Is quantum mechanics relevant in the brain? The primary dynamics of the brain is that there is an electrochemical pulse which travels from one end of a neuron to another. The propagation of this pulse is classical; quantum mechanics is pretty much irrelevant here (as far as we currently know). But the initiation of pulses makes use of the synapses, the small separations between adjacent neurons, and these synapses are small enough—less than a thousand atoms or 100 nm across—that quantum processes are potentially relevant. In fact, using an argument due to Stapp (Ref. 5), we can show that quantum considerations are almost certainly relevant for neural processes. This opens up the possibility that our thoughts and actions are not mathematically or mechanistically determined so we have ‘free will,’

Synapses and calcium ions. The synapses determine whether or not a pulse in one neuron triggers a pulse in the next neuron, and so they control the flow of thoughts. The passing-on or not-passing-on is in turn partly controlled by calcium ions. Classically and simplistically speaking, if a calcium ion is near that edge of a synapse which is next to the synapse of another neuron, •) (, the pulse will be passed on. That is, the positions of the calcium ions, in effect, control the flow of thoughts.

Now the wave function of a calcium ion (or any particle) doesn’t just sit, unmoving, in space; it spreads out. So one way that quantum mechanics can be relevant to the brain is if a single calcium ion spreads out over the whole synapse in a reasonable time. If it does, within a time appropriate for neural processes, then the quantum state of the synapse will be a linear combination of [passing on] (calcium ion near the edge) and [not passing on] (calcium ion not near the edge) the electrochemical pulse. That is, the pulse is simultaneously passed on and not passed on. In that case, quantum mechanical considerations are indeed relevant to the functioning of the brain.

The spread of calcium ions. So the question becomes: Do calcium ions spread out over the synapse in the time, approximately 1 millisecond, relevant to neural processes? To see, we use the Uncertainty Principle
Suppose we have a calcium atom initially centered at the origin and use
From these two equations, we get
where x₀ is the initial spread in the wave function and t is the time of spread.

A reasonable initial spread for the wave packet is 10 nm, and a conservative representative time for brain processes is a tenth of a millisecond. We also have ˜10^-34 and m_Ca=66x10^-27 in mks units. If we put these numbers in, we get x_spread˜500nm, which is more than adequate for the calcium ion to spread around the synapse.

The conclusion is: Because the wave function for a single calcium ion quickly spreads around the synapse, the quantum state of the synapse is a linear combination of passing on and not passing on the pulse. Thus quantum mechanical considerations certainly cannot be ruled out for brain processes.

Free will. Templates. There is a book (Ref. 5) by the Nobel laureate brain researcher John Eccles called “How the SELF Controls Its BRAIN.” Because of the spread of the calcium wave packets, the wave function of the brain is a linear combination of trillions of different possible thoughts and signals for bodily actions. The Mind, if one subscribes to The Mind-MIND interpretation, can ‘freely’ ‘control’ the thoughts and actions by choosing one of those neural states to concentrate on. But the organizational problem, how to pick out just the right combination of firing neurons to cause a particular thought or bodily movement, is formidable (although it is not really not so much more formidable than the classical organizational problem). It must presumably be solved by some combination of the structure of the physical brain along with a set of organizational templates that are indigenous to the ‘non-physical’ Mind.