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So You Want to Learn Physics (2016) (susanjfowler.com)
249 points by apsec112 54 days ago | hide | past | favorite | 124 comments

I like the list! It's very "physics person" oriented. Unfortunately, I have faced an insane amount of frustration trying to learn from the same sources because they "skip" on mathematical detail, often leading to more confusion down the line. I personally enjoyed the books I write down below to learn "rigorous physics":

- Classical mehhanics by VI Arnold: We first abstract define what "space" is, analyze its properties, then move on to build Lagrangian and Hamiltonian formalisms. Is a great book to understand formally (i) what we mean by "observer" in classical mechanics, (ii) variational problems, (iii) the precise relationships between the Lagrangian and the Hamiltonian

- Wald + Misner Thorne Wheeler for general relativity. MTW is the "bible", with great pictorial explanations for everything. Wald prefers to write everything in terms of differential geometric language which makes for an entertaining read. For example, he does not write "the particle is at rest". Rather, he writes "the particle is invariant under time-translational symmetry". It was eye-opening to learn how to "think like a geometer" about these sorts of ideas.

There is also Leonard Susskind's video lectures called as "the theoretical minimum" where he explains, rigorously, classical/quantum/GR/QM/stat-mech: https://theoreticalminimum.com/courses. I've personally watched the GR lectures and found them very informative.

Finally, there is Landau and and Lipschitz: These are dense, terse, often difficult, but honestly, written with extreme clarity. This was the only undergrad stat-mech book I could find which actually formally defines the phase space, the averaging procedure we use, etc.

For a more casual reader interested in the mathematics and practical applications of GR, I'd recommend Peter Wald's book. It still provides a rigorous introduction, but has a slower pacing while building up the mathematical foundation of differential geometry. It provides an enjoyable ~150 page read which can be worked through in a few days/weeks if one is comfortable with Calculus.

- A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity


Peter Collier?

I think all undergrad STEM programs should put A LOT MORE emphasis on mathematics and other fundamentals before bothering with heavy specializations.

The Arnold book is great, but it presumes a level of mathematical sophistication that isn't practical to achieve (at least in the US) until well into graduate school, and realistically?, only for Physics theory students or some Math students that are motivated to dive into Physics.

There are major theorems in the famous "Calculus on Manifolds" by Spivak that are exercises (and not end-of-chapter or starred exercises either) in Arnold.

Is it “a lot more emphasis” or that the math education of STEM students should be rebalanced?

I’m an EE and I think I had a math class every quarter for two years if I remember right. I tend to agree with Strang’s too much calculus essay.


You need the bread around the sandwich too, i.e. if you learnt statistical mechanics solely through Landau I think you'd miss some of the intuition in terms of heat and work and so forth (It's in the book but blurred behind the russian-ness). Bra-ket notation really helps me focus in big equations when battling attention span (certainly not present in my library edition of L&L)

Jackson's book is surprisingly practical considering its reputation (I wasn't expected any discussion of Galerkins method for example)

MTW is great although a little odd by today's standards (how many books talk about tensors as machines with slots and holes)

I am glad you brought up bra-ket notation. I have wasted a lot of time trying to understand how to formalize bra-ket notation. I kept seeing the words "C* algebra" and "rigged hilbert space" being thrown around. I recently learnt the full story:

- Von Neumann's paper "mathematical foundations of quantum mechanics"[http://alpha.math.uga.edu/~davide/The_Mathematical_Foundatio...] builds up hilbert space theory and solves problems without ever using dirac deltas. So if one wants to use bra-ket without dirac deltas, this is the formalism.

- To make dirac deltas themselves precise, forgetting the bra-ket context, one uses the language of distributions. So we view the dirac delta distribution as a linear functional which takes a function `f` and spits out the value `f(0)`, and all that jazz.

- To join distribution theory with Hilbert space theory, we construct rigged Hilbert spaces. This is the theory that carefully delineates from which subset of Hilbert space we can pick kets, and from which larger space of distribution we can pick bras, to allow the bra-ket formalism to continue to work.

I found the reference "The role of rigged Hilbert spaces in QM"[https://arxiv.org/pdf/quant-ph/0502053.pdf] incredibly valuable.

This is the sort of thing that drives me nuts. I bought and tried to read Shankar, because I was told it is "rigorous". It's not. It casually uses dirac deltas and all sorts of "punning" with bra-kets with zero formalism.

Do you have a good recommendation for learning this heat and work perspective? I always found this confusing [eg. "adiabatic work", "infinitely slowly" and all that]. FWIW, I wanted to learn stat-mech for a closer look at entropy and information, which I felt I got with some LL.

I don't have the mathematical maturity to comment on the rigour of the bras and kets, but as to heat and work I was referring to thermodynamics in the sense of Carnot and co.

I picked Zemansky and Dittman off the shelf in the library and it's honestly really nice little book - the aim here is for intuition (particularly for experiment) while also making connections to the more theoretical perspective found in L&L (in my case this is because I can't be bothered to read 300 pages of formalism to get to the applications although YMMV). It is quite handwavey in the ways that you describe but I think that is the jazz that the great physicists played in order to get the result in the first place.

I learned stat mech from L&L, and had the same problem that I never really understood thermodynamics.

I've been working through Bohren and Albrecht's 'Atmospheric Thermodynamics' recently, which I've been really enjoying. They are much more concrete, and very opinionated about ditching notation and concepts that are unclear, such as the differentials that get bandied about in most other books.

I think the key problem is that most thermodynamics books try to develop the axiomatic theory in the abstract, as opposed to introducing real materials and building physical intuition with them first.

