Omg 5 am i couldn’t do 7 am lectures xD. Never again. 8 am is my cutoff but my campus is smol, so it takes like 10-15 mins to walk to that class

Does anyone have a suggestion for a resource specifically on learning Noether’s theorem for the first time? I have smol knowledge of finite group theory and linear algebra and such. No background in classical mechanics

i don't mind learning some

@SillyGoose Noether theorem has several formulations and there are various levels at which you can study it. Depending on the rigour you need you may want to use a CM book (the only English book I can suggest is Goldstein) or a Physics book for a more "naive" approach

You should learn the lagrangian formalism first, though

A nice physical approach is given in Landau&Lifšits volume 1, chapter 2. Noether is not explicitly mentioned though and it deals with three special cases (i.e. angular momentum, momentum and energy)

@Feynman_00 when i lived in shanghai, the bus to school trip was like 40ish min. so i just started sleeping at school

thats how you optimize

I mean, at some point of tiredness you have to ask yourself if you really have to be physically present for the lecture :P

then again I'm used to a system where attending lectures was never mandatory, as long as you handed in all the exercises that needed to be handed in you could in principle sit for an exam without ever having attended the corresponding lecture

thank u nlab

I'm surrounded by pigeons right now, I guess this is how it ends

@ACuriousMind In principle the lecture itself is not mandatory, but I want to attend lectures as long as I have to take that course. We don't have exercises to be hand though, just an exam at the end of the semester

I am studying a bit of renormalization group from the real space pov, to understand fixed points, rg flow and all that (following Nishimori Ortiz book). I am not sure I understand why the behaviour near a critical fixed point reflects the behaviour near a critical point.

I think the point is that the partition function is invariant under the RG transform by construction, so all the points in the fixed critical point's basin of attraction describe the same thermodynamics and the same critical behaviour.

is this correct?

I could study the critical behaviour with any point of the critical manifold, I choose the fixed critical point since the whole linearize the rg transform makes possible to characterize the critical indices in terms of the scaling dimension of the relevant parameters

@ACuriousMind regarding our conversation yesterday about the damped harmonic oscillator placed in an accelerating car...is it correct to say that the oscillator becomes a driven harmonic oscillator due to the acceleration of the car?

@schn formally, sure (but usually people use "driven" to have some sort of time-dependent external force that's being switched on/off)

Ok, thanks

Trying to learn more about the canonical line bundle and the tautological line bundle but I fear this is heavy in algebraic geometry and schemes 😭

Most people talk about them in those terms

Newton's second law for the mass attached to the spring reads $$m\ddot{x}=-b\dot{x}-kx-ma \iff m\ddot{x}+b\dot{x}+kx=-ma.$$ The homogenous solution, i.e. $ma=0$, is simply that of a damped harmonic oscillator. However, I am a little uncertain about the inhomogeneous solution. Naively, $x=-ma/k$ solves the above equation, so I guess it is the solution.

Nevermind, I think I am starting to see how the question doesn't make sense.

Hey, I've got a question about electron spin. I know that in quantum computing, if we decide to represent a qubit using an electron, then that electron is considered to have two possible "pure" spin states (up and down), as well as various possible "mixed" states. Uh... I think.

(I'm ignoring entanglement here.)

Now, suppose I've got an electron sitting here on my desk. Would it be accurate to say that the spin of that electron could be any physical direction—up, down, north, south, east, west, or anything in between those?

(I'm aware that any way of trying to measure the spin could only have two possible results.)

@Tanner-reinstateLGBTpeople Not really. While classically we like to imagine spin as a vector, quantum mechanically the problem is that only one of the components of this spin is ever well-defined as a definite quantity at the same time

i.e. while the question "Is the spin of this electron up or down?" makes sense and can receive a definite answer after a measurement (and likewise for any other direction), the question "What is the direction of the spin of this electron?" is ill-defined - there is no measurement that would measure "the spin"

Let me ask this, then: does the question "is the spin of this electron east or west" make just as much sense as the question "is the spin of this electron up or down"?

yes - but like with all such questions in QM, it only has a definite answer after a measurement

I think I understand.

And theoretically, I could have three machines, one that produces electrons with up spin, one that produces electrons with north spin, and one that produces electrons with east spin, right? And obviously there's no measurement that could take an electron and determine which of the three machines it came from.

And measurement changes the state: If you ask "east or west?" and get the result "east", then ask "up or down?" on that state with spin-east and get the result "up", then asking "east or west?" again of that state with spin-up, the answer is "west" 50% of the time (this is a classic setup of consecutive Stern-Gerlach experiments)

Mmyup.

@Tanner-reinstateLGBTpeople not a single measurement, no - but if you can make repeated measurements, then you can e.g. measure spin north/south and there will be one of the three outputs where this comes up with 100% north all the time and then you know that's the machine that produces spin-north electrons and likewise for the other directions

Makes sense.

hallo