Cheating by having two ideas this week. But they are big ones. We talk about how “parallel transport” of vectors allows us to define curvature intrinsically, and leads us to the Riemann curvature tensor. Then we move to topology, in particular homotopy groups, which show up in physics all the time.

And here is the associated Q&A video, where we talk a bit about embeddings, tensor components, topological defects, and more.

After three videos in a row about quantum field theory, we bring things a bit more down to earth by talking about the sizes of things. Mostly about particles and atoms; the sizes of people and planets will have to come later.

And here is the associated Q&A video:

The third installment of a little trilogy about the basics of quantum field theory. First we explained free fields, and why they led to particles; then we added interactions and used Feynman diagrams to calculate them; and today we’re going to deal with pesky infinities by introducing effective field theories. A wild ride!

And here is the associated Q&A video:

Last time we figured out that when you start with a theory of noninteracting fields and quantized it, you could think of the result as a theory of noninteracting particles. Now we let those particles interact, and describe what happens using Feynman diagrams.

And here is the associated Q&A video:

We’ve talked about the quantum mechanics of particles, now it’s time to apply those ideas to fields. It requires a bit of effort to understand how a quantum field — which is really a wave on top of a wave, when you think about it — ends up looking like particles in the right circumstances. But it’s worth it.

And here is the Q&A video. I talk a bit about different kinds of fields, and why the Dirac or Klein-Gordon equations are not relativistic versions of the Schrödinger equation.

Entanglement is one of the most important features — arguably, when you get down to it, the most important feature — of quantum mechanics, but it’s often glossed over in how we introduce the subject to students. Here we dive in, and I use this as an excuse to eventually talk about some of the different physical theories vying to be a complete formulation of quantum mechanics.

Update: I originally uploaded the wrong file, this should be the right one!

And here is the associated Q&A video. (Sorry I was in a hurry and didn’t do the lighting correctly … I’ll never make it big in Hollywood at this rate.)