More on free will, and why quantum mechanics can't help you understand football

 

I’ve had some stimulating further discussion with Philip Goff and Kevin Mitchell on whether quantum mechanics can illuminate the free-will problem. Kevin has responded to our comments here; Philip’s have been on Twitter. Here’s where it all leaves me at this point.

First, here’s where I think we all agree:

(1) Events at the quantum scale can be adequately described by quantum mechanics – for our purposes, nothing more is needed.

(2) There’s no missing “force of nature” that somehow intervenes in matter as a result of “free will”.

(3) The future is not predetermined, because of quantum randonmess: at any given moment, various futures are possible.

Kevin’s argument is, as I understand it, that agents with free will are able to select from these possible futures.

Philip’s objection is that this is not how quantum mechanics works: those futures are determined by the probabilities they can be assigned from the Born rule.

I’m sympathetic to that observation: it isn’t at all clear to me how anything called free will can somehow intervene in a quantum process, however complex, to “select” one of its possible futures.

My objection to Philip’s point was, however, to the scenario he uses to illustrate it – where he decides whether or not to water his plant (called Susan). It seems to me to be ill-posed. I’m averse in general to thought experiments that don’t stack up in principle, and this seems to me to be one.

To calculate the Born probabilities for this situation, you would need to know the complete initial state of the system and the Hamiltonian that determines how its wavefunction evolves in time. Now, it is no good supposing we can define some generic “state of Philip confronted with thirsty Susan”. I’m not even sure what that could mean. How do we know what we need to include in the description to make a good prediction? What if Philip’s cell phone goes off just before he is about to water Susan, and calls him away on an emergency? How much of the world must we include for this calculation? And we’re looking to calculate the probability of outcome X, which quantum mechanics can enable us to do – so long as we know the target state X. But what is this? Is it one in which Susan stands in damp soil and Philip’s watering can is empty? But how do we know that he added the water of his own free will? What if in the initial state he know someone would shoot him later if he didn’t add the water? Does that still count as “free will”? I mean, he could in principle still refuse to water Susan, but it’s not what we would usually consider “free will”. But perhaps then our initial state needs to be one in which Philip has no such thought in his head. Had we better have a list of which thoughts are and aren’t allowed in that initial state? But whichever initial state we choose, we can never do the experiment anyway to see if the predictions are borne out, because we could never recreate it exactly.

My point is that we should not be talking about scenarios like this in terms of quantum states and wavefunctions, because that’s not what quantum mechanics is for. We can run an experiments many times that begins with a photon in a well-defined state and ends with it in another well defined state as it evolves under a well-defined Hamiltonian, and quantum mechanics will give us good predictions. But people are not like photons. Even though fundamentally their components are of course quantum particles obeying quantum rules, it is not just ludicrous but meaningless to suppose that somehow we can use quantum theory to make predictions about them – because the kind of states we care about (does Philip do this?) are not well defined quantum states, and the trajectories of any such putative states are not determined by well-defined Hamiltonians.

It seems to me the distinction here is really between quantum physics as a phenomenon and quantum mechanics as a theory. I don’t think anyone would dispute that quantum physics is playing out in a football match. But it seems to me a fundamental mistake to suppose that the formalism of quantum mechanics can (let alone should) be used to describe it, because that formalism does not involve the kinds of things that are descriptors of football matches, and vice versa. (Philip’s “watering a plant” scenario is of course much closer to a football match than to a Stern-Gerlach experiment.) It’s not just that the quantum calculations are too complex; the machinery of calculation is not designed for that situation. Indeed, we are only just beginning to figure out how to use that machinery to describe the simplest couplings of quantum systems to their environment, and these are probably probing the limits not just of what is tractable but what is meaningful.

Does all this objection, though, negate Philip’s point that free will can’t determine the outcome of a quantum process, as (ultimately) all processes are? In one sense, no. But my point is really that the answer to this is not legitimately yes or no, because I’m not sure the question has any clear meaning. The scenario Philip is depicting is one in which there is some massively complex wavefunction evolving in time that describes the whole system – him with watering can and potted plant – and somehow that evolution is steered by free will. But – and I think this is where I do agree with Kevin – I don’t believe this is the right way to describe the causation in the system.

 I don’t just mean it is not an operationally useful way to do that. I think it is fundamentally the wrong way to do it.

Here’s an example of what I mean. Imagine a tall tower of Jenga bricks. Now imagine it with one of the bottom brick removed, so that it’s unstable. The tower topples. What caused it to topple? Well, gravity and the laws of mechanics. Fine.

Now here’s the same tower, but this time we see what brought it to the state with the bottom brick removed: a child came along and took the brick. What caused it to fall? You could say exactly the same: gravity and mechanics. But we’re actually asking a different question. We’re asking not what caused the tower with the brick missing to fall, but what caused the tower with the brick still in place to fall – and the answer is that the child turned it into the unstable version. The child’s action was the cause.

When we try to speak of free will in terms of microphysics, we are confusing these two types of causal stories. We’re saying, Ah, the child acting is really just like the tower minus brick falling: physics says that’s the only thing that can happen. But what physics says that, exactly? Unlike the case of the tower falling, we can’t actually give an account of the physics behind it. So we just say, Ah, it’s somehow all there in the particles (why not the quarks? The strings, or whatever your choice of post-standard-model theory? But no matter), and I can’t say how this leads to that exactly, but if I had a really big computer that could calculate all the interactions, and I knew all the initial conditions, I could predict it, because there’s nothing else in the system. But that’s not a causal explanation. It is just a banal statement that everything is ultimately just atoms and forces. Yes it is – but at that level the true cause of the event has vanished, rather in the way that, by the time you have reduced a performance of Beethoven’s Eroica to acoustic vibrations, the music has vanished.

