Measurement problem

In plain terms

Left alone, a quantum system evolves smoothly and reversibly, keeping every superposition intact, where a superposition is a state that combines several possible outcomes at once with none of them selected. Measured, the system delivers one definite outcome and the alternatives vanish. The theory contains both behaviours and refuses to say where one ends and the other begins, so you're left asking what counts as a measurement, whether a detector, an eyeball or a graduate student.

This isn't a philosophical itch, as the two rules are mathematically incompatible. The first is linear, so combinations of states evolve into the same combinations of their evolved parts, and reversible, so the motion can be run backwards, and the second is neither. A theory that holds both without a boundary between them isn't a closed description of anything.

Every serious interpretation is, at bottom, a proposal for which rule to sacrifice. Many-Worlds keeps the smooth evolution and drops definite outcomes, and collapse theories keep the outcomes and modify the evolution. The question is old, unresolved and entirely legitimate.

In CSD

CSD's move is that nothing abrupt ever happens on the substrate. The underlying motion is deterministic and volume-preserving throughout, meaning that it carries any region of the underlying state space to a region of the same size, and what changes at a measurement is which region of the epistemic space, the space of quantum states, the trajectory gets recorded against. Both textbook rules become views of one process.

What keeps this from being just another story is a trilemma, three theorems that stake out what any account must give up. No volume-preserving map implements exact collapse. No continuous dynamics correlates a pointer, the apparatus's readout, perfectly everywhere on a connected arena, a state space in one piece. And approximate collapse has a stated price, as accuracy costs improbability of the apparatus's ready state, and the exchange rate is quantitative.

So the corpus doesn't dissolve the measurement problem by narrative. It proves which combination of desiderata is impossible, then says openly which one CSD abandons, and that's what separates a result from an interpretation.

Mathematically

Three impossibility results on the pointer arena, so there's no exact collapse by a measure-preserving map, no everywhere-correlating continuous propagator on a connected arena, and a quantitative accuracy-versus-improbability bound.

All three are CSD-free in statement, being measure theory, topology and an estimate respectively, so any rival account with the corresponding structure inherits them, and they can't be cited against this programme without being cited against the citer.

Related entries

• CollapseIn CSD the quantum state never jumps, and that's a theorem about volume-preserving maps rather than a preference among interpretations.
• De-isolationNothing collapses, as a measured system stops being isolated, and measurement is what de-isolation dynamics looks like from inside.
• Record layerA measurement is over when the world itself carries which outcome happened, and the record layer is where that fact lives, on the arena and not in anyone's notebook.
• What happens during a measurement in CSD?The system stops being isolated, the joint dynamics of system and apparatus carries the underlying state into one outcome region and leaves a record there, and the famous collapse is the updating of a description, so there's one law and no switch.
• Copenhagen interpretationCopenhagen is the oldest position on quantum measurement and the one that declines the question, as measurement is where the theory stops and not something it explains.