  According to our current conception of physics, any valid physical theory is
supposed to describe the objective evolution of a unique external world.
However, this condition is challenged by quantum theory, which suggests that
physical systems should not always be understood as having objective properties
which are simply revealed by measurement. Furthermore, as argued below, several
other conceptual puzzles in the foundations of physics and related fields point
to limitations of our current perspective and motivate the exploration of an
alternative: to start with the first-person (the observer) rather than the
third-person perspective (the world). In this work, I propose a rigorous
approach of this kind on the basis of algorithmic information theory. It is
based on a single postulate: that universal induction determines the chances of
what any observer sees next. That is, instead of a world or physical laws, it
is the local state of the observer alone that determines those probabilities.
Surprisingly, despite its solipsistic foundation, I show that the resulting
theory recovers many features of our established physical worldview: it
predicts that it appears to observers as if there was an external world that
evolves according to simple, computable, probabilistic laws. In contrast to the
standard view, objective reality is not assumed on this approach but rather
provably emerges as an asymptotic statistical phenomenon. The resulting theory
dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete
predictions for thought experiments like the computer simulation of agents, and
suggests novel phenomena such as "probabilistic zombies" governed by
observer-dependent probabilistic chances. It also suggests that some basic
phenomena of quantum theory (Bell inequality violation and no-signalling) might
be understood as consequences of this framework.
