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 – The extended Hamiltonian for a classical free particle is the classical version of the Klein-Gordon equation. After having seen the classical version of antiparticles we will see the classical version of the Klein-Gordon equation. This is the essentially the extended Hamiltonian for the free particle. Let’s look at the details. 1. Extended Hamiltonian for …
TL;DR – Antiparticle states are those for which time is a decreasing function $t(s)$ of the trajectory parametrization instead of an increasing function (i.e. time and trajectory parametrization are anti-aligned). In a previous post we introduced the extended Hamiltonian equations. In the next few posts we will see that they allow us to create parallels …