Specific guidance suggestions?

[Ringo Hendrix]

Ok. Very long post incoming. I'm kind of in a conundrum where my context is important. I am self-teaching theoretical physics slowly but surely. My end goal is to be able to mathematically comprehend various quantum gravity theories such as LQG and String Theory. My calculus roots go back to 2014 and I learned some major things in physics conceptually but only mid 2021 did I really start formally teaching myself. Started with Leonard Susskind's lectures, and Khan Academy for vector calculus. Improved my intuition of classical mechanics with various texts including David Tong's notes, from orbits to Noether's theorem and Liouville's theorem. Got some Special Relativity intuition there as well but more a refresher of things I learned from 2014-2021. Then, I tackled linear algebra and undergrad quantum mechanics via Griffiths- that went pretty well for almost a year. While the text clearly wants me to just go along with formulae, I truly like to understand everything I'm doing as fully as I can and be able to derive things. So when I got to Chapter 8 with Airy functions it led me on a path to want to study complex analysis... and improve and expand my knowledge of special functions, PDEs, vector calculus, linear algebra, etc etc etc.

So that took me to 2023 where I spent much of my time 'thoroughly skimming' Riley's Mathematical Methods text, more so for intuition rather than full understanding. It has greatly helped enhance my intuition of pretty much everything, from series to Sturm-Liouville theorem to the aforementioned topics that set me on this journey. Late last year I actually started with Griffiths EM while hitting a low point with Riley's math methods but it eventually led me right back to Riley for PDE topics such as Dirichlet boundary conditions. (I supplemented with Tong's notes when confusion arose) I've finally clawed my way up to complex analysis and have been supplementing with Faculty of Khan's extremely helpful series of videos on the matter.

Now I don't know which path to take. Also, I am quite familiar with Susan Rigetti's "so you want to learn physics?" site, it's been somewhat helpful.I sincerely want to resume QM, this time in full with solving way more problems- I feel with my enhanced intuition I could fly through Griffiths (compared to last time) but it is undergrad level and doesn't discuss path integrals, density matrices, etc. Sakurai or Shankar don't seem like convincing routes based on reviews... I'd be better to go graduate from the start but don't know a suitable text.

Besides, before I'm ready for that, it would do me wonders to study thermodynamics/statistical mechanics (for from-scratch knowledge building of subjects like blackbody radiation- I have a copy of Schroeder maybe I could time my studies where its quantum chapter overlaps with Griffiths' statistical chapter?) It's obviously immensely important for my end goal. Will probably need to tackle graduate level.

And of course electromagnetism- but I don't particularly want to go too in depth with it since the EM I intend to study is the quantum field theory and I suspect it can be studied fairly independently- perhaps Tong's notes will suffice? They seem to the point. Polarization and waves seem useful concepts to learn more about- particularly when I get to gravitational waves.

I can't stress enough how eager I am to start GR and differential geometry. I've considered running through Carrol's Spacetime and Geometry since you don't seem to need background knowledge on topology.

In Riley, I'm about on to the Tensors chapter- and Group Theory which I am hyped for.

Through this disjointed experience I'm seeing how all these different topics are intertwined.... That said- I'm beyond itching to study differential geometry. I know for my end goal, I'll need a much more formal approach to mathematics. Like I need Set Theory for topology (don't I?) and I am deeply interested in mathematical/abstract logic... more advanced complex analysis, real analysis, group theory etc for my end goal. Do I start with basics then re-do it all over again formalizing it or just learn the more formal approach first and be done with it?

Now, I don't know if I should resume Riley for Tensors and Group theory or move on entirely- is there a text which better starts from scratch all of this more abstract math? Arfken might be a good place to start? Zill also discusses sets, I believe, but doesn't go past complex analysis. But I like his descriptions.

Sorry, I know this is a very, very long post- I'm clearly lost in the woods but I just am deeply passionate about physics and want nothing more than to be able to get to the level I'm wanting... without having months-long blocks like I've been having. Am I doing better than I think and being hard on myself? Any advice is greatly appreciated.

Bonus- me deriving Pauli spin matrices and Schwarzschild solution.

 

[Vanadium 50]

Very long post

Correct.

My thoughts:

Most people need some help to learn physics (we have places dedicated to such help, called universities). Since you will be asking questions of people, it will help enormously if you learned to pare them down to their essentials. You have eleven paragraphs and two videos and I am still not 100% sure what you are asking.

