Improving an 'eh' undergraduate physics foundation/How to go back to the basics?

[MissSilvy]

I have a slightly bothersome problem with my current body of physics knowledge. I got A's and B's in all my upper-level physics classes and I know the math, at least as much as I need to know to solve the problems, so it's not like I don't know ANYTHING about what I learned. But it was all learned a little superficially. Not much thought given to where this fits in with the grand scheme of things, or symmetries or the really sort of 'deep' understanding that I feel is missing. Obviously going back and redoing it all is out of the question, since I am doing research over this summer and when the fall starts back up I will be taking three of the most fundamental physics classes in the undergraduate track and more research, but I do know that I will have to set time aside to fix this.

I think it was Richard Hamming's talk "You and Your Research" that made the following quote:

``How can anybody my age know as much as John Tukey does?'' He leaned back in his chair, put his hands behind his head, grinned slightly, and said, ``You would be surprised Hamming, how much you would know if you worked as hard as he did that many years.''

I was wondering what the best approach would be from here. I'm already reading the Feynman Lectures (and maybe picking up Landau later, I really enjoyed the little I saw of his classical mechanics book) but there must be more/better ways of doing it? I feel like I'm building more and more physics on a subpar foundation, so this is quite a pressing issue to me. If anyone would have anything to chime in or just any thoughts I would be grateful.

 

[Choppy]

Have you thought about teaching?

Are there opportunities for undergraduates to lead labs? Or maybe tutor? Or grade papers? One of the reasons that graduate students are required to do these things is that they force one to return to the basics and fill in gaps.

 

[deRham]

Not much thought given to where this fits in with the grand scheme of things, or symmetries or the really sort of 'deep' understanding that I feel is missing.

I'm no physicist. However, my comment here is that it often helps to consider what one eventually wants to understand, and then look into reading in that area. Becoming an expert at a single mode of thought exposes you to the basics in several others, and by nature, has you thinking more deeply about how things fit together.

In essence, I think what you're experiencing is the urge to actually become an expert and solve real problems.

A place to start is of course reading the papers of the experts...but obviously you can't go there until you do some introspection as to what perspective you want to take.

On the other hand, since you're already doing research, perhaps you've already thought of all this and are still dissatisfied.

To which I'd say - sometimes, there is no such thing as having a good foundation before you start putting foundational knowledge to the test, i.e. building upon it and strengthening as you go.

But if you're more specific as to what bothers you, there may be more to be suggested?

 

[Mororvia]

Interesting post MissSilvy. I can't really offer any advice but I've felt the same way. My undergrad education in physics felt rushed because I switched from engineering fairly late. I feel as though I'm missing understanding of some fundamentals because of that. That said, I made it through undergrad and a master's degree.

 

[chiro]

I don't think anyone, no matter what field they are in, can learn something non-superficially in their undergraduate degree.

Think about the entire context of what you are learning. You are learning material that has taken thousands of very very bright people working very hard with focus on particular specific areas of some sort.

Also I have to say I have great admiration for physicists. The math is not rigorous, but it is a challenge to really understand what the math means in many physical contexts. I know that other fields have to do the same thing (statistics, engineering, and so on), but I still think you guys (and girls) are amazing.

When you learn things in university all of the excess context that people gained while obtaining or discovering that knowledge is largely gone.

I guess if you want the kind of understanding you are talking about, then you probably need to devote a large chunk of your life to it. Even if you do this, nothing is guaranteed, but like they say: "The harder I work, the luckier I get".

I think research is definitely a good place to get understanding. It's more likely (and this is my own experience) that you will make mistakes and run into dead ends and understand why certain things don't work. This can be just as good as finding why something does work.

I wish you the best in your research and I hope you eventually get out of studying and life what you originally did it for.

 

[I like Serena]

One of the purposes of education, is to quickly learn a new knowledge domain.
To sift through the information and pick up on the global lines, and see through the details.
Always knowing, that if you need the details, you'll know where to find them.

This needs to be practiced to become better at it.

When you will have finished your education, it's likely you'll get into a job in which you will do something entirely different from what you've studied.
The main use of your education then, will be that you know how to quickly deal with lots of the information of the type you're studying.

In my field of expertise (software engineering) we have standards related to the level of expertise.
A junior is allowed to take about half a year to digest a new knowledge domain (related to software engineering).
A senior is supposed to do it within a couple of weeks.

 

[MissSilvy]

In essence, I think what you're experiencing is the urge to actually become an expert and solve real problems.

A place to start is of course reading the papers of the experts...but obviously you can't go there until you do some introspection as to what perspective you want to take.

