Dual Locations

Popular accounts of quantum mechanics often say that “the system evolves in Hilbert space” while “measurements occur in physical space.” This framing produces what a Nature article (here) calls a “duality of location”: as though there were two distinct arenas — one mathematical, one physical — that must somehow remain in perfect synchrony.

But this is a category error. Hilbert space is not a second “place” alongside physical space. It is a system of potential — a structured theory of possible states. To spatialise it, to imagine quantum processes “happening” inside Hilbert space, is to reify representation as reality.

The effect of this metaphor is subtle but profound. It turns a relational model into a parallel universe. It makes the theory itself into a second stage on which events unfold. And then, having invented this unnecessary duplication, physicists are forced to marvel at the miraculous synchronisation between the two.

From a relational perspective, there is no “where” of Hilbert space. What it encodes is potential, not phenomenon. Events are not “located” in Hilbert space but actualised through construal: cuts in the fabric of possibility that manifest as phenomena. To treat Hilbert space as a place is to mistake the map for the territory — worse, to mistake the theory of maps for a second territory.

The problem is not that Hilbert space and physical space are hard to reconcile. The problem is the assumption that Hilbert space is a “space” at all. It is not an arena, but a model of relational potential. Remove the misplaced spatial metaphor, and the so-called “duality of location” dissolves.