[somenameforme]

I'd disagree and have done exactly that. I started with a reasonable basis in physics, but self studying through an entire course dramatically expanded my understanding. For an example of what I mean this [1] is Feynman's lecture on conservation of energy. It's something every schoolkid learns -- I'm fairly sure I saw my first pendulum from the nose demo in middle school, yet Feynman will take this and make you completely rethink your understanding.

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.

--

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.

[1] - https://www.feynmanlectures.caltech.edu/I_04.html

[dr_kiszonka]

> the point of learning should not be to do something, but to expand your own mind and understanding of the world (and beyond)

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.

[gmueckl]

Conservation of energy is simply the invariance of a system to translation in time: the system shows the same time evolution from a well defined starting state regardless of whether that state exists at a time t or a time t+t' with an arbitrary t'. This is one application of Noether's theorem.

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.

[not-a-llm]

Noeter theorem and energy get complicated in General Relativity, because there is no global time translation symmetry

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

[gmueckl]

On the contrary, this is best description of what conservation of energy means: all externally generated forces acting on the system do vary with time. Im other words, this is a closed system as defined in thermodynamics.

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.

[Xmd5a]

> Why is this conserved? Because ∇ᵤ(Tᵘᵥξᵥ) = (∇ᵤ Tᵘᵥ)ξᵥ + Tᵘᵥ(∇ᵤ ξᵥ).

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?

https://news.ycombinator.com/item?id=48699125

[BrandoElFollito]

Noether theorem is one of the nicest ones to derive (together with Maxwell equations). There is such an elegance to go from the axions to the result.

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.

[ndriscoll]

I suppose it depends on what you mean by unstructured (vs. the original claim of self-study). e.g. my method of self-study was generally to find course requirements for a degree program, find corresponding course descriptions and syllabi, find the relevant books, course notes, and/or video lectures and proceed through those.

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.

[gmueckl]

You are following a structured course. I meant unstructured in the sense that topics are not chosen based on a properly designed curriculum or syllabus, but based on personal preferences alone.

[_glass]

I also don't like this focus on practical applications. It is true for me as an engineer, that in the end I want to build something. But when I force myself to focus only on the practical part, just as you said, the whole context is missing. There is this meme of a guy still living with his parents, and trying to acquire all knowledge. This is actually a dangerous mind virus. Learning is an idle activity, often confused with being a do no good. But for me at least this is the only way to really grok something. In university at the summer break, I could only really go through the math and enjoy it, without the stress of exams and cramming. And now it is the same, I learn things idly, and trust in the universe that the application will come, which it always does somehow.

[Ono-Sendai]

energy = frequency of angular rotation in the complex plane of a wavefunction.

[pmontra]

This is new to me (thanks, I'll investigate) and it's the kind of things the books of Physics at University (Computer Science) was full of, completely detached from real world experience. Then there was the book of exercises to prepare for the exams. Sometimes finding the right way to go from theory to calculations was a puzzle in its own. I guess that they were almost the very same books they used at the Physics department and teachers are really interested only in students that can master the subject by themselves with no help. I had one of those students at high school. He was reading university books by 16 and he is a professor now.

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.

[Ono-Sendai]

Are you saying my statement is very abstract? or down to earth?

[pmontra]

I break it down in reverse order to let you understand how I get a gist of that definition

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.

[Ono-Sendai]

Hi, fair enough. I've thoroughly immersed myself in this stuff enough that I sometimes don't realise people aren't as familiar with the concepts and jargon. I'm going to write another article that I think should help about the Klein gordon equation, at some point.

See my last article here https://forwardscattering.org/page/Intuitive%20Quantum%20Ele... Although it is a bit technical. next one will start simpler.