So you want to learn physics (second edition, 2021) | Hacker News Reader

So you want to learn physics (second edition, 2021)

susanrigetti.com

321 pointsazhenley69 comments

I have no idea why these sorts of posts are popular. Past college you're not going to learn physics by trying to self-study an entire university course. The best way to learn is just to pick a small part of physics you'd like to learn (preferably related to your job), i.e. how GPS work or some fluid mechanics etc... Then learn the physics you need for that. Knowledge accumulation can't be organized in a straight line, it happens non-linearly and generally builds upon small wins that are useful for you.

I think it's useful for learning about unknown unknowns. If you don't have a clear direction, it's entirely fine to start with a university course then stop when you get a feeling for what you really need.

I think there is more in this world than is dreamt of in your philosophy. The crowd on HN now is very different than it used to be rest assured there are many people self-teach themselves the equivalent of a university curriculum. I mean, nerds actually exists, they're not all humdrum corpo worker bees trying the maximize their employers' value and then just hiking or whatever.

The analogy seems to be like learning classical music (like piano or violin) after as an adult.

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.

I think this is unnecessarily pessimistic. I think there's actually a surprisingly large number of people who are interested in and have the discipline to study something on their own, and there's value in pursuing a whole course of study from beginning to end. Doing things piecemeal and incrementally has value too (especially in software development), but can obscure the whole shape of a discipline.

Somehow millions of people have learned physics in a "straight-line" at university. Most physics majors have a logical progression from the simplest to most complex ideas.

Let's subject that claim to some basic arithmetic.

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?

much less dopamine, video games are realy good at stimulating that. Studying physics not so much.

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.

Personal curriculum is a positive trend[1] IMO.

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.

[1] https://www.youtube.com/watch?v=Jk4MIYOKapQ

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

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.

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

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.

> 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

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.

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.

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.

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

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.

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

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.

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.

> 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.

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.

I think self-studying a university curriculum is also helpful. I've studied physics at the undergraduate level myself.

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.

> I have no idea why these sorts of posts are popular. Past college you're not going to learn physics by trying to self-study an entire university course.

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.

I have this incredible strong urge to try to understand how our world works. I keep finding new topics in physics I just need to understand to calm this urge. Back to grinding differential geometry for me. Im long past college

I find it is impossible to fetch any skill can applied in real world.

> Past college you're not going to learn physics by trying to self-study an entire university course

And why not? Because humans' brains stop working after they graduate from colleges?

Most college students don't work that hard.

IMO: It's not learning that's the problem. It's learning and verifying you actually learned. I'm not saying "unless you can solve homework problems you haven't learned", but... kinda? With a complex generally-theory subject like Physics, the amount of effort you need to put into verification grows exponentially faster than the "learning" part; it's tough for many to get a "feel" like you could for chemistry or programming or electronics or mechanical stuff, difficult as those definitely can be.

Most of us who learn (and always learned) outside of schools and academia, do so for some purpose and with some intention beyond the learned thing. I didn't learn programming to learn programming, I learned it because that's how you built websites. I didn't learn woodworking just to learn woodworking, but in order to build my own furniture, and so on.

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 think you're possibly generalising your own experience to the masses. That's absolutely not the case for me.

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.

> I think you're possibly generalising your own experience to the masses

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.

My brain only started working after college.

and one wonders even now.

We don't see things as they are, we see them as we are.

https://en.wikipedia.org/wiki/False_consensus_effect

Not necessarily true. A lot of autodidacts have significant gaps. Going through fundamentals can unlock things applied across the board in the field and outside. Sometimes this approach is useful.

I try every couple years. I even got myself to relearn the first part of calculus once.

Of course I've never used it and it's gone again

Some classic soviet-era physics books which one can use as a good supplement to the listed textbooks.

1) Physics for Entertainment by Yakov Perelman (2 vols) - https://mirtitles.org/?s=physics+for+entertainment Great to motivate oneself and learn to think in physics terms.

2) Fundamentals of Physics by B.N.Ivanov - https://mirtitles.org/2018/04/21/fundamentals-of-physics-iva... Nice overview which approaches physics "from atoms to matter".

3) Physics for Everyone by Landau and Kitaigorodsky (4 vols) - https://mirtitles.org/?s=Physics+for+Everyone A nice overview of all the major domains in physics.

4) General Methods for Solving Physics Problems by B.S.Belikov - https://mirtitles.org/2015/12/07/general-methods-for-solving... This is a great book which teaches you by walking through the solutions of various physics problems using a general methodological framework.

I've found pacing to be the biggest problem with self-learning of academic subjects.

Suppose we are learning from a textbook. The things we learn in each chapter are built upon in the subsequent chapters. If we go forward before we have a good enough understanding it can make it very hard to learn that next chapter.

On the other hand if we wait to go forward until we feel we really have mastered the material up to this point it can take a long time to move forward, and that doesn't even really gain you anything.

The best way to master something is to practice it. The textbook author knows this. The author writes each chapter under the assumption that you are OK with the material from the previous chapters but have not yet mastered that material. You now need things to practice that material on, and using it while learning the material of this chapter is perfect for that.

That point where you have gotten good enough with the present material that you can handle the next chapter is almost certainly going to be a point where you do not think you are ready.

Saving this until after I retire and decide to invent my own crackpot Theory of Everything

Perhaps start with https://arxiv.org/abs/2605.21660

"It is certainly true that there are aspects of relativity that are counterintuitive, not only to retired engineers but also to many physicists."

