Theoretical Minimum - Physics

iTunes-U has lectures from Stanford called "The Theoretical Minimum".

I've watched 3 of the topics so far (about 10 lectures per topic, about 90 minutes per lecture). I am enjoying them. Topics so far:

• Classical mechanics
• Quantum theory
• Quantum entanglment

My highlights from Classical Mechanics:
Principle of Least Action. Deriving the Euler-Lagrange equations from the principle of Least Action.

Noether's Theorem: differentiable symmetries (i.e. smoothly parametrised transformations that leave the Action invariant) imply conserved quantities, e.g. x->x+ε for linear momentum, θ->θ+ε for angular momentum, t->t+ε for energy.

Derivation of Hamiltonian formulation (used Legendre transformation L+H=pv). Liouville's theorem: flows in pq phase space are divergence free (like incompressible fluid flow).

Electromagnetic example: particle in magnetic field: guage field needed for Least Action formulation; guage invariance and guage transformations.

From Quantum Entanglement:

Definite highlight from quantum entanglement is Bell's theorem, and the violation of locality: Making an "observation" of one component of an entangled system instantaneously determines the outcome of the other component, irrespective of their spatial separation. I.e. the one component affects the other component instantaneously, and notably: faster than the speed of light!

Note: I also highly recommend the Quantum Mechanics lectures from Oxford by James Binney.