Learning advanced physics without a physics background

[JonnyG]

I am a (pure) math major, but I do have some interest in physics. Sadly, I do not know any physics at all, and my interest comes from watching pop science documentaries. Nonetheless, I would like to learn some physics. I am thinking about taking two courses next school year - one on the mathematical foundations of quantum mechanics and one on general relativity. I know that saying I want to take classes on those topics sounds insane when I say that I know of no physics, but the prerequisites for the classes are only math prerequisites, and the courses are listed in the math department. Furthermore, there are distinct general relativity and quantum mechanics classes in the physics department, which leads me to believe that the classes that I am interested in are from the point of view of a mathematician (actually, the quantum mechanics class most surely is, as it is called "the mathematical foundation of quantum mechanics"). Anyway, I once read that learning quantum mechanics without knowing classical mechanics makes little sense. So my question is, does it make sense for me to take these classes without knowing any physics? Will I actually understand and appreciate the physics or will it just feel like a pure math class? Below are the course descriptions for the classes so you can see exactly what I will be learning.

General Relativity:

Einstein's theory of gravity. Special relativity and the geometry of Lorentz manifolds. Gravity as a manifestation of spacetime curvature. Einstein's equations. Cosmological implications: big bang and inflationary universe. Schwarzschild stars: bending of light and perihelion precession of Mercury. Topics from black hole dynamics and gravitational waves. The Penrose singularity theorem.

Mathematical Foundation of Quantum Mechanics:

Key concepts and mathematical structure of Quantum Mechanics, with applications to topics of current interest such as quantum information theory. The core part of the course covers the following topics: Schroedinger equation, quantum observables, spectrum and evolution, motion in electro-magnetic field, angular momentum and O(3) and SU(2) groups, spin and statistics, semi-classical asymptotics, perturbation theory. More advanced topics may include: adiabatic theory and geometrical phases, Hartree-Fock theory, Bose-Einstein condensation, the second quantization, density matrix and quantum statistics, open systems and Lindblad evolution, quantum entropy, quantum channels, quantum Shannon theorems.

 

[Orodruin]

Clearly, taking a "physics" course at a maths department runs the risk of losing some of the physics insights in favour of the mathematical structure. As a physics background, I would strongly recommend analytical mechanics (Lagrange and Hamilton formalism) before doing either GR or QM. Admittedly, this is not always how it is done even in physics departments, but it does add more physical insight.

There is also a lot to the mathematical description of classical mechanics, in particular in terms of symplectic manifolds.

The best way of checking the courses out is probably to ask the course responsible teachers directly.

 

[micromass]

It really depends on what you want to get out of this course. You will definitely get a nice appreciation of how math is used in physics, and you will see your mathematics courses in a new light. This is already very beneficial as you might only be confronted with very abstract math classes so far which seem to have no application. You will meet some applications now.

But if your goal is to actually learn physics, then no, this won't teach you much physics.