This has the same omission that my undergrad program had: continuum mechanics. Even just the very basics (pressure, velocity, etc in a moving, non-equilibrium system) and translating between the terminology used by different science and engineering fields (static pressure, total pressure, velocity pressure, stagnation pressure, hydrostatic pressure, dynamic pressure, plain old pressure, head, oh my!) is very useful.
Hydraulics are everywhere. Ever used a sink? Flushed a toilet? Contemplated an air filter? Felt both sides of a small fan? Wondered how, exactly, a utility pump causes water to go in the inlet and out the outlet, and tried to read the manufacturer’s spec? Contemplated that the ripples when you throw a rock in an actual pond really don’t resemble the average “look I made water in WebGL” animation very much?
And more fancily, and very much in “Physics”, cosmological models usually model the universe as being full of a spatially varying continuous fluid. Stars are plasma or weirder things, and those are fancy fluids.
Yet, for some reason, the basics are missing from “Physics”. You can sometimes find them in mechanical engineering departments, and Feynman covers it a bit in his lectures.
You might be interested in Kip Thorne (of Gravitation fame) and Roger Blandford's book Modern Classical Physics, which is designed to cover the elements of non-quantum physics that are generally ignored in the first year PhD curriculum. Part headers: statistical physics; optics; elasticity; fluid dynamics; plasma physics; general relativity
I second the recommendation of this book -- it really is quite excellent and covers at an advanced level most of what is commonly left out of a modern physics curriculum (though it is quite imposing in its size/weight).
Idiot who transferred from physics to computer science after year 1 here, so please make allowances. But all of those phenomena are emergent. Shouldn’t physics focus much more on the underlying micro states and micro processes than the emergent phenomena?
Obviously there needs to be a transition, but at some point you go from physics to engineering. I suppose it depends what specialty in physics you go into. Nobody can specialise in everything.
> Shouldn’t physics focus much more on the underlying micro states and micro processes than the emergent phenomena? Obviously there needs to be a transition, but at some point you go from physics to engineering.
1. The boundaries between disciplines are where they are in part by historical accident, and in part because that's what the people working in them find useful - there is no actual fact of the matter.
2. We don't actually know the underlying microprocesses of anything. Effective theories are all we have, and there's no fundamental difference between an effective theory for the vacuum (if it is a vacuum) and one for, say, the bulk of a semiconductor.
Reminds me of a student sketch from my days in nerd school, parodying Star Trek. A student dressed as one of the physics professors demonstrated that FTL travel was impossible, causing the Enterprise’s warp drives to stop functioning. It was fixed when Scotty said, “Wait, I’m an engineer: I don’t need to understand physics!”
As GP said, continuum mechanics is often used for physics research. While not the Truth, the models can often be accurate. My own research involving transport in the quantum domain utilized some models from continuum mechanics.
(I didn't introduce it - it was already being used).
You could say that about a lot of topics. Heck you could say that chemistry is just an emergent phenomenon of physics.
The benefit of taking such a class or reading such a textbook is that these things have been studied extensively, we have good models for them, and it is useful to know because people are still doing fundamental research on it to this day or working on phenomena that are closely related.
I think solid state continuum mechanics are also the optimal place to introduce tensors. For some reason, the first tensors many physics students encounter are very abstract. It would be like if the first vectors you encountered were quantum mechanical states. Stress and strain are, in my opinion, the ideal "prototypical rank-2 tensors", and it's useful to spend time really elaborating what that means, the same way we teach students to think of vectors as "things that look like displacement/velocity".
That’s an interesting idea. The best class involving tensors I ever took was an introductory course on differential geometry, and I still think the coordinate-free approach of thinking of tensors as multilinear functions from some number of vectors to some other number of vectors (or a scalar) is great. Everything else just involves picking coordinates and figuring out where the numbers to :)
But I probably like abstractions like this more than most people.
Oddly, undergraduate physics also seems to be missing another, arguably even more fundamental, tensor: the moment of inertia. You can get quite far (in three dimensions, and only in three dimensions) by thinking of rotation as a vector. (Or a quaternion if that floats your boat.) But you can’t get very far by pretending that the moment of inertia is a scalar, and you get very confused very quickly if you treat it as three scalars in the magical coordinate system in which you can write it like that.
