Measurement context

In plain terms

Quantum mechanics is contextual. You can't assign answers to every possible measurement at once, as you can only assign them to the measurements one actual arrangement of equipment can perform together, so the measurement is never just a quantity written on paper. It's a physical context, and which context is in place makes a difference to what can happen, and the measurement context is the concept that records this.

CSD takes the context seriously enough to make it a definite piece of data. A context is the information the apparatus contributes, so for every possible state of the world it gives a set of rates, one per outcome, saying how strongly each outcome is favoured. Fix the context and the regions of the arena that lead to each outcome are fixed, and if you change the context a genuinely different division of the arena applies.

A useful comparison is a referee's rulebook. The rulebook belongs to the referee, exists before the match starts, and doesn't consult the players, and in the same way the context belongs to the apparatus, is fixed before the run, and doesn't depend on which state was prepared. The comparison stops there, as a rulebook is written by people, whereas in CSD the natural context is read off the geometry of the state space.

In CSD

Formally a context is a rate field on the base of the arena, the space of quantum states, so to every point of the base it assigns a list of outcome weights, each non-negative and all summing to one, in a way that lets the resulting regions be measured. The preparation plays no part in this assignment, and that independence is one of the programme's stated requirements, so the corpus builds its outcome basins from the context's field alone. The canonical context reads its rates off the moment map, the map that extracts the Born weights from the geometry of the state space, so even the rates are geometry rather than bookkeeping.

Contextuality then has a precise home. Distinct contexts induce distinct partitions of the arena. The no-go theorems against assigning context-independent answers to every measurement at once are proved in the corpus, and alongside them stands a positive witness, a contextual model that reproduces the statistics of the singlet state, the standard two-particle entangled state, in full.

Mathematically

A ContextField consists of rate functions p -> Fin N -> R, measurable per outcome, nonnegative, summing to one at every point, and the preparation-independence of the field is the A7 requirement.

The induced basins are measurable and pairwise disjoint with Born-weight epistemic probabilities, and the canonical instance takes rate := momentMap with measurability supplied by the moment-map infrastructure.

Related entries

• ContextualityFor some sets of quantum questions no consistent answer sheet exists at all, and CSD's response is to stop demanding one answer per question and to say instead what the answer depends on.
• CarvingCarving is the programme's own word for the move it refuses to count as a derivation, which is cutting a region to have exactly the size you wanted to explain.
• Luders ruleThe textbook's second rule, which says how a state changes when it's measured, isn't a second rule in CSD, as it's what the record layer does.
• Kochen-Specker theoremThere's a finite list of directions in space that admits no consistent yes-or-no labelling, so contextuality follows by pure counting, with no experiment, no statistics and no separated particles.
• Pointer basisA measuring apparatus doesn't record what you ask it to, as it records what it can keep, and what it can keep is decided by its interaction with the surroundings and not by the experimenter.