The Hilbert Space as a Physical Container

Popular accounts often describe Hilbert space as a “location” in which quantum states live, or a “space” through which vectors move. In a Nature article (here), this metaphor underpins the notion of synchronising time between Hilbert space and 3D space.

From a relational perspective, this is deeply misleading. Hilbert space is not a physical container or backdrop. It is a mathematical abstraction encoding the potential relations among possible measurements — a symbolic structure, not a place in which anything literally exists. Treating it as a “space” encourages an ontological misreading: that quantum states somehow inhabit a reality separate from physical systems, awaiting interaction with instruments to materialise.

This metaphor obscures the relational character of quantum phenomena. A quantum state is not “somewhere”; it is a pattern of dispositional potential, defined only in the context of interactions and symbolic cuts. The “movement” of vectors in Hilbert space is not a literal motion but a way to calculate relationally structured probabilities.

Relational ontology reframes the story: the physics is not about objects floating in an abstract space but about how potentialities co-occur, actualise, and align with measurement contexts. Hilbert space is a tool for representing these relations, not a new dimension of reality.

Punchline: Quantum states do not dwell in a hidden space; they describe the unfolding possibilities that emerge when systems and measurements interact.