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Free will theorem

The Free Will Theorem is a theorem in quantum mechanics, proved by mathematicians John H. Conway and Simon B. Kochen in 2006, which demonstrates that if experimenters possess free will in selecting measurement directions for spin-1 particles, then the particles' responses to those measurements cannot be fully predetermined by their past states or information accessible to them, implying a form of indeterminism or "free will" at the quantum level.^[1] The theorem relies on three foundational axioms derived from established principles of quantum mechanics and relativity. The SPIN axiom states that for a single spin-1 particle, measuring its squared spin components along three mutually orthogonal directions always yields the values 1, 0, and 1 in some permutation, consistent with quantum predictions for such systems.^[2] The TWIN axiom describes the perfect correlation in measurements of entangled "twinned" spin-1 particles: if one particle is subjected to a triple measurement yielding a specific outcome for a direction, the distant twin particle will produce the same outcome when measured along that parallel direction, regardless of space-like separation.^[2] The third axiom in the original formulation, FIN, posits that information transmission is bounded by a finite speed, aligning with special relativity's light-speed limit.^[2] The theorem's proof proceeds by assuming that particle responses are deterministic functions of all prior accessible information (a hidden variable hypothesis) and deriving a contradiction using the Kochen-Specker theorem, which shows that quantum mechanics prohibits non-contextual hidden variables for spin-1 systems.^[1] Specifically, it constructs a scenario with two space-like separated experimenters, A and B, each measuring entangled particles; the correlations enforced by TWIN and SPIN force the particles' outcomes to evade any predetermined assignment compatible with the experimenters' free choices, thus mirroring the assumed freedom of the experimenters.^[2] In 2009, Conway and Kochen published a strengthened version, dubbed the Strong Free Will Theorem, which replaces the FIN axiom with MIN—asserting that experimenters can freely select from a sufficiently large set of measurement directions (e.g., 33 for one and 40 triples for the other) without their choices being constrained by prior cosmic history in any inertial frame.^[3] This revision addresses potential loopholes related to information propagation, broadening the theorem's applicability by emphasizing the minimality of assumptions about experimental freedom.^[3] The implications of the theorem are profound for interpretations of quantum mechanics, as it rigorously excludes relativistic hidden variable theories and relativistic objective collapse models (such as relativistic versions of Bohmian mechanics or GRW theory) that seek to restore determinism while respecting quantum correlations and special relativity.^[1] Philosophically, it challenges reductionist views by suggesting that if human free will exists, it must extend analogously to fundamental particles, underscoring quantum mechanics' inherent indeterminism and prompting debates on the nature of causality, consciousness, and the universe's fabric.^[3]

Background

Historical Development

The Free Will Theorem emerged from efforts by mathematicians John H. Conway and Simon B. Kochen to address longstanding debates on determinism in quantum mechanics, particularly the implications of quantum indeterminacy and special relativity for the nature of experimental choices. Their initial formulation was motivated by the desire to explore whether human free will in selecting measurements could imply similar indeterminacy at the particle level, building on earlier no-go theorems in quantum foundations. This work was first presented in the paper "The Free Will Theorem," submitted to arXiv on April 11, 2006, and published later that year in Foundations of Physics.^[4] The theorem draws foundational influence from the 1967 Kochen-Specker theorem, which demonstrated the impossibility of non-contextual hidden variables in quantum mechanics, providing a key conceptual precursor for analyzing measurement outcomes without predetermined values. In 2009, Conway and Kochen published a strengthened version titled "The Strong Free Will Theorem" in the Notices of the American Mathematical Society, introducing the MIN axiom to broaden the theorem's applicability by relaxing assumptions about the finiteness of possible measurement directions while preserving the core argument against deterministic particle responses. This revision aimed to make the theorem more robust against potential counterexamples in infinite-dimensional Hilbert spaces, further engaging with philosophical questions about supradeterminism in quantum theory. The preprint appeared on arXiv in July 2008.^[5] Subsequent developments by Kochen alone refined the theorem for greater empirical relevance. In 2017, he elaborated in "Born's Rule, EPR, and the Free Will Theorem" that the MIN axiom could be replaced by the LIN axiom, which invokes experimentally testable Lorentz invariance instead of the more abstract MIN condition, allowing potential verification through quantum experiments without relying on unproven minimality assumptions. This shift was intended to align the theorem more closely with observable relativistic symmetries in particle physics. A further simplification came in 2022 with Kochen's preprint "On the Free Will Theorem" on arXiv (2207.06295), which presents a more general, frame-invariant proof that strengthens the spontaneity conclusion for particles without presupposing experimenter free will, emphasizing absolute rather than relative indeterminacy in response to measurements. This version ties back to ongoing discussions of quantum nonlocality and determinism, offering a streamlined argument accessible to broader audiences in mathematical physics.^[6]

