Quantum Mechanics and Free Will

"In their hearts humans plan their course,

but the Lord establishes their steps."     -  Proverbs 16:9

See here for my earlier blog post on the issue of free will from a theological viewpoint.
Disclaimer: My only formal experience with quantum theory is a very introductory undergraduate course. Someone much further from an expert than I one would struggle to find.

Introduction 

We wish to determine whether or not free will exists, so let us toss a coin and let it decide for us.

The coin soars out of my hand high into the air, spinning rapidly; neither of us have any idea whether or not free will is going to exist or not.

Hang on a second, though. The fact that we can't predict the outcome of the toss is a measure of our incapacity more than it is a testament to the universe's fundamental unpredictability. If we knew more about the coin toss (exactly how heavy the coin is, how fast it is spinning etc) we surely could know which side would land face up.

This was the dominant view of physicists before quantum mechanics. All the main theories of the time (Newton, Maxwell, ...) were entirely deterministic in nature; they all said "tell me about a system at a certain time, and I'll tell you what happened before, and what will happen in the future".

If the universe right now contains enough information to predict with certainty what will happen for the rest of its course, then that includes information about everything you'll ever do. On absolute determinism, then, in what sense can free will remain except than as a pitiable illusion?

For the sake of clarity, we henceforth define an action to be free if it cannot be determined, and say that an action is willed if it is a non-arbitrary choice made by some conscious being. So we get for free that determinism definitely rules out free actions.

It is easy to see that it also rules out us willing actions too; on determinism the state of the universe before we were born determines what we do, and we weren't around to will anything then!

Though it is of course true that we could still want things to occur that do, but as Schopenhauer puts it, "we could not will what we willed".

This is contentious philosophical ground, and has severe implications for the way we view religion, truth, and morality. At the turn of the 20th century it certainly seemed that physics and the notion of free will were in conflict, if not outright contradictory.

However, a lot has changed in physics world since then. Now the debate is much more open, largely due to the development of quantum theory, and its introduction of fundamental uncertainty into physical theories of the universe. The aim of this post is to briefly discuss the theory itself, and then explore its implications regarding the plausibility of free will.

Quantum Theory

"If you think you understand quantum mechanics, you don't understand quantum mechanics" - Richard Feynmann

Little hope have I, then, of providing an adequate introduction here, but it seems I have no choice.

Quantum theory says, in brief, that God plays dice with the universe.

Back to the coin toss. Suppose you knew was that the coin toss was fair, but weren't allowed to see the result. The best thing you could say regarding the state of the coin is "According to the information I've been given, the best I can do is assume that the coin has probability 1/2 of being heads, and 1/2 of being tails".

Quantum theory says that, in actual fact, no matter what we know about the system, the best we can say is "the probability of one event is this, the probability of another event is that, ..." until we actually take a look at what has happened.

There might be many possible events, so instead of listing them like this we encode them neatly into something called a wave-function. This tells us about the system, and so might change over time as the system does, and the way it does that is governed by Schrodinger's equation.

Observing the system corresponds to operating on the wave-function. Upon observation, we know that we observe an actual event, and not probability superpositions of events. Thus at this point the probabilities must collapse so that the event that you observe has probability 1, and all the others have probability 0. Mathematically this means the wave-function instantly changes to become an eigenfunction of the Hamiltonian of the system. Take or leave the formalism, it will not be needed.

If we want to observe two facts about a system, we must do two successive measurements (observations). Sometimes the order in which we do these measurements makes a difference to the results we get. This results in Heisenberg's uncertainty principle, which says that there are some pairs of observables that we cannot know simultaneously, like position and momentum. 

A related result tells us that information about any physical system is necessarily incomplete. These are very problematic results to interpret philosophically!

Free will

"I used to be indecisive but now I am not so sure" - Tommy Cooper

We used to think that the universe was predictable. But now we are pretty convinced that it is not deterministic. The possibility of free actions arises from the murky depths of incoherence, but it is not at all clear what we know beyond that.

Quantum theory doesn't abandon determinism completely. In fact, if it did something would have gone wrong somewhere, as science itself presupposes the intelligibility of the universe. Instead, we have moved to semi-determinism; we don't know what will happen, but we do know the probabilities of various events occurring. Or at least the latter are still, in principle, calculable!

This still seems to interfere with free will. We instinctively associate probabilities with randomness, especially when the probabilities are not simply making up for our lack of knowledge.

But randomness, while allowing free actions as we defined them, doesn't allow for free willed actions so easily.

To move us along at pace, I am going to claim:

(i) God exists, and created and sustains everything else that exists.

(ii) Humans are immaterial and eternal souls, that temporarily inhabit material bodies.

(iii) A human soul has free will in that he or she can choose to what state the wave-functions collapse within regions of space-time that their brains occupy.

