[Paper Review] The Free Will Function

Sabine Hossenfelder|arXiv (Cornell University)|Feb 3, 2012

Free Will and Agency4 references3 citations

TL;DR

This paper proposes an operational definition of free will in physics by introducing a 'free will function'—a non-deterministic, irreducible function that generates choices not predictable from prior information. It argues that such a function, while not derivable from differential equations, could underlie decision-making in a deterministic universe, offering a scientific framework for free will without metaphysics.

ABSTRACT

It is argued that it is possible to give operational meaning to free will and the process of making a choice without employing metaphysics.

Motivation & Objective

• To provide a scientifically operational definition of free will that avoids metaphysical assumptions.
• To resolve the tension between determinism in physics and the subjective experience of making choices.
• To explore whether free will can coexist with a deterministic universe by introducing a new mathematical construct.
• To challenge the assumption that all physical laws must be expressible as differential equations.
• To offer a framework where choices are not predictable from past information, even in principle.

Proposed method

• Define an agent as a subsystem of the universe with degrees of freedom, treating its internal state as a black box.
• Introduce the 'free will function' as a non-deterministic, irreducible function that outputs choices not derivable from prior information.
• Require that the free will function not be a solution to any forward-deterministic differential equation.
• Propose that such a function could coexist with deterministic laws of physics if formulated via axioms rather than differential equations.
• Use thought experiments to illustrate that even with full knowledge of the universe, the agent's next action remains unpredictable if governed by such a function.
• Compare with backward-deterministic evolution as a less satisfying alternative, since it relies on future boundary conditions.

Experimental results

Research questions

• RQ1 Can free will be given operational meaning in a physical theory without invoking metaphysics?
• RQ2 Is it possible to define a decision-making process that is not predictable from any prior information, even in principle?
• RQ3 How can a non-deterministic function coexist with deterministic laws of physics?
• RQ4 What kind of mathematical structure could serve as a foundation for free will if not differential equations?
• RQ5 Does the existence of such a function suggest limitations of differential equation-based theories when describing the whole universe?

Key findings

• A free will function can be defined as a non-deterministic, irreducible function that generates choices not predictable from any prior information.
• Such a function does not need to be a solution to any differential equation, thus avoiding the constraints of forward determinism.
• The existence of such a function implies that free will is compatible with a deterministic universe if the fundamental laws are not required to be differential equations.
• The free will function acts like a fundamental law of nature—self-contained, not derived from anything else, and not predictable from initial conditions.
• The framework suggests that theories based on differential equations may fail to describe the universe as a whole, and free will could be a hint of this limitation.
• The paper concludes that while free will is not proven real, it can be given a scientifically meaningful operational definition through this function.