Isn't doing physics in a mathematically rigorous way very hard or close to impossible? I think Quantum Field Theory and the Standard Model remain non-rigorous because of their dependence on path integrals.

Yes, doing QFT rigorously is hard because of path integrals. It's possible to do QM rigorously, as the "rigged Hilbert spaces" formalism suffices.

Ballentine's book is a modern textbook that relies on that (as opposed to Shankar which you mentioned)

Nice, thank you, this was exactly the kind of resource I was looking for :)

Carroll as an intro to general relativity is a great recommendation from the OP. I have been learning it (albeit with preexisting differential geometry knowledge) from Carroll and MTW.

An unmentioned benefit of MTW is that, because it is so heavy, it is perfect for placing on my forehead while lying down with a migraine.

> Leonard Susskind's video lectures called as "the theoretical minimum"

This is apparently a book too, co-authored by Susskind and Hrabovsky [1].

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

I own the series. Combine them with video's and you have a pretty good combination. What you don't understand from one, you can pick up from the other.

Susskind deliberately set out to create something an amateur could use to understand physics. Accordingly he doesn't just teach the physics, he teaches the math too as you need both, of course. It seems so obvious, but he's the only one I've seen that does both.

It's one of a series, even. There is The Theoretical Minimum, Special Relativity and Classical Field Theory: The Theoretical Minimum, and Quantum Mechanics: The Theoretical Minimum.

>ecause they "skip" on mathematical detail, often leading to more confusion down the line. I personally enjoyed the books I write down below to learn "rigorous physics":

That is possibly because it would require too much space to explain those concepts in greater detail. The books are already very long even when skimping on the details.

Is this a joke? He wrote that he liked Arnold's and Wald's books. I have tried to study from typical physics undergrad books and was also missing some rigour which I would assume most people coming from a math background would appreciate more in introductory physics books. Arnold's book or also Spivak's book are much better in that regard.

Hilariously wrong reply to OP. Reading Wald means you’re comfortable with differential geometry which an undergrad in math encounters several years after calculus. Not to mention that other texts mentioned cover Lagrangian and Hamiltonian mechanics which rely on calculus of variations and differential equations.

"Everyone can learn physics" is a flat out lie to make other people feel better. Without a proper tutorium and insufferable fits of frustration it's only possible to learn such complex subjects on your own you if have the right mind (whatever that is) for it. That arrogance some people have saying "If I can do it, why can't you?!" is beyond tolerable.

The knowledge transfer process is different for every person, because people learn things differently. The school doesn't teach you HOW to learn, only WHAT you are supposed to know to be a productive member of society with some value to companies. More inquisitive minds go to sciences and engineering, only to discover that universities are just a next level of schooling. Only people aiming for PhD learn how to do "independent" research, only to discover that research paper business is dirty.

The article only lists books and what the author thinks about them. It doesn't say how to learn physics. Also, learning physics without experiments is as valuable as learning to drive without ever getting in the actual car.

> It doesn't say how to learn physics.

OK, but can any article ever hope to give a real prescription for "how" to learn physics?

Far more important than "how" is "why" or "to what end". It's no different than obtaining mastery in any other big subject. The article is perfectly fine as a reading list or set of suggestions for students that have some passion for learning physics. There's other advice out there consisting of long lists of exactly which topics to study and in what order. All good advice, but totally fungible and not critical to anybody's path.

I would not take her other article "If Susan can learn physics, so can you" as a "lie". It's a piece of inspiration. So many folks don't live up to their potential because they prematurely self-select themselves out of endeavors which they feel passionate about. If I remember correctly (the link seems to be down), in Susan's case, she was a home-schooled kid living in a not wealthy rural place with few resources and low expectations from her family and peers. She ended up at University of Pennsylvania in a Physics PHD program. Does that mean "everyone" can literally do that? No, but rather, there's no excuse not to try (whether it's a PHD or any other seemingly infeasible challenge). Sometimes people people really need to hear that and she told her story eloquently.

i was a physics PhD student once and i might have some thoughts on how to learn physics, but i think the parent commenter is spot on -- the only reliable way we have is to have an apprenticeship with someone who works well with you.

there are a tons of posts along the lines of this one, which are largely lists of books that people like to romanticize or as the parent comment says, lists of things that someone thinks you should know.

the Feynman lectures are a good example of that, actually. i've read them a couple of times and they are wonderful -- like most things Feynman. but very unhelpful. even Feynman was disappointed at how the students they were given to weren't quite learning the physics. Feynman is to explaining science as, eg Joshua Bell is to performing music for the violin. but in terms of actually trying to learn what a physical theory says, to what degree it holds, what are the current open problems with it, and what might be good approaches to solving them, Feynman explanations outside of highly technical works (like his papers or maybe his lecture notes on statistical mechanics) are not too useful. and the more technical works are very difficult to approach by yourself, you'll need a mentor.

My frustration comes from the sentiment that supposedly everyone with a can-do attitude can learn Quantum Mechanics (which is addmitedly quite easy to grasp after you have had years and years in studies of the whole physics curricula) It makes physics sound SO easy! I fell for that lie when I was inspired by my physics curriculum in high school which was quite advanced. I dropped out of physics after just 1 semester, because the courses where horrible. I have learned physics in my engineering school and I finally understood what the problems were I was facing: I had approached my physics studies the same way I was learning physics in high school.

Inspiration is an illusion, an illusion is a lie, it's concealing the thruth. The physics faculty, instead of taking the realistic approach aka "forget everything you know about physics", had chosen to reinforce the sentiment that everybody can do it. In truth, the faculty needs numbers of students to get grants from the government. The faculty doesn't care about your inspiration. Many of the books she lists I actually do possess and have read them partially, watched a lot of lectures. But nothing can replace how the learn that stuff, how to translate it so that it fits in your own head.

