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I suspect this question deserves to be closed on a number of grounds, but I am posing it anyway in the hope that some of you might find it interesting (most of the near duplicates were asked some years ago, so with luck you will have forgotten about them!).

John Bell famously proposed a test to determine whether the effects predicted by quantum theory could be the result of local hidden variables. Has there been any systematic work to develop analogous tests to rule in or out the possibility of free will? It seems to me, superficially at least, that there is a parallel, in that either things akin to hidden variables are driving our decisions or they are not.

I realise the question assumes an agreed definition of free will, but I am happy to leave that aside.

Marco Ocram
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  • A question would be more complete, if a brief description of Bell's test is included. Also, it seems to imply a specific definition of free will, whereas there are many. E.g., I consider it as a non-issue, since determinism is not equivalent to predictability. – Roger V. Mar 21 '23 at 10:01
  • @RogerVadim those are great points. I'll try to update the question later today if I can free-up some thinking time. – Marco Ocram Mar 21 '23 at 10:05
  • There can be no such theorem. Free will has nothing to do with physics, there are no variables or equations. Besides, any valid definition for free will would tell for certain whether it is a real or an imaginary phenomenon. If you need to rule out or in the possibility of free will, you have an invalid definition. – Pertti Ruismäki Mar 21 '23 at 11:04
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    The Conway-Kochen "free will theorem" implies, according to the authors, that "if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe." They sort of axiomatize what "free will" is. – Conifold Mar 21 '23 at 12:25
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    Clever to try and preempt question closure and requests to clarify "free will" - but I don't know if you can really "be happy" to not define "free will" :-) The penalty is that the discussion might be vague or unproductive :-) – Frank Mar 21 '23 at 14:21
  • @Frank Ha! Mea culpa! Yes, I am guilty as charged. I really should have made the question longer, and included something to the effect of 'assuming free-will means x, y or z', but I didn't have time. I might extend it later if I get the chance. – Marco Ocram Mar 21 '23 at 14:23
  • That kind of test may be possible, maybe there is something in the literature in experimental psychology? But even if it is possible or has been tried, the results may be open to interpretation since humans and psychology are much more complex than the particles to which Bell's theorem applies. – Frank Mar 21 '23 at 14:23
  • Maybe you could propose such a test as a thought experiment, and we could see how it would work or where it would break down. – Frank Mar 21 '23 at 14:27
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    I think it's going to require at least some degree of definition of free will. Testing if something exists requires you have at least some vague idea of the properties. – Boba Fit Mar 21 '23 at 14:30
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    Two points a) contrary to Roger Vadim's comment, determinism does imply predictability and b) Bell theorem only rules out local hidden variables. Theories with non-local hidden variables like Bohm's theory is compatible with Bell inequalities. – Nikos M. Mar 25 '23 at 18:38
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    I guess all we need is a reliable way to generate two intricated people, take them far away from each other, check what one of them does and see if the other one does the opposite... – armand Nov 11 '23 at 00:22
  • @armand ingenious +1 ! – Marco Ocram Nov 11 '23 at 07:03

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When I first read this question I was quite dismissive. However, I re-read The Emperor's New Mind by Penrose in the last week. Now I'm pausing to consider.

The basic idea of Bell's theorem is that, for certain specific types of measurement, it is possible to distinguish between quantum mechanics and a very broad range of deterministic theories called "hidden variable" theories.

This type of theory says that reality is really deterministic. It's just that there are control factors that we cannot see. These factors, if we could see them, would determine the outcome of experiments that, in quantum mechanics, are said to be randomly selected from a distribution. The control factors are called hidden variables.

Bell's theorem allows us to perform experiments that distinguish between quantum mechanics and hidden variables. There are situations that are physically possible, in which any hidden variable theory will predict results that are different from what QM will predict. And, in several well known experiments, QM has been shown to be the "victor."

Penrose's thesis is that consciousness can not be algorithmic. That is, he claims that digital computers, being entirely deterministic, will not be able to produce the equivalent of human thought. He then speculates (in a manner I found interesting) about how it could arise in matter such as brains. One of the speculations he proposes is that quantum mechanics is required for human consciousness.

Some of the issues Penrose touches are things such as Goedel's theorem and self reference, the Turing test, existing tech w.r.t. AI, etc.

One section of the book deals with measurements of nerve impulses in various situations, including direct stimulus of the brain of volunteer subjects. There are some unusual results about the time of build up of a nerve signal (indicating the subject is mentally preparing for an action) as compared to the time the subject reports preparing. And these are then compared with the subject's response to surprise stimulus, with the result that there is very much less prep time. This seems to indicate that preparation takes longer than we are aware of, but is not always required. Thus, quite ironically, indicating that a substantial part of consciousness is unconscious.

There is a great deal more than I am explaining, but this post is already growing.

As to free will and a "Bell's test": It would require a specific theory of what constituted free will, and how it connected to matter. That is, it would not be a context free test with Result A meaning free will, Result not-A meaning no free will. We could only test a specific hypothesis.

For example: Suppose we speculate, along with Penrose, that free will arises due to quantum mechanics. (I still have the problem that I have not given any useful definition of free will.) In principle we could test this speculation by attempting to construct a device explicitly based on (somewhat) hidden variables. That is, a completely deterministic device such as a digital computer. If we could p+roduce a digitial computer device that could exhibit free will (to whatever definition we have yet to supply) then it would put a lot of pressure on the speculation that free will requires QM.

BillOnne
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    If you refer to Libet-style experiments, this interpretation has been debunked since 2012, see free will and Libet experiments – Nikos M. Mar 25 '23 at 19:08
  • QM is not really a victor. Experiments demonstrate that 3 properties of Bell's theorem really cannot hold at the same time (universe being real, local and freedom exists in choice of measurement).

    QM assumes freedom and localism, and abandons reality (state of the universe is not hidden and then observed, it just does not exist).

    QM says measurement creates reality. It is as crazy as it sounds. The cat is both dead and alive and measurement made it really dead (or really alive). Local realism is a possibility with the experiment results, but then there is no freedom in our measurements.

     – Looft Aug 01 '23 at 23:14
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I recommend looking at the free will theorem of Conway and Kochen. Quantum entanglement has been cited as an example of consciousness at the quantum level. Some panpsychists propose a form of realism in which matter and consciousness are inextricably linked.

Meanach
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I don't know for free will, but there are several theories for consciousness that proposes testable mathematical formulas. I am not betting on any one of them but am aware of 2: Integrated Information Theory (IIT) and Global Working Space Theory (GNWT). The proponents of both have agreed to an "adversarial scientific collaboration" to test their rival theories by an independent lab. However, the collaboration soured recently, after the publication of the initial results, that apparently slightly favored the ITT. The GNWT guys have called the IIT pseudoscience...

I could try and dig a description of both theories, if anyone is interested. But it's all over the interwebs.

Olivier5
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You should not be happy to leave the definition aside. It is totally impossible to discuss anything, if the subject has not been clearly defined.

Once you have settled on a valid definition, you have already ruled out or in the possibility of free will. No valid definition defines free will as a possibility.

Some definitions define free will as an impossible imaginary phenomenon.

Some definitions define free will as a real everyday phenomenon.

In either case there is no need for testing.

Pertti Ruismäki
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