(This analogy goes deeper, because in truth the music is not in the acoustic waves at all, but in the influence they have on the auditory system of people attuned to hearing this kind of music so that they have the appropriate expectations. There is music because of the history of the system, including the deep evolutionary history that gave us pattern-seeking minds. So it makes sense to explain the effects of the music in terms of violations of expectation, enharmonic shifts and so on, but not in terms of quantum chromodynamics. You will simply not get a causal explanation that way, but just an (absurdly, opaquely complicated) description of underlying events.)

And you see that this argument has nothing to do with quantum mechanics, which is why I think quantum indeterminacy is a bit of a red herring. Free will – or better, volition – needs to be discussed at the level on which mental processes operate: in terms of the brain systems involved in decision-making, attention, memory, intention and so on.

The basic problem, then, is in the notion that causation always works from the bottom up, aggregating gradually in a sort of upwards cascade. There is good reason to suppose that it doesn’t – and that it is especially apt not to in very complex systems. Looked at this way, the microphysics is irrelevant to the issue, because the issue itself is not meaningful at the quantum level. At that level, I’m not sure that the matter of whether “things could have been otherwise” is really any different from the fact that things only turn out one way. (It could be interesting to pose all this in a Many Worlds context – but not here, other than to say I think Many Worlds makes the same mistake of supposing that quantum mechanics can somehow be casually welded onto decision theory.) Beyond quantum randomness, the notion that “things could have been otherwise” is a metaphysical one, because you could never prove it either way. Best, then, to jettison all of that and simply consider how decision-making works in cognitive and neurological terms. That’s how to make sense of what we mean by free will.

Does quantum mechanics rescue free will?

 

Philip Goff has challenged Kevin Mitchell’s interesting supposition that the indeterminacy of quantum physics creates some “causal slack” within which free will can operate. In essence, Kevin suggests (as I understand it) that quantum effects create a huge number of possible outcomes of any sufficiently complex scenario (like human decision-making), among which higher-level mechanisms of organismic agency can act to select one.

Philip responds that this won’t do the trick, because even though quantum mechanics can’t pronounce on which outcome will be observed for a quantum process with several possible outcomes, it does pronounce on the probabilities. He gives the example of his decision to water his dragon tree Susan (excellent name):

“Let’s say the Born rule determines that there’s a 90% chance my particles will be located in the way they would be if I watered Susan and a 10% chance they’ll be located in the way that corresponds to not watering Susan (obviously this is a ludicrously over-simplistic example, but it serves to make the point). Now imagine someone duplicated me a million times and waited to see what those million physical duplicates would decide to do. The physics tells us that approximately 900,000 of the duplicates will water Susan and approximately 100,000 of them will not. If we ran the experiment many times, each time creating a million more duplicates and waiting for them to decide, the physics tells us we would get roughly the same frequencies each time. But if what happens is totally up to each duplicate – in the radical incompatibilist sense – then there ought to be no such predictable frequency.”

It’s a good point, insofar as it needs an answer. But I think one exists: specifically, Philip’s scenario doesn’t really have any meaning. In this respect, it suffers from the same defect that applies to all attempts to reduce questions of human behaviour (such as those that invoke “free will”, a historically unfortunate term that deserves to have scare quotes imposed on it) to microphysics. The example Philip chooses is not “ludicrously over-simplistic” but in fact ill-defined and indeterminate. I don’t believe we could ever determine what is the configuration of Philip’s particles that predisposes him to water Susan. It’s not a question of this being just very, very difficult to ascertain; rather, I don’t see how such a configuration can be defined at the quantum level. We would presumably need to exclude all configurations that lead to other outcomes entirely – but how? What are the quantum variables that correspond to <watering Susan> or <not watering Susan (but otherwise doing everything else the same, so not cutting Susan in half either)>? What counts as “watering Susan”? Does a little water count? Is watering Susan before lunch the same as watering Susan after? This is not a simple binary issue that can be assigned Born probabilities – and neither can I see how any other human decision-making process is. (“Oh come on: what about ‘Either I press a button or I don’t’”? But no, that's not the issue as far as free will is concerned – it’s ‘Either I decide of my own volition to press the button, and I do it, and the botton works’ or not. And what then is the quantum criterion for ‘of my own volition’? How do we know it was that? What if I was bribed to do it?... and so on.)

Obviously such scenarios could go on ad infinitum, and the reason is that quantum mechanics is the wrong level of theoretical description for a problem like this. We simply don’t know what the right variables are: where the joints should be carved in an astronomically complex wavefunction for many particles that correspond to the macroscopic descriptions. And again, I don’t think this is (as physicists often insist) just a problem of lack of computational power; it’s simply a question of trying to apply a scientific theory in a regime where it isn’t appropriate. The proper descriptors of whether Philip waters Susan are macroscopic ones, and likewise the determinants of whether he does so. At the quantum scale they don’t just get intractably hard to discern, but in fact vanish, because one is no longer speaking at the right causal level of description.

This is, in fact, the same reason why Schrödinger’s cat is such an unhelpful metaphor. No one has ever given the vaguest hint at what the wavefunctions of a live and dead cat look like, and I would argue that is because “live” and “dead” can’t be expressed in quantum-mechanical terms: they are not well-defined quantum states.

I don’t necessarily argue that this rescues Kevin’s idea that quantum indeterminacy creates space for free will. I’m agnostic about that, because I don’t think what we generally mean by free will (which we might better call volitional behaviour) has any meaning at the quantum level, and vice versa. It’s best, I think, to explain phenomena at the conceptual/theoretical level appropriate to it. As Phil Anderson said years ago, it’s wrong to imagine that just because there’s reducibility of physical phenomena, this implies a reductive hierarchy of causation.

You’ll see very soon in Physics World why I’m thinking about this…