Since then, all I read when I see "If Susan can do it, so can you!" is in actuality "If Susan can do it, good for her, moving on!"

> Inspiration is an illusion, an illusion is a lie, it's concealing the truth.

Well, that's a grim and somewhat dramatic view!

We're all motivated in large part by inspiration of some form. I think of inspiration as a kind of fuel that gets one through the inevitable rough patches on the way to mastery (it doesn't matter what subject or what aspect of life). It helps drive both curiosity and grit. People without inspiration in life's-work or career are apt to take the path of least resistance, they appear incurious and bored. That's not necessarily a bad thing if there's inspiration in other parts of life.

So you dropped the undergrad physics major after ONE semester because the "courses were horrible"?? I don't think so. You dropped it because you were 18 and people at that age are flighty and unsure of what to do, that's totally OK.

I do agree, however, that more curricula should take the "forget-everything-you-know-and-start-from-fundamentals" approach. IMHO, undergrad students would be better off if all STEM majors were basically one merged curriculum with a few courses different towards the end. That won't ever happen, of course, as long as people see universities as strictly vocational training and employers think they want subject-matter-experts who can "hit the ground running" on entry level jobs.

Oh, and to make the whole matter more ridiculous, I have been told repeatedly "maybe studying is not your thing?" and after a while I got it and answered "That's it! Studying on your courses in your university is not my thing! Thanks!"

Everyone can learn!

The problem is many people don't know how to learn, or haven't developed good habits-of-mind. That goes under the terms executive function and metacognitive skills. They are force multipliers throughout your education, and you're right that schools don't teach them.

If I can do it, so can you! It just takes a few years developing those skills, and ideally a little bit of mentorship to point you on the way.

And no, people don't learn differently. That's one of the biggest lies fleeced upon us. The reference there is: "Learning Styles: Concepts and Evidence." Turns out we all learn more-or-less the same way. Many of us believe we learn differently, but we actually don't. A big part of executive function is differentiating between activities which /feel/ like learning, and ones where skills actually grow.

Everyone can learn, but not everyone can learn any arbitrary subject or discipline to an arbitrary level of depth. We all have different levels of intellectual capacity.

The arrogance displayed here by saying “If I can do it, so can you!” when that’s exactly what OP is complaining about is astounding.

Does everyone have the same level of intelligence? Are you really telling me that absolutely any member of the public could learn QFT, even people with a severe learning disability and low-IQ? Anyone you just randomly plucked off the street? Just no.

As a practicing physicist, i would compare the amount of time, effort and skill needed to complete a PhD to that needed to become a professional session musician. Some people will find aspects of it much easier than others because of talent, some will get a big head start in childhood, some will learn much faster than their peers because they practice 6 hours per day and are driven by their passion. Some people get lucky and have the trifecta.

This doesn't mean that there isn't value in an adult choosing to learn an instrument (i.e. study physics). It can be enriching even if one never reaches the point of quitting their day job to play music full time.

Apologies if I came off as needlessly combative, my phrasing could certainly be improved.

Don’t get me wrong, I completely agree with what you’re saying. In fact, I encourage anyone with even the slightest inclination to study essentially anything, but especially physics, in their own free time to do it. You’re spot on in saying that there’s value in doing that.

The only assumption I wanted to challenge was that absolutely every human on Earth could do it. I just think that’s patently untrue, and betrays an inability to view things from other people’s perspective.

I assume this was flagged for being combative, but it's spot-on, so I vouched it.

How many people with Down syndrome have mastered calculus? Let's please attend to reality in these matters.

Thanks, and apologies if it came off as needlessly combative. I probably could’ve phrased it better.

I wasn't referring to mental disability, but aside from that, yes, a typical random person plucked off the street could generally learn quantum field theory, given about a decade of appropriate focused effort.

Mathematical maturity takes about a half-decade to develop, maybe a little more. Working through physics up to QFT takes a bit under a half-decade, in my experience. It's slow-going at first, and then accelerates.

I've seen people go through very similar transitions before.

Ain't nobody got time for that.

> Everyone can learn!

No they can't. Thinking so is just the Dunning-Kruger effect on show. You don't realise your own strengths.

It's probably easier to understand through the lens of your weaknesses. Pick something you've never been good at. Maybe it's art, or singing, some sport like pitching a baseball, training animals, rally driving, working with 2 years olds 8 hours a day, or god help me making the perfect weld. And now imagine someone saying whose really good at it (and anyone who truly understands basis for the 2nd law of thermodynamics is such an outlier) oh, anybody can be as good as me - your just not trying hard enough.

> And now imagine someone saying whose really good at it (and anyone who truly understands basis for the 2nd law of thermodynamics is such an outlier) oh, anybody can be as good as me - your just not trying hard enough.

I'd agree with them!

Seriously. I can't get good at all of those -- there isn't enough time in my life -- but I could get good at any one of those given time and effort. I'm really bad at art. Would I be Van Gogh? No. But I could get up to the same level as a professional illustrator in a few years. Anyone* can. Could I learn to sing? Sure, again, given a few years of hard training. I wouldn't be the next Susan Boyle, but I could definitely go from zero to where I could perform in a local performance or sing as well as a professional backup singer or chorist.

Going back to quantum field theory, I'm not claiming anyone can make the next breakthrough in physics, but anyone* can learn quantum field theory at the level of a e.g. a typical grad student in the field.

And a perfect weld just ain't that hard. Anyone can learn to do that. I've seen welding artwork which is hard (people building up metal to make beautiful artwork completely additively, for example), but you could be a professional welder if you set your mind to it.