Hydraulics are everywhere. Ever used a sink? Flushed a toilet? Contemplated an air filter? Felt both sides of a small fan? Wondered how, exactly, a utility pump causes water to go in the inlet and out the outlet, and tried to read the manufacturer’s spec? Contemplated that the ripples when you throw a rock in an actual pond really don’t resemble the average “look I made water in WebGL” animation very much?
if you can understand the PDEs of GR and QFT, you can apply it to this too
I noticed that too, and my explanation was that physics education needs to set itself apart from engineering.
Classical ( non relativistic ) field theories by now are undergrad engineering topics, but there are only a few quantum engineers.
Most of the non quantum topics in modern undergrad physics curricula, is needed to make sense of quantum[ thermodynamics, filed theory, optics, something ]
Halliday & Resnick Fundamentals of Physics is what we used in AP as well as in freshman year at college. Covers most sections one needs to be familiar with to be physics literate (solid/fluid mechanics, waves, thermo, electromagnetism, optics, relativity).
For the mathematically inclined, the best I've seen is An Introduction to Continuum Mechanics by Morton Gurtin from 1981. At one point, it could be purchased from Google books directly as a pdf.
I don’t know much about continuum mechanics (unless you count stat mech but I wouldn’t), however Goldstein has a few chapters on the topic that might serve as an introduction
You've described the core of a usual Chemical Engineering curriculum. A school with a good engineering program would definitely offer these classes, maybe under a name like "transport phenomena" (in my experience).
The undergraduate Physics program is, in my opinion, heavily influenced by the working physicists in the field. Lots of physicist who work in fundamental physics is either particle physicists or work with models that are in particles. Those are the ones who teach physics in undergrad.
This is simply not true, condensed matter physics makes up the largest sub-field of physics (about half by some estimates).
I think the more relevant aspect is that to reach the frontier in a wide array of fields you a solid grounding quantum physics (and several other "new" -- i.e. within the last century or so -- topics) that have displaced more "old-fashioned" topics like continuum mechanics.
A point that's rightfully emphasized by the author:
> Solving problems is the only way to understand physics. There's no way around it.
This generalizes well to other fields. I don't want to discourage anybody from trying to educate themselves in a difficult field (be it physics or something else), but that's a very common and immediately visible problem with autodidacts. If you haven't worked through enough hard problems you lack the intuition that ties together theory.
That’s a POV I’ve grown to adopt as I got older (like many, perhaps). I used to heavily privilege theory, believing that everything could (and maybe should) be derived from first principles.
Now I place the concrete over everything else; theory is nice when it can illuminate why the practice works. Otherwise, it’s just words.
The most frustrating is when I have friends who have derived their entire understanding of a subject I know as a practitioner (typically something tech/programming related) from watching YouTube videos/listening to podcasts.
Because they’ve heard hours and hours from experts, they have a feeling of deep understanding. But talking to them about this topic is extremely frustrating because their knowledge clearly has never had to be applied to the real world, and is grounded in nothingness, so they misunderstand lots, but they feel like they know what they’re talking about as much as you do.
> That’s a POV I’ve grown to adopt as I got older (like many, perhaps). I used to heavily privilege theory, believing that everything could (and maybe should) be derived from first principles.
> Now I place the concrete over everything else; theory is nice when it can illuminate why the practice works. Otherwise, it’s just words.
That mirrors the trajectory of all humankind, doesn’t it? From lofty Platonic ideals to nitty gritty empiricism and experimentation.
I only became reasonably proficient in physics when I took the summer off between undergrad and graduate school and spent three months, six days a week, ten hours a day, doing nothing but working through four years of undergraduate physics curriculum by solving problems from my textbooks.
Like another commenter, I'm curious what drove you to this. Seems like clearly A Good Idea I Could Have Benefited From, but my attitude was always: I finished the class, whatever I need to learn through application, life will point me toward. Yet I wish I had done something similar to what you did. What gave you the impetus?
But you will spend the rest of your life arguing with people who insist that there must be a ("quick and dirty") substitute and you're responsible for finding it.
Totally 100% with this. When younger I thought I could read the material and say "Oh, okay that makes sense I understand this." Only to fail miserably when on a test or somewhere I had to apply what I "knew" and realizing I didn't actually know it. I lean strongly toward autodidacticism and learned that if I could solve problems with the technique then I knew it.
My calculus 1 professor gave the advice that the best way to study is to do every problem in the book, then go and get another book and do every problem in that book, and keep doing that until you look at a problem and know exactly every step to do immediately.
