Hydrodynamic formulations rewrite the Schrödinger equation as a fluid flowing through configuration space. The probability density becomes a fluid density; the phase gradient becomes a velocity field. Quantum mechanics looks like classical fluid dynamics on a high-dimensional space. The many interacting worlds (MIW) interpretation discretizes this: a finite number of particle-like worlds interact through forces, and quantum probabilities emerge from counting worlds.
Poirier and colleagues (arXiv:2602.21106) identify a fundamental obstacle for the discrete version: the problem of sparse ontology. As the wavefunction branches during decoherence — when a quantum system interacts with its environment and different outcomes separate — the discrete worlds get partitioned into smaller sub-ensembles. Each branch claims a fraction of the finite world population. The density of worlds in configuration space thins out.
When the density drops below a critical threshold, the inter-world forces that produce quantum behavior lose their statistical foundation. The discrete fluid no longer approximates the continuous Schrödinger dynamics. Quantum mechanics breaks down — not because the formalism fails, but because there aren't enough worlds left in each branch to sustain the quantum behavior.
The conclusion is sharp: a successful hydrodynamic model of quantum mechanics plausibly requires an essentially continuous ontology. You need uncountably many worlds, not merely a large finite number. Any finite number, no matter how large, eventually thins to sparsity under repeated branching. The branching is exponential; the world budget is fixed. The budget runs out.
This is a no-go result for a specific class of interpretations. It doesn't affect operational quantum mechanics — just the discrete-ontology version of the hydrodynamic picture. But the mechanism is general: any interpretation that distributes a finite resource (worlds, configurations, tokens) across exponentially branching outcomes will eventually run sparse.
The general observation: when a system branches faster than its ontological substrate can support, the substrate's discreteness becomes visible. Continuous approximations fail when the density they assume drops below the threshold that makes averaging valid. The finite cannot track the exponential indefinitely.