Prerequisites in Quantum Mechanics

Quantum entanglement is a fundamental phenomenon in quantum mechanics where two or more particles become correlated such that the quantum state of each particle cannot be described independently, even when separated by large distances; measuring the state of one particle instantaneously determines the state of the other.^[7] This correlation arises from the particles' shared wave function and persists regardless of the spatial separation, challenging classical intuitions of locality.^[8] In the context of the Free Will Theorem, experiments often involve entangled pairs of spin-1 particles, such as photons or atoms with integer spin quantum number 1, where spin refers to the intrinsic angular momentum of the particle.^[9] Measurements of spin components along different directions yield outcomes that are probabilistically determined by quantum mechanics, with eigenvalues of 0 or 1 for squared spin operators in three-dimensional Hilbert space.^[10] The Kochen-Specker theorem establishes that quantum mechanics is incompatible with non-contextual hidden variable theories, which would assign definite pre-existing values to all observables independent of the measurement context.^[9] Specifically, for a single spin-1 particle, it proves impossible to consistently assign values (0 or 1) to the squared spin components along all possible directions in three-dimensional space without violating the functional relations imposed by quantum mechanics, such as the orthogonality of spin states.^[9] This contextuality implies that the outcome of a spin measurement depends on the compatible set of observables chosen, ruling out predetermined values for all spin directions simultaneously.^[10] Bell's theorem demonstrates that local hidden variable theories cannot reproduce the statistical predictions of quantum mechanics for entangled particles, implying inherent non-locality in quantum correlations.^[11] It derives inequalities based on the assumption of local realism, where outcomes are determined by local factors and no faster-than-light influences occur, but experiments consistently violate these inequalities, confirming quantum non-locality.^[12] For instance, in entangled spin measurements, the correlations exceed classical limits, as verified in loophole-free tests achieving statistical significance beyond 30 standard deviations.^[13] In special relativity, space-like separation describes two events whose interval is such that no causal signal traveling at or below the speed of light can connect them, ensuring no direct influence between the events.^[14] The no-signaling principle, a cornerstone of relativistic quantum mechanics, prohibits the transmission of information faster than light, even through entangled systems; while correlations exist between space-like separated measurements, they cannot be used to send controllable signals.^[14] This principle maintains compatibility between quantum mechanics and relativity by preventing superluminal communication in experiments involving distant entangled particles.^[15] In the experimental context of quantum mechanics, "free will" refers to the assumption that the experimenters' choice of measurement settings, such as the direction for spin measurement, is not predetermined as a function of all accessible past information or hidden variables.^[4] This freedom ensures that the selection of experimental parameters is independent of the particles' prior states, allowing for genuine randomness in the setup.^[4]

Axioms

Original Axioms (2006)

The original formulation of the Free Will Theorem, proposed by John H. Conway and Simon B. Kochen in 2006, relies on three axioms: FIN, SPIN, and TWIN. These axioms encapsulate key principles from relativity and quantum mechanics, serving as the foundational assumptions from which the theorem derives its conclusion about the indeterminacy of particle responses. They are designed to be experimentally verifiable where possible and to reflect established physical laws without presupposing any particular interpretation of quantum mechanics.^[16] The FIN axiom states that there is a finite upper bound to the speed with which information can be effectively transmitted, typically taken as the speed of light. This axiom embodies the principle of relativistic causality, ensuring that no influence or signal can propagate superluminally, thereby preventing effects from preceding their causes in any reference frame. It derives directly from special relativity, where the invariance of the speed of light imposes a universal speed limit on information transfer, a cornerstone of modern physics that has been confirmed through numerous experiments, such as those involving electromagnetic waves and particle accelerators. In the context of the theorem, FIN ensures that measurements on spatially separated particles cannot influence each other instantaneously, isolating the experimenters' choices from prior causal chains.^[16] The SPIN axiom addresses the measurement outcomes for a single spin-1 particle. It posits that for any triple of orthogonal directions, defined by unit vectors \mathbf{n}_1, \mathbf{n}_2, \mathbf{n}_3, a measurement of the squared spin components yields values that are a permutation of $1, 1, 0 in units of \hbar^2. Mathematically, this is expressed as:

(\mathbf{S} \cdot \mathbf{n}_1)^2 + (\mathbf{S} \cdot \mathbf{n}_2)^2 + (\mathbf{S} \cdot \mathbf{n}_3)^2 = 2\hbar^2,

where each individual (\mathbf{S} \cdot \mathbf{n}_i)^2 takes the value $0 or \hbar^2. This property arises from the algebraic structure of quantum mechanics for spin-1 particles, where the spin operators satisfy the commutation relations of angular momentum, and the eigenvalues of (\mathbf{S} \cdot \mathbf{n})^2 are determined by the representation theory of the rotation group SU(2). Experimentally, this has been verified through spin measurements on particles like photons or atoms in controlled quantum states, confirming the non-classical distribution of outcomes without reliance on hidden variables. The SPIN axiom thus captures the intrinsic quantum behavior of individual particles, independent of entanglement.^[16] The TWIN axiom pertains to pairs of entangled spin-1 particles, known as "twins," produced in a singlet state. It states that if one experimenter measures the squared spin components in three orthogonal directions \mathbf{x}, \mathbf{y}, \mathbf{z} on the first particle, obtaining outcomes j, k, \ell (where j + k + \ell = 2 and each is 0 or 1 in units of \hbar^2), and the second experimenter measures the squared spin in a direction \mathbf{w} that coincides with one of \mathbf{x}, \mathbf{y}, \mathbf{z} on the second particle, then the outcome will match the corresponding value from the first measurement. This perfect correlation holds regardless of the spatial separation between the particles, as long as the measurements are space-like separated to respect causality. The TWIN axiom stems from the quantum mechanical phenomenon of entanglement, first highlighted in the Einstein-Podolsky-Rosen paradox, where the joint wave function of the pair enforces non-local correlations without allowing superluminal signaling. These correlations have been empirically demonstrated in numerous Bell test experiments, such as those using photons or ions, ruling out local hidden variable theories and underscoring the theorem's reliance on verified quantum predictions. Together, FIN, SPIN, and TWIN provide a minimal set of physically grounded assumptions that bridge relativity and quantum mechanics for the theorem's logical derivation.^[16]

Revisions and Strong Version (2009 and Later)

In 2009, John H. Conway and Simon B. Kochen published a strengthened version of the Free Will Theorem, replacing the original FIN axiom with a weaker condition known as the MIN axiom.^[5] The MIN axiom states that for space-like separated experimenters A and B, experimenter B can freely choose any one of 33 particular directions, with A's response independent of this choice, and vice versa for A's choice among 40 triples, ensuring the experimenters' choices are not functions of past accessible information.^[5] This revision addresses criticisms regarding information transmission speeds by focusing solely on the independence of experimenter choices from each other's selections in space-like separated scenarios, thereby enhancing the theorem's robustness without relying on strict light-cone constraints.^[5] The Strong Free Will Theorem, derived from the SPIN, TWIN, and MIN axioms, asserts that the response of a spin-1 particle to a triple experiment is free, meaning it is not a function of properties of that part of the universe earlier than the response with respect to any inertial frame.^[5] This formulation implies that outcomes for all possible such experiments cannot be predetermined by past events, extending the theorem's applicability to broader relativistic theories, including those like GRW where particle responses might depend on past half-spaces rather than light cones.^[5] In 2017, Simon B. Kochen further refined the theorem by replacing the MIN axiom with the LIN axiom, which asserts the Lorentz covariance of experimental outcomes.^[17] The LIN axiom specifies that the result of an experiment is Lorentz covariant: a change of Lorentz frames does not alter the results, as seen in spin measurements where outcomes like up/down spots remain consistent across frames (e.g., above/below a diagonal).^[17] This update emphasizes full Lorentz invariance, separating the role of experimenter free will and focusing on a single experimenter's setup, while LIN's covariance is experimentally verifiable through high-precision tests of Lorentz symmetry, such as lunar laser ranging.^[17] Kochen's 2022 proof provides a frame-invariant version of the theorem, simplifying assumptions by relying on invariant light cones rather than specific inertial frames.^[6] Unlike prior formulations, it eliminates the need for assuming experimenter free will, proving unconditionally that a particle's response to the 40 triple experiments is free—not determined by events in its past light cone—using only the SPIN, TWIN, and FIN axioms.^[6] This approach avoids frame-dependent reasoning, as light cones are invariant across inertial frames, broadening the theorem's scope to apply absolutely without conditional links to human choices.^[6] Overall, these revisions expand the strong version's applicability to wider classes of quantum theories, including those with relativistic extensions, by progressively weakening and refining axioms for greater generality and empirical alignment.^[5]^[17]^[6]

