“Einstein could not bring himself to believe that ‘God plays dice with the world,’ but perhaps we could reconcile him to the idea that ‘God lets the world run free’.” – John Conway & Simon Kochen, “The Free Will Theorem”[1]
Are fundamental particles the source of free will in the universe? More specifically, does the unpredictable quantum behavior of electrons and other micro particles enable macro-level free choice?
Philosophers have puzzled over questions like these since Democritus and Epicurus.[2] The free will theorem of mathematicians John Conway and Simon Kochen addresses the quantum version of the question, famously asserting that if humans have free will, then electrons also have free will.[3] The theorem proves mathematically that the universe cannot be deterministic because the quantum behavior of particles is not determined by the past history of the particles or the past history of the entire universe. Quantum behavior is non-deterministic, therefore “[n]ature itself is non-deterministic.”[4]
Why do particles behave in unexplained ways?
Physicists have long observed that particles behave in a curious and unpredictable way during quantum evolution. In the initial phase of evolution, particles and their wave functions evolve over time according to the Schrödinger equation, with predictions of particle behavior changing in an expected and deterministic way. In this phase the future direction and behavior of a particle and its wave function is determined by its prior direction and behavior. In a later phase of quantum evolution, however, when the predicted behavior of a particle is tested with a measurement, something different happens. Instead of behaving in a predicted and determined way, the wave function seems to collapse, and the particle jumps to a specific measured state which cannot be predicted with specificity.[5] Physicists cannot say why or how the specific result occurs in that instance. It is in the range of possible results predicted by the Schrödinger equation, but the mechanism by which the particular result is chosen remains unclear.
Theorists have attempted to explain this behavior by suggesting the existence of unknown or hidden factors which determine the result. The theories assume that the relevant variable simply has not been discovered yet, but its discovery will explain the particular path taken by the particle and its wave function to reach the particular result in each instance. These are called hidden-variable theories.
Electrons make “free” choices
Conway and Kochen analyzed mathematically whether it is possible for hidden variables to determine the outcome of quantum reduction. Relying on non-controversial facts of quantum mechanics, they showed that if an experimenter is free to choose the experiment conducted on a particle, then it can be proven mathematically that the particle is “free” to choose the particular measurement result.[6] In other words, if the experimenter’s choice of how to conduct the experiment is not predetermined by an unknown factor, then it is impossible for the particle’s choice to be predetermined by an unknown factor.[7] The particle is as “free” as the experimenter, and the measurement result chosen by the particle can never be predicted by any preexisting event, variable, or information in the prior history of the universe.
Does the unpredictability of fundamental particles help explain human free will?
The established view among many physicists and philosophers of science is “no”. Fundamental physics is said to offer only two choices—strict determinism or pure randomness—neither of which leaves any room for human judgment or free will.[8]
In contrast, Conway and Kochen argue that the choices made by electrons are not purely “random” or “stochastic” but are more accurately described as “free” or “semi-free”. They believe that a form of “free” choice built into the quantum foundation of the universe may offer a basis for human “free” choice and will.[9]
Free or random
Quantum reduction does have some features not fully consistent with pure randomness. The seemingly “random” results of measurement are not arbitrary but fall within the range of possible results predicted by the Schrödinger equation. Over repeated measurements, the results also average out and approximate the results predicted by both the Schrödinger equation and deterministic principles of classical physics. Perhaps most significantly, particles in a state of superposition produce correlated measurement results. When one entangled particle is measured, with an unpredictable result, a measurement performed on a second twinned particle, entangled with the first, is correlated to the result of the first measurement and therefore more predictable. The twinned, entangled particles do not behave in a completely random way.[10]
Some believe that the alternative to determinism is randomness, and go on to say that “allowing randomness into the world does not really help in understanding free will.” However, this objection does not apply to the free responses of the particles that we have described. It may well be true that classically stochastic processes such as tossing a (true) coin do not help in explaining free will, but … randomness also does not explain the quantum mechanical effects described in our theorem. It is precisely the ‘semi-free’ nature of twinned particles, and more generally of entanglement, that shows that something very different from classical stochasticism is at play here.[11]
Conway and Kochen wrote as mathematicians, not neuroscientists, so offered no empirical evidence or theories to explain how the quantum behavior of particles might influence macroscopic entities such as ourselves.[12] But they had a strong belief that it was possible.[13]
Can random occurrences in the microcosm enable non-random evolution in the macroscopic world?
