Many Worlds in Theory Space: A Quantum Origin for the Constants of Nature

TL;DR

This work reframes the fine-tuning problem by promoting the constants of nature to dynamical quantum variables and embedding them in an extended Wheeler–DeWitt framework. By enlarging the configuration space to include theory space $\mathcal{T}$, the universe is described by a Grand Hilbert Space that is a direct sum of inequivalent U-sectors, each with its own Hamiltonian constraint. Early-universe decoherence then selects a habitable sector, turning the problem of choosing physical laws into a quantum-weighting and branching process. A falsifiable prediction follows: no purely mathematical derivation of the Standard Model parameters exists; instead, a Bayesian-like weight over theory space should peak in habitable regions, guiding comparisons among high-energy theories.

Abstract

Many of the numbers appearing in the laws of physics, such as the strength of electromagnetism or the masses of elementary particles, must lie in precise ranges for stars, planets, and chemistry to exist. Why the universe has these values is one of the deepest questions in science. Here we propose that these constants arise from quantum mechanics itself. By enlarging the configuration space of quantum cosmology, we treat the constants of nature as part of the wavefunction of the universe. The universal wavefunction contains support for many possible sets of constants, and early-universe processes cause these possibilities to decohere into distinct classical universes. Our universe is one such branch, compatible with complexity and life. We defined the Grand Hilbert Space as the direct sum of U-sectors, each representing a distinct set of physical laws. We derived the Meta-Wheeler--DeWitt equation, which governs the dynamics of the theory parameters. We showed that in the Planck era, the kinetic terms for these parameters are active, creating a state of primordial coherence where the laws of physics effectively fluctuate. This formalism offers a quantitative tool for high-energy physics. We proposed that the total integrated amplitude over theory space serves as a Bayesian evidence metric, allowing for the statistical comparison of rival microscopic theories based on their fertility in generating habitable sectors. Finally, this work makes a specific, falsifiable prediction: there will never be a successful, purely mathematical derivation of the Standard Model parameters.