TL;DR Galilean boosts do not leave Hamilton’s equations and phase space volumes unchanged. They give good approximations only for small changes in velocity. When studying physics, you learn that relativistic mechanics is more “correct” and non-relativistic mechanics is just an approximation. But you may also get a sense that non-relativistic mechanics is self-consistent: it just …
TL;DR – Classical Hamiltonian mechanics already includes an uncertainty relationship that is similar to Heisenberg’s uncertainty principle of quantum mechanics. In previous posts we have looked at information entropy, the number of yes/no questions you need to identify an element within a distribution, and the fact that Hamiltonian dynamics conserves that. Here we will show …
TL;DR – Time loops don’t really work. Either they degenerate into sources of infinite mass or they violate thermodynamics. My last thought experiment on time travel struck a chord. “Surely, you must know about wormholes!” someone assailed me. “You could go through a black hole and come out in a totally different era!” “There could …