The trouble with recording devices
Eric Tesse
TL;DR
The paper identifies a fundamental mismatch between the standard Born rule and the probabilities for recording-device states in quantum experiments. It introduces the physical subspace and a start-time concept $T_s(X,t_f)$ to constrain histories so that recorded outcomes are self-consistent with past events, and then proposes an amended Born rule that remains valid when conditioning on recorded histories. Key contributions include formalizing $X(t)$, $t_c$, and subspaces $ ext{P}_Z$ and $ ext{P}_W$, along with a verifiability criterion for probabilities in both pre- and post-condition times, and applying the framework to continuous measurements such as tracking detectors. The resulting quantum probability calculus yields a unified, observer-inclusive description of measurements in closed systems, clarifying how probabilities are verifiable and providing a coherent treatment of continuous measurements and observers without mandating wavefunction collapse or preferred interpretations.
Abstract
Quantum theory encounters a difficulty when attempting to describe recording devices. If the recording is of events in which quantum uncertainty plays a role, such as an experiment on a quantum system, quantum theory is unable to correctly predict the probabilities of both future and past states of the recording. The nature of this difficulty will be laid out at the outset. A resolution then will be presented, in which the Born rule will be lightly amended so as to correctly predict all probabilities. The resolution will have the further benefit of clarifying how quantum theory applies to an array of situations in which the theory can be ambiguous, such as the descriptions of continuous measurements, and of closed systems containing all observers.