You are using "real" in a way I don't recognize. In my view, the past that is real is that which corresponds to and is consistent with records of past events. This allows for many different pasts, and many can have some plausibility. But if my diary on a given date says I popped my knee, then any past which is inconsistent with this record is not real.
In orthodox quantum theory, past events, even those that happened in experiments showing quantum effects, such as double-slit experiment with single particle, are determinate in the sense they can sometimes be retrodicted from the present knowledge, even when they could not have been predicted before they happened (e.g. which hole the particle went); only future events are not determined by psi.
In orthodox quantum theory, past events, even those that happened in experiments showing quantum effects, such as double-slit experiment with single particle, are determinate in the sense they can sometimes be retrodicted from the present knowledge, even when they could not have been predicted before they happened (e.g. which hole the particle went); only future events are not determined by psi.