Even if quantum behavior were random, is there reason to believe that random action at the quantum level gives rise to non-random evolution, or something like choice, at the macroscopic level?
We know that random variation in nature can result in non-random evolution. An obvious example is quantum reduction itself, which is governed by the laws of probability. Those laws cause seemingly random results to average out and produce the appearance and reality of non-random macroscopic evolution. Natural selection is also an obvious example; it is based on the principle that random changes and genetic variations drive non-random evolution of species over time.
A less obvious example is the role that randomness and indeterminacy may play in the evolution of reason-based decision-making and free agency. In his book Free Agents: How Evolution Gave Us Free Will, neuroscientist Kevin Mitchell challenges the position that “indeterminacy or randomness doesn’t get you free will.”[14] He argues instead for a direct connection between indeterminacy and the development through natural selection of reasoned judgment and meaning.
The idea is not that some events are predetermined and others are random, with neither providing agential control. It’s that a pervasive degree of indefiniteness loosens the bonds of fate and creates some room for agents to decide which way things go. The low-level details of physical systems plus the equations governing the evolution of quantum fields do not completely determine the evolution of the whole system. They are not causally comprehensive: other factors—such as constraints imposed by the higher-order organization of the system—can play a causal role in settling how things go.
In living organisms, the higher-order organization reflects the cumulative effects of natural selection, imparting true functionality relative to the purpose of persisting…. The essential purposiveness of living things leads to a situation where meaning drives the mechanisms. Acting for a reason is what living systems are physically set up to do.[15]
Uncertainty leads to interpretation, prediction, and the creation of meaning
Mitchell maintains that “indeterminacy at the lowest levels can indeed introduce indeterminacy at higher levels.”[16] If that is true, and indeterminacy is ubiquitous at both microscopic and macroscopic levels, the process of resolving that indeterminacy becomes a fundamental feature of physical existence.
For living systems, resolving indeterminacy means confronting uncertainty. Organisms, as a matter of biological necessity, must deal with a level of unreliability and randomness in the environment. It is built in. There is no escape from it.
With incomplete knowledge about expected occurrences in the environment, organisms learn to interpret events and predict what will happen in order to adapt behavior to threats or opportunities. Organisms that do this well tend to persist better than organisms that predict less well.
For organisms with neural systems such as ours, interpretation of events further leads to the imposition of meaning on the world in order to act and persist within it. The meaning given to events becomes important to survival, and acting in ways that are consistent with that meaning becomes crucial.[17] Creating meaning and acting for reasons helps us survive in an environment of uncertainty and indeterminacy. Natural selection therefore results in organic systems that specialize in interpretation and meaning and choice.
Indeterminacy means organisms can choose to behave randomly
Living systems also learn to use randomness to their benefit. Mitchell describes how the neural structures of our brains have evolved to reflect and take advantage of the uncertainty around us.
There is an inherent unreliability and randomness in neural activity that is a feature in the system, not a bug. The noisiness of neural components is a crucial factor in enabling an organism to flexibly adapt to its changing environment—both on the fly and over time.[18]
The system succeeds, not just despite uncertainty and randomness, but also because of it.