* Standard exclusions apply. No, a blind quadriplegic with cerebral palsy might not be able to train to run a marathon, or by "everyone," I mean everyone from, say, the 20th percentile up.

I enjoyed the theory and problems much more than doing "experiments" in high school and university.

In fact, I loathed the lab components. I always felt they were highly contrived, and offered little value beyond having to learn the structure of writing out a formal lab.

I get that experimentation and laboratory work is a vital part of science. I just appreciated the problem solving components more.

I think it’s sort of even between undergrad experiments and problems in degree of contrivance.

I think you're partially right. In order to learn from a list of textbook recommendations you need to know how to read effectively and comparatively, how to take proper notes, how to record your thoughts and questions for future reference, how and when to summarize the information you just read to support learning and understanding (chunking it and fitting it in to your mental schema along with information from other sources), and you need to be disciplined enough to go back and review your notes and the text so that you will actually remember the material.

I don't think it's a matter of "having the right mind" or any sort of innate ability. It's a matter of acquiring the skillset and perspective necessary to learn. I agree that school does not teach this, you're simply expected to either be a good or a bad student and any failing is entirely your own. We'd have many more "inquisitive minds" if our education system taught kids how to be inquisitive, literally how to ask questions of themselves and others, instead of test taking.

The knowledge transfer process is different for everyone insofar as everyone tends to be at varying levels of competency in the set of skills needed to acquire that knowledge. This is generally the case because training of those skills is so neglected or hodgepodge and left up to blind chance, peer groups, and parents.

Experiment is key because all knowledge requires some grounding in actual physical experience. The base of the framework that you build upon is made up of your interactions with the world. Another failing of our current system is shuttling people between home and school with less and less "free" time in the wider world. We have it backwards, thinking that we need to frontload all the information and book-learning and then explore the world after that's done. We couldn't be more wrong, our physical experience must precede or coincide with our education. You have to walk the halls and avenues of the world in order to build up a store of places and things upon which you can hang the names and concepts that you learn.

I was not sure how to say "having the right mind". I didn't say the right brain, because that is what determines "innate ability". But the brain has plasticity, so then the mind must also be flexible and can be prepared to understand new stuff.

So, "having the right mind" can also mean "prepared mind" having the right mental tools to understand and apply knowledge to new problems. I do not know the right words for describing "the right mind" in context of learning. But, intellectual competence is also partially determined by the innate ability of people to observe things and make connections which is not a given.

No, "learning physics is easy" is a flat out lie. For some it will be very frustrating depending on the path they take.

"Most people give up" is probably the truth. People don't want to put in the effort.

Another truth is that many people never recover from finding that some fact of physics strongly contradicts their intuition. That is what flat earth is all about: people just cannot accept when their intuition is wrong.

I agree that physics requires some level of experimenting to truly internalize the knowledge. I don't think "everyone can learn physics" is a lie, though. If you are interpreting that phrase as being able to make breakthroughs in our understanding of physics, then sure. However, if you interpret it as having an solid understanding of the fundamentals to the point that you can actually apply some of it to your day to day reasoning and problem solving, then I don't think the phrase is a lie. Everyone already has a grasp of physics, getting a bit more formal about it is doable by anyone who has a high school diploma.


In the past, I have made no secret of my disdain for Chef Gusteau's famous motto: "Anyone can cook." But I realize, only now do I truly understand what he meant. Not everyone can become a great artist, but a great artist can come from anywhere.

>"Everyone can learn physics" is a flat out lie to make other people feel better. Without a proper tutorium and insufferable fits of frustration it's only possible to learn such complex subjects on your own you if have the right mind (whatever that is) for it. That arrogance some people have saying "If I can do it, why can't you?!" is beyond tolerable.

But people find being told they cannot do something, also bad. Telling someone that they are not mart enough to do something is demoralizing even if it is grounded in reality. is it worse to tell someone they cannot do something, or give them false hope? It really depends on your ethical and value system. In the case of physics, the worst that happens is thy try it and get bored.

>It doesn't say how to learn physics

Presumably by reading the books

I think the right phrasing ought to be that anyone can learn physics if they want to. The problem is that learning anything deeply is really hard, much harder than you think it'll be upfront. So, unless you're really motivated and really want to see it through, you're likely going to give up.

That being said, I believe that if you're a reasonably intelligent person (say at least above the median) then I don't see any major issue with you learning physics to some decent extent.

I earned my PhD in physics at Penn and Columbia, helping build a satellite still taking data (XMM-Newton). I love physics. I loved learning physics.

Physics is not math. It is an experimental field. Ctrl-f experiment yields no results on that page. Ctrl-f lab shows only results in the comments. I love that that page exists, but it's missing the physical component of physics. Learning only theory may serve many people, but it doesn't serve the field.

Now that I teach project-based learning, albeit in leadership not physics, I see huge gaps in my physics education about experiment, curiosity, doing things with our hands, realizing we can test things ourselves. Most lab classes I took walked us through known results so we could write the data we were supposed to find if we measured wrong -- the opposite of science.

If you want to be a theorist, great, but distancing physics from what anyone can do seems to make it less accessible.

For example, I work on sustainability. People routinely seem shocked that their turning on a light switch or air conditioner necessarily today means somewhere some power plant had to convert that energy from something else, polluting in the process.

"If you want to be a theorist, great, but distancing physics from what anyone can do seems to make it less accessible." Well said. I also dont fully understand this strong desire to push everyone towards the theoretical boundaries of physics.

"Physics is not math." I would lean towards agreeing with this statement however its pretty much considered heresy.

"Most lab classes I took walked us through known results so we could write the data we were supposed to find if we measured wrong " This is extremely unfortunate. Perhaps it was a time/resource constraint issue. Real labs can be very time intensive but I found them to be very rewarding and motivating.

