An attempt is made to reconstruct the postulates of quantum mechanics a priori from rationalist first principles, based on an algorithmic epistemology. The result, I suggest, is close enough to quantum mechanics to potentially serve as the basis for a consistent algorithmic interpretation of it. As a variation on the many worlds (or Everett) interpretation, such a framework provides a natural solution to the two most persistent objections to Everettianism: the preferred basis and probability problems. While there are gaps in the reconstruction, I argue that these are well-motivated in terms of traditional rationalist philosophical axioms, which have their own rationale and justification independent of quantum mechanics. The reconstruction is in two parts. Part I is a “toy” reconstruction, based on a general metaphysical and epistemological framework called “algorithmic synthetic unity” (or ASU). It does not yield quantum mechanics, but does exhibit some of the puzzling qualitative features of quantum theory. ASU provides an alternative to the outcome-counting formulations of probability that are assumed in many versions of both the probability objection to Everett, and the frequentist Everettian responses to it, and it yields the Born rule when added to the other quantum postulates. Part II is the “full” reconstruction, which yields specific analogues to the traditional quantum postulates, and takes us much closer to quantum mechanics, but also requires an additional assumption. This assumption is not a traditional rationalist principle, but is well-motivated within that tradition, and draws on contemporary experience with information theory and digital signal processing. The resulting reconstruction is “Periodic ASU”, which I suggest may have the potential to deliver a simpler formulation of quantum theory.
A Rationalist Algorithmic Reconstruction of Quantum Mechanics