You mention "intuition" a bunch of times. You don't wake up one morning and say "Now I have some intuition!". You gain it from experience.

You are trying to get to where a senior undergraduate or new graduate student is. In college, this would take 4-6 years. On your own, longer. Lots of people come here with the plan of learning physics 10x faster than those fools at Harvard or Caltech. It has yet to work out that way.

 

[Ringo Hendrix]

Most people need some help to learn physics (we have places dedicated to such help, called universities). Since you will be asking questions of people, it will help enormously if you learned to pare them down to their essentials. You have eleven paragraphs and two videos and I am still not 100% sure what you are asking.

University is simply not an option for me right now. Unless there were some online program where I could specifically study my interests. And perhaps intuition wasn't my best phrasing, right. I wrote that late last night, after working all day. By "gain intuition" I just mean to expand my understanding even if I couldn't necessarily past a test per se. While being able to derive/explain a topic certainly displays a level of understanding of a topic, it doesn't necessarily mean that I would be able to apply that knowledge to problem solving. (I can in some cases)

And I hope I didn't come off like trying to "learn 10x faster than those fools at Harvard" so to speak. I'm just simply passionate and want to see a path through the forest even if it takes me 10 years (I would hope not)

 

[PeroK]

Graduate level material is likely to be a lot harder without a supervisor or mentor of some sort. Especially if and when you go beyond regular textbook material.

You are on the right track, but how do you compete with full-ime PhD students and post docs?

At some point, I suggest, something has got to give if you want to pursue the physics further.

 

[Orodruin]

The thing is that "I don't have the time to go to university right now" is something that we hear pretty often. But then how will you have the time to learn what people go to university to learn - without the guidance of university teachers?

 

[Ringo Hendrix]

The thing is that "I don't have the time to go to university right now" is something that we hear pretty often. But then how will you have the time to learn what people go to university to learn - without the guidance of university teachers?

Not a time issue per se. Personal and living situation issue.

 

[BvU]

In threads like this one I am reminded of the inventory Gerard 't Hooft compiled:

https://www.goodtheorist.science/index.html

##\ ##

 

[Muu9]

If you're cool with continuing your 10,000 foot overview, you might find these notes useful: https://knzhou.github.io/notes/phy.pdf

You could probably start differential geometry now with Needham and/or Renteln, and GR with Schutz and/or Zee

 

[gleem]

Ok. Very long post incoming.

Likewise

You have set a lofty goal. It seems to me that while fixated on that goal you are generally stumbling forward toward that goal. I know nothing about quantum gravity except what I read in Carlo Rovelli's little book "Reality Is Not What It Seems". That said what I can say about understanding physics is that there is no shortcut. You say frequently that you have improved your intuition on various topics. What do you mean by intuition? You sort of answered that question yourself.

So that took me to 2023 where I spent much of my time 'thoroughly skimming' Riley's Mathematical Methods text, more so for intuition rather than full understanding.

Of course, skimming a book does not lead to an understanding of its content. So how do you "study" or teach yourself? I estimate that a typical physics major through grad school has in the neighborhood of 2000+ hrs of face time with a professor over six or more years. add about 4 + hours of study and problem-solving per class hour and you have over 10,000+ hours of directed learning experience with evaluation of your understanding. I would think a self-learner should be expected to take longer to achieve the same level of understanding for various reasons, including available time, the distraction of day-to-day activities, the lack of a regular schedule, and the natural competition of fellow learners to keep you on track.

Your apparent haphazard approach and being prone to try and jump over what might seem irrelevant topics to reach your goal faster is counterproductive as in this statement:

I sincerely want to resume QM, this time in full with solving way more problems- I feel with my enhanced intuition I could fly through Griffiths (compared to last time) but it is undergrad level and doesn't discuss path integrals, density matrices, etc. Sakurai or Shankar don't seem like convincing routes based on reviews... I'd be better to go graduate from the start but don't know a suitable text.

No, you do not skip Griffith and go straight to Sakurai, you are shorting your experience in QM. Why do we teach Intro to QM and Advanced QM instead of just getting on with it and teaching one extensive course in QM in one fell swoop? It takes time and effort (practice) to learn and understand a subject. Skimming is not a learning technique. You learn with pencil and paper in hand as you work through the texts and as you test your knowledge by working out problems.

Schools and universities are there to manage the learning experience, providing direction on what courses to take and to what depth, the order of the courses, assignment of texts, the availability of resources to expedite the learning as professors and libraries, and producing an efficient learning experience. Without a university, you must manage the learning yourself which you obviously are having difficulty with.