On the other hand, since you're already doing research, perhaps you've already thought of all this and are still dissatisfied.

To which I'd say - sometimes, there is no such thing as having a good foundation before you start putting foundational knowledge to the test, i.e. building upon it and strengthening as you go.

But if you're more specific as to what bothers you, there may be more to be suggested?

That is a good point. I suppose that's why even something like classical mechanics is presented three or more times; freshman-level mechanics, undergraduate-level, and then graduate-level before you get to deep symmetries and things. Or maybe I just need to revisit these ideas later in my educational career periodically. I don't have specific grievances, just a foreboding feeling that my knowledge is shaky, but that can be fixed with experience I suppose.

Interesting post MissSilvy. I can't really offer any advice but I've felt the same way. My undergrad education in physics felt rushed because I switched from engineering fairly late. I feel as though I'm missing understanding of some fundamentals because of that. That said, I made it through undergrad and a master's degree.

It's good to know that I'm not alone in this. It's probably not even an actual phenomenon, just a silly notion. They do say learning is lifelong though. As long as you remain critical and seeking to understand, maybe it will correct itself later. I am really reluctant to just trust that it'll work out, despite the advice of a lot of very smart people on this forum and elsewhere.

One of the purposes of education, is to quickly learn a new knowledge domain.
To sift through the information and pick up on the global lines, and see through the details.
Always knowing, that if you need the details, you'll know where to find them.

This needs to be practiced to become better at it.

When you will have finished your education, it's likely you'll get into a job in which you will do something entirely different from what you've studied.
The main use of your education then, will be that you know how to quickly deal with lots of the information of the type you're studying.

In my field of expertise (software engineering) we have standards related to the level of expertise.
A junior is allowed to take about half a year to digest a new knowledge domain (related to software engineering).
A senior is supposed to do it within a couple of weeks.

That is a very good point. I think your comments about seeing the forest through then trees in a sense in exactly what I was aiming at. I guess picking up global lines and not getting bogged down in details is a skill I need to develop more. But thank you for putting it so clearly.

Have you thought about teaching?

Are there opportunities for undergraduates to lead labs? Or maybe tutor? Or grade papers? One of the reasons that graduate students are required to do these things is that they force one to return to the basics and fill in gaps.

Teaching I have thought about and been offered a TA position but in the great race to assemble a grad school application, I chose to do research instead. It would be a good idea though. Especially in grad school. Thank you Choppy, I never thought of that as a possibility for reinforcing the basics!

I don't think anyone, no matter what field they are in, can learn something non-superficially in their undergraduate degree.

Think about the entire context of what you are learning. You are learning material that has taken thousands of very very bright people working very hard with focus on particular specific areas of some sort.

Also I have to say I have great admiration for physicists. The math is not rigorous, but it is a challenge to really understand what the math means in many physical contexts. I know that other fields have to do the same thing (statistics, engineering, and so on), but I still think you guys (and girls) are amazing.

When you learn things in university all of the excess context that people gained while obtaining or discovering that knowledge is largely gone.

I guess if you want the kind of understanding you are talking about, then you probably need to devote a large chunk of your life to it. Even if you do this, nothing is guaranteed, but like they say: "The harder I work, the luckier I get".

I think research is definitely a good place to get understanding. It's more likely (and this is my own experience) that you will make mistakes and run into dead ends and understand why certain things don't work. This can be just as good as finding why something does work.

I wish you the best in your research and I hope you eventually get out of studying and life what you originally did it for.

True, maybe I am expecting too much too soon. I still enjoy physics and math, make no mistake, but part of this post was just to see if I was the only doofus plodding around in the dark. It always seems like most people have their stuff together and figured out and you're the only one struggling, but I know rationally that such a thing isn't true. Still, it's hard to remember at 1AM when you're finishing a problem set that took you hours because you forgot some bit of knowledge you need to solve a problem. Thank you for the advice though, you seem to know what you're talking about.

And thank you everyone. I feel a little more at ease now thanks to your sound advice.

 

[aalaniz]

MissSilvy, it took me about a decade to become comfortable with what math and physics are about, their limits, their utilities, and their possibilities. This comfort has come from applications (nuclear weapons physics, computational physics, accelerators, lasers, financial physics, molecular dynamics, etc.), and from much reading of historical sources, textbooks, and current research papers--not to mention plenty of conversations with many mathematicians, physicists, and engineers pursuing diverse areas at national laboratories and other places.

During this time, I have made maps and guides of how physics and math fit together, and what a person needs to learn these foundations for themselves.

