The late philosopher Robert Nozick, talking about the deep question of why there is something rather than nothing, quipped: "Someone who proposes a non-strange answer shows he didn't understand the question." So, when Scott Aaronson began a talk three weeks ago by saying it would be "the looniest talk I've ever given," it was a good start. At a conference on the nature of time—a question so deep it's hard even to formulate as a question—“loony" is high praise indeed. And indeed his talk was rich in ambition and vision. It left physics überblogger Sabine Hossenfelder uncharacteristically lost for words.

As part of his general push to apply theoretical computer science to philosophy, Aaronson has been giving thought to that old favorite of college metaphysics classes and late-night dorm-room bull sessions: free will. Do we have autonomy, or are our choices preordained? Is that a false choice? What does it mean to be free, anyway? For some of Aaronson's earlier thoughts, see his lecture and blog post. Though hard to summarize, his talk (slides here) can be broken down into two parts.

First, he sought to translate fuzzy notions of free will into a concrete operational definition. He proposed a variation on the Turing Test which he calls the Envelope Argument or Prediction Game: someone poses questions to you and to a computer model of your brain, trying to figure out who's the human. If a computer, operating deterministically, can reproduce your answers, then you, too, must be operating deterministically and are therefore not truly free. (Here, I use the word "deterministically" in a physicist's or philosopher's sense; computer scientists have their own, narrower meaning.) Although the test can never be definitive, the unpredictability of your responses can be quantified by the size of the smallest computer program needed to reproduce those responses. Zeeya Merali gave a nice summary of Aaronson's proposal at the Foundation Questions Institute blog.

The output of this game, as Aaronson portrayed it, would be a level of confidence for whether your will is free or not. But I think it might be better interpreted as a measure of the amount of free will you have. Last year, quantum physicists Jonathan Barrett and Nicolas Gisin argued that free will is not a binary choice, live free or die, but a power that admits of degree. They proposed to quantify free will using quantum entanglement experiments. Freedom of will enters into these experiments because physicists make a choice about which property of a particle to measure, and the choice affects the outcome. Such experiments are commonly taken as evidence for spooky action at a distance, because your choice can affect the outcome of a measurement made at a distant location. But they can also be interpreted as a probe of free will.

If there are, say, 1000 possible measurements, then complete freedom means you could choose any of the 1000; if your choice were constrained to 500, you would have lost one bit of free will. Interestingly, Barrett and Gisin showed that the loss of even a single bit would explain away spooky action. You wouldn't need to suppose that your decision somehow leaps across space to influence the particle. Instead, both your choice and the outcome could be prearranged to match. What is surprising is how little advance setup would do the trick. The more you think about this, the more disturbed you should get. Science experiments always presume complete freedom of will; without it, how would we know that some grand conspiracy isn't manipulating our choices to hide the truth from us?

Back to Aaronson's talk. After describing his experiment, he posed the question of whether a computer could ever convincingly win the Prediction Game. The trouble is that a crucial step—doing a brain scan to set up the computer model—cannot be done with fidelity. Quantum mechanics forbids you from making a perfect copy of a quantum state—a principle known as the no-cloning theorem. The significance of this depends on how strongly quantum effects operate in the brain. If the mind is mostly classical, then the computer could predict most of your decisions.

Invoking the no-cloning theorem is a clever twist. The theorem derives from the determinism—technically, unitarity—of quantum mechanics. So here we have determinism acting not as the slayer of free will, but as its savior. Quantum mechanics is a theory with a keen sense of irony. In the process of quantum decoherence, to give another example, entanglement is destroyed by… more entanglement.

As fun as Aaronson's game is, I don't see it as a test of free will per se. As he admitted, predictable does not mean unfree. Predictability is just one aspect of the problem. In the spirit of inventing variations on the Turing Test, consider the Toddler Test. Ask a toddler something, anything. He or she will say "no." It is a test that parents will wearily recognize. The answers, by Aaronson's complexity measure, are completely predictable. But that hardly reflects on the toddler's freedom; indeed, toddlers play the game precisely to exercise their free will. The Toddler Test shows the limits of predictability, too. Who knows when the toddler will stop playing? If there is anybody in the world who is unpredictable, it is a toddler. What parents would give for a window in their skulls!

Yet no one denies that toddlers are composed of particles that behave according to deterministic laws. So how do you square their free will with those laws? Like cosmologist Sean Carroll, I lean toward what philosophers call compatibilism: I see no contradiction whatsoever between determinism and free will, because they operate at two different levels of reality. Determinism describes the basic laws of physics. Free will describes the behavior of conscious beings. It is an emergent property. Individual particles aren't free. Nor are they hot, or wet, or alive. Those properties arise from particles' collective behavior.

To put it differently, we can't talk about whether you have free will until we can talk about you. The behavior of particles could be completely preordained by the initial conditions of the universe, but that is irrelevant to your decisions. You still need to make them.

What you are is the confluence of countless chains of events that stretch back to the dawn of time. Every decision you make depends on everything you have ever learned and experienced, coming together in your head for the first and only time in the history of the universe. The decision you make is implicit in those influences, but they have never all intersected before. Thus your decision is a unique creative act.

This is why even the slightest violation of free will in a quantum entanglement experiment beggars belief. "Free will" in such an experiment means simply that your choice of what to measure is such a distant cousin of the particle's behavior that the two have never interacted until now.

This is where we get into the second big point that Aaronson made in his talk, about just how creative an act it was. Even if the influences producing a free choice have never interacted before, they can all be traced to the initial state of the universe. There is always some uncertainty about what that state was; a huge range of possibilities would have led to the universe we see today. But the decision you make resolves some of that uncertainty. It acts as a measurement of those countless influences.

Yet in a deterministic universe, those is no justification for saying that the initial state caused the decision; it is equally valid to say that the decision caused the initial state. After all, physics is reversible. What determinism means is that the state at one time implies the state at all other times. It does not privilege one state over another. Thus your decision, in a very real sense, creates the initial conditions of the universe.

This backward causation, or retrocausality, was the "loony" aspect of Aaronson's talk. Except there's nothing loony about it. It is a concept that Einstein's special theory of relativity made a live possibility. Relativity convinced most physicists that we live in a "block universe” in which past, present, and future are equally real. In that case, there's no reason to suppose the past influences the future, but not vice-versa. Although their theories shout retrocausality, physicists haven't fully grappled with the implications yet. It might, for one thing, explain many of the mysteries of quantum mechanics.

In a follow-up email, Aaronson told me that the connection between free will and cosmic initial state was also explored by philosopher Carl Hoefer in a 2002 paper. What Aaronson has done is apply the insights of quantum mechanics. If you can't clone a quantum state perfectly, you can't clone yourself perfectly, and if you can't clone yourself perfectly, you can't ever be fully simulated on a computer. Each decision you take is yours and yours alone. It is the unique record of some far-flung collection of particles in the early universe. Aaronson wrote, "What quantum mechanics lets you do here, basically, is ensure that the aspects of the initial microstate that are getting resolved with each decision are 'fresh' aspects, which haven't been measured or recorded by anyone else."

If nothing else, let this reconcile parents to their willful toddlers. Carroll once wrote that every time you break an egg, you are doing observational cosmology. A toddler playing the “no” game goes you one better. Every time the toddler says no, he or she is doing cosmological engineering, helping to shape the initial state of the universe.

Quantum art courtesy of garlandcannon. Slide courtesy of Scott Aaronson.