TL;DR – States are identified by position and momentum because this is the space that allows us to define coordinate-invariant densities. As we saw in many of our posts, Hamiltonian mechanics describes the deterministic and reversible evolution of states. This leaves one question: why are states fully described by position and momentum? Why not only …
TL;DR – Inverting the direction of time and space is equivalent to inverting the direction of the parametrization. In previous posts we have seen the classical equivalent for anti-particles. Here we see something that looks similar to the CPT theorem. Naturally, it’s not a complete analogue because we are not really looking at fields at …
TL;DR – Events with low probability happen all the time, even ones with probability zero. When I was in high school, a friend of mine vehemently told me: “Me with him? It’s more likely that donkeys start raining. It’s more likely that hell freezes over. It’s more likely that I enter a convent and never …