Further, it should be noted that since relativistic quantum theories (such as quantum field theory) can always be expressed in terms of a local Lagrangian density, it follows that probability mass in such theories always flows locally through configuration space, and therefore that a classical configuration of the system’s (field) variables can still be made to evolve locally in a way that simply tracks the flow of the conserved probability current in configuration space.
The Free Will Theorem, published in 2006 by John H. Conway and Simon Kochen, says in rough terms, that if we (as humans) have free will then so do elementary particles. As you would ordinarily take it for granted that you have “free will”,Â and if you follow their argument, then elementary particles, or, since all of matter is said to be made up of them, matter has free will too. Certainly a spectacular situation, and if you read their writings, I think you will agree that they think it is spectacular too, and they are quite proud of their discovery.
The theorem does not assert that we have free will whatsoever. But if we do then we would not be so free as to withhold the same from those elementary particles; Conway and Kochen’s operative keywords are SPIN, FIN and TWIN. Earlier this year, they announced the Strong Free Will Theorem, which came to my attention and puzzled me quite a lot.
In my experience, it is very hard to cross from science or mathematics to philosophy or metaphysics; in many ways, philosophy and metaphysics are a lot more difficult. In the case of this Free Will Theorem, one might like to perform an experiment to make sure the mathematics corresponds to reality. At the end of section 9, “Historical remarks”, on page 21 of the (earlier) Free Will Theorem article, Conway and Kochen discuss possibilities of such an implementation.
This is because our Free Will assumption requires decisions by a human observer, which current physiology tells us takes a minimum of 1/10 of a second. During such a time interval light will travel almost 20,000 miles, so the experiment cannot be done on Earth.
This is were the following gedanken experiment commences: namely, despite those difficulties, some scientists apply for grants, devise an experiment that can be carried out on Earth, design the equipment, and soon realize that the average person’s free will does not elicit a measurable amount of free will on the part of the elementary particles, at least within their budgetary constraints. They perform some back-of-the-envelope calculations and happily notice a gap: one person in a billion will have sufficient free will.
So they call him up and explain the situation, and ask him whether he wants to participate. Jimi reluctantly agrees after some hesitation. They arrange a time, tell him where the lab his, he arrives, and they show him their machine, explain how it works. They tell him that they regret it is loud and noisy, after all it is the first of its kind. When one of its lamps turns from orange to green, he is to push away at the three buttons that they point out, any way he wants to. They will then compare his choices with the elementary particle’s, and graph the results to correlate the free will. He nods, sits down at the chair that is provided, and they start the final preparations. Finally, the lamp turns to green.
Jimi is not pushing any buttons.
They cancel the experiment, and ask him (quite annoyed), why he didn’t follow the instructions. To which he responds, “Well, I wanted to increase volume of your machine, but I couldn’t find the control.”