What sort of models of physical reality are compatible with free will?

Question

Metaphysical subtleties aside, I'm willing to consider free will as a solid experimental fact. If we accept this premise, we can rule out the models of physical reality that are not compatible with free will. For example we can rule out:

• Deterministic models (e.g. classical physics).
• Non deterministic models entirely driven by pure randomness (e.g. random quantum collapse).
• Models entirely driven by an external entity (e.g. God makes all decisions).

What is left?

Comments

How can you rule out determinism? Free will doesn't mean doing something completely arbitrary, but doing something from a motivation that may be unrelated to the current circumstances but still is usually determined by the past. 

To answer your question in the context of physics you'd have to give a definition of free will that refers only to physical facts and not to unphysical entities like mind.

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@ArnoldNeumaier - I don't know what "unphysical entities" are (sounds like a self-contradictory concept), so to me the mind is a (poorly understood at this moment) physical entity. That my physical mind now chooses to add the off-topic statement "Juventus won 2-0 against Monaco last night" is a physical fact (you can verify it).

I agree that free will doesn't mean doing something completely arbitrary (random), in fact I ruled out also my second category (Non deterministic models entirely driven by pure randomness (e.g. random quantum collapse). Now, if I rule out also my third category (doesn't sound like free will to me), I don't see what is left.

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An unphysical entity is anything that cannot be completely described in terms of physics. To make free will a physical entity you need to give a model of free will, i.e., say how it is expressed in terms of classical or quantum fields or N-particle systems. 

I know how to do this in principle for a brain, so a brain may be considered to be a physical object. But how to do it for ''will'' and for ''free''??

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Re "To make free will a physical entity you need to give a model of free will, i.e., say how it is expressed in terms of classical or quantum fields or N-particle systems."

That's what I am asking! What physical model based on fields and particles can support free will, defined as ability to make choices that are a) not uniquely determined by the past, b) not random, and c) not uniquely determined by another entity?

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What you are asking is not the same as what is required for making the question a physics question. Without having already a specification of what free will means in physical terms, the question is metaphysics, not physics. Only with such a definition given we'll know what you mean by free will in a physical context, and then one can ask whether a particular kind of dynamical system is compatible with such a definition. 

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Let's try, how about this:

Free will is a property of a physical entity whose evolution is: a) not uniquely determined by the past, b) not random, and c) not uniquely determined by another entity.

Conway and Kochen seem to imply a similar definition in the strong free will theorem.

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Well, this defines something and excludes by definition the three items in your question. And it leave open the question, why this something deserve the name ''free will''. I think a physically and philosophically sound definition should first define ''will'' and then define a condition under which this will should be called ''free''.

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Given this definition, my question can be formulated as just "Does free will exist?" or "Does anything in the universe have free will?"

A problem with "free" and "will" is that these terms are used in everyday language, and any definition that is usable in physics would deviate from popular usage. As you say, it's questionable if this definition deserves the name "free will." In fact, this definition allows to think that a chaotic system goes one or another way near a bifurcation because it freely wills to go that way.

I can reformulate the question without using "free will":

Does a physical entity exist whose evolution is: a) not uniquely determined by the past, b) not random, and c) not uniquely determined by another entity?

What do you think of Conway-Kochen theorems?

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What do you think of Conway-Kochen theorems? - a blind alley

If you want your original question to mean the question in your last comment, you should add this to your original post, so that one can address it in an answer.

Answer 1

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Let me first address what happens when you try to grasp free will "as a solid experimental fact". I will then also go on and provide a physicist version of a classical philosophical argument about free will in a wider cosmological sense.

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Let us define pure free-willness of a phenomenon as the extent to which it is independent of initial conditions (or the completely idealized preparation of the system, possibly including a human). I.e., your choices are determined by circumstance and motivation, but if we want to have purely free decisions which cannot be planted into our minds from the outside, there must be a factor X which is not determined by any conditioning.

Now take a look at it from the point of view of the scientific method: would any empiric construction of a theory be able to distinguish between free-willness and randomness? No, it would not. Pure free-willness and randomness will be the same thing in any strictly scientific theory. There might be an ontological distinction between free-willness and randomness, but it is not, by its very definition, accessible to the scientific method.

So, theories which allow for the ontological postulation of free will are those which, at least for now, contain a fundamentally random, undetermined element. This was also the basis of the idea of Roger Penrose to somehow link the element of randomness in quantum mechanics with the free will of the human brain.
 

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However, there is a loophole which allows for free will even in a purely deterministic theory, and that is to zoom out on the whole cosmology and realize that the scientific method fails at that level. There is no experimenter which determines the given conditions in the universe to test the outcomes. Even if someone, in a monstrous hypothetical scenario, were to raise and "program" a child to a certain behavior, they would never have complete control of their conditioning. If, then, you erase the extremely conventional and arbitrary distinction between "an individual" and "their environment", the behavior of the child has the same "freeness" as its conditions.

To give a concrete example: you go to your favorite bakery to buy a croissant and the baker Jacques smiles at you while handing you the croissant. You may ask yourself: why did Jacques smile at me today? And you might say: well, because it was a sunny day and he knows me since I have been going there, also he is a human and as a typical human he likes sunlight and company, and humans have developed like this because... This allows you, in principle, to construct a deterministic chain of argumentation, but ultimately does not allow you to explain why these unique conditions determining Jacques' smile have come to be.

Getting a little bit more into physical terms, if we believe that the evolution of the universe is in some sense "unitary", that is, no new information is created by the time evolution, Jacques' smile has always been "out there" in the initial conditions of the universe. But the initial conditions of the universe are undetermined by the scientific method or any physical law in the classical sense. You can thus say that these initial conditions are "free". In this sense, if you ask about Jacques' smile in a cosmological frame, it is as free and undetermined as can be.

(I just want to repeat that I very much realize that this is a notion which is strongly different from the intuitive idea of free will of the totally distinct individual vs. the totally distinct exterior universe.)

Comments

Nice answer (even if the topic is philosophical, which might not be appropriate for this site). To follow up on your last comment, do you think there is a uniquely 'human' aspect of free will, that would distinguish it from, say, the analogous property of a hypothetical life form with a completely different physical structure? On a related note, do you think that an individual's experience of observing their environment consistently at every moment of time (as opposed to another branch of the multiverse), despite being part of a macroscopic quantum state of the universe, could be relevant to the topic of free will?

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mmm... free will is operationally indistinguishable from randomness, very interesting point. I'll think about it some more before upvoting the answer.

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Now take a look at it from the point of view of the scientific method: would any empiric construction of a theory be able to distinguish between free-willness and randomness? No, it would not...

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I am not sure about this claim. Surely, if we mean by the latter "quantum randomness" it can be distinguished from the existence of a certain factor "X" which for me sounds like very much a "hidden parameter" of the system.