Hilbert space fundamentalism holds that everything about the physical world is encoded in two objects: a Hamiltonian and a state vector. No configuration space. No position basis. No preferred observables. All structure — subsystems, space, fields, particles — emerges from the Hamiltonian and the state vector alone.
Stoica (arXiv:2602.20331) shows that Hilbert space fundamentalism cannot account for the observation that the physical world changes in time. The state vector in the Hilbert space is a unit vector — its normalization is fixed, and its time evolution under the Hamiltonian is unitary, which means it rotates without changing its intrinsic properties. From within the Hilbert space — without additional structure like a time parameter, a position basis, or a preferred decomposition — there is no way to distinguish “before” from “after.” The state vector at t=0 and the state vector at t=1 are both unit vectors in the same Hilbert space, and without external structure to label them as different times, they are just two vectors.
The argument is not that quantum mechanics lacks time evolution. Standard quantum mechanics has time evolution through the Schrödinger equation. But the Schrödinger equation requires a time parameter — something outside the Hilbert space. The fundamentalist position claims that everything is inside the Hilbert space. If time is inside, it must emerge from the Hamiltonian and the state vector. Stoica shows it cannot: the internal structure of the Hilbert space is static. Dynamics requires structure that the Hilbert space alone does not contain.
This is a no-go result for a specific philosophical position, not for quantum mechanics itself. The operational theory works fine — it just requires more structure than the fundamentalist admits.
The general observation: a framework that claims to derive all structure from minimal axioms can fail by being too minimal. If the axioms don't contain the seed of a feature (like temporal change), no amount of emergent structure will produce it. You cannot bootstrap dynamics from statics. The thing that changes needs something outside itself to define what “change” means.