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The Born Rule and Free Will

Ruth E. Kastner

Published Feb 1, 2016• 3 citations
OpenAlex

Abstract

In the libertarian ``agent causation'' view of free will, free choices are attributable only to the choosing agent, as opposed to a specific cause or causes outside the agent. An often-repeated claim in the philosophical literature on free will is that agent causation necessarily implies lawlessness, and is therefore ``antiscientific." That claim is critiqued and it is argued, on the contrary, that the volitional powers of a free agent need not be viewed as anomic, specifically with regard to the quantum statistical law (the Born Rule). Assumptions about the role and nature of causation, taken as bearing on volitional agency, are examined and found inadequate to the task. Finally, it is suggested that quantum theory may constitute precisely the sort of theory required for a nomic grounding of libertarian free will.

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In the libertarian agent causation'' view of free will, free choices are attributable only to the choosing agent, as opposed to a specific cause or causes outside the agent. An often-repeated claim in the philosophical literature on free will is that agent causation necessarily implies lawlessness, and is therefore antiscientific." That claim is critiqued and it is argued, on the contrary, that the volitional powers of a free agent need not be viewed as anomic, specifically with regard to the quantum statistical law (the Born Rule). Assumptions about the role and nature of causation, taken as bearing on volitional agency, are examined and found inadequate to the task. Finally, it is suggested that quantum theory may constitute precisely the sort of theory required for a nomic grounding of libertarian free will.
It is often argued that bottom-up causation under a physicalist, reductionist worldview precludes free will in the libertarian sense. On the one hand, the paradigm of classical mechanics makes determinism inescapable, while on the other, the leading models that allow a role for quantum effects are noncommittal regarding how conscious agents are supposed to translate indeterminacy into self-formed choice. Recent developments, however, not only imply that self-formed decisions are possible, but actually suggest how they might come about. The cornerstone appears to be causality superposition rather than quantum-state entanglement, as is usually assumed, and the natural arena for applying these developments is (perhaps ironically) a framework that was built without any consideration for quantum effects.
The basic question in the long-standing debate about free will (FW) is not whether FW can be demonstrated to exist nor even whether it exists, but instead how to define it scientifically. If FW is not dismissed as an illusion nor identified with a variety of unpredictability, then logical paradoxes arise that make FW elusive to define. We resolve these paradoxes through a model of FW, in which FW is a new causal primitive empowered to override physical causality under guidance. We develop a simple mathematical realization of this model, that when applied to quantum theory, suggests that the exercise of FW corresponds to a nonlinear POVM causing deviations from the Born rule. In principle, these deviations would stand in conflict with known conservation laws and invariance principles, implying that the brain, the presumed seat of FW, may be an arena of exotic, non-standard physics. However, in practice it will be difficult to distinguish these deviations from quantum and neural noise, and statistical fluctuations. We indicate possible neurobiological and neurological tests, implications and applications of our proposed model.
Our discussion in the first five sections shows that little new can be said about compatibilism, that van Inwagen's argument for incompatibilism still stands, and that the view of free agency for a libertarian has little chance unless she believes that agency contains elements that are not within the natural order. Borrowing from a suggestion from Russell we expanded the Nozick-Kane model of libertarian free agency and connected it to the Wignerian interpretation of quantum measurement. As such, free decisions and choices may well violate the Born rule of probability distribution and yet it is shown how such violations are unlikely to be detected in experiments. This model is probably the only model in which Loewer's van Inwagen style argument for the incompatibility between free agency and quantum indeterminism does not apply, and it is a model in which free agency is not only compatible but necessary. It is compatible with indeterminism and it is necessary for the determinateness of any measurement outcomes.
QBists insist that theirs is a realist position while denying that the quantum formalism represents a mind-independent world. The insistence is hard to place. The realism debate is throughout a dispute about represented content, so a theory that denies standing in the representation relation appears not to take up a position within that debate at all. This paper examines the most developed attempt to make good on the QBist claim--David Glick's perspectival normative realism--and argues that it fails instructively. Glick seeks the ground of the Born rule's objectivity among states of affairs and construes an agent's perspective as a location within an already-constituted world; finding no state of affairs fit to bind every agent at once, he must book the ground as brute. Phenomenology supplies the third thing his picture lacks. A horizon is not a position within the world but the condition under which a world is given. Read as an agent's weighting--her curvature--of such a horizon, the quantum state is neither a defective description nor a brute posit, and the Born rule articulates the invariant lawfulness by which any sense confers a curvature at all.
The "consequence argument", together with the "luck objection", which are summed up by the "standard argument against free will", state that if our volition were dependent on physical causally indeterministic processes, our actions would lack control and, thereby, result in random behavior that would be a mere matter of luck and chance. In particular, quantum indeterminacy is supposed to be of no use in support of libertarian agent-causation theories because any volitional act interfering with the probability distributions defining quantum laws would lead to its violation. Building upon recent conjectural work questioning this assumption (Clarke 2010, Kastner 2016, Masi 2023), it is shown, with a concrete example involving quantum indeterminacy, how a hypothetical agent with access to the temporal ordering of events can pre-determine the result of a process taking place in time without modifying the probability laws defining it. This conclusion is then taken as a basis for a libertarian panpsychist interpretative model.