If measurements of quantum phenomena can show results that are truly random wouldn't it be possible to establish a macroscale-dependence on such a non-statistical result and thereby introduce randomness and an interruption of determinism - if it exists - into the classical realm?
This is similar to the Schrödinger's Cat thought experiment, about which Schrödinger wrote:
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation.
Some speculate that "determinism can emerge from underlying indeterminism (via the law of large numbers)" and that "the universe could be conceived of as having alternating layers of causality and chaos".
Here it says:
According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. That is, in an experiment that controls all causally relevant parameters, some aspects of the outcome still vary randomly. For example, if a single unstable atom is placed in a controlled environment, it cannot be predicted how long it will take for the atom to decay—only the probability of decay in a given time. Thus, quantum mechanics does not specify the outcome of individual experiments but only the probabilities. Hidden variable theories reject the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, properties with a certain statistical distribution are at work behind the scenes, determining the outcome in each case.
This debate is relevant because it is easy to imagine specific situations in which the arrival of an electron at a screen at a certain point and time would trigger one event, whereas its arrival at another point would trigger an entirely different event (e.g. see Schrödinger's cat - a thought experiment used as part of a deeper debate).