Which exactly describes the problem with today's culture of people watching a 10 minute youtube clip and then thinking they are experts on the subject matter.
Yes, and I'd take it further. What I'd like to see more of in physics texts is presenting a problem before offering the solution. Too often you get what amounts to a laundry list of techniques and ideas, which are the components to the answers to hard problems, but the student isn't motivated to learn them. If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill. For example, I think calculus is probably better learned after trying to write down some force laws, and perhaps doing some numerical analysis. Then when you learn them you realize those nice closed-form solutions aren't busywork, they are huge labor saving tools that eliminate ad hoc labor intensive analysis.
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this!
I suffer from this. Sure, I'd like to learn physics, but what I don't want to do is learn all of it. Right now. Because what I'd rather learn is what I need to solve the problem I have. It's a silly problem, it's not real world, but it's my problem that I'd like solved.
As I've grabbed my horse and lance and rushed at this windmill from assorted directions, I quickly run into my limitations that prevent the problem being solved. I run into vocabulary problems with the math, the fact that I simply don't have the math to approach the problem (which appears to be some vector calculus -- I think. "No, you idiot, it's XYZ instead", but I don't know enough to know that it's not vector calculus, if, indeed, it isn't). I try to apply basic kinematics to the problem, but I don't know if that's enough. And, finally, it could be all of those things plus, oh, some optimization issues and, also, would you like to be introduced to the several different techniques for computing numeric integration and the differential equation solvers?
"Eeep!"
To quote the film "Addams Family Values":
Wednesday: Pugsley, the baby weighs 10 pounds, the cannonball weighs 20 pounds. Which will hit the stone walkway first?
Pugsley: I'm still on fractions.
So, yea, that's me, I'm Pugsley. It seems I need 2+ years of mechanics, calculus, and differential equations, and, probably, some time with computer based simulation all to chart the course for a spaceship to a planet for a 40 year old role playing game. Of course, I don't know what the, perhaps, abbreviated path I could take through those domains to get to be able to answer my question. That might knock a year off the study, but, unlikely. "Better to have all of the foundation" and all that. Which is true, but I'm kind of after the "reward" part here, not so much the "journey".
> What I'd like to see more of in physics texts is presenting a problem before offering the solution.
Yes.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill.
No.
If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
I never taught at the university level, but with middle and high school math students I taught them to how (re)discover the solutions, rather than teaching them the solutions directly.
As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution -- or tell us to learn it between classes and bring questions back.
>> Solving problems is the only way to understand physics. There's no way around it.
The reason is that you think you understand what you read, but as Richard Feynman said:
> The first principle is that you must not fool yourself, and you are the easiest person to fool.
You think you understand 90% of what you read, but in reality it's probably only 20-30%. By doing the exercises, at the very least you'll know that you don't know that much. And if you then reread the materials a few pages before, you'll realize that you have skimmed (or worse, skipped) some parts because you mistakenly thought you already understood it.
Another tips from my personal experience: When you're reading a textbook, keep asking in your mind questions with the types of "what if" and "how about," which are sometimes not yet explained in the section you're reading. Also, keep associating what you've recently learned with what you've already known (days ago, years ago).
Be curious and validate that you really understand what you think you understand.
Although, I think what you're describing doesn't completely lie on the reader. Oftentimes, the author has plain just not explained things clearly or even remotely well, and the reader has to play a little bit of 20 questions to get to the meat of something. When a book is properly written, then the shared load between the reader and the writer is much more balanced.
In college, I was always the first one out of my friends to “get” a concept, like fast Fourier transforms, anything with signal processing or even coding or any labs we had to do etc so I would spend time teaching them in the library. However I never did any of the exercises, mostly due to laziness and not arrogance. They would get A’s and I would get C’s and D’s.
I emphasize this story to my kids because knowing isn’t important because everyone eventually figure it out. It’s the ones who can do the problems and get good marks that succeed in the end.
I think this shows a lack of self-doubt, which can be deadly. Those problems acted as verification to yourself that you understood the theory and its application. If you truly understood the material, then the problems would be zero effort. However, if you struggled with them it's a signal that you don't know what you think you know.
This is kind of interesting to hear because I was the other way around. I found the best way to understand something was to teach it to others. That way I took what I already understood and was able to see what other people misunderstood, which was often something I'd never expected to be an issue, and add their experience in learning the topic on to what I already knew which expanded my overall understanding.
