Month: July 2017

Hamiltonian mechanics is conservation of information entropy

Hamiltonian mechanics is conservation of information entropy

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 …

What is information entropy?

What is information entropy?

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 …

Time travel and a walk in the past

Time travel and a walk in the past

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 …