Sunday, December 13, 2020

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.

8 comments:

Peter said...

"this argument has nothing to do with quantum mechanics, which is why I think quantum indeterminacy is a bit of a red herring." FWIW, I agree with that.

"the notion that causation always works from the bottom up" can only be the case if there is a bottom. For us, in the middle, where we can have no knowledge of whether there is or is not a bottom, it seems best to think of and mathematically describe causation as working from the middle out. There's a math for that: quantum field theory in the Wightman and Haag-Kastler axiomatic formalisms, in which there are measurements and operations that can be expressed as sums and other combinations of more refined measurements and operations, but there are no smallest measurements.

If there is no bottom and there is noise all the way down, then both classically and QMically the axiom of choice and analysis done properly introduce considerable mathematical difficulties for anyone who wants to say that the bottom (we've just said there is no bottom, but people seem to think they can get away with saying something like "infinitesimals" loudly enough) determines the middle.

Owen said...

"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."

Agreed, and this statement just translates to some form of determinism/compatibilism. There is no room in an emergent theory of consciousness for true free will, not even close. If there were ground-up effects at the quantum scale to the giant waveform of the neurological system as a whole, they would surely be so complex that it could never be understood as choosing one decision over another. It would surely just be more unpredictability.

Having said that, the strictly materialist ideas of emergence also don't make sense on a phenomenological level. I.e., the “Experiential Gap”. There is still something missing, but quantum indeterminacy isn't going to solve that.

Jayarava said...

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

We can make predictions quantum scale events, but we have no adequate description of them. We do not have a good explanation of the measurement problem yet. Without that quantum mechanics is a useful black box but nothing like an adequate description.

You cannot really be arguing that "shut up and calculate" is good philosophy, can you?

Moreover, the Schrodinger equation cannot be solved, even in principle, for any system more complex than a hydrogen atom. In order to deal with deuterium and beyond we have to introduce simplifying assumptions. That these work without us really understanding why is again, fine for physics but bad philosophy.

And please, please, put some moderation on your comments to keep the penis enlargement crowd out!

Peter said...

Definitely seconding the wish for some comments moderation!

Jayarava, in reply to one aspect of your comment, the collapse of the quantum state can to some extent be explained, I think, as a mathematical tool to enable the use of two or more noncommutative operators to generate a joint probability density.
That is:
(1) if we model two measurements using two operators that commute and using simple multiplication, we can generate a joint probability density;
(2) if we model two measurements using two operators that do not commute and using only simple multiplication, we cannot generate a joint probability density;
(3) if we model two measurements using two operators that do not commute and use what I would call a "collapse product", we can generate a joint probability density.

I present the essentials of the mathematics in a talk I gave last week at a workshop in Frascati (remotely, of course), if you care to watch it, starting at 14'10". It's not yet available on the arXiv or in published form. I think from your comment above and from looking at a few of your posts that you may think this approach is too much at the level of description, but I see this as establishing that this mathematical method could equally be used by a classical physicist, insofar as it results in a simpler and more effective construction of physical models, if that classical physicist is not too hamstrung by what is or is not acceptable mathematics.

I should say that I have been trying to persuade Philip that the approach I present in a paper in Annals of Physics 2020 (and also findable on the arXiv), "An algebraic approach to Koopman classical mechanics", includes some tools that would be useful to him in his attempts to reduce the weirdness of QM. This comment is an early attempt to articulate a new aspect of that approach, somewhat directed by your comment but, with apologies, mostly to my own needs and with a very slight background of wondering whether Philip monitors the comments here (I'm not expecting that he does, because if he notices them at all, surely he would delete some of them!) Best wishes.

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