The universal path integral

TL;DR

This paper introduces a universal path integral that sums over all computable structures, providing a comprehensive framework that encompasses various quantum theories and supports a quantum theory of the universe.

Contribution

It defines a universal path integral that includes all computable path integrals, unifying different quantum theories within a single framework.

Findings

Contains all possible computable path integrals including field theory and string theory.

Has a well-defined measure ensuring finiteness.

Supports a quantum theory of the universe based on interference of all structures.

Abstract

Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness, together with a method for extracting probabilities for observable quantities. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.