So, what does this have to do with our feeling of free will? Suppose that you are such a collection of entangled particles existing throughout your brain, nervous system, or perhaps every cell in your body. We’ve already discussed the challenges of maintaining quantum entanglement in such an environment, but, there is a way, in theory. Entangled systems become “One” system in the 3^rd-person quantum description and this manifests as your feeling of being “One” entity in your 1^st person experience. Measurement in 3^rd person is choice in the 1^st, while the eigenstates that result from measurement/choice manifest as memories in the 1^st. The crisscross entanglement generates a nonlinear Schrödinger equation in the 3^rd person quantum description, and manifests in the 1^st person as your “mind’s eye“. This is how you focus your thoughts – how you control where you project your attention. When you focus your mind on something, and direct your thoughts, this is like the part of you near end “B” focusing yourself at end “A”. It could be you choosing to focus onto life choices, onto the possible actions you may take, onto the subject matter you wish to think about, or on sensations you want to detect, for example.

Quantum probabilities always manifest themselves to you as preferences. You are more likely to direct your thoughts to those states with higher state coefficients, that is, you are more likely to direct your thoughts to those things you prefer. You freely choose what to think about. And, once you’ve chosen where to direct your thoughts, the choices you make there, too, follow quantum probabilities corresponding to your preferences. So, your will is free and indeterminant, but it is constrained to follow the probabilities of quantum mechanics – you are constrained to probably do what you want and need to do.

Is this truly free will, though? Descartes famously said: “the will is by its nature so free that it can never be constrained“. But, if we examine our will certain things are very hard to do. For example, it would be very hard to, on a whim, stab ourselves in the gut with a knife. Search your feelings, do you think you can even will yourself to do that? I have a very strong preference to not do this action. The quantum coefficients there are very small. Even though my will is free it is probabilistically constrained. On the less dramatic side, I have a very hard time resisting chocolate. My best strategy is to not even think about eating chocolate. I have made this mistake in the past and felt terrible later. I have learned over time, and, relying on my ability to store long-term memories, my quantum probabilities have adjusted to avoid this trap. Nowadays, I am aware of the consequences of my choices, my preferences have adjusted, and I don’t “go there”. This illustrates how our preferences can be recursively affected. Furthermore, the more I think about chocolate the more tempting it becomes – the mere act of thinking about something can recursively alter the state we are in, change our preferences. The quantum state coefficients may be altered the more and more we think about something. And, once I eat one bite, it becomes almost impossible to not eat more. My choices feel constrained probabilistically to my preferences which are dual to the quantum state coefficients.

Figure 14: Artist’s illustration of the mind’s eye. The focus of our thoughts can feel like a third eye. From Psychology Today here.

Let’s consider a Gedänken experiment in free will. Think about whether you would like to go out to dinner tonight. Let’s suppose in your brain somewhere there is a “button” that, if pressed, will set in motion a chain of events that will lead to going out to dinner. We will defer the discussion of the physical nature of this button until the subsequent section. For now, just suppose it exists. Last, let’s suppose that you feel 50%/50% about it – you are on the fence and could go one way or the other with no clear preference. In your brain, you are using your mind’s eye to think about and explore the idea – focusing your thoughts on this button. This consideration is crudely like you using end “B” to focus end “A” on that button to measure yourself. This is called a weak measurement in quantum mechanics. You make an inconclusive measurement that gives only partial information about the state of the system. It leaves you open to many possibilities without committing to one. Many weak measurements will give you an idea of the quantum probabilities. If you feel 50%/50% it means that the projection of yourself onto that “go-out-to-dinner” button has an aggregate quantum probability of 50%. That is to say, 50% of the probability-weighted states in the quantum superposition that makes up you, projected onto this button, have a value of, say, “1”, meaning go out to dinner, and 50% have a value of “0”, meaning stay at home. Of course, you can choose not to think about going for dinner, and the whole projection onto the button becomes irrelevant. Also, thinking about this choice and its consequences and ramifications can recursively affect the probabilities and alter your preferences too. You can definitely think about something so much you talk yourself out of it, “paralysis by analysis” as it were. Note, however, at the time you do make the decision, if you make it 100 times over, being that you are on the fence each time and under otherwise identical circumstances, you will freely choose to go out to dinner about 50 times – the results of your choices reconcile with the quantum probabilities. Also, we should say that this quantum system takes inputs from the outside world as well. For example, sensors that register sights and sounds as well as your own hunger level influence the state of the system. If you are very hungry, relevant sensors could strongly affect the system near end “B” skewing your preferences to strongly consider focusing on the problem of getting something to eat!

“You can choose a ready guide

In some celestial voice

If you choose not to decide

You still have made a choice

You can choose from phantom fears

And kindness that can kill

I will choose a path that’s clear

I will choose free will.”

– the song Free Will by Rush (1980)

Of course, thinking about the prospect of going to dinner, and actually doing it are two different things. If we make too many weak measurements too quickly we will ascertain the state of the system definitively and collapse the wave function – a strong measurement. If that’s what you want to do – if you choose to push the button – you focus on it sufficiently to activate it. You make enough weak measurements of yourself to reveal sufficient information about yourself to push the button, you make a definitive choice. You make a choice in the 1^st person to push the button, and a measurement is made of you in the 3^rd person by the button. Then, this button triggers a whole chain of events, including pressing other buttons, related to going out to dinner.

A great question naturally arises: can you “game” the system”? In other words, can you do what you don’t want to do? The mere act of thinking about this, however, changes the game. You no longer are just thinking about whether you want to go out for dinner, but are now considering a much more abstract topic. Indeed, you are projecting yourself now onto a whole different button – a “game the system” button!

“Free will is neither fate, nor chance. In some unfathomable way it partakes of both.” – Martin Gardner. Hat tip here for the quote