Physics is not math. It is an experimental field.

Isn't this kinda what Sabine Hossenfelder has been saying for the past couple of years?

But that itself seems to be a reaction to the way so much of physics has become "just math". One can bemoan this state of affairs (and people have, obviously. Hossenfelder, Peter Woit, Lee Smolin, etc.), but it seems like that's kinda where we're at these days... at least for a large portion of the physics community.

There's plenty of experimental physics, but everyone seems to think physics means theoretical particle physics. It bugs me.

While I don't particularly disagree with you, I can assure you that there are plenty of physics PhDs who focus on theoretical physics and know as little about the experimental world as the archetype you are trying to criticize.

You definitely can get a PhD in physics and be fairly clueless about the experimental world.

> experiment, curiosity, doing things with our hands, realizing we can test things ourselves

Partially-related, I have heard it claimed that would-be surgeons are showing less dexterity than previous generations, presumably from lack of hands-on hobbies when younger.

I have found that there is a world of everyday physics, related to things like temperature, humidity, weather, materials (durability, permeability etc.), clothing, nature, cooking, farming, cars, and also now in covid times about droplets and droplet evaporation, turbulence, breathing and face masks. These are fascinating and come up in everyday life. And maybe they might come up in your work if you're an engineer and work about manufacturing physical things.

But typical university physics curriculum is, I guess understandably, focused on fast-tracking you to the borders of known fundamental physics: quantum mechanics, particle physics, astrophysics. Whereas the everyday physics builds on more classical things like thermodynamics, fluid mechanics, heat transfer, structural mechanics, which are usually covered only quickly, and partially only in elective courses.

So if you want to learn physics for more practical purposes than understanding the progress of research in quantum and particle physics, a normal physics curriculum does not serve you too well. But it still gives you the foundations to self study these topics.

Have a Phd in physics, agree fully. I love talking to people about the physics and chemistry in every-day life, and you need very little of quantum mechanics or advanced electromagnetism. Perhaps statistical physics (thermodynamics) is the single most useful topic.

Also, if you want to understand the science in every-day life, chemistry (or more broadly materials science) is arguably more relevant than physics per se.

Do you know any books or courses that focus on every day /chemistry? That would be a nice way to learn.

I've always thought that one could write a book of recipes that also goes into the chemistry of things (pressures, heat, types of reactions, acid-base stuff, etc). Making delicious things while understanding what goes on, which coincidentally is what sometimes chefs do pretty well when explaining their recipes (I've discovered Kenji Lopez on HN and he does a bit of that in many of his videos)

Also in his cook book, The Food Lab: Better Home Cooking Through Science

The thing is the math gets hard really quickly in problems related to everyday life.

Reminds me of Feynman's quip along the lines of "Why do we use linear approximations? Because we can solve them."


Learning physics is not the same as learning to do physics. If you want to learn how to really do it, you need to work problems.

This means you to learn the techniques, and you need problem books, with solved examples, that you can work through on your own, or with a small group. This is absolutely critical. This includes both complex mathematical calculations as well as back-of-the-envelope calculations.

Moreover, while textbooks are great references, nothing replaces a good video lecture or presentation, that gets to the heart of the physical concepts without being overly technical. n And remember that physics is fundamentally an experimental science. It is not just advanced mathematics. Even if you yourself are not an experimentalist, you need to understand the basics.

I should mention that "good video lectures" are extremely hard to come by. Experts appreciate a clean narrated delivery, and novices like it too, but students generally don't learn from a monologue.

You can't just watch videos. You have to work through the problems.

If you have a lot of free time, and you're curious about designing effective educational multimedia, check out Derek Muller's (of Veritasium fame) dissertation: http://www.physics.usyd.edu.au/super/theses/PhD(Muller).pdf

The right sort of textbook is just as good as a good lecture. In math, books like Rudin's Principles of Analysis are extremely thorough, rigorous, and a great source of problems, but not a good book to start learning from. On the other hand, Abbott's Analysis is a less detailed book but a much better introduction. Any textbook that takes itself too seriously is probably not going to be as good as a lecture.

My biggest struggles with Physics are psychological.

Because of how the universe works, if you fire a gun and drop a bullet from the same height they both reach the ground at the same time.

Maybe it's because I have a cartoonish version of physics in my head, my first instinct is "no that can't be right" and I start from a place of extreme skepticism that gnaws at me even as I watch myself being proved wrong.

The other common struggle I face is that so much of the physics you learn at a basic level comes with caveats like "assuming no air resistance" or "in a vaccuum" or "at sea level" and perfect weights and I end up wondering how futile all of it seems because in reality I'll never be able to apply this stuff the way it's being presented. If I have to actually apply it - I'd have to start thinking all the possible ways in which the system can be affected, then measure those ways and add them to my calculation.

Then I feel overwhelmed by all the possible things I would need to factor in. Did I forget friction? Is this surface 100% horizontal? Is it windy right now? Am I really at sea level? I feel like the street I'm on is 30m higher.

Then I start thinking about the practicality of measuring things. Even if I eventually learned all of the physics in theory, if I was one of the last 100 people on Earth and the person with the best physics knowledge, could I use it to build even something as simple as a bridge? How precise would my tools need to be? Is it ok for my execution to be off by 0.1 degree? Is that too much of an error? How would I even know?

With programming I feel like there are more opportunities to blackbox things and focus on building practical solutions, whereas with the material world I would have to worry about whether I got a faulty batch or whether the manufacturer was reputable or whether I should have spent more money on a better manufacturer. By comparison it feels incredibly inaccessible to do anything tangible with.

