Free Will and Quantum Clones: How Your Choices Today Affect the Universe at its Origin
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.