Quantum Measurement? ... MEH

Abstract

We formulate a residual-and-information framework for continuous quantum measurement in which non-Markovian record history is represented by an exact anchored accumulation and conditional measurement ambiguity is represented by a residual whose zero set is the extremal record manifold. The construction is deliberately layered on established quantum instruments, nondemolition filtering, and quantum-trajectory theory rather than presented as a replacement for them. The central objects are the branch log-likelihood accumulators and the normalized posterior weights. Under an objective record filtration, the weights are bounded martingales. For a QND measurement, the conditional pointer variance has a universal negative predictable drift; its martingale coefficient depends on the spectrum and is written in full generality. Divergent accumulated record information then forces the posterior to an extremal simplex vertex. Martingale conservation yields the terminal Born probabilities, while the projective case gives the L¨uders state. Counting and diffusive records, finite-memory Gaussian environments, and completely positive detector dilations are treated in a common framework. We also isolate what is and is not structurally new: the paper proves uniqueness only inside explicitly defined AAC/RCC admissible classes, and it separates that internal uniqueness from any historical priority claim. Finally, a no-free-actualization theorem shows that exact history re-expression, conditional filtering, and residual coordinates cannot by themselves turn deterministic closed-system unitary dynamics into an objectively unique outcome. The remaining ontological input is therefore made explicit rather than hidden.

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