recognize wrong stuff is large enough to drown out those who upvote everything that sounds cool, actually reads most posts, and then actually votes on them.
@JohnRennie : yes, I know. And I now know that when you say comments welcome and why not post your view as an answer? along with the point of a canonical question is to gather all the arguments into one place, I should take it with a pinch of salt.
@JohnDuffield I hereby formally encourage you to post an answer that is an answer. That is, imagine my answer didn't exist and you wished to post the perfect answer, then write what you would post under those circumstances.
I did not vote to delete your answer because I disagreed with it. I voted to delete because it was not an answer to the question posted.
Re the undelete: normally it takes three votes from high rep users to undelete a deleted answer. We were a bit surprised to find the author has that right with just a single vote.
@DanielSank although it doesn't seem to be the case these days, in my days in the British educational system much emphasis was placed on using English in subtle ways.
I am wondering how an Archimedean screw (https://en.wikipedia.org/wiki/Archimedes%27_screw) could be made. Especially, I would be interested who ancient civilizations would do it, say early Greek or Romans.
physics.stackexchange does not look like the place to ask this, but for all *.stackexcha...
@0celo7 Of course, your school has a party school reputation, but so what? People in physics and engineering know that the physics and engineering programs are rigorous and that the ones who party hard discover that $$ \lim_{\text{GPA} \to 0} \text{ENGR} = \text{ECON} $$ (or even COMM).
My undergrad institution hosted what Playboy Magazine called the "third biggest part of the year" on Halloween while I was there. It didn't affect the value of my degree because the Physics program was know to be rigorous.
While I was in Tuscaloosa more than one student mentioned friends who went to Knoxsville for the party atmosphere. They took it for granted, but I suppose that is was a regional reputation because I'd never heard that before then.
@0celo7 Logistics is very important to the modern world and is definitely a technical discipline these days, but I still think of it as "studying to be a supply sergeant".
Someone has to do it and they can't be bumbling oafs, but it doesn't attract the best and the brightest.
@JohnRennie It's used in all gaelic languages as far as I know...and due to the long-standing problems between gaelic people and brits, I don't think it is meant to be exactly positive...
Two Questions:
1) What are the basic interpretations of quantum mechanics and what does each have to say about the nature of reality and the role of the observer (or anything else of interest)?
2) Are there any good references out there (free or otherwise) which address the question above at th...
I've fallen accross the following curious property (in p.10 of these lectures): in order to be able to apply Stokes theorem in Lorentzian manifolds, we must take normals to the boundary of the volume we integrate on that are :
inward pointing (with respect to the interior of the volume I guess,...
Integration over chains does not care for a metric or an orientation at all. $\int_M \mathrm{d}\omega = \int_{\partial M} \omega$ doesn't care for metrics, orientations, or anything besides the smooth structure
Yes, you have to choose to sign of the integral, essentially. It's as arbitrary as deciding whether the Lebesgue integral over $[a,b]$ is $\int_a^b$ or $\int_b^a$ in terms of the Riemann integral
The way you get the vector calculus formulation of Stokes' theorem with the oriented normal from the differential forms formulation is by considering expressions in which a Hodge star appears
Ask yourself this: How does the statement $\int_V f\mathrm{d}V = \int_{\partial V} \nabla f \cdot \mathrm{d}\vec S$ follow from Stokes' theorem for forms?
I am wondering how an Archimedean screw (https://en.wikipedia.org/wiki/Archimedes%27_screw) could be made. Especially, I would be interested who ancient civilizations would do it, say early Greek or Romans.
physics.stackexchange does not look like the place to ask this, but for all *.stackexcha...
Two Questions:
1) What are the basic interpretations of quantum mechanics and what does each have to say about the nature of reality and the role of the observer (or anything else of interest)?
2) Are there any good references out there (free or otherwise) which address the question above at th...
I've fallen accross the following curious property (in p.10 of these lectures): in order to be able to apply Stokes theorem in Lorentzian manifolds, we must take normals to the boundary of the volume we integrate on that are :
inward pointing (with respect to the interior of the volume I guess,...
