I was reading about the light cone in relativity and I got to the point where in order to avoid paradoxes one can introduce the causality principle:
Causality Principle: For every inertial observer , there is no event whatsoever that can affect past events . Only past events can affect future events .
This principle states that time has a direction. That is related to the second law fo thermodynamics,
Second law of thermodynamics: the entropy of an isolated system can increase, but not decrease. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future.
This again states that time has a direction.
Whats the relation between both statements ?, Does one imply another ?
Best Answer
There are several possible approaches to this question, but I've always been a fan of the one taken by Edwin Jaynes in his 1965 paper Gibbs vs Boltzmann Entropies. (See sections V and VI for the discussion, which I think can be read in isolation from the rest of the paper.) Here he derives the second law from the empirical fact that we as scientists and engineers are able to manipulate the initial conditions of an experiment, but we can't directly manipulate the final conditions. (The only way we can affect the final conditions of an experiment is via the initial conditions and the boundary conditions.) Together with Liouville's theorem this is enough to derive the second law.
Jaynes doesn't mention relativity explicitly, but if we take his view then the causality principle can be seen as a common assumption in both relativity and thermodynamics.
Of course, this doesn't address the other side of this issue, which is why there would be a causality principle at all, given that the microscopic laws of physics are reversible in time. This is known as Loschmidt's paradox, which itself has many possible resolutions.