The Observer Class Hypothesis

Abstract: The discovery of a small cosmological constant has stimulated interest in the measure problem. One should expect to be a typical observer, but defining such a thing is difficult in the vastness of an eternally inflating universe. We propose that a crucial prerequisite is understanding why one should exist as an observer at all. We assume that the Physical Church Turing Thesis is correct and therefore all observers (and everything else that exists) can be described as different types of information. We then argue that the observers collectively form the largest class of information (where, in analogy with the Faddeev Popov procedure, we only count over "gauge invariant" forms of information). The statistical predominance of the observers is due to their ability to selectively absorb other forms of information from many different sources. In particular, it is the combinatorics that arise from this selection process which leads us to equate the observer class $\mathcal{O}$ with the nontrivial power set $\hat{\mathcal{P}}(\mathcal{U})$ of the set of all information $\mathcal{U}$. Observers themselves are thus the typical form of information. If correct, this proposal simplifies the measure problem, and leads to dramatic long term predictions.