[O]rganisms have developed numerous mechanisms to directly harness the underlying randomness in neural activity. It can be drawn on to resolve an impasse in decision making, to increase exploratory behavior, or to allow novel ideas to be considered when planning the next action. These phenomena illustrate the reality of noisy processes in the nervous system and highlight a surprising but very important fact: organisms can sometimes choose to do something random.[19]
The ability to harness randomness enables the creativity that characterizes brains like ours and enhances our ability to survive and grow and persist. Mitchell cites the two-stage model of free will proposed by William James as a model for how organisms use randomness and indeterminacy to broaden the options available for decision-making.[20] Ideas spring to mind in a seemingly, or actually, random way, but then the organism applies judgment and decision-making to choose the option that suits the requirements of the system in that moment.
In humans, we recognize this capacity as creativity—in this case, creative problem solving. When we are frustrated in achieving our current goals or when none of the conceived options presents an adequate solution to the current problem, we can broaden our search beyond the obvious to consider new ideas. These do not spring from nowhere but often arise as cognitive permutations: by combining knowledge in new ways, by drawing abstract analogies with previously encountered problems in different domains, or by recognizing and questioning current assumptions that may be limiting the options that occur to us. In this way, humans become truly creative agents, using the freedom conferred by the underlying neural indeterminacy to generate genuinely original thoughts and ideas, which we then scrutinize to find the ones that actually solve the problem. Creative thoughts can thus be seen as acts of free will, facilitated by chance but filtered by choice.[21]
Similar to how new biological variations appear randomly in nature, but then are selected or eliminated through natural selection, humans rely on inherent randomness for creative inspiration, while implementing the constraints and systems of meaning that determine how we persist and why.
This model thus powerfully breaks the bonds of determinism, incorporating true randomness into our cognitive processes while protecting the causal role of the agent itself in deciding what to do.[22]
Quantum evolution and natural selection have given us the ability to resolve the indeterminacy at the heart of the universe by confronting uncertainty and harnessing it to the service of creativity, decision-making, and meaning. That is our superpower.[23]
We choose like electrons
So if Mitchell is correct that quantum indeterminacy permeates the universe and enables the evolution of choice and free agency, are Conway and Kochen also correct? Are we like electrons in a truly fundamental way?
Electrons make something like free choices through the process of quantum reduction. In that process the universe around the electron undergoes a deep transformation. Before the process the electron exists in an unrecognizable quantum world of infinite superpositioned possibilities; after the process the electron becomes part of a recognizable reality of finite events and things. The process transforms possibilities into mathematical probabilities which resolve into one unique occurrence in spacetime. The electron therefore has a superpower, too—it can resolve probabilities into unique outcomes.
Our superpower is very much like that. We are made of fundamental particles like electrons and we are creatures like electrons. The universe we inhabit is constructed through the process of quantum reduction. Second by second, the quantum world of possibilities transforms itself into the concrete world of spacetime. Our world is fundamentally about uncertain possibilities and probabilities resolving into the certainty of actual events.
That ubiquitous uncertainty is reflected in the structure and operation of our brains. By making decisions amidst uncertainty, we participate in the universal process of transforming possibilities into unique, concrete events. Natural selection has taught us to use the randomness that is foundational to that process; we use it for creative inspiration and to generate options for decision-making. We sometimes make random choices—intentionally.
The ability to make random choices—just as an electron does—may be crucial to the ability to make non-random, reasoned choices. John Conway perhaps had this in mind when he said that the free will theorem also could be called the “free whim theorem”.[24] Without the freedom to make random choices, making reasoned choices through judgment and logic may amount to nothing but determinism. True free will necessitates freedom to choose, and the “free whim” of the electron may be exactly what gives us that freedom.
Electrons R us.
[1] Conway and Kochen (2006), p. 27.
[2] Democritus argued that all action in the universe is determined by the movements of atoms. Epicurus, one of his followers, theorized that atoms swerve periodically in a way that breaks the chain of deterministic causation and preserves a conceptual basis for human freedom of action.
[3] In a follow-up article Kochen broadened the proof to demonstrate that the free behavior of particles is not dependent on the free behavior of humans. Kochen (2022).
