Expert: Daniel Mazur - 5/18/2009

Question
Hello Daniel,

How is everything with you? Perhaps you remember me, I am Siddharth Ahuja, 26 years old, from India. I wrote you some time ago about the criteria for getting into a Physics PhD in the US. Your advice is proving most valuable to me and I am working on the things you had suggested.

I have run into a peculiar situation here and your advice would again prove indispensable to me. So I am hoping you would guide me further in my quest. As I mentioned earlier that I have been studying all the undergraduate physics on my own (since I don’t have a degree in Physics) and I have been reading ‘Resnick Halliday’ and ‘Feynman lectures’ to cover up the basic course work. I am pretty much done with them now. I have done the Special Theory of Relativity and Quantum Mechanics...however, I have not done General Relativity yet(as it is not usually taught at the undergraduate level) but I am planning to do it anyhow. And since Quantum Mechanics and General Relativity are the basic building blocks of all the physics today, as Brian Greene and Michio Kaku so fondly tell us on Discovery :) I was wondering whether after doing General Relativity, shall I venture out to see what lies in those Grand String theories and their famous off spring, the Super String theory leading to M-theory and so on.

I have books on these things available in stores around my place so I can get hold of them, whichever I would need to buy. But will this be a right approach for me? Or will I be better off doing the field theories first? There seem to be so many field theories around(both successful and failed ones) and there is also QED (Feynman) and Quantum Gravity (Hawking) to confuse me further. To be most honest, Daniel, I am pretty much lost here. I don’t know which ones to do and which ones to leave, if at all. And also in what order I approach them. Please help out this poor student and also, your advice on the names of the books I should read will be more than welcome.

I am trying to be best prepared before applying to a Master or PhD program, so at that time I don’t look like a fool to the professors :)

Thanks a ton in advance for all your help and time, I know you are busy but you are always so generous with your time, its incredible!

Best Regards,
Siddharth Ahuja
India


Answer
Dear Siddharth,
it's nice to hear that I helped, I hope to be as useful again.

It sounds to me, as if you are now looking to make not so much the next step as the next leap! There is something of a gap between Halliday et al., Special relativity and Quantum mechanics on one end and General Relativity, QED and string theory on the other. Apart from the need to master a great amount of maths to delve into QED one also needs to be familiar with statistical mechanics, electromagnetism and optics.

Secondly and more importantly, by choosing the study of General Relativity, QED and string theory you are already choosing your specialization, as these are by no means part of undergraduate curriculum. General relativity and string theory are, I believe, both part of the Masters studies in astrophysics. Quantum electrodynamics is more a subject for particle physics and high-energy physics, who might benefit from string theory knowledge as well. Apart from these there is a large amount of theoretical physics of solids, plasma and other materials - theory, which benefits from QED, but as the conditions are very different (mainly many-body effects), it becomes a completely different branch.

I suggest you now reflect on two things:
1) Have I learned all there is to learn at the undergraduate level?
2) What specialization do I really want to have, when I become an official graduate physics student?

I should add to the first point that in USA most examinations are test-based, so "learning" something really means that you are able to solve almost any textbook problem. I leave it to you to judge, if you can do that - Feynmann's textbooks and Halliday's are good base but by no means they are enough! To pass the Qualifier in the USA you will have to be able to solve without any reference material problems like Laplace/Poisson/wave/telegraph equation with boundary conditions, electrical circuit using Laplace transform and complex-plane integration calculus, find the magnetization of spins in the Ising model, calculate energy levels in hydrogen, energy levels of model systems that require higher-order perturbation calculus, Doppler effect in a gas with special kinetic energy distribution. And other things.

As I know how difficult it is to know all this at the same time, I warn before the rush to advance to the next book if you "only" understand the previous ones. It will be the problem solving that will determine your first success in the USA - passing the Qualifying Exam. The QE never contains anything of string theory or general gravity, and the QE demands quantum particle physics don't go beyond what's covered in the basic course plus quantum mechanics. Even quantum field theory is a tad too advanced for what you really need.

So, now you are aware of all that, so we can talk about the advanced books. Or can we? Of all the advanced theoretical subjects I only ever read A.Zee's "Quantum Field Theory in a Nutshell", which is really nicely written and makes the subject - provided you know all the prerequisites - really easily accessible. I also studied from several "Solid State Physics" books by various authors, but as you didn't ask about physics of materials, maybe you are not interested. With everything else I regret to say that you will need to ask a theoretical physicist or an astrophysicist. Before you jump into it, be sure that you really want to become a theorist. :-)

I am sorry for not being able to advise you better on the subject of the books, it really goes beyond my specialization and I don't want to give you a badly founded advice.

Good luck with your studies and all!
Daniel