Understanding of the core material comes eventually if you bang your head against it enough. Electrodynamics at the junior level (say Griffiths text level) is straightforward enough. Electrodynamics at the graduate level (Jackson text) took me working at accelerator facilities to really appreciate the content intuitively. I recently wrote a kind guide/syllabus for core material which I would be happy to share.

On the other hand, until recently I felt something was missing in the sense that you have expressed, and I have spent decades pursuing things to pin them down to my satisfaction. A simple case in point was my understanding of thermodynamics and statistical physics (I recommend Fermi's book on Thermodynamics, and Reichl's on Statistical Physics to get started; Riechl covers more of the field that other introductory graduate texts.) Of course I got this stuff in undergrad and grad school. Then I worked a little in molecular dynamics. I also worked on a trading floor doing "econophysics". Eventually I came to Los Alamos to work on nukes, involving particle transport. Accordingly, my understanding evolved in stages. Prior to my doctoral program in physics, I earned a non-thesis, 36 hour MS in mathematics. I studied analysis at the graduate level. The abstract approach quickly lost contact with any sense of intuition until I practiced financial physics. The analysis, placed in the context of probability and stochastic differential equations suddenly had context to finance and diffusion processes. Understanding the applications of Kolmolgorov and Ito and others made realize that my training in physics had only exposed me to a limited view of thermodynamics and statistical physics, but in the trading pits we actually practiced Monte Carlo techniques to extract numbers. This experience with Monte Carlo methods grew at Los Alamos, and I realized that this method is not bad, and that my deeper, analysis-based understanding of stochastic processes was nice, but not necessary. Still, I suppose I would have always felt a sense of incompleteness without knowing the math approach to stochastic processes. Only recently, interested in this stuff about the holographic principle, that the universe is a kind of computer, have I read C. Shannon's works on information theory, and I realized that I had erroneously thought I had a pretty good foundation on thermodynamics and statistical physics. Okay, maybe now I do.

What is math? What are its limits? Can we get rid of things like the Banack-Tarski paradox? The short answer I leave to Morris Klein, his multivolume history of math book (how. why, and the difficulties of how math got built), and his book "Mathematics, The Loss of Certainty". The books are great, but in between them are years spent studying Cantor, Ramanujan, the history of vector analysis, the continuum hypothesis, the axiom of choice, and so on. In other words, Klein's books give you a start, and I have to say that part of understanding his books lay in my graduate training in mathematics, and a part in heavy self eduction. Coming to a comfort with this kind of math foundations took me more time than it should have because there is no guide out there. You do it on your own, with little likelihood of success, or get lucky to find a good mentor. I've been drawing up a guide for this. Ditto for physics foundations.

Yes, I have a reasonable and operational understanding of general relativity and the Standard Model (and a guide for how to do this on your own) but general tools that allow theoreticians to cook up fantastical universes took me a long time to gather, unnecessarily long. I studied a lot of abstract (modern) algebra in my math training, and it just got more abstract. e.g., Lang text. Where was the contact with physics that I so often read about? I happened on "Groups, Representations and Physics", 2nd ed., H. F. Jones for a good start. I then fought with Georgi's "Lie Algebras in Particle Physics", poorly written in my opinion, but worth the fight for physics understanding. Then I ran into "Topology, Geometry, and Gauge Fields, Foundations" by Naber--so full of promise--so difficult its math jargon is to read, but I got a big picture: gauge fields have a more general language than just terms put into a Lagrangian to make it relativistically invariant, e.g., the Dirac equation. Frustration with Naber led me to the much more readable text by Nakahra, "Geometry, Topology and Physics". Again, that MS training in math helped, and pure a physicist would be more hindered in my opinion. Lastly has come an older, but readable and highly relevant book: "Lie Groups, Lie Algebras, and Some of Their Applications" by R. Gilmore. One begins to see physics in a general language. Yes, the Standard Model and General Relativity were "extruded" from experiment, but early on, people began theorizing more general constructs, such as Kaluza-Klein theory. (Only experiment can choose among all the theorizing fantasies). The books in this paragraph (plus reading of the literature concurrently throughout the years) have given me this more elevated, general view. With these books, and from various great texts on QED and QFT, I have learned that physics has some big, general ideas: how to add, e.g., Feynman's history over paths, and how to group, e.g., particle spectra, and how this adding and this grouping can come together using algebraic topology (Lie, Homology, Homotopy) to produce GUTs, string theories, etc. These foundations are nowhere as intellectually challenging as they are difficult to put together in the absence of proper mentorship.

PS--Once you get Lie groups and Lie Algebras (R. Gilmore text) you're ready to start seeing good, old fashioned mathematical physics as a very unified subject. I've gone back to Goldstein's Mechanics, and realized I had only partially understood some of the key chapters without a full appreciation of Lie Groups and Lie Albebras.