Then again, in the process of teaching I always found myself teaching people to work problems, which required me to be able to work the problems myself. In a way, it's kind of impressive you managed to avoid doing that.
It used to pose as a difficulty for self leaners because they did not have access to assignments, exams and solutions unless they register for classes.
Nowadays it's a lot easier when there are so many free materials from top school online. And stack exchange and reddit is available almost 24-7 if one ever has a question.
> It used to pose as a difficulty for self leaners because they did not have access to assignments, exams and solutions unless they register for classes.
Many textbooks still employ the deplorable practice of not presenting the answer to all exercises at the end, unfortunately.
It's kind of a tautology though. Physics isn't remotely special in this regard at all, and it doesn't need generalizing from physics. One needs to work through anything to truly learn it: music, sports, gardening, life, writing, etc.
> Classical Electrodynamics by Jackson (essential). This is the bible of classical electrodynamics, and everyone who works through either loves it or hates it (I loved it).
I agree that there is a division between who loves that book (like the author) and the majority of the graduate students who had nightmares (and sometimes still gets). I like this goodreads review of the book [1]
> A soul crushing technical manual written by a sadist that has served as the right of passage for physics PhDs since the dawn of time. Every single one of my professors studied this book, and every single one of them hates it with a passion. While I've no intention of becoming a professor, I still wonder, will my colleagues also inflict this torture on their students? Will the cycle be perpetuated ad infinitum? How many more aspiring physicists will we leave battered and bruised at the gates of insanity before switching to a textbook that seeks to make electrodynamics clear and intuitive rather than a mind-numbing trip through the seventh circle of hell?
It is interesting that 2 years later the same reviewer changes their mind a bit:
> Now, a few years after writing that review, I must return to say that as much as I hate this book, it's probably the best textbook that I have. I constantly return to it to reteach myself basic concepts or math. The problem with the text is that in order for it to be useful, you pretty much have to already understand the material. It's a dense, technical manual that, when paired with an easier to understand text such as Griffiths, grants tremendous power. Don't get me wrong, if there is a hell, I personally hope John David Jackson is burning in it right now, but I also have to tip my hat to him
Well yes, but curious what book you would recommend instead for graduate electrodynamics? Note that she already recommends first studying Griffith's Introduction to Electrodynamics at the undergraduate level (and that one is a true pleasure to read imho).
I'm happy that many professors start to use Zangwill's Modern Electrodynamics [1] textbook. It seems more focused on explaining things and don't assume that you know too much (which you usually have no idea if you should have known something or you just an idiot) like Jackson.
From what I've heard, the value of Jackson is not the EM you'll learn, but the mathematical techniques you'll learn, which are widely applicable beyond EM.
the author's IQ is high enough that I don't think this opinion is applicable to anyone reading it
Classical Electrodynamics by Jackson (essential). This is the bible of classical electrodynamics, and everyone who works through either loves it or hates it (I loved it).
If you're smart enough that advanced college physics comes as easily as learning to talk, I guess this would be true. The author of this guide is such a huge outlier in every respect of life. I have seen and read many smart people and she's easily in Witten or Tao territory of just being otherworldly smart. I don't think she ever encountered anything being hard. Jackson for her is like a walk in park, which is otherwise regarded as a formidably hard text.
The title should probably be: "So you want to learn theoretical physics".
While generally little known and appreciated among modern theorists and mathematical physicists, physics is actually an empirical science. In other words, every single section of that reading list is based directly or indirectly on a diverse and sophisticated set of devices and measurement configurations (aka experiments). Also, most progress in our understanding the physical universe follows simply from inventing ever better probes and opening new observation windows.
A computer analogy of the theoretical/empirical physics relation might be fun: You can spend your whole life writing application software and never even know what digital devices you are actually using. That's totally legit. But if you want to write a new computer language (= a new theory) you most likely will have to dig into memory architectures and caches and all that stuff. If you want to dramatically increase the speed of computation (= a new observation window) you have to design a new chip. And if you want to go really deep and invent new computing paradigms, well then you need to learn quantum mechanics :-)
In fairness, she does have a final sentence about that weird place called laboratory (= a place of labor).
> And, finally, a note on learning in a laboratory vs. learning from textbooks. Physics is both an experimental and theoretical science, and while research happens in laboratories and on blackboards and computers, the majority of any physics education does not take place in a laboratory but in lecture classes that teach from textbooks and assign homework problems that are found in textbooks.
