Abstract
The unification of quantum mechanics and general relativity remains one of the central open problems of modern theoretical physics. In this work, a stochastic swarm-based process termed GenI ((Generic Inference process)) is introduced as a simple dynamical model that connects probabilistic quantum measurement statistics with emergent geometric structure.
The model describes a population of interacting entities evolving according to local stochastic transition rules that generate a competitive selection process among possible outcomes. The swarm state can be mapped onto a complex amplitude representation of the available alternatives. Analytical arguments and numerical simulations indicate that the probability distribution of the selected outcome depends solely on the initial amplitudes and reproduces the statistical structure associated with the Born rule of quantum mechanics. The process design does not rely on hidden variables and so does not satisfy the precondition for the Bell inequation to hold.
In addition, the internal dynamics of the stochastic process can be represented as trajectories in an effective four-dimensional Riemannian manifold. The resulting metric structure satisfies the consistency conditions required for Einstein’s field equations, suggesting a possible connection between the swarm dynamics and spacetime geometry.
These results indicate that stochastic collective dynamics may provide an alternative perspective on the relationship between quantum measurement statistics and gravitation. The proposed framework therefore offers a simple conceptual model that may contribute to ongoing investigations of emergent spacetime and the foundations of quantum theory.