[4] Conway and Kochen (2009), p. 230.
[5] This unexplained behavior is called the “collapse of the wave function”, also quantum state vector reduction, quantum state reduction, or simply quantum reduction.
[6] “[O]ur assertion that ‘the particles make a free decision’ is merely a shorthand form of the more precise statement that ‘the Universe makes this free decision in the neighborhood of the particles’.” Conway and Kochen (2006), p. 15.
[7] Conway and Kochen did not give credence to the proposition that experimenters are not free to choose their own experiments. “It is hard to take science seriously in a universe that in fact controls all the choices experimenters think they make. Nature could be in an insidious conspiracy to ‘confirm’ laws by denying us the freedom to make the tests that would refute them. Physical induction, the primary tool of science, disappears if we are denied access to random samples. It is also hard to take seriously the arguments of those who according to their own beliefs are deterministic automata!” Conway and Kochen (2006), p. 24.
[8] See e.g., Hossenfelder (2022).
[9] “Indeed, it is natural to suppose that this latter freedom [of particles] is the ultimate explanation of our own.” Conway and Kochen (2009), p. 230.
[10] “Although we find ourselves unable to give an operational definition of either ‘free’ or ‘random,’ we have managed to distinguish between them in our context, because free behavior can be twinned, while random behavior cannot (a remark that might also interest some philosophers of free will).” Conway and Kochen (2006), p. 25.
[11] Conway and Kochen (2009), p. 230.
[12] “In the present state of knowledge, it is certainly beyond our capabilities to understand the connection between the free decisions of particles and humans, but the free will of neither of these is accounted for by mere randomness.” Conway and Kochen (2009), p. 230.
[13] “The world [the free will theorem] presents us with is a fascinating one, in which fundamental particles are continually making their own decisions. No theory can predict exactly what these particles will do in the future for the very good reason that they may not yet have decided what this will be! Most of their decisions, of course, will not greatly affect things — we can describe them as mere ineffectual flutterings, which on a large scale almost cancel each other out, and so can be ignored. The authors strongly believe, however, that there is a way our brains prevent some of this cancellation, so allowing us to integrate what remains and producing our own free will.” Conway and Kochen (2006), pp. 26-27.
[14] Mitchell (2023), p. 280.
[15] Mitchell (2023), pp. 280-281.
[16] Mitchell (2023), p. 159.
[17] “[T]he higher-order features that guide behavior revolve around purpose, function, and meaning. The patterns of neural activity in the brain have meaning that derives from past experience, is grounded by the interactions of the organism with its environment, and reflects the past causal influences of learning and natural selection. The physical structure of the nervous system captures those causal influences and embodies them as criteria to inform future action. What emerges is a structure that actively filters and selects patterns of neural activity based on higher-order functionalities and constraints. The conclusion—the correct way to think of the brain (or, perhaps better, the whole organism) is as a cognitive system, with an architecture that functionally operates on representations of things like beliefs, desires, goals, and intentions.” Mitchell (2023), pp. 194-195.
[18] Mitchell (2023), p. 175 (emphasis in original).
[19] Mitchell (2023), p. 175 (emphasis in original).
[20] Mitchell (2023), pp. 187-192, citing Doyle (2010).
[21] Mitchell (2023), p. 191 (emphasis in original).
[22] Mitchell (2023), p. 188.
[23] “This capacity to generate and then select among truly novel actions is clearly highly adaptive in a world that refuses to remain 100 percent predictable.” Mitchell (2023), p. 191.
[24] As reported by Jasvir Nagra in notes on a talk given by Conway in 2004. “He said he did not really care what people chose to call it. Some people choose to call it ‘free will’ only when there is some judgment involved. He said he felt that ‘free will’ was freer if it was unhampered by judgment—that it was almost a whim. ‘If you don’t like the term Free Will, call it Free Whim—this is the Free Whim Theorem.’” Nagra (2020).
