So for instance, what is energy? Somebody who knows a little would probably tell you something like the capacity to do work, and so it feels quite abstract. But the interesting thing is that energy really "exists" so to speak. If you paused the universe somehow, and then resumed it - you'd need to know exactly how much energy was and where in order to keep things moving as they were. Yet there is no known 'thing' that is energy - just a wide array of mathematical abstractions.
And then this thing is also perfectly conserved such that the amount in play will never change. It's completely bizarre to think about, and this is something you initially "learned" in grade school, and probably never even really though twice about.
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And more generally I think the point of learning should not be to do something, but to expand your own mind and understanding of the world (and beyond). Outside of this being arguable alone as a philosophical point of view, I also think there's even a practical reason for it - unknown unknowns. There are things you can't even imagine that you don't know, and the only way you can reconcile this is trying to dive into things across a wide breadth.
This is an example of a topic that unstructured self study would likely skip. But it is included in every properly structured course because this theorem puts a fundamental explanation to all conserved quantities that occur in classical mechanics.
https://curtjaimungal.substack.com/p/what-is-energy-actually
Ignoring that, saying "energy must exist because of Noether and time-translation" doesn't really tell what energy actually is, not a very satisfactory response
The nature of energy is really just a result of this property.
The difficulties with energy in GR are related to the fact that those equations alone allow for space-times that are truly bizarre. Some that are technically solutions to the field equations are clearly nonphysical (e.g. Goedel's solutions). There is also a priori no reason why e.g. expanding metrics should actually yield proper conservation of energy.
Interesting.
> This is an example of a topic that unstructured self study would likely skip.
I'm not studying physics – could you take a look at some unstructured reflexions I wrote a couple weeks ago?
e.g. I did formal study of basic physics in an engineering program, but Noether's theorem was never mentioned. I came to that through self-study, and can't really imagine how anyone would miss it unless "self-study" means "read random blogs and watch random youtube videos." I expect even browsing Stack Exchange and Wikipedia would expose you to most core topics fairly quickly.
I still have a trauma associated with this, though, because it popped out in one exam and I could see the pages in my notes where it was derived but they were quite blank.
Luckily the books of Physics at high school started from practical experience and then showed the equations. So, my advice to somebody willing to learn physics, with plenty of time, no ambition to become a researcher is: go through high school books to get the gist of the subject, then go deeper with one of those university books.
wavefunction, for example light or any particle, this can't be argued.
the complex plane, because? But a complex number is only a pair of numbers and I know that in polar notation it's handy for:
rotation! And I remember that the electric and magnetic components are on orthogonal planes so we are back to complex numbers and maybe the components rotate, but how about neutral particles? But they are not neutral inside. I think that I'm already off track, very lost.
Energy = frequency, because I know that higher frequency photons are more energetic.
Finally, usually we learn about kinetic energy, then E = mc^2 and maybe about the relativistic effects, without the formula. Those things can be understood easily and are taught at school. The jump to angular rotation and the complex plane is something that few people are exposed to and, as I hope to have demonstrated, it's not easy to map to common experiences, which could be inevitable.
See my last article here https://forwardscattering.org/page/Intuitive%20Quantum%20Ele... Although it is a bit technical. next one will start simpler.
I agree with your comment overall, but people have different reasons for learning and it may not be productive to tell them they are learning for the wrong reason. Let's celebrate all learning for I fear we are heading in a direction where it will become increasingly uncommon.
You have no idea, because you have no motivation or interest to self-study.
But if you pay attention, you will notice that your personal motivation and interest does not match the ones from all the people engaging in this discussion.
The reason why this sort of topic is popular is because others have different interests, motivations, and ability to do it.
You should not spend time trying to convince others that they cannot, and instead you should look inside and see what you can do for yourself.
When you're forced to use AI instead of the skills you've put decades learning; it's time to learn new skills to keep the brain from becoming mushy.
I think dense personal curriculum like this is the way forward.
And why not? Because humans' brains stop working after they graduate from colleges?
Most college students don't work that hard.
Same can be applied here I'd say, and probably must (at least for me) be applied that way, for the learning to even be engaging. So don't learn physics just to learn physics, but learn it in order to be able to execute on something else, then learn the related parts to that.
Then the verification becomes part of what you're doing, and fun as well, as you're progressing on other stuff :)
Of course, YMMV and all that.
I love learning to learn. I learned programming because I found a quick basic compiler / IDE on my dad's computer, along with some shipped examples, and it was actually magic to me.
I read our encyclopedias as a kid because it was just really cool. Likewise, I did physics in university not for a job (the jobs are shit), but because it gives me that feeling of expansive possibility and wonder that Carl Sagan gave me when I watched Cosmos growing up.
Most of my most passionate self learnings came about because of that feeling of magic, not because I was chasing an end goal.
Yeah, that's fair and probably true, it's limited to my own experience and the experiences of the people around me, not gonna claim it's universal so you're right.
> I did physics in university [...]
My comment is also explicitly not about you and your type ;)
> Most of my most passionate self learnings came about because of that feeling of magic, not because I was chasing an end goal
One could argue that the end goal you were chasing was feeling that magic again :) Jest aside, I do understand what you mean.
A university would expect maybe eight undergraduate level courses, four credit hours per course, and you are expected to do three hours of study per hour of credit per week. That's 1,500 hours.
How does that compare to the "hours played" on a typical strategy game Steam review?
Don't get me wrong Physics can be satisfying in its own ways but the amount of dopamine rushes you get from cracking a hard problem are few and far between. Often enough you just get frustrated and once you find the solution you think to yourself oh is that easy how didn't i get that before and feel absolutely stupid.
Quantum mechanics, for example, is useful enough as a general background, and going through fluid dynamics and GPS problems is also helpful. But if you just follow the application problems, you can learn what you need, but the bigger risk is that you might miss the larger framework that defines those problems. That's not necessarily a bad thing. In fact, the entire university curriculum training is ultimately a process of translating complex phenomena into the Western scientific way of understanding things. It's a mental model that says 'this phenomenon can be interpreted with this kind of formula.'
In other words, it's about building mental models. In a formal university curriculum, you usually learn things like vectors, topological spaces, energy conservation, and how to map real-world phenomena onto these perspectives. It's about learning to simplify the world using mathematical tools. I didn't go to a top university, so I didn't learn things like tensors, but I hear they're taught now. I used tensors in grad school.
Of course, when I actually code and deliver factory equipment, I've done motor-related work under NDA, and the actual formulas aren't always perfectly accurate. There are corrections and adjustments. But the important thing is not just problem-solving itself, but building the mental model of 'how to approach the problem' before solving it. And I think the curriculum helps with that.
Of course I've never used it and it's gone again
You learn the basics like scales and chords to build and build to modern jazz.
But if you’re an adult, life is too short, just go straight to a few pieces you like. Get a simplified version and learn the bits you need from there from a teacher.