  The aim of this paper is to argue that the (alleged) indeterminism of quantum
mechanics, claimed by adherents of the Copenhagen interpretation since Born
(1926), can be proved from Chaitin's follow-up to Goedel's (first)
incompleteness theorem. In comparison, Bell's (1964) theorem as well as the
so-called free will theorem-originally due to Heywood and Redhead (1983)-left
two loopholes for deterministic hidden variable theories, namely giving up
either locality (more precisely: local contextuality, as in Bohmian mechanics)
or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's
cellular automaton interpretation of quantum mechanics). The main point is that
Bell and others did not exploit the full empirical content of quantum
mechanics, which consists of long series of outcomes of repeated measurements
(idealized as infinite binary sequences): their arguments only used the
long-run relative frequencies derived from such series, and hence merely asked
hidden variable theories to reproduce single-case Born probabilities defined by
certain entangled bipartite states. If we idealize binary outcome strings of a
fair quantum coin flip as infinite sequences, quantum mechanics predicts that
these typically (i.e.\ almost surely) have a property called 1-randomness in
logic, which is much stronger than uncomputability. This is the key to my
claim, which is admittedly based on a stronger (yet compelling) notion of
determinism than what is common in the literature on hidden variable theories.
