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

TL;DR

This paper formalizes the stochastic dynamics of the universe's entropy as a time-symmetric Markov process, disentangling various hypotheses about the universe's past, the second law, and Boltzmann brains to clarify their assumptions and relationships.

Contribution

It introduces the entropy conjecture as a formal framework to analyze the assumptions behind the Boltzmann brain hypothesis and the second law, avoiding circular reasoning.

Findings

All hypotheses assume conditioning on a single event in time.

Boltzmann brain hypothesis and second law are based on similar assumptions.

Formal disentanglement clarifies the legitimacy of different cosmological hypotheses.

Abstract

Are your perceptions, memories and observational data, a statistical fluctuation out of the thermal equilibrium of the universe, having no correlation with the actual past state of the universe? Arguments are given in the literature for and against this "Boltzmann brain" hypothesis. Complicating these arguments have been the many subtle -- and very often implicit -- joint dependencies among these arguments and others that have been given for the past hypothesis, the second law, and even for Bayesian inference of the reliability of experimental data. These dependencies can easily lead to circular reasoning. To avoid this problem, since all of these arguments involve the stochastic properties of the dynamics of the universe's entropy, we begin by formalizing that dynamics as a time-symmetric, time-translation invariant Markov process, which we call the entropy conjecture. Crucially, like all stochastic processes, the entropy conjecture does not specify any time(s) which it should be conditioned on in order to infer the stochastic dynamics of our universe's entropy. Any such choice of conditioning times and associated entropy values 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 these all make an arbitrary assumption that the dynamics of the universe's entropy should be conditioned on a single event at a single moment in time, differing only in the details of their assumptions. In this aspect, the Boltzmann brain hypothesis and the second law are equally legitimate (or not).