Disentangling Boltzmann brains, the time-asymmetry of memory, the H theorem, and the second law

Abstract: Are you, with your perceptions, memories and observational data, a Boltzmann brain, i.e., a statistical fluctuation out of the thermal equilibrium of the universe? Arguments are given in the literature for and against taking this hypothesis seriously. Complicating these analyses have been the many subtle - and very often implicit - entanglements between related arguments that have been given for the past hypothesis, the second law, and even Bayesian inference of the reliability of experimental data. These entanglements can easily lead to circular reasoning. To help disentangle those arguments, since almost all of them involve Boltzmann's H theorem, we begin by formalizing the H theorem as a time-symmetric, time-translation invariant Markov process over the entropy values of the universe. Crucially, this process does not specify the time(s) on which we should condition it in order to infer the stochastic dynamics of our universe's entropy. Any such choice of conditioning events must be introduced as an independent assumption. This observation allows us to disentangle the standard Boltzmann brain hypothesis, its "1000CE" variant, the past hypothesis, the second law, and the reliability of our experimental data, all in a fully formal manner. In particular, we show that they all adopt the H theorem's stipulation that the universe's entropy evolves as a Markov processes, and all make an arbitrary assumption that the process should be conditioned on a single moment in time. Their only difference is what single time to condition on. In this aspect, the Boltzmann brain hypothesis and the second law are equally legitimate (or not).