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Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the experimenter needs to know all past outcomes at the end of the experiment, and that requires the presence of probes carrying the corresponding records. In this picture a composite system+probes can be seen to undergo an unbroken unitary evolution until the end of the trial, where the state of the probes is examined. For these two descriptions to agree one requires a particular type of coupling between a probe and the system, which we discuss in some details. With this in mind, we consider two different ways to extend the description of a quantum system's past beyond what is actually measured and recorded. One is to look for quantities whose values can be ascertained without altering the existing probabilities. Such "elements of reality" can be found, yet they suffer from the same drawback as their EPR counterparts. The probes designed to measure non-commuting operators frustrate each other if set up to work jointly, so no simultaneous values of such quantities can be established consistently. The other possibility is to investigate the system's response to weekly coupled probes. Such weak probes are shown either to reduce to a small fraction the number of cases where the corresponding values are still accurately measured, or lead only to the evaluation of the system's probability amplitudes, or their combinations. It is difficult, we conclude, to see in quantum mechanics anything other than a formalism for predicting the likelihoods of the recorded outcomes of actually performed observations.