Wednesday, May 31, 2006

Free Will: All the Way Down

I really enjoyed this paper: The Free Will Theorem, by Princeton Mathematics Dept. luminaries John H. Conway and Simon B. Kochen (HT: Clark’s sidebar, which linked to this Garden post, which linked in turn to this Times article).

Using axioms which implement an idealized EPR-style quantum spin measurement experiment (and assuming relativity), the authors set out to prove that:

If the choice of directions in which to perform spin 1 experiments is not a function of the information accessible to the experimenters, then the responses of the particles are equally not functions of the information accessible to them.

They call this the Free Will theorem since we in practice assume experimenters are free to set up the experiment the way they wish. So, the authors are not proving free will exists, they are proving that if free will exists at the human level, then the outcome exhibited by elementary particles will also be free.

The proof seems fairly straightforward once one accepts the earlier Kochen-Specker theorem (it can’t be said that the spin values for each direction already exist prior to measurement).

Following the presentation of the proof, the authors show (by discussing a way to modify Bohm’s theory) that QM is logically consistent if one assumes the assumption of particles expressing free will in a relativistic framework. Next, they relax some of the idealized assumptions to establish the robustness of the result in a more real world context.

The next section discusses how this result furthers the process (earlier marked by the K-S theorem and Bell's Theorem) of making hidden variable theories unworkable. They also argue it is an obstacle for GRW-type collapse models.

Further tidbits:

The authors argue that it is incorrect to interpret EPR-style experiments as meaning there is faster-than-light communication between particles; the particles are entangled as a collective system, but one will not confirm the predicted correlation until the future measurement of the other member of the pair. This is congruent with the perspective of Smerlak and Rovelli’s recent paper which interprets EPR from the perspective of relational quantum mechanics (RQM).

In terms of interpreting quantum mechanics: the authors argue quantum states (between measurements) are merely predictors (with probabilities) of what will happen if various measurements are performed. It is a mistake to ascribe concrete reality to the quantum states. This again is consistent with RQM’s perspective that it is the measurement events which are concretely real. The authors also state briefly that they don’t believe a conscious human mind is needed for collapse, but they don’t discuss in detail what they think is necessary. They think a future physics will explain what sort of “texture” surrounding a system will cause collapse.

The authors offer some philosophical remarks on free will. First, they remind the reader that they don’t claim to prove free will. They say “determinism, like solipsism, is logically possible.” They themselves do subscribe, however, to what a philosopher would call a naïve folk conception of libertarian free will. They don’t see how science could be taken seriously if its practitioners weren’t free to investigate nature by choosing what experiments to perform.

In any case, the linking of free will at the human level to free or spontaneous outcomes at the level of elementary quantum systems is an important result. It is also an especially appealing idea to a panexperientialist like me. While I appreciate the substantial problems which afflict the folk conception of free will, the results of this paper fit with my view that the conscious experience, intentionality, and (at least limited) free agency of human beings are all sourced from fundamental and ubiquitous properties of the natural world.

I also want to comment on a section toward the end entitled “Free versus Random?” It is extremely common to interpret QM as meaning the universe contains a fundamental indeterminism, but it is unusual to say it implies the existence of a fundamental freedom. Here’s a point the authors make in favor of the latter:

“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).”

“Twinned” here refers to the entanglement of two particles. The measurement of the first of the twinned pair enables us to predict the outcome of the measurement of the second, so they aren’t individually random events. But I’m not sure this is a good argument: are we conflating the idea of a particle’s randomness with its independence? I’ll have to give this more thought.

I’m very interested in arguments which support my contention that the worldview implied by QM is richer and much more interesting than just classical physics plus an overlay of randomness. It isn’t just that the measurement outcome is random vs. determined. The quantum measurement event has intrinsically more to it than a classical billiard-ball notion of a causal event. It is an interaction between two systems where one system’s propensity toward an outcome is actualized by the second (measuring) system. I believe this actualization event or process carries with it the raw material of agency (as well as experience).


Anonymous said...

A lot of links to read through but from your summary this is definitely intriguing.

I subscribe to a similar view to yours in regard to panexperientialism and QM.

As always you've dug out some great stuff to read. (I check in every couple of days)


Steve said...

Thanks Richard.
With regard to this paper, I'm hoping to find some expert commentary or critique of it, but haven't seen anything yet.

Steve said...

Actually, a more careful search reveals a few comments on physics and quantum-computing blogs back in April. See for example this post by 'the quantum pontiff' Dave Bacon.

Tom Clark said...

I'm not sure randomness does much to give us the sort of freedom that grounds responsibility, which is usually what people are looking for when they claim to have free will. After all, anything indeterministic that contributes to behavior can't be ascribed to one's character or motives. So it's hard to see how quantum indeterminacy helps to make one responsible. As Hume's fork has it: if things are determined, I don't have free will, and if they are random I don't have free will either.

Nevertheless, interesting stuff at your blog, keep up the good work.


Tom Clark
Center for Naturalism

Steve said...

I agree indeterminism per se can't do the whole job.

Thanks alot, Tom. I've enjoyed your site and appreciate your work.

Mike Wiest said...

Hi All,

I recently looked back through the free will paper. A couple question/comments:

1) How do you interpret their "free state" version of the theorem? It's brief enough that I'm not sure I'm getting it, but it seems to be more powerful (if less provocative) than the free will version. I mean, doesn't it just omit the human free will assumption and get the same result about indeterminacy in quantum measurements? I'm sympathetic to the idea that we have some kind of genuine free will, but obviously that's controversial; and probably most neuroscientists would see no problem with assuming that deterministic brain dynamics decide what experiments we will perform.