Rather than defend the truth of these propositions, I would like to instead defend that if free~will does exist in a way that is compatible with physical theories this is the most plausible mechanism by which it would occur. Most of us feel (perhaps by no choice of our own!) that we do have free will, and so to find such a theory would be nice.

Mainstream interpretations

“You say: I am not free. But I have raised and lowered my arm. Everyone understands that this illogical answer is an irrefutable proof of freedom.” - Leo Tolstoy

We have said that until an observation of a system is made, the wave-function evolves according to Schrodinger's equation, but that at the instant of observation the probabilities collapse to give a definite event. However, the physical significance of the evolving of the unobserved wave-function is an area of great philosophical contention.

All we really know is how to use the theory to predict things. The wave-function evolves in the sense that if we observe the system at time t=0, we can leave it until some later t=T and know (by solving the Schrodinger equation at t=T) what the probabilities of observing all possible states is.

Maybe one can cling to determinism by insisting that, upon an observation, the wave-function doesn't collapse.  Rather, the observer becomes part of the quantum system. The necessary consequence of these presuppositions is that the universe itself is a superposition of all possible universes that could have occurred, given the beginning of the universe. If you like, traditional determinism is the trivial special case of this. Free~will probably can't be salvaged from here. 

Or perhaps there never is any uncertainty to begin with. This is not an easy one to explain, and in fact it has received criticism on the grounds of its seemingly unnecessarily complicated nature. But in essence, it postulates that the universe follows a path through the space of all possible universes, guided probabilistically by Schrodinger's equation. This is compatible with God having sovereign free will, but gets tricky when considering multiple locally free agents.

Regarding these theories (for the former is the simplest!), Budziszewski remarked: "In order to avoid believing in just one God we are now asked to believe in an infinite number of universes, all of them unobservable just because they are not part of ours. The principle of inference seems to be not Occam's Razor but Occam's Beard: 'Multiply entities unnecessarily.'"

Consciousness 

"To determine by what modes or actions light produceth in our minds the phantasm of colour is not so easie" - Isaac Newton

If we expect to be able to glean free~will from an interpretation of quantum mechanics, it should be expected that it somehow physically distinguishes between human (and possibly animal) minds, and everything else. Of course, this goes against materialism and notions of complete causal closure.

When you observe a system, what you do clearly depends on what you observe. Thus we see that any quantum mechanical must be functionally causally closed. So we must consider the whole material universe. But everything in the system is decomposable into mere fundamental particles. So who is to say that a given collection of these at any given time qualifies as an observer? 

The case of no observers would lead us back to the previous theories. 

But an alternative suggestion is that human minds (or souls) are actually non-material observers.

Further, as we need an actual (and therefore observed) world to exist for a human to even be created, we must further say that there existed a non-material being (God) "collapsing wave-functions since time immemorial"!

There is an amount of time called a Planc length, which is the smallest time interval that has any physical meaning in current physical theories. Conceivably the universe quantum~collapses every planc length of time in a way controlled by your immaterial mind in various regions of your material brain, by everyone else in their respective brains, and everywhere else by God - or randomly. 

In other words, quantum indeterminacy leaves well~defined fundamental gaps in any theory of this kind. It is in these scientifically unreachable regions that consciousness could act. This should not really be seen as a scientific theory, let alone a good one.  But it is, nevertheless very interesting. 

As a Christian I am convinced that we do have some measure of free will - though as a Calvinist I inhabit somewhat of a superposition of beliefs! - and I believe that God has set up the universe so that miracles are unusual (again, a topic for a later discussion!); that is, that the universe obeys mathematical laws almost all of the time. But without the framework discussed above, the only way one could really justify belief in free will would be to claim that a tiny miracle occurs in our brains every time we make a decision!

What the consciousness interpretation of quantum mechanics does is provides a mechanism by which these mini-miracles could happen, that is consistent with our current body of physical theory, This seems to be the closest thing to a reconciliation between quantum physics and dualism that we currently have. 

Such a theory is essential if we are to ever rid ourselves of the all permeating, dogmatic reductionist philosophy plaguing modern physics, and more broadly reconcile faith and science. In fact, the tension felt here is not between faith and science. It is between faith and reductionism. These are diametrically opposed. One is true; the other false. And currently, the wrong one is dominating scientific thought.

Quantum theory isn't going to disappear any time soon, because it is probably close to representing reality. But I believe it can be reconciled with Christianity, and more specifically, with free will. 

Of course, if I want to say these things with any authority I need to dedicate my working life to studying the theory. 

That's a big commitment. For now, this blog will have to do.

Until next time!

“For you will certainly carry out God's purpose, however you act, but it makes a difference to you whether you serve like Judas or like John.”  - C.S. Lewis