Cheers,

Alex A

 

[chiro]

Hey there aalaniz and welcome to the forums.

I am very interested to read your guide if you don't mind sharing it. I myself am a mathematics student, but am still interested in anything you have to share whether it pertains to physics, mathematics, or a mixture of the two.

I hope you like it here at PF: this place is a fountain of knowledge, experience, and wisdom with a lot of talented, hard working, and smart, and open minded people and I hope you enjoy your time here.

 

[aalaniz]

Dear Chiro,

I've attached my "guide" to the student physicist, mathematician and engineer as a Word document. It has come about from much interaction with undergrad and grad interns with indomitable curiousities. Let me know if it uploads; this is my first uploading to this forum.

The audience is physicist, mathematiciand, and engineer from the sophomore level to the PhD level and beyond. Any typos or suggested changes would be greatly appreciated.

Cheers,

Alex A.

 

[chiro]

Dear Chiro,

I've attached my "guide" to the student physicist, mathematician and engineer as a Word document. It has come about from much interaction with undergrad and grad interns with indomitable curiousities. Let me know if it uploads; this is my first uploading to this forum.

The audience is physicist, mathematiciand, and engineer from the sophomore level to the PhD level and beyond. Any typos or suggested changes would be greatly appreciated.

Cheers,

Alex A.

Hey Alex,

Many thanks for the material. I have skimmed over it and it looks pretty comprehensive and interesting and very diverse. It's good when you read books by an author that has a wide perspective like yourself (i.e. studied a variety of things with the ability to merge a variety of ideas into something that is cohesive).

Looking forward to reading it.

 

[deRham]

I think your comments about seeing the forest through then trees in a sense in exactly what I was aiming at.

I think this then reinforces what I felt is the root of your anxiety - it can be tough to see the forest until you are forced to really contribute (or at least prepare to contribute) to the body of knowledge. You're right, I think, as to why the same fields are presented again and again at various levels of sophistication.

The feeling of not having really understood it tends to have to do with motivation for all that junk one is manipulating. But the reality is there's often not just one piece of motivation but many, found in different publications by people who think about the subject very differently.

As someone training in mathematics, I've many times experienced a lack of motivation for various things, and it's something I've found only gets cleared up painfully over time. You'll have the right conversations with various people, read the same thing over and over again (NOT AT ALL during the same stretch but sometimes even months later), and suddenly things will start to have meaning.

I don't think one is meant to have an appreciation for all one learns as an undergraduate, but rather to cover things well enough so that the basic vocabulary and ideas are somewhere injected into the system.

 

[MissSilvy]

Hello Alex! Thank you very much for such a wonderful and comprehensive reply. I enjoyed reading it immensely and I'm sure a lot of other people will find it useful as well.

I have downloaded your guide and I look forward to reading it tomorrow. It seems daunting how much there is yet to learn. I think one gets complacent in university; simply do the homework and take notes and eventually you get to call yourself a physicist but that is really nowhere near the end of the line as far as learning and understanding the field goes. The problem is the tendency to want to go in five different directions at once; the theory, the concepts behind the theory, the math, the other area of that the theory applies to, the applications and so on. I am very glad, however, that you had the desire for a deeper, more comprehensive understanding and not only went through the necessary work to get there, but did not regret it. I can only hope that I come across a mentor like yourself at some point in my education.

Electrodynamics at the graduate level (Jackson text) took me working at accelerator facilities to really appreciate the content intuitively. I recently wrote a kind guide/syllabus for core material which I would be happy to share.

I did hear from many physicists in high energy that Jackson was a lifesaver when designing accelerators and I admit to being curious myself. Would you mind posting this, if that wouldn't be too much trouble?

I think this then reinforces what I felt is the root of your anxiety - it can be tough to see the forest until you are forced to really contribute (or at least prepare to contribute) to the body of knowledge. You're right, I think, as to why the same fields are presented again and again at various levels of sophistication.

Thank you. It's just hard to get your teeth into the subject. I feel like it's an endless chain. You don't understand the concept behind a particular theory, so you look it up. It needs an understanding of some bit of math that is a little beyond what you currently know, so you look that up as well. And then you patch up the math but by that time you've found not only a whole section of math you need to think about, but two more theories. I am incredibly impressed with people who have learned how to truly learn physics because it is a sort of art. Your comment on undergraduate education being about vocabulary and basic ideas is heartening. Things sometimes do seem impossibly difficult when you are learning them but in retrospect, might be pretty basic.