Disentangling Boltzmann brains, the time-asymmetry of memory, and the second law
David Wolpert, Carlo Rovelli, Jordan Scharnhorst
TL;DR
The paper reframes the Boltzmann-brain debate by modeling the universe's entropy as a time-symmetric Markov process and by formalizing how current data are conditioned on independent assumptions. It introduces a rigorous probability framework for laws, formalizes the entropy conjecture as a Boltzmann process, and clarifies how BB, PH, and the second law reduce to different conditioning choices rather than distinct physical predictions. It shows that the entropy conjecture alone cannot decide whether BBs or the PH/second law hold, and that conclusions depend on priors about data reliability and cosmology. The work exposes circular and unstable reasoning in common arguments and provides a formal toolkit to analyze these issues, with a notable 1000CE variant illustrating the subtle continuity between BB and PH. Overall, it advances a principled, math-grounded approach to foundational thermodynamics and the epistemology of memory in cosmology.
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).