> my first instinct is "no that can't be right"

There's nothing wrong with that. It's also the normal reaction when you are presented with more advanced concepts, like relativity and quantum mechanics.

It's just a matter of accepting that facts and your instinct can diverge... and it means that your instinct is wrong!

Which is not to say that you are stupid, no way! On the contrary, it's a sign that you have embarked on an adventure to discover how the world really works, which is beyond what evolution may have imprinted in you DNA in order to survive daily struggles.

> I end up wondering how futile all of it seems because in reality I'll never be able to apply this stuff the way it's being presented.

That's a common misconception by non-physicists: that years of advanced studies can be compared with trivial experience in everyday life, as if the value of a senior software developer could be judged by how fast he can install a new version of Visual Studio.

Funnily, when I was in high-school and made a "trailer" for some programming lectures I was attending, one of the lines in it I meant to sound "epic" was "You must use the new version of Visual Studio!"

I'm a physicist. I think the way to overcome this hurdle is to get into the lab. These days you could do worse than getting an Arduino and learning to make different kinds of measurements with it. And then finding out how and why there are better things than an Arduino. ;-)

When you make a measurement, think about how and why you believe it, to what degree of accuracy. Build things. Break things. Fail early and often.

In any event, electronic measurements is one of the things you'd have to learn as a physics student. One of my textbooks was The Art of Electronics.

But also, one of the hurdles to learning physics is motivation, and I think somehow engaging with the physical world needs to be part of that motivation. I hate to say that's what makes physics different than engineering, but there are a lot of engineers who like to blackbox things, and I owe a certain portion of my job security to being willing to do things like figuring out if we got a faulty batch.

> I think the way to overcome this hurdle is to get into the lab. These days you could do worse than getting an Arduino and learning to make different kinds of measurements with it.

Last year I took Electronics 101 and 102 at my local community college; validating circuits with a multimeter just became second nature. It was only a small next step to validating them with a SPICE simulator (TI Tina) :-)

I worry when I see movies like Star Wars which preach believe your instincts (aka trust the "force"). In reality vast majority of our instincts are either flatout wrong and works only in very narrow situations. In fact, virtually every scientific law is a statement of how our instinct was so wrong. Does Sun rotates around Earth? Is Earth flat? Can an object move endlessly when applied a force? Can two objects of different mass hit the surface at same time? Science is essentially a bandaid to fix our instincts. Vast majority of people will fail at basic probability questions. This is why there are so few people who finally managed to become quantum physicists. They had to break pretty much every single instinct about how world works. So I've always looked at Star Wars's "May the force be with you" slogan with dose of irony. If force is actually with you, you are probably not using your mammalian instincts :).

> I worry when I see movies like Star Wars which preach believe your instincts (aka trust the "force")

I thought that The Last Jedi was interesting because it very deliberately subverted that -- there are multiple pivotal scenes where people fail or endanger others because they're trusting their instincts. I'm not sure I've ever seen a blockbuster with such a cohesive thematic element.

Consciously or not I suspect that's why some folk didn't like it.

Why don't you approach it like this: forget about the real world, and think about building a virtual world with all these theories in place. I get you are a programmer so this shouldn't be too hard.

Now don't go building a real physics engine, that is not the point. The point is to calm down the anxiety in your head by working in this very limited virtual world instead of the real world.

After you figured it out in the virtual world, you can do the next more difficult step of looking how much your application in this virtual world would differ from the real one. Or you could just stay in the virtual world of course :).

If there was some kind of VR physics lab I think it would be fantastic because it would democratize access to all the tools without having to spend money to learn in that setting. In fact you could even simulate large scale things and see how they interact (boulder crashing into car, etc).

Is there educational software like this which is aimed at beginners?

It sounds like you want engineering, not physics. Physics tries to understand why something falls to the ground, and to make any progress on that problem you have to idealise the problem and neglect other factors (i.e. Air resistance) so you can focus on just one aspect. Engineering is all about understanding which things you have to take into account and which things you can ignore, and what level of precision or approximation is necessary to get you a useful answer.

Not sure I understand. If you fire a gun toward the ground from the leaning tower of Pisa, and you drop a bullet at the same time, the bullet that was fired from the gun will reach the ground before the other one. The thing is that the explosion gave the bullet additional momentum toward the ground (and a corresponding inverse momentum to the person holding the gun, more or less, ignoring other factors)

You fire the gun horizontal to the ground. That way it will theoretically reach the ground (although far away) at the same time the ball does.

>The other common struggle I face is that so much of the physics you learn at a basic level comes with caveats like "assuming no air resistance" or "in a vaccuum" or "at sea level" and perfect weights and I end up wondering how futile all of it seems because in reality I'll never be able to apply this stuff the way it's being presented. If I have to actually apply it - I'd have to start thinking all the possible ways in which the system can be affected, then measure those ways and add them to my calculation.

That is because otherwise the math would be considerably more difficult than it already is, which is already quite difficult for most people for an introductory or undergrad course. Advanced courses cover such stuff, in which approximation techniques are used to account for less than ideal conditions. Also, adding some conditions such as air resistance or other friction does not make the problems too much more difficult and are good enough approximation to reality for most cases.

This advice might seem too simple, but the solution is to just start doing a ton of physics problems rather than trying to resolve any of these issues. Your heuristics for real world physics will probably change faster than you think, and it's very satisfying to feel like you really understand a common phenomenon in depth.

It does sound more like you want to study engineering from your latter paragraphs, but I'd argue a lot of that stuff is just industry knowledge you'd gather over time actually building things. Physics gives you the ability to do some back of the napkin maths to see if something seems to be the realm of feasibility though.