The Theorem

Statement

The Free Will Theorem, proposed by John H. Conway and Simon B. Kochen, asserts that under certain foundational assumptions in quantum mechanics and relativity, the behavior of elementary particles cannot be predetermined if the choices made by experimenters are not determined by prior information. Specifically, in its original formulation, the theorem states: "If the choice of directions in which to perform spin 1 experiments is not a function of the information accessible to the experimenters, then the responses of the particles are equally not functions of the information accessible to them."^[1] This implies that if experimenters possess free will—meaning their selection of measurement settings is independent of the past state of the universe—then the responses of the particles to those measurements must also be free in the same sense, not dictated solely by information in their backward light cones.^[4] The theorem applies primarily to experiments involving spin-1 particles, such as entangled pairs where measurements of squared spin components in three orthogonal directions are performed. In such setups, the outcomes follow the quantum mechanical prediction that the squared spins yield values of 1, 0, and 1 in some order (summing to 2), and for twinned particles separated by a space-like interval, parallel measurements yield identical results.^[1] The scope is limited to these spin-1 systems but has been noted as extensible to other quantum contexts where similar entanglement and measurement independence hold, though the core proof relies on the Peres configuration of 33 directions for experimenter choices.^[1] In the strong version, developed to address potential loopholes in deterministic hidden-variable theories, Conway and Kochen refined the axioms and the notion of accessible information. The Strong Free Will Theorem states: The axioms SPIN, TWIN, and MIN imply that the response of a spin 1 particle to a triple experiment is free—that is to say, is not a function of properties of that part of the universe that is earlier than this response with respect to any given inertial frame. Here, the MIN axiom replaces the original FIN, allowing particle responses to depend on past half-spaces rather than strict light cones, thereby ruling out broader classes of deterministic theories, including some relativistic collapse models like GRW, while maintaining the conclusion that no such theory can reproduce quantum predictions if experimenter choices are free. This version reinforces that particles must exhibit unpredictable responses akin to free will, ensuring the theorem's robustness against attempts to localize influences within space-time. One experimenter chooses from 40 orthogonal triples, the other from 33 directions.^[5]

Proof Overview

The proof of the Free Will Theorem relies fundamentally on the Kochen-Specker theorem, which demonstrates that quantum observables cannot be assigned predetermined values independently of the measurement context, as certain configurations of directions lead to logical contradictions in any non-contextual hidden variable theory.^[4] This contextuality is central to showing that particles' responses to spin measurements cannot be preassigned without inconsistency. The overall proof structure proceeds by assuming, for contradiction, that the responses of elementary particles to measurements are predetermined by factors in their past light cones, independent of the experimenters' free choices.^[4] It then employs two key experimental setups involving entangled spin-1 particles: the Twin experiment, where two particles are measured in space-like separated locations with parallel directions yielding perfectly correlated outcomes (either both +1 or both 0), and the Spin experiment, where a single particle's measurements in three orthogonal directions yield outcomes summing to 2, as per the SPIN axiom.^[3] By considering a scenario with two experimenters, Alice and Bob, performing such measurements on twin particles separated by a vast distance (e.g., Earth and Mars), the proof derives that Alice's free choice of measurement directions forces predetermined responses on Bob's particle that violate the Kochen-Specker no-go theorem when extended across multiple compatible contexts.^[4] In the original version, the axioms SPIN, TWIN, and FIN play crucial roles in isolating the contradiction by ruling out hidden influences or dependencies that could correlate outcomes across space-time. FIN (finite speed of information) ensures no signals faster than light propagate between experiments, preserving locality.^[4] In the strong version, MIN (measurer independence) replaces FIN and guarantees that each experimenter's choice of directions is not a function of the complete past state accessible to their particle, preventing superdeterministic loopholes.^[3] Together, these axioms ensure that the assumed predetermination leads to an impossible assignment of values (a "101-function") for all possible measurement directions, as prohibited by Kochen-Specker contextuality.^[3] A pivotal step occurs in space-like separated experiments, where the experimenters' free choices of incompatible direction sets compel the particles' responses to satisfy correlations that cannot be predetermined without contextual inconsistency. In the original proof, this uses the Peres configuration of 33 directions; the strong version extends to 40 orthogonal triples for one experimenter and 33 directions for the other.^[4] This forces the conclusion that particle responses must be indeterministic, matching the freedom in experimenters' choices. A 2022 simplification of the proof by Kochen reformulates it in a frame-invariant manner, using light cones as invariant space-time structures to avoid reliance on specific Lorentz frames or coordinate choices, while preserving the core reliance on SPIN, TWIN, and Kochen-Specker elements.^[6]

