I’ve posted an update to the notes with some reorganization of the section on quantum symmetry. Specifically, I included a subsection describing the momentum state eigenbasis and the Fourier relation between position and momentum bases.

I came across a fun article the other day that highlights something that is rather surprising about how length contraction would appear in the real world. Usually when I’ve described length contraction, we imagine it from the side in a rather two-dimensional sort of way. We draw a picture of a 2D car with the car’s image squeezed along the direction of its motion. This is fine for getting the idea across, but it doesn’t actually reflect what we’d really see. You see, objects are three dimensional and light from different parts of the object would reach us at different times. It turns out that as a result of this, length contraction would actually appear to be something like a rotated version of the object.

For more details and some very helpful graphics that explain what’s going on, check out this article from Physics World:

https://physicsworld.com/a/the-invisibility-of-length%E2%80%AFcontraction/