> if you fire a gun and drop a bullet from the same height they both reach the ground at the same time

This is incorrect if you consider drag.


“ @BrandonEnright Yeah, I have. I agree that the difference in time for the two bullets will be so tiny that it doesn't even really matter. I'm just asking if there would be a tiny difference. – chbaker0 Dec 13 '14 at 2:20”

> I start from a place of extreme skepticism that gnaws at me even as I watch myself being proved wrong.

I had the same kind of issues: I thought that energy should be E=mv, not E=1/2m*v^2. The latter seemed really baroque. I set up a ballistic pendulum trying to demonstrate my idea. I finally got it when I was thinking about how if you accelerate a projectile, the force has to be applied over more distance per unit time to achieve the same acceleration, so the amount of work being done goes up quadratically.

Even then, I was annoyed that "the" kinetic energy wasn't a unique value -- it depends on the velocity, which depends on your frame of reference. I finally got over that one when I realized that the kinetic energy in a collision is uniquely defined b/c of the center-of-mass frame.

In graduate stat mech, I basically got lost at the point where the prof said we're supposed to assume that every point in phase space is equally likely -- how the hell should we know that?!? It wasn't until I read the Bayesian derivation by Jaynes, based on Galilean invariance & entropy maximization as a form of being unbiased, that I finally got it - years after I squeaked by with a B in the class.

Relativity -- same deal, the time dilation / length contraction stuff seemed really contrived with all the little square root factors that drop out at low velocities. I finally started to get it when I saw someone write it all in terms of geometry instead of algebra.

QM -- can't say that I grok it yet, but I think I'm in good company on that front. One thing I worry about is that physicists have gotten so good at accepting initially-counterintuitive concepts, that it's gotten to be a badge of honor. I think it's always better to find a way to make the concepts intuitive. Maybe quantum physics cannot ever be made intuitive, but I think we should keep trying to find better ways to understand it instead of gatekeeping the profession by whether people can stomach the Copenhagen interpretation of QM.

>overwhelmed by all the possible things I would need to factor in.

I experienced that too. I made peace with it eventually, by accepting that it's a trade-off. Often times it doesn't make a big difference in the result, but it does make a big difference in how easy it is to understand what's going on (and to solve the math problems). It's generally better to work with the oversimplified problem first, and then you can test changes afterwards to see if they matter.

I have the same struggle. It's just neuroticism. Physics becomes fun when you ignore precision.

When you know the theoretical (perfect world) model, it can still be applied in the real world as long as you're aware that you won't get an exact answer, but it will often be "good enough". One of the few times I was able to apply my physics knowledge in my job, I was able to hack together the relevant equations and constants to give realistic answers (to do with still-air cooling of a mobile phone on a charging pad in a car) and I was able to estimate roughly how accurate the answers were, given the remaining unknowns.

I guess I also struggle with knowing when it's ok to be a little vs a lot imprecise, and what that means in terms of units. If I'm building something at kilogram scale can I be off by a few milligrams?

Theoretical physics is like computer science. You focus on algorithmic complexity, etc and neglect the actual HW architecture, latency, and cache concerns.

Susan Fowler is legit terrifyingly brilliant. In only a year and a half she went from pre-algebra to grad QM while being a writer at NYT. Some people are just set to a higher gear.

> In only a year and a half she went from pre-algebra to grad QM while being a writer at NYT

I found this hard to believe, so I looked it up. It appears she _did_ go from pre-algebra to grad quantum within a short time [1], but that was many years before she joined NYTimes in 2018.

[1] https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgli...

I still find it implausible. Would a university realistically allow someone who didn't know anything beyond 6th-grade math (in her own words) to sign up for such an accelerated syllabus that she went from doing introductory physics to quantum field theory in 6 months (also according to her own account)?

"In only a year and a half" --> How do we know she is not exaggerating? People have strong incentives to lie about their own accomplishments.

“Now, she tells her full story for the first time: a story of extraordinary determination and resilience that reveals what it takes—and what it means—to be a whistleblower. Long before she arrived at Uber, Fowler's life had been defined by her refusal to accept her circumstances. She propelled herself from an impoverished childhood with little formal education to the Ivy League, and then to a coveted position at one of the most valuable companies in the history of Silicon Valley. Each time she was mistreated, she fought back or found a way to reinvent herself; all she wanted was the opportunity to define her own dreams and work to achieve them. But when she discovered Uber's pervasive culture of sexism, racism, harassment, and abuse, and that the company would do nothing about it, she knew she had to speak out--no matter what it cost her.”

— blurb for her book “Whistleblower”

I have no doubt she is smart and resilient. But there is a huge gap between "smart" and "one-in-a-million genius".

You quoted a marketing blurb. Of course it is supposed to sell the author.

It's a distraction; care about your own learning at whatever pace.

u can learn it in 2 months https://www.youtube.com/watch?v=RGD6KQ6bRS8

To put this into context: The video is from the same guy who plagiarized a paper and replaced "quantum gates" with "quantum doors" and "complex Hilbert space" with "complicated Hilbert space".


It is conceivable her IQ is in the order of 1 in 100 million rarity in which it is possible to perform such feats of learning. Read the bios of some of the Nobel laureates in physics or those who revolutionized the field,and a similar pattern emerges of being able to learn things very quickly.

Gerard 't Hooft, Nobel laureate in physics has a list of resources to learn theoretical physics here:


Basically, whenever you become a physicist, especially a Nobel-prize-winning theorist (this even happened some to me during my non-theoretical PhD), you get a bunch of emails from cranks that believe they have "figured it out" without ever having engaged with the centuries of work and results that we are building on. So he made this reading list that he requires people to be familiar with before he engages with them. All the information you need is available and easily accessible and he just curated it into a full course.