2) Objective collapse vs. Lorentz invariance: this result that an objective collapse mechanism breaks Lorentz invariance is very interesting to me. I just wanted to point out that this "obstacle" might be a truth that we have to accept. I mean, as Bergson pointed out, there is neither an arrow of time nor any psychological "duration" in relativity theory. I tend to think that means that relativity theory is incomplete because it can't account for our subjective sense of time. The quantum measurement dynamic would seem to give us an irreversible arrow of time missing from relativity, if we can accept that it is real, objective, ontological.

3) An idea or two for getting past this impasse that says neither indeterminism nor determinism give us freedom:
a) A simulated annealing toy model for how pure randomness can be used for non-random cognitive purposes. In this picture, the system's randomness keeps it from getting stuck in a local minimum sub-optimal solution to a computational problem. If the system bounces into a better state, the system recognizes that it's a more advantageous state and keeps it. So the system's behavior is technically not determined, but it's not random either because there are definite criteria for accepting or rejecting candidate solutions/behaviors. This model might be mildly interesting...but I don't think it gets us all the way to moral responsibility.
b) To try to clarify the authors distinction between twinnable freedom and untwinnable randomness, could we think of freedom as "spontaneous coordination," since it is undetermined but still maintains determinate relations among parts of the system? This doesn't EXPLAIN anything, but at least lets us broaden our conceptual space to include distinct possibilities besides pure randomness and pure determinism.


Steve said...

Hi Mike-
With regard to your 1), I can't respond until I reread the paper. But I wanted to say that I agree wholeheartedly with what you say in 2). This is why I'm excited by a new strand of quantum gravity research which sees a causal network of quantum events as fundamental, and sees relativity (as well as the matter fields of the standard model) as emergent. Causality and one directional local time would be real and basic.

3a) This kind of attractor model with randomness and local minima/maxima is interesting, but there may be a limit to how useful it is if we ponder how to build the whole system up from the ground level. But your 3b) idea of spontaneous coordination may be a good way to think about how a quantum measurement works...

Mike Wiest said...

Hi Steve,

1. OK, the "free state theorem" is tabled.

2. Won't you tell me what this new strand of quantum gravity is called? Is it renormalizable or finite? Is it related to the relational interpretation of quantum mechanics (which I'm just starting to learn about)? Dmitri Nanopoulos has a string field theory story about the emergence of time...(a popular account on the web is called "As Time Goes By.")

3. a) I think I get your point about the "ground level"--it would seem there is no functional organization that corresponds to a simulated annealing algorithm down there, so our panpsychist theory would never get off the ground. But then again, we might think of the quantum mechanical path integral that minimizes the action in these terms: that basic quantum dynamic evolves the system according to global "optimality" criteria rather than deterministic local mechanisms. (Maybe the path integral is what I should have suggested from the start.)

In this paper Behera constructs a quantum model to describe eye movements in a saccade-to-target task:

It's an example of how behavior can be adaptive even though it is stochastic (and claims to model the phenomenon better than classical Kalman filter models). This other paper describes a flexible motor coordination algorithm that uses "quantum clustering" that seems closely related to the classical simulated annealing paradigm:

Again, these examples neglect the moral responsibility dimension, but do show how adaptive behavior could be technically indeterminate even though guided or constrained by definite goals, desires, or reasons.

3. b) I've wondered whether the randomness of quantum mechanics could all be accounted for in terms of non-local EPR type connections. Even if that can't be the whole story, "spontaneous coordination" could refer to situations in which dynamics were determined by global, delocalized or distant factors, so they necessarily APPEAR random to a local observer. Then we might be able to build a story about how non-local factors amount to "reasons" or "motivation" to act in a certain way, again giving us a way to see unpredictable adaptive behavior as distinct from random behavior.

I don't know how you feel about the idea of randomness, but I feel the power of Einstein's and Leibniz's strong feelings that nothing happens without a cause. The idea of randomness seems like it should express our ignorance rather than an intelligible feature of objective reality. Now, I'm aware that we have been told for decades that quantum randomness is genuine and irreducible, and we have all gotten used to it, and we talk smugly about Einstein's quaint mental inflexibility. But as far as I can tell the basis for this is Bell's proof against "hidden variables." But the proof of course is about LOCAL hidden variables, so it seems we are free to contemplate non-local hidden variables, although I don't think anyone knows HOW.

BUT, I wonder if this free state theorem (or the free will version) have something to say about my conjecture that all the randomness might go away if we knew all the non-local entanglements (which incidentally would extend to future and past times as well, so "free will" might still be a meaningful concept in this kind of deterministic universe, because it's locally indeterministic!). I suspect it might prove me wrong...but I can't quite see that--can you?

Steve said...

1) From a quick read, I think the free state version just replaces the parameters freely chosen by the experimenter with parameters chosen in an unspecified way. Either way the outcome of the experiment cannot be deduced from the information "available" to the system (as defined). In this version, I think the model is just an extension of the Bell and K-S no-go restrictions on hidden variable theories without the distracting free will talk(?).

2) There are several research efforts in this strand: Causal set theory, quantum causal histories, causal dynamical triangulations and Lloyd's quantum computing inspired model. Here are the series of my posts with links to relevant papers:

BTW, I have started to read a couple of the Nanopoulos papers - thanks.

3) Thank you for those links as well.

While we can't evidently rule out non-local hidden variable theories, they seem to need to be very contrived to do the job. I'd rather accept measurement events as implementations of a new kind of causality. While probabilistic, its not just classical mechanics with some randomization. Measurement is a two-sided (or more) interaction where the both sides have a propensity toward an outcome involving the other and come together to actualize the outcome, rather than the one-sided billiard-ball impact of classical thinking (whether strictly deterministic or stochastic).