My recommendation for a comprehensive intro into theoretical physics is The Road to Reality by Roger Penrose. Alas there is no such profound review of all experimental physics.
She just lists the standard curriculum through undergraduate and graduate degrees. I clicked the links to all the books and my Amazon has the purchase dates from when I took those courses. It's not specific at all to theoretical physics.
After reading this blog, I'm ashamed. I just graduated from college. In my high school, the education of physics was so boring and tiresome that I even hated it at one point. For this reason, I chose computer science rather than physics as my major in college. Later, I gradually became interested in physics, however, due to the lack of good enough study habits, atmosphere and courage (which is a self-deprecating way of saying cowardice and laziness), until now I have not taken a step forward. This is the decision I regret most in my life. I am going to the United States to study for a master's degree in CS. Maybe I can learn some physics during the freetime of the two-year program because the educational resources in the United States are more abundant(perhaps).
I feel the same way about pursuing CS instead of Physics. But at some point, a pragmatic solution had to be made. So don’t go hard on yourself for that, you probably would have felt the same way about CS too.
Yeah thanks. The difference of CS and physics, and other natural science, I think, is that it's more about engineering even though it's name is computer "science". However the pupolar deep learning may satisfy the needs of a natural science enthusiast. Since Hinton sayed the way neural network workss resembles the mechanism of human brain[^1]. It's quite exciting.
I dropped out of Physics back in the day, because I loved computers a bit more, and now that I'm kind of fed up with computers I'd like to remove the thorn and do something like this.
But I find that so much time has passed that I would need to brush up parts of my high school maths first, and this kind of discourages me before even starting.
I decided to start self learning theoretical physics late last year. I have been now studying physics every day for almost a year (before and after work). I did have to brush up on calculus and matrices but it came back very quickly (within a few days) after a 25 year gap so I'd say don't let that discourage you.
I'm preparing to do something similar but attack a lesser beast that is the general relativity. I had a Master's degree in Statistics but unfortunately 1) Statistics does not really match Pure Mathematics and 2) I forgot most of it.
A beast it still is, I think it is contained in its own walls. I can skip any topic in Quantum Physics and others that is irrelevant.
I'm wondering if it's helpful to you too to focus on something smaller.
Using math to model a system instead of learning math qua math does wonders for ease of understanding. Derivates and integrals become easy if you're using them to model the relationship between position/velocity/acceleration. I don't think I really got linear algebra until using it to learn quantum computing.
Rather than 27 (or however many) books, an ambitious student may be able to use just one big-ish book: Ian D. Lawrie's "A Unified Grand Tour Of Theoretical Physics". This even has a little 18 page "Snapshots of the Tour" which might be a trip down memory lane for those who studied physics long ago.
Of course, it might also be impenetrable if you haven't had prior exposure to most of the material.. I have zero experience trying to teach physics from it.
It will be impossible to learn physics from this book, even in the unlikely event that you already have all the requisite mathematical background (partial differential equations, vector calculus, tensors, etc.). Degree of “ambition” doesn’t come into it; you just can’t start out with special and general relativity and spacetime and quantum fields; you need to solve a lot of problems in newtonian mechanics and electromagnetism and thermodynamics and get a solid foundation in classical physics first. There is no royal road to this stuff: Susan’s list lays out the standard curriculum and it’s really the only way we know to produce physicists.
That said, this book does look like a great text for someone with a graduate level physics knowledge who wants to refresh their memory.
It was mostly just a recommendation to check out. I did not actually do it myself, but I tend to think I could have right after lin.alg./multivar calc freshman year and would have preferred it. Can't prove that, of course, since I didn't do it, but a year later I was loving Landau's Classical Theory of Fields which has a very similar relativity-first approach, and I did know a lot of relativity in high school. Wolfram went right from high school to grad school in physics at Caltech. The only very recently deceased late great Ed Fredkin got to be head of the MIT CS department with naught but a high school degree due to various life interventions and had some interesting "digital physics" ideas.
There are lots of pathways to learn & do. That is especially true of people coming to topics later in life, as I might expect is more common for HN comment thread readers. I know someone who learned to program in x86 assembly before they learned C (in fact one of the best programmers I know). If you talk to such people, I think you will find that their more varied backgrounds / ages in life when they approach things make anyone's dogmas more suspect. A great numerical relativist didn't study physics until his 30s. No idea what order he did things in, but I heard it was very non-standard.
