This post originally appeared in longer form at Bob’s place. There’s a lot of meat here; I recommend biting it off in small chunks.
“Of course I believe in free will. I have no choice.” —The Salon Interview, 1987, Isaac Balshevis Singer
“There is no evidence for determinism.” —Princeton Lectures, John H. Conway
“Philosophy is too important to be left to philosophers” —Unification beyond the Core, Frank Wilczek (also attributed to John Wheeler)
“Does it even matter if God plays dice?” —Rachel Thomas’ Plus-math Interview of John Conway
“…[D]early beloved…be not disturbed by the obscurity of this question; I counsel you first to thank God for such things as you do understand; but for all which is beyond the reach of your mind, pray for understanding from the Lord, observing at the same time peace and love among yourselves…” —On Free Will and Grace, St. Augustine of Hippo
In one of the later Foundation novels, Isaac Asimov envisages a world, Gaia, in which a super-conscious mind pervades the world, from the smallest virus or rock to the humans (and robots). In such a world it would be natural that quantum entities have free will, and there would be nothing remarkable in the Conway-Kochen Free Will Theorem:
It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. (The Strong Free Will Theorem, John Conway and Simon Kochen.)
See Rachel Thomas for a rigorous proof. Or read John Conway’s six Princeton lectures on his Free Will Theorem. I should note that Conway does not claim his Free Will Theorem disproves determinism; indeed, he says there is no way to disprove determinism, despite the fact that there is no evidence for it.
Here I use the Free Will Theorem (abbreviated as FWT) as a springboard to discuss several issues in interpreting quantum mechanics, namely how randomness and consciousness might enter into interpretations of quantum mechanics. (Fear not, gentle reader–this will not be a “What the Bleep” presentation, or a jump into Eastern mysticism.)
What do Conway/Kochen mean by “free will”? Both for the investigator and for particle system they mean that the choice–what is done–does not depend on previous history. A more conventional interpretation might be that free will is the ability to freely choose amongst several options. The term “freely” is susceptible to a number of definitions. (As with Justice Potter Stewart’s definition of pornography, “I know it when I see it”.) In his Princeton lectures and interviews for Rachel Thomas, Conway is quite emphatic that this freedom is not just “randomness”.
To show how randomness might enter, he sets a backgammon tournament as an example. The tournament director casts all the throws of the dice the night before the tournament, and then calls them out sequentially as each game is played, so that there is a level playing field for each contestant.
An example more familiar to me is that of a duplicate bridge tournament. At each table, four hands are dealt out randomly and teams rotate from table to table, so that (eventually) each team has played at each table with the same dealt hands. There is a predetermined initial lay of the cards, but the players are free to deal with the sets of hands as they will. (Is this an example of what philosophers call “compatibilism” in free will?)
Conway strongly argues that the FWT forbids randomness as an agency, whether occurring at the event or predetermined:
That’s why it doesn’t matter if God plays dice with the Universe, or not. Even if we allowed random numbers into the Universe, which I’ll think of as God’s dice, that’s not sufficient to explain the lack of pre-determinism in quantum physics.
I have a problem understanding this assertion. Granting that the FWT shows that the particle response cannot be predicted by a function involving past history, how exactly does this dispense with pseudo-randomness, predetermined before the world began? What can we learn from physics, in general, and quantum mechanics, in particular, to understand Conway’s argument?
Let’s consider first “random noise” in electronic devices, my old friend from nmr spectroscopy and MRI. Such noise can be characterized by mean square amplitude and correlation times, which in turn can be related to physical parameters. Molecular motion candidates for randomness also obey functional relationships. I’ve cited these as examples that don’t contradict Conroy’s argument about predetermined randomness. Can the reader cite others that might? I can’t.
If we turn to quantum mechanics, the state function, which most generally can be put as a superposition of basis states (e.g. “Schrodinger’s Cat“), evolves deterministically. The randomness comes at measurement, when the state function collapses, except for that basis state which gives the measured result. Chance/randomness for the measured result comes from the component nature of basis states, and should be distinguished from weighting in a mixture of states (also see Quantum divine intervention). Quantum Mechanics does not include this state function collapse on measurement as part of the general theory, and thus results the so-called Measurement Problem.
Amongst the various interpretations and alternative theories which attempt to resolve the measurement problem, I’d like to focus on two: 1) the relation between the observer, consciousness and measurement in quantum mechanics; 2) many worlds/many minds (relative state theory). From the earliest days of quantum mechanics, the great thinkers–Von Neumann, Wigner, Schrodinger–have posited that the final step in the measurement process was observation by a mind, a consciousness, and thus the mind and quantum mechanics were entwined. The delayed choice experiment adds weight to this belief, I believe.
There are many physicists (not abashed by the popularization of this notion in quantum leap science fiction) who subscribe to the Many Worlds interpretation of quantum mechanics that at each measurement one option is made apparent and the rest branch (into alternative universes; or alternative minds?).
With John Wheeler, I believe there is a participatory universe created by the observer, by conscious minds (ours? God’s? both?). The free will of the quantum entity is our own free will. There is an infinitude of possible universes and our ego, our consciousness traverses these as it makes choices. If there is a universe where we measure the particle going through one slit, there is another (with other conscious minds) where it goes through both. Such a view resolves a conflict between free will and God’s omniscience and omnipotence–if God knows what our future actions will be, how can our will be free? And the answer would be a type of Molinism, God is aware of all possible counterfactuals, but they are only counterfactuals for our mind, our ego, not for God.