Implications

For Physics

The Free Will Theorem challenges local deterministic hidden variable theories by demonstrating that, under its axioms, the outcomes of certain quantum spin measurements cannot be predetermined by any information accessible from the particles' past, extending the no-go results of Bell's theorem to a broader class of experiments involving spin-1 particles.^[4] Specifically, the theorem proves that if experimenters' choices of measurement settings are not functions of prior particle information, then the particles' responses must also be unpredictable in advance, ruling out local realistic models that attempt to restore determinism to quantum mechanics without invoking non-locality.^[18] This implication holds robustly even in the strong version of the theorem, which weakens the finiteness assumption while preserving the core argument against such theories.^[5] The theorem is fully compatible with standard quantum mechanics, as its axioms—derived from quantum predictions for entangled particles—are empirically verified and align with the indeterminacy central to the Copenhagen interpretation, where measurement outcomes are inherently probabilistic rather than predetermined.^[4] By emphasizing that particle responses evade deterministic functions of past states, it reinforces the view that quantum mechanics requires genuine randomness at the fundamental level, without necessitating modifications to the theory's core formalism.^[19] Regarding relativity, the theorem's framework incorporates principles that prevent superluminal signaling. In a 2017 revision, the LIN axiom—formulated as an experimentally testable form of Lorentz covariance—replaces the MIN assumption, ensuring that experimental outcomes respect relativistic causality by prohibiting influences outside light cones.^[17] This reinforces the no-signaling condition inherent in quantum field theory, maintaining consistency between quantum non-locality and special relativity. A further 2022 strengthening by Kochen proves particle spontaneity unconditionally, without relying on experimenter free will, providing even stronger evidence against deterministic hidden variables.^[6] However, the theorem has limitations, as it excludes deterministic non-local theories, such as Bohmian mechanics, but allows stochastic models where randomness is intrinsic rather than hidden, provided they satisfy the axioms.^[19] Experimental verification of the Lin axiom's Lorentz covariance can be pursued through high-energy particle collisions in accelerators like the Large Hadron Collider, where deviations from invariance would manifest in scattering processes or decay rates, providing indirect support for the theorem's relativistic assumptions.^[20] Such tests, combined with quantum entanglement experiments, strengthen the theorem's physical foundation without directly probing free will itself.^[21]

For Philosophy of Free Will

The Free Will Theorem, developed by mathematicians John Conway and Simon Kochen, establishes an analogy between human agency and the behavior of elementary particles, positing that if experimenters possess free will in choosing measurement settings, then particles must exhibit a comparable form of freedom in their responses. This implication directly challenges strict determinism by demonstrating that particle outcomes cannot be fully predetermined by prior physical states, thereby extending the notion of agency to the fundamental level of nature.^[4]^[5] In philosophical terms, the theorem lends support to libertarian conceptions of free will, which emphasize genuine indeterminacy and the capacity for uncaused choices that influence the future, rather than mere compatibility with causal laws. Conway and Kochen argue that the particles' responses represent active decisions not dictated by historical antecedents, aligning with libertarianism's rejection of determinism as incompatible with true agency. This view critiques compatibilist accounts, which reconcile free will with determinism by redefining freedom as acting in accordance with one's desires; the authors dismiss such positions as relics of a pre-quantum worldview, unnecessary in a universe where indeterminacy is inherent.^[4]^[5] Later developments, such as the 2022 unconditional version, prove inherent particle freedom without presupposing human free will, which may weaken the direct analogy but strengthens the case for fundamental indeterminism as a basis for agency across scales.^[6] The theorem's broader impact questions reductionist philosophies that seek to derive human consciousness and volition solely from deterministic physical processes, suggesting instead that agency permeates all scales of reality and cannot be reduced to mechanistic explanations. By ascribing "free will" to particles—deliberately to provoke reflection on indeterminacy—Conway and Kochen intend to defend the idea that quantum unpredictability provides a foundational basis for human agency, free from the constraints of a clockwork universe.^[4]^[5]

