The trouble with recording devices

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.