William M. Briggs

Statistician to the Stars!

Quantum Mechanics & Free Will: Guest Post by Bob Kurland

Quantum mechanics and duplicate bridge share the same idea of randomness

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”.

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.

Quantum Measurement

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.

Enter Minds

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.

16 Comments

  1. Briggs

    February 4, 2014 at 9:13 am

    Only a side comment, but I had no idea about those kind of backgammon and bridge tournaments. I love them!

    Terrific illustration that random means unknown. I’m stealing these ideas forthwith.

    I’m so delighted by this that I haven’t fathomed whether God could have picked out, “in advance”, all the “random” outcomes. At first blush, why not? The idea that the counterfactuals are propositions and not actual “worlds” I find especially pleasing. Not a great argument in its favor, naturally, but that is infinitely more parsimonious than the alternative.

  2. Didn’t “they” make a movie with this as the underlying theme…Avatar…

  3. Matt Lewis (@_scarymatt_)

    February 4, 2014 at 11:43 am

    Neal Stephenson’s Anathem does some exploration of the many worlds hypothesis as both ego traversal and physical travel between the universes. It’s occurred to me that a similar phenomenon (ego traversal) could explain prescience in the Dune series.

  4. Matt, thanks for your comments. With respect to the notion that counterfactuals as propositions, rather than “actual” worlds, is a more parsimonious take, I would agree. But does God need to be parsimonious?

  5. Ken,Matt Lewis: There was a great TV series, “Quantum Leap”, that explored the Many Worlds notion, with Scott Bakula and Dean Stockwell. See http://en.wikipedia.org/wiki/Quantum_Leap or the many entries from a Google search.

  6. Briggs

    February 4, 2014 at 12:01 pm

    Bob,

    Nope. But I quail at the idea that there are billions (trillions? more?) of Briggses who keep branching off me each time a wave function must “collapse.” The physicality of MW seems to be the polar opposite of idealism, which posited all is thought. The idea you outline is in between these two extremes.

  7. I’m with Omnes on this: the wave function does not “collapse” on measurement, it is supplanted by additional information derived from the measurement. The map is not the territory, and the wave function is not the object being measured. A wave function is epistemological in nature: it says as much as we can know about the properties of the world, it does not replicate the properties of the world in itself. It is a category error to take the properties of a description as identical to the properties of that which is being described.

  8. Jupp, I liked the coment from JT and its true.

    The delayed choice corrolates with what I persive as observed reality, is a function of the past, and is been reproduced in the “present” as the Now.

    Scarey, hehe, we create what we persive.
    No wounder people getts freeked out when the bounds of the process, mentioned above, is been manipulated/interfered with, by warious means.
    This is where I belive, the future lies.

    Our ability to interface with “machins” and/or matter in realtime, will not ocure before we fully ynderstands this process.
    Like the movie Elysium.
    I belive thats possible, but the “code” the process plan and its function is stil in the dark.

    peace

  9. As my old stat perfesser used to say, “Random is another word for ignorance.”

    There is no such thing as “random” in the real world. Random is a concept, not a reality. Even the concept is suspect. Random cannot be truly “generated” even by the most sophisticated computers in the world.

    The duality of random vs. determinate is a false one. They are not two sides of a coin. Neither actually exists in the real world.

    As to the quantum world, it is ignorance, not mythical randomness, that is mainly in play in the Physics Dept.

    As to free will, I command you to stop reading this note now.

  10. Time Travel — It’s been tested & demonstrated false:

    On June 28, 2009, Stephen Hawking hosted a party for time travelers, but he sent out the invitations only afterward.

    No one turned up.

    He offered this as experimental evidence that time travel is not possible.

    “I sat there a long time,” he said, “but no one came.”

  11. RE: “The free will of the quantum entity [whatever that is] is our own free will…”…’Counterfactuals, God,….’

    Ponder this (copied from Futility Closet):

    If all moral obligations originate from God’s commands, then so must our moral obligation to obey these commands. He commands us to obey his commands. But what is the moral reason to obey that command? An earlier command? What is the reason to obey that?

    Do we have a moral obligation to follow God’s commands because we love him? This implies that we ought to love him. Why? Because he commands it? That’s a circle. Because he’s good? That seems to mean only that he follows his own commands — or else that goodness is a standard independent of God.

  12. RE: “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?”

    That derived from:

    “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.”

    That last perspective is a core plot feature plagiarized right out of a Dean Koontz novel — I forget which, but from there it came & anybody can check it out with little effort for themselves…

    AS FOR THE omniscience and omnipotence of God knowing what our future actions will be, how can our will be free?

    THAT was addressed in an episode of the X-Files (at least I’m pretty sure it was an X-Files episode) — the dilemma, properly understood, is one of broad context…really really broad context: a deity figure, or just a deceased loved one coming back for a chat, has the ability to envision all possibilities of any choice one might make. For us mere mortals the finite possibilities of a chess game might seem impossible, but that’s child’s play for a spectral entity, who can see, comprehend and grapple with the infinite–not infinite universes to contain the corresponding possibilities, just a “mind” capable of whittling them down as we make our endless choices…until we drop dead, at which point the outcome is certain. It’s all really quite simple, conceptually…the trick is just making sure one watches the right sci-fi movies/reads the right sci-fi books and everything quantum becomes un-mysterious’d (or “demystified”…for those preferring real words).

  13. Ken, thank you for your comment. I don’t read Dean Koontz and have never watched the X-files, so it must be that universal mind reaching out its tentacles.
    Bob

  14. yo, JT…There are lots of interpretations/theories of QM that attempt to deal with the measurement problem/collapse. One variety of such are modal interpretations, the first of which was by a mathematical philosopher, Bas Van Fraasen. Van Fraasen is an empiricist, so he doesn’t credit the reality of the state-function… From the Stanford Encyclopedia of Philosophy article on modal interpretations of QM:
    “It relied, in particular, on a distinction between what he called the “dynamical state” and the “value state” of a system at any instant:
    The dynamical state determines what may be the case: which physical properties the system may possess, and which properties the system may have at later times.
    The value state represents what actually is the case, that is, all the system’s physical properties that are sharply defined at the instant in question.
    Like Omnes interpretation, that doesn’t appeal to me; I like the notion of QM and mind intertwining, but as far as I know there’s know scientific “proof” for any interpretation–Operationalists are on the soundest ground… The calculations and predictions are really good, so why worry about an interpretation?

  15. This is, of course, incompatible with holographic principle, the theory that a description of a portion of space–time is determined by conditions on its boundary. The future is a portion of space–time whose boundary is the present. That means either the premises of the Free-Will Theorem are false or the holographic principle is false.

    I am neither a physicist or a philosopher so I’m not taking sides right now.

  16. Joseph, interesting comment.

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