Does this have anything to do with the question how many rotations it takes for a circle rotating over another circle until it is head up (starting point up) again? 16:00 I was imagining a rubber band over a spherical ball.
I keep going back to this video. It shows true pedagogical skill, showing that when the point that you are making is deep enough it deserves tender loving care even if that might seem to those who don´t care it might seem tedious. Go for clarity!
Great job! I'm hapoy to live in that time when there are such youtube channels) I also have a question. Why SO(3) ~ RP³ and SU (2) ~ S³ if SU(2) is COVER of SO(3) but it seems to be that RP³ is cover of SU(2) in some sence and not vice versa ?
To me p implies q is simply a propositional logic function that takes truth values and spits out other truth values. It's just a convenient way of stating mathematical theeorems. Just like conjunctions or disjunctions. When you come across a math theorem claiming "p then q" is true then you should take it as a simple, formal, succint, lacconic way of telling you "in case p is true you'll also have q true and in case p is not true then I don't know which value q might take on". In a way, one is solving for the value of q: I tell you p->q=1 then you know p=1 yields q=1. All the semantics and philosophical garble that mudy the waters are simlply outside the realm of mathematics and much confusion could have been spared if propositional logic functions were seen in that fashion.
This video put together courses I took during my undergraduate time together and beautifully. I have known that abstract algebra and linear algebra is used extensively in Inorganic Chemistry, and I don't think much more of it. I took abstract algebra because I was bored and wanted to challenge myself during my undergrad studies, having poor math skill and complete garbage rigor. In physical chemistry, I was taught quantum mechanics using only differential equation and just a line of equation, only used matrices in Slater's determinant, but I know that matrices are going to be useful if I were to study quantum mechanics like the people of physics do, so I took linear algebra. Then for laughs I took complex analysis with the hope of evaluating some crazy integrals I see in P-chem without looking it up on the table. The fact that these mathematics idea are put together in such a fundamental theory, and the history that goes into developing it is really beautiful
Hi Noah, your videos and notes are really awesome! i read your A Crash Course in Statistical Mechanics and couldn't believe how useful it is for me as a high school student doing my independent research project in computational chemistry! please don't stop making those notes and videos you are so talented in explaining complex physics intuitively!!!
The true nature of implication is not entailment but opposition: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-supEdKORfNw.html (English subtitles available) The "False imply true" problem is solved once and for all!
I have to admit, a lot of important parts of this video are a bit confusing. First off, with regards to why S'-S is 0 at all. It makes sense if that's making use of the premise about time translation symmetry (time transformation needs to not change the action). But here it's framed in terms of the principle of extremal action. Which then begs the question of where the premise of time translation symmetry even is or went. And things get even more confusing once one starts thinking about the fact that the Lagrangian may have explicit time dependence. The fact that it may is just ignored here of course. But adding a ε ∂L/∂t factor to L' is only something that gets absorbed into dL/dt anyway. And that would sound like it meant that the quantity called energy would have a total time derivative of 0, even if the Lagrangian had explicit time dependence. Not only does this sound wrong, but I certainly know that it is from other sources (like just working out the total time derivative of E and using the Euler-Lagrange equation to cancel out most terms). Right now it seems to me like the issue is that, if there is time translation asymmetry, S'-S=/=0, but I can't tell how that could be used to deduce something concrete like dE/dt=-∂L/∂t. I guess that something has to be done to separate the time transformation from the path variance. Because the latter is always true whereas the former might have an effect on the path (in the even there are asymmetries).
I’m taking a university QM class now, and studying spin 1/2. I have about 5 books that cover the topic. I have watched my own professor’s lectures and Susskind and Binney online. After watching this video, for the first time I think I could solve a lot of practice problems. I do have one question. Once you have designated one axis as the z axis (I assume arbitrarily), how is it determined which axis is the x axis versus the axis?
I’ve looked at many references on this subject. This is by far the best explanation which I was able to follow step by step. Really appreciate the time you put into preparing this video.
From what I understand, the equation of motion correspond to the action being stationary with respect to the variation in path q(t). In this derivation, the action is being made stationary with respect to the variation in time (t). I doubt if the result we get corresponds the equation of motion in such case. Moreover, it seems like we do not require time symmetry to get to the result in this derivation. Where is the symmetry constrained imposed?
Everyone talks about lAgrange mechanic etc but no one understands nor explains how virtual velocity by Bernoulli , virtual work and Dalemberts principle actually mean … clearly the way olden days guys developed
How does the Stern Gerlach experiment enter into this? I gather it can be used to sort the spin-up objects from the spin-down objects. In that case I don't understand how changing the coordinates could change spin up into spin down - surely the experimental apparatus doesn't know if it has been rotated 360 degrees around the electron. Getting the citation of the recommended algebraic topolgy book is awkward. It is presented on the screen briefly at 56:47, the title is "Algebraic Topology", and the author is Allen Hatcher. Edit: I see you have a series of 8 videos about quantum spin and the 8th one is about the Stern-Gerlach experiment. More edit: Stern Gerlach sorts particles by angular momentum. There are two possible spins for each angular momentum. As the video states, you have to do interference experiments to distinguish spins.
