How to seriously learn (theoretical) physics?

[Dr Flame]

Hi All!

thanks a lot for this great forum!... I really love it and spend a lot of time reading the threads (when I have time of course, hehe).

I am searching some advice and I think this is the best place to get it!. I apologize in advance for the long post! and thank you all for reading!

My story in short:

I always wanted to study physics (100% interested in theory), but I was scared of the job market and therefore decided to study something with a lot of physics in the curriculum, but more marketable, just to be sure I could get a job. But I always kept in mind I would learn the rest of the physics of my interest on my own (someday).

So, I studied Mechanical Engineering and then went to grad school for more theoretical/mathematical stuff: My PhD thesis was in Combustion Theory with the main focus in turbulent combustion. I really like the field. Lots of physics, lot of math and plenty of very challenging problems =). But of course, even when lots of maths are involved in my research, and even when turbulent combustion is almost purely physics, there are several other fields in physics which I do not dominate (at least not in a formal, mathematical way: I have read lots of pop-science books, hehe).

Things are currently going very well for me: I got an assistant professorship, got good evaluations (from students and dean), and finally I think I have some time to continue learning physics and I want to pursue it to the highest possible level (hopefully as high as my research in theoretical combustion). I estimate I have at least 5 hours a week to do it and I want to start covering Classical Mechanics, Electromagnetism, Quantum Mechanics and Relativity (one by one, probably one semester or year per subject). My very long term goal is: learning Quantum Field Theory (If I get tenure, I will have life-long time to do it!)

From my situation (some background already available in mathematics and some physics), I think it would be nonsense to start from zero, at least for classical mechanics, since it would take too much time and I would probably see lots of thinks I already know. It would be probably better to start with some not so basic, but not so complicated, book, which I will probably not completely understand in the first read, but which I could eventually understand after some analytical thinking. In the process I will for sure find some mathematics unknown to me, which I will end mastering in order to understand the physics: This is the way how I learned Combustion Theory!.

The question then is: How to approach this?.. which books should I use?.. Some recommended videos?

I thank you all again for the advice!

Best regards

 

[NathanaelNolk]

I own 'An Introduction to Mechanics' from Kleppner and Kolenkow which I think might be a good refresher on the subject of (Newtonian) mechanics. It doesn't cover the Lagrangian/Hamiltonian formalism though and I haven't studied it deeply enough yet to consider giving you advice on which books to choose. That being said, I think the books titled 'Classical mechanics' from both Taylor and Goldstein are two popular textbooks for a more advanced treatment of mechanics.
But what is your current background on maths and physics? Did you have a complete exposure to linear algebra? diff. eqs?

 

[Dr Flame]

But what is your current background on maths and physics? Did you have a complete exposure to linear algebra? diff. eqs?

Yes sure, as a mechanical engineering student I had several courses on calculus, linear algebra, differential equations, numerical analysis, statistics and probability. As a PhD student and now as a researcher focussed on theoretical combustion I have gone much deeper in those subjects and learned continuum mechanics (with all the tensor stuff involved).

In Physics I had algebra based classical mechanics, electromagnetism, fluid mechanics, thermodynamics, heat transfer, optics, very basic special relativity, very basic quantum mechanics, statics, dynamics, etc.

 

[NathanaelNolk]

Then do you really feel the need of a classical mechanics textbook? I'd suggest going straight into E&M otherwise, especially if you already know the Hamiltonian formalism (which will come in handy later when you'll want to learn QM, it'll make more sense).
Something else I'd like to point out is that knowing the theory and applying it to physical problems are indeed two different things. I'm no mechanical engineering student so I don't know exactly your physics background, but you might find useful to pick up one of the classical mechanics books I mentioned earlier and go through the problems to make sure you're comfortable with them. If you're interested in QFT and especially research, real exercices practice will be of utmost importance, especially to really grasp the theory.

 

[Dr Flame]

Then do you really feel the need of a classical mechanics textbook? I'd suggest going straight into E&M otherwise, especially if you already know the Hamiltonian formalism (which will come in handy later when you'll want to learn QM, it'll make more sense).
Something else I'd like to point out is that knowing the theory and applying it to physical problems are indeed two different things. I'm no mechanical engineering student so I don't know exactly your physics background, but you might find useful to pick up one of the classical mechanics books I mentioned earlier and go through the problems to make sure you're comfortable with them. If you're interested in QFT and especially research, real exercices practice will be of utmost importance, especially to really grasp the theory.

It was probably my mistake to assume that everyone knows that mechanical engineers normally only have Newtonian mechanics. Unfortunately, I do not know the Hamiltonian formalism. But yes, you are probably right: I should start checking how far I can go with the exercises to see what is really clear and what not, so I can skip what I already know and go faster. Probably I can start with Hamiltonian mechanics.

I will try to get the books you mentioned :).

 

[NathanaelNolk]

It was probably my mistake to assume that everyone knows that mechanical engineers normally only have Newtonian mechanics. Unfortunately, I do not know the Hamiltonian formalism. Probably I can start with Hamiltonian mechanics.

Actually the only graduate student I knew in mechanical engineering took classes called analytical mechanics where he learned Lagrangian/Hamiltonian formalism, hence why I thought it was the same for you. But yeah, consider working your way through the first problems to see if you can tackle something like Goldstein or Taylor, and then proceed to move on.
Also don't forget to make sure your maths skills are on par with your physics skills. A graduate student told me he was learning group theory and Lie groups for some of his advanced QM courses. Of course, right now what you know is enough, but don't forget to always check what mathematical prerequisites you might need for the branches of physics you're interested in.

 

[limetea]

Have you seen this page before?
http://www.staff.science.uu.nl/~gadda001/goodtheorist/index.html
The sidebar on the left is a concise high-level summary on what kind of topics are essential for a theoretical physicist (at least according to one), and I think you'd find it useful. I myself have perused through them, and I like the layout and brevity. The notes attached to each section are of good quality to my knowledge.
Your mechanical engineering/mathematical background should be invaluable, as quite a lot of the physicist skillset overlaps.