This is a pretty good list. I used it is a starting point for my own studies. I just have two comments to make:

1. It's very likely you do not have good enough math skills to start learning physics. I have a math minor and CS major, but after being out of school for a few years I had forgotten a lot of stuff. I needed to spend a week reviewing algebra and trigonometry and then longer reviewing calculus. This is humbling but will make your progress a lot easier. If you don't do this there will be examples you can't follow because you don't know what trick the author is using to go from one step to another in a solution.

2. If your mathematical preparation is good you can skip a lot of the introductory stuff. I.e. just go straight to Taylor's Classical Mechanics, and Griffith's Introduction to Electrodynamics. You can also learn QM from the graduate texts. No need to read Griffith's QM book first. I'm working through Shankar's Principles of Quantum Mechanics and it is definitely doable. He introduces all the math you need for the rest of the book in the first chapter, so if you can make it through that (it is mostly linear algebra) you will be ready for the rest of the book.

Regarding math, one topic that is often neglected: Asymptotic approximations. I would often read a grad level textbook, and the author would whip up some fancy approximation, and it always seemed like brilliant magic. It was demoralizing: I could never come up with that. Do I not have what it takes to be a physicist?

Then my math department offered a (rigorous) course on doing asymptotic approximations. I took it, and it all made sense. There are well known techniques, and the physics authors were merely using them. Yet it's rarely taught formally in physics programs. I've occasionally seen it covered as part of a "Mathematics for physicists" course, but they can cover only so much.

There are books out there on the topic.

That's interesting. Are there any books in particular you can recommend?

I was recommended

J.D. Murray "Asymptotic Analysis"

when I was having trouble understanding a particular technique (method of steepest descents), and it definitely had clearer explanations than other texts.


Thanks, this looks a little more accessible than other texts, I'll try to find a copy of it.

I haven't read any, but some the professor recommended:

Asymptotic Methods in Analysis by de Bruijn

Concrete Mathematics by Knuth, et al.

He said the latter is a bit elementary, and the former is fairly advanced.

Searching for '"asymptotic methods" course' on Google will hopefully get you some free lecture notes.

Thanks! I actually own Concrete Mathematics, but have not worked through it yet. I'll check out the other book too.

I will second any and all recommendations for reading Griffiths, I have not met better written textbooks in any field.

His E&M book is the best, bar none. I know people talk a lot about Jackson, but a physicist friend gave the best description of Jackson's book: "The best book to teach me about all kinds of mathematical techniques used in solving physics problems. My problem solving skills went through the roof because of Jackson. My understanding of E&M was not at all affected, though."

For E&M intuition, Griffiths is fantastic.

His quantum mechanics book, while decent, is not that great. I don't know if I've found a single great book on QM.

Beware the first link inside the article redirects you to a phising site (someone's server got compromised)

The questions is, why do you want to learn physics? And once you answer that we can give you the contents that will satisfy that "Why", but just giving a list without any connection with the interests of the reader is useless.

It is assumed that the reader already has a reason

Sure, and depending on it the approach changes


Is this the full book? I'm confused by some items' being marked as "third volume".

Course of Theoretical Physics by Lev Landau, Evgeny Lifshitz was considered the gold standard at the graduate level, although not very pedagogical. It's better to read the particular books after one has already taken a course on the corresponding subject. Affectionately known as L^2

There was a nice list of good popular physics books in the beginning of the article. I wonder if anyone has similar lists for other science disciples?

You'd like to know more about the author?


I wish there’s a similar list for modern math.


There are others, but this one explicitly says

"Math is a much more diverse subject than physics, in a way: there are lots of branches you can learn without needing to know other branches first... though you only deeply understand a subject after you see how it relates to all the others!"

"It's a warm summer evening..."

The Character of Physical Law by Richard Feynman

was a waste of money and time. It was one of the worse books I've ever read.


It's hard to explain because I found it so unremarkable and banal.

But there was a small part of the book I took particular issue, "Your expectation on answering the question why goes deep. (No duh!) You might need to adjust your expectations of understanding to be less rigorous." He says the same thing in this video: https://www.youtube.com/watch?v=36GT2zI8lVA It's basically his book.

I think not only does this not match my personal experience, experience I've understood from others at large, but in particular Einstein who had deep insights because of his depths of understanding "why" in broad categories of topics. Einstein's brilliance was a synergistic understanding. Better, if we don't know something, it's best to say, "It's not yet understood" and explain expected horizons for exploration.

I would compare this attitude to Sabine Hossenfelder who says, "Yes! We can figure things out including quantum gravity. It's not our 'why's' that are wrong, but almost certainly our (amazingly crazy) assumptions."

This is a good and accurate list (albeit rather aspirational!) For context, I did my PhD in physics.

Although, referring to Wald as a "high level overview" is not right. In my mind, Wald is a very abstract and rich book and one that should not be read until you've mastered GR reasonably well.

She appears to have taken her "If Susan can..." blog post offline [0]

I do not believe she's coming clean on her learning journey.

[0] https://news.ycombinator.com/item?id=24089263

I think it's just an accidentally fubared link. It's still published: https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgli...

The problem with learning physics is there is little to no money involved in spite of all the work required, unless you plan to teach it or get a job that requires it. There are plenty of very difficult problems in which finding the answer can yield an immediate payoff. One such problem is, how do you create and use cheap google adwords threshold accounts that do not get suspended . Answering such a question is as intellectually challenging as the hardest of physics problems but the answer means getting effectively free ads from google. Same for similar problems in regard to Twitter and Facebook ads. Fingering out how to evade a social network's spam filter can man a lot of $ if exploited.

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