What I can say is this; study the traditional physics course sequence as a foundation; general physics, classical mechanics, E and M, thermodynamics, modern physics, and intro to quantum mechanics maybe condensed matter physics, or relativity, classical field theory then Electrodynamics, advanced mechanics, advanced QM, Statistical Mechanics, QFT, General Relativity, special courses in Cosmology, or astophysics that might be relevant. As far as math is concerned concentrate on the math that is relevant to the next physics topic you want to study. For the undergraduate sequence calculus, vector calculus, linear algebra PDE, and special functions, a little analysis seems to be sufficient. Tensor analysis when you see general relativity on the horizon and other advanced maths as will be needed for upcoming topics but not too early to distract you from the foundational topics. The text that you use for a topic should tell you the math or background that you will need. If they say something would be useful take their word for it. I never particularly liked the math tutorials that are often offered in a physics text they should be used only as a review.

Don't be so anxious to get to your final destination. Enjoy the "scenery" on your trip to it.

 

[CrysPhys]

My end goal is to be able to mathematically comprehend various quantum gravity theories such as LQG and String Theory.

You should expand upon your end goal. Are you doing all this merely to satisfy your own intellectual curiosity (physics as a hobby)? Or are you aiming for a paid job/career in physics research?

 

[Ringo Hendrix]

Intellectual curiosity, absolutely. Hobby would be underselling it. It's been there since I was 12, life's just got in the way. The career/paid job thing would be only if I happened upon it, so to speak.

 

[Ringo Hendrix]

Likewise

You have set a lofty goal. It seems to me that while fixated on that goal you are generally stumbling forward toward that goal. I know nothing about quantum gravity except what I read in Carlo Rovelli's little book "Reality Is Not What It Seems". That said what I can say about understanding physics is that there is no shortcut. You say frequently that you have improved your intuition on various topics. What do you mean by intuition? You sort of answered that question yourself.

Of course, skimming a book does not lead to an understanding of its content. So how do you "study" or teach yourself? I estimate that a typical physics major through grad school has in the neighborhood of 2000+ hrs of face time with a professor over six or more years. add about 4 + hours of study and problem-solving per class hour and you have over 10,000+ hours of directed learning experience with evaluation of your understanding. I would think a self-learner should be expected to take longer to achieve the same level of understanding for various reasons, including available time, the distraction of day-to-day activities, the lack of a regular schedule, and the natural competition of fellow learners to keep you on track.

Your apparent haphazard approach and being prone to try and jump over what might seem irrelevant topics to reach your goal faster is counterproductive as in this statement:

No, you do not skip Griffith and go straight to Sakurai, you are shorting your experience in QM. Why do we teach Intro to QM and Advanced QM instead of just getting on with it and teaching one extensive course in QM in one fell swoop? It takes time and effort (practice) to learn and understand a subject. Skimming is not a learning technique. You learn with pencil and paper in hand as you work through the texts and as you test your knowledge by working out problems.

Schools and universities are there to manage the learning experience, providing direction on what courses to take and to what depth, the order of the courses, assignment of texts, the availability of resources to expedite the learning as professors and libraries, and producing an efficient learning experience. Without a university, you must manage the learning yourself which you obviously are having difficulty with.

What I can say is this; study the traditional physics course sequence as a foundation; general physics, classical mechanics, E and M, thermodynamics, modern physics, and intro to quantum mechanics maybe condensed matter physics, or relativity, classical field theory then Electrodynamics, advanced mechanics, advanced QM, Statistical Mechanics, QFT, General Relativity, special courses in Cosmology, or astophysics that might be relevant. As far as math is concerned concentrate on the math that is relevant to the next physics topic you want to study. For the undergraduate sequence calculus, vector calculus, linear algebra PDE, and special functions, a little analysis seems to be sufficient. Tensor analysis when you see general relativity on the horizon and other advanced maths as will be needed for upcoming topics but not too early to distract you from the foundational topics. The text that you use for a topic should tell you the math or background that you will need. If they say something would be useful take their word for it. I never particularly liked the math tutorials that are often offered in a physics text they should be used only as a review.

Don't be so anxious to get to your final destination. Enjoy the "scenery" on your trip to it.