So, I would encourage you to have more imagination of what might be possible / be less dismissive / jumping to conclusions. That is needlessly discouraging to many here were bemoaning "soooo many books/years/etc". "Ambition" might be "first learn diffgeo, then learn physics". I've been recommending that lately to a friend with extreme mathematical sophistication (a professor even) but no physics exposure, actually, but already some diffgeo exposure.
And, of course, "to learn physics" is maybe not to be a "produced physicist" any more than "to learn networks" means to "build a hardware router". It all depends. IMO, there are too many levels (& even directions/dimensions) of "having learned" to really even make "just can't", "only way" statements like you did. Elsethread, the diversity of even what "physicists" wind up having learned is shown to vary considerably (e.g. continuum mechanics). I find such absolutist statements needlessly discouraging to someone who might be hopeful to do it in "fewer steps". The way for most need not be the way for all or even the recommended way for any one person. People vary.
This guide does contain the books that are usually recommended in a university course setting! So, it will require significant amount of time and effort to master it. One of the series of books that physicists religiously stick to is Landau and Lifschitz. But my experience has been that it's worth it only if you already have some basic understanding.
I never got on very well with Landau and Lifschitz it's pretty intense. I mostly used pdf lecture notes from different courses. They can be a bit mixed but many are very good quality and you can easily pick up a couple for the same topic if you don't understand some part of one of them
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Hydraulics are everywhere. Ever used a sink? Flushed a toilet? Contemplated an air filter? Felt both sides of a small fan? Wondered how, exactly, a utility pump causes water to go in the inlet and out the outlet, and tried to read the manufacturer’s spec? Contemplated that the ripples when you throw a rock in an actual pond really don’t resemble the average “look I made water in WebGL” animation very much?
And more fancily, and very much in “Physics”, cosmological models usually model the universe as being full of a spatially varying continuous fluid. Stars are plasma or weirder things, and those are fancy fluids.
Yet, for some reason, the basics are missing from “Physics”. You can sometimes find them in mechanical engineering departments, and Feynman covers it a bit in his lectures.
Obviously there needs to be a transition, but at some point you go from physics to engineering. I suppose it depends what specialty in physics you go into. Nobody can specialise in everything.
1. The boundaries between disciplines are where they are in part by historical accident, and in part because that's what the people working in them find useful - there is no actual fact of the matter.
2. We don't actually know the underlying microprocesses of anything. Effective theories are all we have, and there's no fundamental difference between an effective theory for the vacuum (if it is a vacuum) and one for, say, the bulk of a semiconductor.
(I didn't introduce it - it was already being used).
The benefit of taking such a class or reading such a textbook is that these things have been studied extensively, we have good models for them, and it is useful to know because people are still doing fundamental research on it to this day or working on phenomena that are closely related.
Engineering: practical implementation
That’s how it goes in my brain. It’s physics until we can build it reliably, then it’s engineering.
But I probably like abstractions like this more than most people.
Oddly, undergraduate physics also seems to be missing another, arguably even more fundamental, tensor: the moment of inertia. You can get quite far (in three dimensions, and only in three dimensions) by thinking of rotation as a vector. (Or a quaternion if that floats your boat.) But you can’t get very far by pretending that the moment of inertia is a scalar, and you get very confused very quickly if you treat it as three scalars in the magical coordinate system in which you can write it like that.
if you can understand the PDEs of GR and QFT, you can apply it to this too
Classical ( non relativistic ) field theories by now are undergrad engineering topics, but there are only a few quantum engineers.
Most of the non quantum topics in modern undergrad physics curricula, is needed to make sense of quantum[ thermodynamics, filed theory, optics, something ]
I think the more relevant aspect is that to reach the frontier in a wide array of fields you a solid grounding quantum physics (and several other "new" -- i.e. within the last century or so -- topics) that have displaced more "old-fashioned" topics like continuum mechanics.
> Solving problems is the only way to understand physics. There's no way around it.
This generalizes well to other fields. I don't want to discourage anybody from trying to educate themselves in a difficult field (be it physics or something else), but that's a very common and immediately visible problem with autodidacts. If you haven't worked through enough hard problems you lack the intuition that ties together theory.
