The Strong Free Will Theorem (0807.3286v1)

Abstract: We strengthen "The Free Will Theorem" [1] in several ways, by replacing the axiom FIN by a weaker axiom MIN, and also by allowing the particles' responses to depend on past half-spaces rather than on on past light cones. This change allows us to directly apply our theorem to relativistic theories of the GRW type.

• The paper proves that if experimenters freely choose measurement settings, then elementary particles must display an intrinsic form of non-determinism.
• The paper employs the SPIN, TWIN, and MIN axioms to derive its conclusions, rigorously challenging classical deterministic interpretations of quantum mechanics.
• The paper's findings have significant implications for unified theories in physics, questioning the viability of deterministic hidden variable models.

A Summary of "The Strong Free Will Theorem"

John Conway and Simon Kochen present a significant extension of their work in the paper titled "The Strong Free Will Theorem." Their research revolves around foundational questions about quantum mechanics, relativity, and the implications for determinism versus free will. The primary assertion of their theorem is that if humans have the ability to exercise free will in choosing experimental settings, then elementary particles must also exhibit a form of this freedom.

Core Axioms

The theorem rests on three axioms: SPIN, TWIN, and MIN.

1. SPIN Axiom: This axiom draws from the Kochen-Specker Paradox and asserts that specific measurements of squared spin for a spin-1 particle in orthogonal directions yield results in the sequence of (1,0,1), challenging the classical notion of predetermined properties in quantum systems.
2. TWIN Axiom: Derived from the EPR paradox, this axiom deals with correlated results of entangled particles. It suggests that paired "twinned" particles will produce the same response to spin measurements along parallel directions.
3. MIN Axiom: This axiom introduces the concept of free will by assuming that experimenters can freely choose the measurement settings in relativistically separated experiments. Specifically, it asserts that the choice of measurement by one experimenter does not influence the outcomes at the other location, reflecting the relativity principle that the temporal order of spacelike separated events is not absolute.

The Theorem and Its Implications

The authors' Free Will Theorem postulates that, under the axioms mentioned, the results produced by a spin-1 particle in a series of experiments are not a function of the entire history of the universe prior to those results—implying a form of independence or "free will" in particles akin to human-level free will.

This theorem challenges deterministic interpretations of quantum mechanics by positing a fundamental non-determinism rooted within physical laws themselves. The authors argue this not only sustains the probabilistic nature of quantum mechanics but raises philosophical implications for understanding free will in humans versus determinism in the universe.

Practical and Theoretical Considerations

The authors meticulously detail their formal proof, ensuring that the theorem’s robustness is maintained across varying interpretations of quantum mechanics and relativistic contexts. They emphasize that even approximate adherence to the stated axioms retains the theorem's core conclusions. Furthermore, in their discussion, experimental verification is considered, though they acknowledge the idealized nature of the needed experimental setup.

The paper also touches on the potential incompatibility of determinism with the FWT, emphasizing that no deterministic theory would suitably account for the free nature of responses in quantum systems as depicted in rGRWf theories and collapsing wave functions.

Future Directions

Future developments in the field will need to reconcile the non-deterministic implications of the FWT with the quest for a comprehensive theory of quantum gravity or a unified approach to quantum mechanics and relativity. The implications on interpretations such as Bohmian mechanics or other hidden variable theories need rigorous exploration, especially in light of potential general relativistic influences.

In summary, Conway and Kochen's "The Strong Free Will Theorem" challenges preconceived notions about determinism in the universe, suggesting that particle behavior challenges classical ideas of cause and effect in fundamental ways. It demonstrates that the nature of freedom and determinacy in quantum mechanics is complex, potentially impacting our understanding of fundamental physics and the universe's structure.