For my study day this week I spent a lot of time working through Lecture 7 of the Theoretical Minimum Quantum Mechanics course. The theme of the lecture is Quantum Entanglement. At this stage we’re limiting ourselves to considering a singlet state, as I described in the previous post.

The thrust of the lecture involved Density Matrices and ultimately Bell’s Theorem. These are deep results and are not something which come easily, hence the need to repeat the material and carry it out over two lectures. It is interesting that having a bit of a background in stochastic processes and financial engineering certainly helps with the probabilistic concepts.

I’m glad that I’m finally beginning to get a solid grasp of elementary QM concepts. Once the course is over I’m going to work my way through the Special Relativity and Electrodynamics course. At this stage I really want to make sure I’m up to scratch on Classical Mechanics, QM, SR and EM by virtue of working through some textbooks and questions on the respective topics. Essentially, if I’m happy with the Landau & Lifshitz topics for Vols I (Classical Mechanics), II (Classical Theory of Fields) and III (Non-Relativistic Quantum Mechanics), then I feel I am in a good position to have a go at more complicated topics.

I am currently deciding on whether to pursue a deeper study of Quantum Field Theory or General Relativity, as a means of getting closer towards independent research. At this stage I am drawn towards both Quantum Gravity and Numerical Relativity as potential research areas. Perhaps I need not restrict myself to either. Nevertheless I am going to require a solid education in QFT, String Theory and GR in order to continue.

The next logical step is to “parallelise” learning of QFT and GR via the Theoretical Minimum lecture series, which has a specific GR module, and study QFT via some of the introductory textbooks. This is because there isn’t a specific QFT course at the Theoretical Minimum, although a lot of the necessary material is covered in the Advanced Quantum Mechanics course.

However, once I cover General Relativity via a number of textbooks (and even a workbook), I will have to decide whether to push hard on Numerical Relativity. This is a *logical* continuation of my PhD research into compressible fluid dynamics, so I should be able to begin researching more rapidly. But I am still very interested in the prospect of *theoretical* research into Quantum Gravity. Watch this space!