Popular in 2023 (528 points, 165 comments) https://news.ycombinator.com/item?id=37200615

> the vacuum (if it is a vacuum)

Here is a five-hour video essay explaining that we actually live inside a superconductor: https://youtu.be/DkH1citHtgs

That is, the reason the weak nuclear force has limited range in our "vacuum" seems identical to the reason the electromagnetic force has limited range in an electric superconductor. Therefore we live in a weak nuclear superconductor. Whatever that means.

(Furthermore and even weirder, the electromagnetic force is a shadow of the weak nuclear force, the one-dimensional projection of it that retains an unlimited range even inside the superconductor, which happens because of reasons)

In case if any Physics learner finds this useful: Susan Rigetti's list is great if you are planning to do a late life PhD in Physics but not if you are re-learning it on the sideline of normal career as a hobby.

I've found many hard-core Physics textbooks to be off putting. Because the syllabus and its progression makes it seems like we are jumping from one special formula to another and there's just so much to learn! I was trying to search for a physics book that will try to cover as much ground as possible in fewer ideas and mental models. Roughly similar to Elon's idea that knowledge is a semantic tree and one should focus on trunk and big branches first.

Thomas A Moore did this experimental syllabus / series called "six ideas that shaped Physics". Each textbook takes one idea like "conservation laws constrain interactions". It's an excellent series, each book is relatively short and has amazing explanation. Especially look out for 2nd edition because later editions were probably "mainstreamed" by editors / publishers. The series is great choice for self learners. It uses non-standard notation and terminology at places to get the point across effectively so maybe not a great textbook lol.

2 standout examples for me : the first unit starts from the idea of interactions -> change in momentum -> to talk about change in kinetic energy. This motivates the idea of work done from first principles instead of directly throwing a definition "force . displacement". The unit on electromagnetic fields similarly has a beautiful discussion to motivate why one would use the ideas of curl and divergence.

I personally recomend Halliday as an everything important in Undergrad thats not Theoretical Physics book. Use that in conjunction with your favorite Flavor of Math for Scientists and Engineers book. And you get a pretty wide understanding of Physics.

It really depends on what the individual goal actually is.

I think engineering curriculums “stop short” on mathematics just as it starts becoming interesting, more generalized and before connections start becoming easy to see and remember. Math is often handled as a bag of tricks.

A lot of engineers would do well to review mathematics at a deeper level than their undergrad days, and that can mean hitting up real analysis, abstract algebra and other topics from scratch in a proof theoretic way.

Once that mathematical fluency is achieved, it becomes possible to ingest other topics at higher levels of sophistication, IMHO.

I have never reached that level of Mathematic fluency very honestly. I came by with my very mediocre level of Math, and I still somehow managed to pass General Relativity.

I still couldn't Mathematically proof anything if a gun were held against my head. I however do apreciate the precise language of math, which I greatly enjoy for describing problems and solutions with incredible precision and little room for interpretation.

The only bold-faced sentence in the post is this:

"Solving problems is the only way to understand physics."

This is key! If you have the discipline to follow through on this, then learning via self-study is possible.

If you don't have the time or determination to do that (which is hard, by the way), the other option is basically to pursue "Physics appreciation" via popular science books (some of which are mentioned in the post). You will not have achieved understanding of physics, but you will have an appreciation for it, which is not a bad thing either. (But do not confuse the two.)

if you really, really want to understand physics and are not afraid of hard math I highly recommend this youtube channel in particular

* https://www.youtube.com/@PhysicsExplainedVideos/videos

"Physics Explained"

But I am not kidding about hard math

He starts off slow and gentle but most of the videos 10 minutes in my brain is screaming and cannot keep up

Which is probably why textbooks are superior for some kinds of learning

But his videos are very well done

Why this rather than Motion Mountain?

https://www.motionmountain.net/

Pointing to someone else's comments that advised against it:

https://news.ycombinator.com/item?id=37201037

Thanks!

I no longer regret that it has not yet made it to the top of my TBR stack (and is being removed instead).

The person who wrote the guide is more unusually interesting than the guide itself. I knew something sounded familiar.

Just using an opportunityto promote guys making really great videos about basic physics, focusing on experiments:

https://youtu.be/kUkgKsEq330?is=uxc8zlUy0z1eng6M

Unfortunately, English version are somewhat reduced from Russian, but still.

The Feynman Lectures and/or Berkeley Physics Course [1] would give one the basics one would ever need.

[1] https://en.wikipedia.org/wiki/Berkeley_Physics_Course

Is there a math edition?

Yep. Linked in the header. It's very good.

https://www.susanrigetti.com/math

That seems like a very physics focused of mathematics. What about statistics or optimization?

No surprise, since she is a physicist.

I wonder how much all the textbooks that the author recommends would cost in total...

How many are available on Safari? ($43/month)

Older editions (second hand or new) often have largely the same content at a fraction of the price...

How does one know whether they actually learnt physics this way. Seems a lot of reading and structure, that's great. Not convinced about whether there is a change in understanding. Typical university/college classes have assignments, quizzes, exams etc.. don't see the equivalent.

The post explicitly calls out that solution manuals are available and that one should do most/all problems. For highly mathematical topics you can also do derivations (or proofs in math) yourself before reading the one in the book.

I'd recommend Shankar's books as a starting point.

"It's a warm summer evening, circa 600 BC. You've finished your shopping at the local market or agora, and you look up at the night sky..."

i learn with AI lol

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