This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling (...) principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness. (shrink)

The Free Will Theorem of Conway \& Kochen on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will. Although Conway and Kochen informally claim that their theorem supports indeterminism and, in its wake, a libertarian agenda for free will, inferring the former from the Free Will Theorem is a \emph{petitio principii}. Of course, this also considerably weakens the case for (...) the latter. A recent reformulation of the Free Will Theorem due to Cator and the author uses a mathematically precise formulation of the idea that experimentalists freely choose their settings even in a deterministic world, and thence construes the theorem as providing constraints on determinism. In the present paper we argue that the concept of free will used in this version of the theorem is essentially the one proposed by Lewis, also known as `local miracle compatibilism'. To do so, we give a mathematical reformulation of this idea, which we believe to be well within its spirit and which may be of independent interest. On this double reformulation the Free Will Theorem shows that local miracle compatibilism contradicts the parts of modern physics used in its assumptions. Therefore, although the intention of Conway and Kochen was to support free will through their theorem, what they actually achieved is the opposite: a well-known, philosophically viable version of free will now turns out to be incompatible with physics! (shrink)

Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In (...) this paper I show that the finite precision loophole does not apply to the Conway–Kochen Theorem. (shrink)

A well known logical loophole for Bell’s theorem is that it relies on setting independence: the assumption that the state of a system is independent of the settings of a measurement apparatus probing the system. In this paper the implications of rejecting this assumption are studied from an operationalist perspective. To this end a generalization of the ontic models framework is proposed that allows setting dependence. It is shown that within this framework Bell’s theorem reduces to the conclusion that no-signaling (...) requires randomness at the epistemic level even if the underlying ontology is taken to be deterministic. The ideas underlying the framework are further used to defend setting dependence against the charges of being incompatible with free will and scientific methodology. The paper ends however with the sketch of a new problem for setting dependence: a necessary gap between the ontic and the epistemic level that may prevent the formulation of a successful setting dependent theory. (shrink)