Reception and Criticisms

Scientific Responses

Physicists Eric Cator and Klaas Landsman praised the Free Will Theorem for relying on fewer assumptions than Bell's theorem, as it does not require probability theory and instead uses a minimal fragment of quantum mechanics focused on spin measurements and locality constraints.^[22] A notable critique came from Sheldon Goldstein and collaborators, who argued that the theorem primarily constrains deterministic hidden variable models but does not exclude indeterministic frameworks, which can accommodate quantum predictions without violating the theorem's key conditions like the MIN axiom.^[23] David Hodgson supported the theorem's implications for quantum foundations, viewing it as evidence against strict determinism by demonstrating that particle responses cannot be fully predetermined independently of experimental choices, thereby bolstering anti-deterministic interpretations.^[24] Regarding experimental feasibility, Simon Kochen proposed in 2017 replacing the MIN axiom with the LIN axiom, which asserts Lorentz invariance of measurement outcomes and is designed to be testable through experiments verifying covariance in entangled particle systems, prompting discussions on practical implementations using advanced quantum optics setups.^[17] In 2025, discussions in quantum neuroscience have linked the theorem to wave function collapse models as mediators of free will, suggesting potential experimental resolutions to determinism debates.^[25]

Philosophical Debates

Philosophers engaging with the Free Will Theorem have debated its implications for libertarian conceptions of free will, which posit that agents can make choices undetermined by prior causes. In their 2009 paper, John H. Conway and Simon B. Kochen argue that the theorem demonstrates if human experimenters possess free will in the sense of being able to choose measurement settings independently, then elementary particles must exhibit a comparable form of freedom, thereby implying a non-deterministic foundation for human agency.^[3] They contend this "semi-free" behavior of particles underpins human free will, stating that "if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity," and that particle freedom provides "the ultimate explanation of our own."^[3] This defense bolsters libertarianism by ruling out superdeterminism, a deterministic loophole in quantum mechanics, and asserting that the universe is inherently non-deterministic.^[3] Critics, however, contend that the theorem's conception of "free will" is narrowly defined as mere unpredictability or causal independence in choices, falling short of the robust moral agency central to philosophical free will debates, which involves rational deliberation and the ability to do otherwise in a morally significant way. For example, philosopher Klaas Landsman argues that a reformulation of the theorem removes the need to presuppose indeterminism by assuming a deterministic framework with independence for choices, and aligns more closely with compatibilist views, such as David Lewis's local miracle compatibilism, rather than strengthening libertarianism, as it does not address deeper questions of agency.^[26] This narrow interpretation limits the theorem's metaphysical reach, rendering it philosophically shallow for discussions of moral responsibility.^[26] These tensions were highlighted at the SOPhiA 2025 conference in a talk by Ella van Dalen, who examined whether the Free Will Theorem truly defends libertarianism. Van Dalen argued that the theorem fails to establish meaningful free will for particles and cannot prove the indeterminism required for libertarianism due to its circular assumptions, while also noting ambiguities in equating quantum unpredictability with philosophical agency.^[27] The theorem has indirect implications for debates on non-human agency, including artificial intelligence and consciousness, by suggesting that quantum indeterminacy could enable forms of decision-making beyond classical determinism in complex computational systems. For instance, discussions in quantum models of brain processes propose that particle-level freedom might contribute to emergent conscious agency, potentially extending to AI systems exhibiting unpredictable behaviors akin to free choices.^[28] Ongoing philosophical debates explore the theorem's compatibility with emergent free will in complex systems, where macro-level agency arises from micro-level quantum indeterminacy without requiring libertarian indeterminism at every scale. Critics like Landsman suggest this emergence aligns with compatibilist frameworks, allowing free will to coexist with underlying physical laws in hierarchical systems, though proponents of libertarianism maintain it underscores irreducible freedom at the fundamental level. A 2025 philosophical reframing emphasizes that modern physics, including the Free Will Theorem, supports a non-deterministic universe, challenging determinism-based arguments against free will.^[26]^[29]

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