you have to distinguish the fiction of the non-rel. limit from the real world at low energy - of course the limit is meant to describe a lot of what happens in the real world, but the two are not 1:1
phew, i just cleared all the reviews i could. hit the dayum limit on the close votes
I would have just asserted that a decay uses creation and annihilation operators, a concept that does not exist in NRQM, only in QFT. And it is really only sensible in SRQFT, with NRQFT just inheriting them from SRQFT.
The usual NRQM that we play with, is quite the inconsistent mess. It is only after studying SRQFT and carefully extracting out the NRQFT and reinterpretating the stuff in NRQM formalism, that you realise that, actually, one single SRQFT matter field leads to a pair of NRQM, one for the particle, the other for the anti-particle. Having just one of them alone is not ok.
@bolbteppa I know that. I just exited from condensed matter research. We aren't talking about that, and I specifically phrased it in a way with it in mind, that the NRQFT creation and annihilation are inheritances from SRQFT
@nickbros123 earlier today @SillyGoose and i were talking and they mentioned reading jackson and griffiths for days and i was like nobody in their right mind enjoys that and sillygoose was well like nickbros would love it XD
@naturallyInconsistent well theres a part in the show of it where this guy just starts blasting everyone to death semirandomly and sillygoose and i were watching it and i was like bro this is naturallyinconsistant when ryder rude says anything
@Relativisticcucumber most anime and live-action stuff in Japan start out as manga. The other possibility is light novel. Of course, there is also a healthy industry making stuff directly for TV
@Relativisticcucumber I'm already very seriously staying out. There is a limit to caring after the recipient obviously does not intend to learn.
@Relativisticcucumber you have no idea how much of an existential crisis you have just dealt onto this kitty. Decade after reading the dayum manga, wondering where Alice was, and only dayum now I read on wiki that it is the dayum protagonist GUY.
@nickbros123 He has fun, scathing remarks, but I never made sense of his texts.
One of the nice things about studying in Western Europe is that you get the chance to totally immerse yourself in the completely racist yet utterly amusing national stereotypes, more so when the field of study is full of eccentric personalities.
@naturallyInconsistent I have copy of his Classical mechanics book, which i hopefully will start by this December in my emphatic return to classical mechanics
Also, I liked his DE book, from the little I've read from it. A bit advanced for me though
I'm the kind of person who can tolerate some arbitrary stuff, but not a lot; I do not just want to absorb some mathematical structure / fact, but rather I want to know why particularly must I pick this structure in the particular way given to us, and no other alternative would do.
Needless to say, QFT is a tremendous disaster to study. Every slightest deviation is a potentially decades long trek to discover a dead end
@nickbros123 There are too many jokes for meow to pick from.
Say, there is a joke about a mathematician going to Russia and wanting to present some theorem he found. As he goes on to write some stuff down and want to prove them, some big shot in the audience goes "That's obvious, just move on". After a few more attempts of that, he just writes down a few more statements, pausing only to ask if they are still obvious and doesn't require proofs. Finally, upon writing down a last statement and obtaining that, yes, it is indeed obvious,
and does not require a proof, he goes on to point out that the statement is false. So, then he restarts the presentation, going to prove things step-by-step
Arnold particularly fits this stereotype, partly when you consider his anecdotes about "Russian schoolchildren have learnt about" X avart-garde uni maths topic, just because he taught them.
@nickbros123 I realized I didn't actually enjoy doing research in theoretical physics all that much, I didn't want to move around the world chasing academic positions because I like where I am right now and I wasn't all that in love with string theory and QFT anymore after actually having studied them for a while (but I could've changed fields, sure).
while there's also general problems with academia it was mostly a personal decision
@123 Maybe this will help. For a single particle, generalized coordinates are any set of coordinates (e.g. Cartesian, Polar, Spherical, etc...) convenient for the problem. $\mathbf{F} = m\mathbf{a}$ in Cartesian coordinates is $F^i = m \frac{d^2 x^i}{dt^2}$, however in polar coordinates it's not $F^r = m \frac{d^2 \theta}{dt^2}$, $F^{\theta} = m \frac{d^2 \theta}{dt^2}$,
You need very basic differential geometry to see it's now $F^i = m ( \frac{d^2 x^i}{dt^2} + \Gamma^i_{jk} \frac{dx^j}{dt} \frac{dx^k}{dt})$. The $\frac{dx^i}{dt}$ are the 'generalized velocities'. For example $\dot{r}$ and $\dot{\theta}$ are generalized velocities in polar coordinates.
Setting $T = \frac{1}{2} g_{ij} \frac{dx^i}{dt} \frac{dx^j}{dt}$, we can re-write the equation as $F_i = g_{ij} F^j = \frac{d}{dt}(\frac{\partial T}{\partial \dot{x}^i}) - \frac{\partial T}{\partial x^i}$, which is almost LM. If $F_i = - \partial_i V$ then setting $L = T - V$ we get the E-L equations $\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}^i}) - \frac{\partial L}{\partial x^i} = 0$ from $F = ma$ just by potting it in generalized coordinates
(Should read $F^r = m \frac{d^2 r}{dt^2}$ above)
So if you had no idea LM existed, you can see from this that it's telling us setting up $F = ma$ basically amounts to fixing this scalar $L$ function in the cases where $F = - \partial_i V$. If $F$ is not in this simple $F_i = - \partial_i V$ form, the idea is that really $F$ is not a 'fundamental' force it's some approximate model encompassing non-specified degrees of freedom (e.g. friction is really a gross approximation of tons of interactions etc)
@Relativisticcucumber Fear not, for I'm here, my young padawan
Although I'd be happier if to migrate this from Star Wars to Halo
@ACuriousMind Today during an exam, the Professor and I had a brief digression and so he asked me to define a connection and the first thing that came to my mind was
Quick physics question: Is there a formula in terms of F that gives the pressure (In PSI, Pa, etc.) required to compress air to 1/F of its volume? Or water? Or iron?
