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 …
TL;DR – Hamiltonian systems are those that conserve information entropy during time evolution. The idea is the following: suppose you have a distribution over position and momentum $\rho(x, p)$. Suppose you evolve it in time and get a final distribution $\hat{\rho}(x, p)$ using Hamiltonian evolution. That is: you take each little area in phase space …
TL;DR – Information entropy tells you the average number of bits (i.e. answers to yes/no questions) you need to identify an element from a distribution. Starting from the 1950s, the connection between information theory and thermodynamics has been increasingly made clear. What I believe is still largely unnoticed is that there is a deep link …
TL;DR – Time travel violates physical laws way before you get to the point where you can kill your own grandfather. A person bumped into me the other day. “Time travel has always fascinated me,” he said. “Is it possible? Could we go back in time and kill Hitler and prevent Nazism? There are so …
TL;DR – Inertial mass tells us how many states are there within a given range of velocity. More massive bodies are harder to accelerate because they have to go through more states to reach the same change in velocity. In this post I want to look a bit more closely at the concept of mass. …
TL;DR – Classical mechanics describes a divergence-free flow of states. The Hamiltonian is the time component of its vector potential. The Lagrangian is the scalar product between the flow and the vector potential. For the longest time I didn’t know what the Lagrangian was and why its integral is minimized along trajectories. A couple of …