I'd like to specify to those I've mislead with the skimming line. I fully intend to gain a full knowledge. I mainly went through Riley- mind you, I'd spend weeks on some chapters, to enhance my math foundations and skills for when I go into a textbook next, which will be soon. Sometimes if I don't understand something I'll stay on it way longer than I should until I get it. While I'm not a pro by any means (that'll come with further problem solving applications) reading through Riley has greatly improved my clarity and understanding of topics such as linear algebra, convergence tests, PDEs and ODEs, Green's functions, eigenfunction methods, special functions (Hermite, Legendre) Sturm-Liouville, integral transforms, complex analysis (residue theorem is amazing)- again, I'm no pro (yet- in due time) but I once knew nothing about these and now some of the results I can derive, I have new problem solving skills and at worst my foundations are much sturdier for the future. The sheer volume of those topics was beyond overwhelming prior to going through this book. So it was definitely methodic and useful on my behalf. Get my foot in the door, my foundation down, then build from there. I would never intend to leave it at that, these things obviously need to become 2nd nature.

 

[Ringo Hendrix]

Tensor analysis when you see general relativity on the horizon and other advanced maths as will be needed for upcoming topics but not too early to distract you from the foundational topics. The text that you use for a topic should tell you the math or background that you will need. If they say something would be useful take their word for it.

Don't be so anxious to get to your final destination. Enjoy the "scenery" on your trip to it.

Yeah, I probably need to work on that. Griffiths QM in places would have things along the lines of "this result can be derived from subject X but that's out of this book's scope"- and I could very well just accept it and could do better by just memorizing some of the rules and get on with the physics, but I feel I'm not getting a full understanding all the way through by doing so... I probably just need to pace myself and work with it's in front of me and expand that knowledge later rather than going on a tangent. There's a reason they don't go into that, yet, I'm sure. I do appreciate your post, btw.

 

[romsofia]

You need structure, and you NEED to problem solve. Yes, it's tough. Yes, you'll feel dumb, but physics is a lot about problem solving. So you need to be doing problem sets, otherwise, you're bound to be stuck feeling like you don't really know anything.

Places like MIT OCW should be the first place you look, but feel free to google a course+a university and see if they have lecture notes, problem sets, past tests, etc. For example, if I google 'analytical mechanics+caltech' this pops up: https://labcit.ligo.caltech.edu/~ajw/ph106/ So, this has everything you'd need. It has a timeline for you to follow, it has the problems, it has the solutions, it has the exams, and it has the notes.

Now that you know where to get problem sets, and exams from, you need to plan out what to study, and when. Once again, pick a university, and follow their suggestions on what their course pre-reqs are. For example, let's say I pick university of Maryland, I google university of Maryland physics, I go to their website and lucky us, they provide a sample course schedule for a physics student: https://docs.google.com/document/d/13mrCBmbCNwebJ7A9OrlZsoAKeckJXBnhifAwOYnf1Zk/edit Of course, it's just a guideline, but it'll give you a sense of structure.

Self education is hard enough, don't make it harder by freestyling your own plans, when people have worked them out. So, i'll conclude with a quote: “The most foolish of all errors is for clever young men to believe they forfeit their originality by recognizing a truth which has already been recognized by others”.

 

[Ringo Hendrix]

You need structure, and you NEED to problem solve. Yes, it's tough. Yes, you'll feel dumb, but physics is a lot about problem solving. So you need to be doing problem sets, otherwise, you're bound to be stuck feeling like you don't really know anything.

Places like MIT OCW should be the first place you look, but feel free to google a course+a university and see if they have lecture notes, problem sets, past tests, etc. For example, if I google 'analytical mechanics+caltech' this pops up: https://labcit.ligo.caltech.edu/~ajw/ph106/ So, this has everything you'd need. It has a timeline for you to follow, it has the problems, it has the solutions, it has the exams, and it has the notes.

Now that you know where to get problem sets, and exams from, you need to plan out what to study, and when. Once again, pick a university, and follow their suggestions on what their course pre-reqs are. For example, let's say I pick university of Maryland, I google university of Maryland physics, I go to their website and lucky us, they provide a sample course schedule for a physics student: https://docs.google.com/document/d/13mrCBmbCNwebJ7A9OrlZsoAKeckJXBnhifAwOYnf1Zk/edit Of course, it's just a guideline, but it'll give you a sense of structure.

Self education is hard enough, don't make it harder by freestyling your own plans, when people have worked them out. So, i'll conclude with a quote: “The most foolish of all errors is for clever young men to believe they forfeit their originality by recognizing a truth which has already been recognized by others”.

Thank you.