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

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 such 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.

• The paper introduces a novel quantum cosmological framework where physical constants emerge as dynamical quantum variables via symmetry breaking.
• It employs an extended configuration space and a meta-Wheeler–DeWitt equation to unify many-worlds and multiverse concepts.
• The study demonstrates decoherence-induced sector separation, offering a testable selection principle for effective laws in cosmology.

Quantum Dynamical Emergence of Physical Constants: Extending Many Worlds in Theory Space

Overview and Context

"Many Worlds in Theory Space: A Quantum Origin for the Constants of Nature" (2512.03251) presents a non-semiclassical, canonical quantum cosmological framework where the physical constants—traditionally inserted into the Lagrangian as immutable background parameters—are promoted to quantum dynamical variables. This paradigm enables the universal wavefunction to be defined on an enlarged configuration space comprising both geometries/matter fields and the ensemble of low-energy laws, i.e., theory space. The result is a physically rigorous model in which Everett-style branching extends to fundamentally different effective theories, unifying the Many-Worlds Interpretation (MWI) and landscape-style multiverse approaches without reliance on external mechanisms such as inflationary bubble nucleation.

Quantum Origin and Structure of Physical Constants

The paper critiques the standard practice of treating dimensionless parameters (gauge couplings, mass ratios, cosmological constant) as fixed c-numbers even in quantum field theory and canonical quantum gravity. In the proposed model, these constants arise dynamically as quantum degrees of freedom, with their values set via symmetry breaking and stabilization processes at or above the GUT/Planck scale. The physical constants are not only consequences of emergent vacuum structures but are fundamentally encoded in quantum operators acting on an underlying theory space manifold, $\mathcal{T}$.

A detailed hierarchy is established:

• Dimensional Compactification: The initial selection of the spacetime dimensionality via modulus stabilization, determining the macroscopic geometry.
• Flux Integers: Discrete flux quantum numbers generate a potential landscape for vacuum energy, contributing to the cosmological constant stabilization.
• Moduli Fields: Continuous moduli (e.g., volume modulus, dilaton) set the strengths of interactions and blueprints for particle spectra (e.g., $G$, $\alpha$, $\alpha_s$, Yukawa couplings).
• Symmetry Breaking: Discrete choices in Wilson lines or flavor structure define generations and mixing matrices.

These features recast the anthropic fine-tuning problem: physical constants compatible with complexity/life are weighted by their quantum mechanical amplitude within the meta-wavefunction, and the observed values are the result of dynamical stabilization rather than external selection or external multiverse sampling.

Enlarged Configuration Space and U-Sector Construction

The mathematical formalism extends superspace (space of all 3-geometries and fields) to include the full space of physical laws. Each point in $\mathcal{T}$ labels a distinct “U-sector”—a sector characterized not just by different quantum states, but by different defining Hamiltonians and operator algebras. This results in a grand Hilbert space as a direct sum:

$$\mathcal{H}_{\rm grand} = \bigoplus_{(D,X) \in \mathcal{T}} \mathcal{H}^{(D,X)}$$

States in different U-sectors are not merely orthogonal but physically disjoint, as their Hilbert spaces are inequivalent representations due to differing operator structure, commutation relations, and spectra. This is a crucial distinction from standard quantum superpositions and ensures sector superselection is dynamically realized rather than imposed by fiat.

Meta-Wheeler–DeWitt Equation and Path Integral Formulation

The canonical quantization of gravity is generalized to a meta-Wheeler–DeWitt equation, acting on the full configuration space (geometry, fields, and laws). This operator includes not only usual gravitational and matter terms but Hamiltonians governing the quantum dynamics in theory space—the transitions and kinetic terms associated with moduli, fluxes, and discrete choices.

In the path integral picture, the gravitational functional integral is extended to include summation/integration over theory space:

$$\mathcal{Z}_{\rm ext} = \int \mathcal{D}_\mathcal{T} \mathcal{D}_g \mathcal{D}_\phi\; e^{iS[g,\phi,\mathcal{T}]}$$

Probability weights for entire effective theories are thus derived as intrinsic quantum amplitudes, not assigned by hand. Once decoherence and symmetry breaking freeze the moduli, all observable physics is constrained within a single U-sector; the amplitude for each sector constitutes a rigorous Bayesian measure supporting comparative model selection in fundamental physics.

Dynamical Sector Separation and Decoherence

A central technical result is the demonstration that sector separation—a physical “many worlds” structure where U-sectors are causally and dynamically isolated—emerges naturally from the quantum-to-classical transition associated with cosmic expansion. During the Planck era, sector transitions (tunneling in theory space) are unsuppressed, but the rapid increase in the effective mass associated with theory-space degrees of freedom causes superpositions over constants to decohere early. Consequently, the universal quantum state fragments into a direct sum over classical branches, each with fixed, immutable laws.

This mechanism has two notable implications:

• No Observable Mixing: Observable low-energy processes are completely insensitive to amplitudes in other U-sectors due to the superselection induced by decoherence of global parameters, not environmental noise or explicit symmetry.
• Quantum Weighting of Fine-Tuning: The "fine-tuned" values we observe are reinterpreted as quantum-selected outcomes weighted by path integral measure, not statistical accidents or anthropically rare draws.

Cosmological Evolution: Boundary Conditions and Branching

Backward evolution from the observed, sharply defined constants yields a broad quantum superposition over theory space at early times due to vanishing effective mass. Using this boundary condition, the forward time evolution leads to entanglement between matter-field dynamics and theory-space variables. Ultimately, moduli stabilization splits the meta-wavefunction into localized, effectively classical packets associated with discrete effective parameter sets.

A crucial prediction is that the observed constants likely reside near the peak of the quantum probability distribution within the anthropically habitable region of theory space. If empirical values are found in low-probability tails, the framework would be falsified or require a revised selection mechanism.

Bayesian Evidence and Model Selection

By identifying quantum measure over theory space as a rigorous Bayesian evidence functional, the model offers a formal selection principle for candidate UV theories (e.g., compactification scenarios or string vacua) based on the quantum weight assigned to habitable U-sectors. The degree to which a fundamental theory “naturally” produces a fertile region in the low-energy parameter landscape directly impacts its plausibility.

Implications for Theoretical Physics and Future Directions

The framework postulates that no “Theory of Everything” can deduce the Standard Model parameters uniquely from algebraic first principles. Instead, any complete quantum theory will yield at most a probability distribution over the constants, a claim that is specific and falsifiable. This sharply contrasts with approaches that seek absolute mathematical determinacy for the low-energy effective parameters.

On a practical level, the formalism provides a pathway for constraining microscopic models via path-integral-based quantum evidence, potentially computable for classes of compactifications or moduli stabilization scenarios. There are also implications for the measure problem, as this approach supplies an intrinsic probability measure on theory space without extraneous assumptions.

Conclusion

This work presents a mathematically rigorous extension of canonical quantum cosmology, where physical constants arise as quantum degrees of freedom, and Everett branching extends to the effective laws of nature themselves. The grand Hilbert space construction, meta-Wheeler–DeWitt equation, and quantum path integral over theory space collectively enable a dynamic, quantum-mechanical explanation of fine-tuning and the origin of physical laws. The prediction that fundamental theoretical physics will only provide probability distributions (not absolute values) for the constants is robust, eminently testable, and imposes significant conceptual constraints on model building in high-energy theory.