Now I place the concrete over everything else; theory is nice when it can illuminate why the practice works. Otherwise, it’s just words.
The most frustrating is when I have friends who have derived their entire understanding of a subject I know as a practitioner (typically something tech/programming related) from watching YouTube videos/listening to podcasts.
Because they’ve heard hours and hours from experts, they have a feeling of deep understanding. But talking to them about this topic is extremely frustrating because their knowledge clearly has never had to be applied to the real world, and is grounded in nothingness, so they misunderstand lots, but they feel like they know what they’re talking about as much as you do.
> Now I place the concrete over everything else; theory is nice when it can illuminate why the practice works. Otherwise, it’s just words.
That mirrors the trajectory of all humankind, doesn’t it? From lofty Platonic ideals to nitty gritty empiricism and experimentation.
Dead Comment
Dead Comment
There is no substitute for solving problems.
But you will spend the rest of your life arguing with people who insist that there must be a ("quick and dirty") substitute and you're responsible for finding it.
Be it microservices, coronavirus or taxation.
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.
As I've grabbed my horse and lance and rushed at this windmill from assorted directions, I quickly run into my limitations that prevent the problem being solved. I run into vocabulary problems with the math, the fact that I simply don't have the math to approach the problem (which appears to be some vector calculus -- I think. "No, you idiot, it's XYZ instead", but I don't know enough to know that it's not vector calculus, if, indeed, it isn't). I try to apply basic kinematics to the problem, but I don't know if that's enough. And, finally, it could be all of those things plus, oh, some optimization issues and, also, would you like to be introduced to the several different techniques for computing numeric integration and the differential equation solvers?
"Eeep!"
To quote the film "Addams Family Values":
So, yea, that's me, I'm Pugsley. It seems I need 2+ years of mechanics, calculus, and differential equations, and, probably, some time with computer based simulation all to chart the course for a spaceship to a planet for a 40 year old role playing game. Of course, I don't know what the, perhaps, abbreviated path I could take through those domains to get to be able to answer my question. That might knock a year off the study, but, unlikely. "Better to have all of the foundation" and all that. Which is true, but I'm kind of after the "reward" part here, not so much the "journey".Yes.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill.
No.
If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
I never taught at the university level, but with middle and high school math students I taught them to how (re)discover the solutions, rather than teaching them the solutions directly.
As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution -- or tell us to learn it between classes and bring questions back.
Issue is that often times people don't know that a certain tool exists, so they re-invent a 100x worse version and just hack something.
The reason is that you think you understand what you read, but as Richard Feynman said:
> The first principle is that you must not fool yourself, and you are the easiest person to fool.
You think you understand 90% of what you read, but in reality it's probably only 20-30%. By doing the exercises, at the very least you'll know that you don't know that much. And if you then reread the materials a few pages before, you'll realize that you have skimmed (or worse, skipped) some parts because you mistakenly thought you already understood it.
Another tips from my personal experience: When you're reading a textbook, keep asking in your mind questions with the types of "what if" and "how about," which are sometimes not yet explained in the section you're reading. Also, keep associating what you've recently learned with what you've already known (days ago, years ago).
Be curious and validate that you really understand what you think you understand.
I emphasize this story to my kids because knowing isn’t important because everyone eventually figure it out. It’s the ones who can do the problems and get good marks that succeed in the end.
Then again, in the process of teaching I always found myself teaching people to work problems, which required me to be able to work the problems myself. In a way, it's kind of impressive you managed to avoid doing that.
The gap between knowers and doers will only get larger as math explainers improve their content.
Nowadays it's a lot easier when there are so many free materials from top school online. And stack exchange and reddit is available almost 24-7 if one ever has a question.
Many textbooks still employ the deplorable practice of not presenting the answer to all exercises at the end, unfortunately.
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I agree that there is a division between who loves that book (like the author) and the majority of the graduate students who had nightmares (and sometimes still gets). I like this goodreads review of the book [1]
> A soul crushing technical manual written by a sadist that has served as the right of passage for physics PhDs since the dawn of time. Every single one of my professors studied this book, and every single one of them hates it with a passion. While I've no intention of becoming a professor, I still wonder, will my colleagues also inflict this torture on their students? Will the cycle be perpetuated ad infinitum? How many more aspiring physicists will we leave battered and bruised at the gates of insanity before switching to a textbook that seeks to make electrodynamics clear and intuitive rather than a mind-numbing trip through the seventh circle of hell?
