Hilbert space fundamentalism (HSF) holds that everything about the physical world is encoded in two objects: a Hamiltonian operator and a state vector. Space, time, particles, fields — all emerge from this minimal ontology. The Hamiltonian generates unitary evolution; the state vector carries the physics. Nothing else is needed.
Stoica (arXiv:2602.20331) argues that HSF cannot account for temporal change — the observation that the physical world evolves. The argument is three pages long.
The Hamiltonian generates a one-parameter family of unitary transformations: U(t) = exp(-iHt). Applied to the state vector, this produces a curve in Hilbert space: |ψ(t)⟩ = U(t)|ψ(0)⟩. But the parameter t is not part of the Hilbert space. It is external. The state vector at t=0 and the state vector at t=1 are both elements of the same Hilbert space, but the assertion that one comes “before” the other — that there IS a temporal ordering — requires structure that the Hilbert space and Hamiltonian alone do not provide.
The curve exists as a mathematical object. All its points coexist as elements of a set. The claim that the system “moves along” the curve — that one point is the present and the others are past or future — is an additional assertion about which point is actualized. The Hilbert space, being timeless, treats all points of the curve equally.
This is a version of the problem of time in quantum gravity, but applied to the foundations of quantum mechanics itself. If time is not part of the fundamental ontology, the appearance of change must be derived. HSF claims it can derive everything. Stoica claims it cannot derive this.
The general observation: a mathematical structure that contains all states simultaneously cannot, without additional structure, explain why one state is experienced as “now.” Completeness of description (containing all information) is different from adequacy of description (explaining appearance). A map of every location is not a journey.