Probabilistic inference in very large universes
I came across a recent article on the arXiv with the title Probabilistic inference in very large universes by Feraz Azhar, Alan H. Guth, Mohammad Hossein Namjoo.
The paper discusses a conceptually challenging issue in cosmology, which I’ll put simply as follows. Suppose we have two cosmological theories: A, which describes a very large universe in only a tiny part of which low-energy physics turns out like ours; and B in which we have a possibly much smaller universe in which low-energy physics is like ours with a high probability. Can we determine whether A or B is the “better” theory, and if so how?
The abstract of the paper is below:
Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a theory that describes such a mostly unobservable universe? We propose a Bayesian method based on theory-generated probability distributions for our observations. We focus on basic principles, leaving aside concerns about practicality. (We also leave aside the measure problem, to discuss other issues.) We argue that cosmological theories can be tested by standard Bayesian updating, but we need to use theoretical predictions for “first-person” probabilities — i.e., probabilities for our observations, accounting for all relevant selection effects. These selection effects can depend on the observer, and on time, so in principle first-person probabilities are defined for each observer-instant — an observer at an instant of time. First-person probabilities should take into account everything the observer believes about herself and her surroundings — i.e., her “subjective state”. We advocate a “Principle of Self-Locating Indifference” (PSLI), asserting that any real observer should make predictions as if she were chosen randomly from the theoretically predicted observer-instants that share her subjective state. We believe the PSLI is intuitively very reasonable, but also argue that it maximizes the expected fraction of observers who will make correct predictions. Cosmological theories will in general predict a set of possible universes, each with a probability. To calculate first-person probabilities, we argue that each possible universe should be weighted by the number of observer-instants in the specified subjective state that it contains. We also discuss Boltzmann brains, the humans/Jovians parable of Hartle and Srednicki, and the use of “old evidence”.
arXiv:2602.02667
I haven’t had time to read the paper in detail yet, and I don’t think I’m going to agree with all of it when I do, but I found it sufficiently stimulating to share here in the hope that others will find it interesting.
In the Dark 
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