[1] https://www.goodreads.com/review/show/1266180525
* personal note: If this book is really the bible of classical mechanics, then I'm atheist.
> Now, a few years after writing that review, I must return to say that as much as I hate this book, it's probably the best textbook that I have. I constantly return to it to reteach myself basic concepts or math. The problem with the text is that in order for it to be useful, you pretty much have to already understand the material. It's a dense, technical manual that, when paired with an easier to understand text such as Griffiths, grants tremendous power. Don't get me wrong, if there is a hell, I personally hope John David Jackson is burning in it right now, but I also have to tip my hat to him
[1] https://www.amazon.com/dp/0521896975/
Classical Electrodynamics by Jackson (essential). This is the bible of classical electrodynamics, and everyone who works through either loves it or hates it (I loved it).
If you're smart enough that advanced college physics comes as easily as learning to talk, I guess this would be true. The author of this guide is such a huge outlier in every respect of life. I have seen and read many smart people and she's easily in Witten or Tao territory of just being otherworldly smart. I don't think she ever encountered anything being hard. Jackson for her is like a walk in park, which is otherwise regarded as a formidably hard text.
While generally little known and appreciated among modern theorists and mathematical physicists, physics is actually an empirical science. In other words, every single section of that reading list is based directly or indirectly on a diverse and sophisticated set of devices and measurement configurations (aka experiments). Also, most progress in our understanding the physical universe follows simply from inventing ever better probes and opening new observation windows.
A computer analogy of the theoretical/empirical physics relation might be fun: You can spend your whole life writing application software and never even know what digital devices you are actually using. That's totally legit. But if you want to write a new computer language (= a new theory) you most likely will have to dig into memory architectures and caches and all that stuff. If you want to dramatically increase the speed of computation (= a new observation window) you have to design a new chip. And if you want to go really deep and invent new computing paradigms, well then you need to learn quantum mechanics :-)
In fairness, she does have a final sentence about that weird place called laboratory (= a place of labor).
> And, finally, a note on learning in a laboratory vs. learning from textbooks. Physics is both an experimental and theoretical science, and while research happens in laboratories and on blackboards and computers, the majority of any physics education does not take place in a laboratory but in lecture classes that teach from textbooks and assign homework problems that are found in textbooks.
My recommendation for a comprehensive intro into theoretical physics is The Road to Reality by Roger Penrose. Alas there is no such profound review of all experimental physics.
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[^1]: https://www.youtube.com/watch?v=2EDP4v-9TUA&t=2418s
But I find that so much time has passed that I would need to brush up parts of my high school maths first, and this kind of discourages me before even starting.
A beast it still is, I think it is contained in its own walls. I can skip any topic in Quantum Physics and others that is irrelevant.
I'm wondering if it's helpful to you too to focus on something smaller.
Of course, it might also be impenetrable if you haven't had prior exposure to most of the material.. I have zero experience trying to teach physics from it.
That said, this book does look like a great text for someone with a graduate level physics knowledge who wants to refresh their memory.
There are lots of pathways to learn & do. That is especially true of people coming to topics later in life, as I might expect is more common for HN comment thread readers. I know someone who learned to program in x86 assembly before they learned C (in fact one of the best programmers I know). If you talk to such people, I think you will find that their more varied backgrounds / ages in life when they approach things make anyone's dogmas more suspect. A great numerical relativist didn't study physics until his 30s. No idea what order he did things in, but I heard it was very non-standard.
So, I would encourage you to have more imagination of what might be possible / be less dismissive / jumping to conclusions. That is needlessly discouraging to many here were bemoaning "soooo many books/years/etc". "Ambition" might be "first learn diffgeo, then learn physics". I've been recommending that lately to a friend with extreme mathematical sophistication (a professor even) but no physics exposure, actually, but already some diffgeo exposure.
And, of course, "to learn physics" is maybe not to be a "produced physicist" any more than "to learn networks" means to "build a hardware router". It all depends. IMO, there are too many levels (& even directions/dimensions) of "having learned" to really even make "just can't", "only way" statements like you did. Elsethread, the diversity of even what "physicists" wind up having learned is shown to vary considerably (e.g. continuum mechanics). I find such absolutist statements needlessly discouraging to someone who might be hopeful to do it in "fewer steps". The way for most need not be the way for all or even the recommended way for any one person. People vary.