Position in the Foundations Landscape

Constraint-Surface Dynamics (CSD) is a realist, deterministic, single-world framework for quantum mechanics. It belongs to the family of approaches, alongside Copenhagen, Many-Worlds, Bohmian mechanics, GRW, and QBism, that offer distinct resolutions of the measurement problem. CSD’s position within this landscape is defined by a specific combination of commitments that no established approach shares simultaneously.

CSD is deterministic.

A single ontic microstate evolves continuously under Hamiltonian flow on a compact geometric surface. There is no fundamental randomness in the dynamics. Apparent stochasticity arises from ignorance of the microstate’s precise location within this surface, not from indeterminacy in the laws of motion. In this respect, CSD aligns with deterministic programmes such as Bohmian mechanics and contrasts with Copenhagen and GRW, which treat randomness as primitive.

CSD is single-world.

There is one geometric surface, one trajectory, and one outcome per measurement. Branching in the Many-Worlds sense does not occur. What appears as branching is instead the dynamical partitioning of the surface into disjoint outcome regions during measurement interactions. The underlying surface remains unified at all times. This places CSD against Many-Worlds and alongside single-world realist approaches.

CSD treats the wavefunction as epistemic in role rather than ontic in substance.

The wavefunction does not represent a physical field or object. Instead, it encodes an observer’s coarse-grained information about which region of the geometric surface the microstate occupies. Measurement updates this information by revealing the realised outcome region. While this informational role parallels aspects of QBism, CSD sharply diverges from QBism’s subjectivism: the underlying geometric surface and its dynamics are fully objective and mind-independent.

CSD fixes the Born rule through symmetry and geometry rather than postulating it.

The SU(n) symmetry of complex projective space selects a unique invariant measure, the Fubini–Study measure. Gleason-class operational constraints then restrict admissible probability assignments to the Born form. Combined with the deterministic volume-typicality result of Paper A, this yields outcome frequencies matching |ψ|² as a consequence of geometric structure. By contrast, Bohmian mechanics requires an additional quantum equilibrium hypothesis, Many-Worlds relies on decision-theoretic arguments, and Copenhagen and GRW postulate the Born rule directly.

CSD introduces no collapse mechanism, no stochastic dynamics, and no dual ontology.

Unlike Bohmian mechanics, it does not posit a guiding wave or value-definite hidden variables for observables. Unlike GRW, it does not modify Schrödinger evolution. Unlike Copenhagen, it does not appeal to an undefined measurement cut. The framework operates entirely within the established mathematics of geometric quantum mechanics, adding only the interpretive commitment that the geometric structure is physically real.

The table below summarises CSD’s position relative to the principal alternatives:

CSD occupies a unique position in this landscape.

No established framework is simultaneously deterministic, single-world, non-ontic about ψ, and able to recover the Born rule from symmetry and geometry without additional postulates. This distinctive combination motivates the CSD research programme.

For more information please read the papers here.