1. Is the Brain Purely Classical and Deterministic? 

In classical physics, your brain (along with the rest of physical existence) is deterministic.  Even though you feel you have free choice of your thoughts and actions, classical physics says you do not.  It says your thoughts and actions are doomed to slavishly follow the deterministic, only-one-allowed-future path predicted by classical mathematics.  Many neuroscientists and others say that the working parts of the brain, although small on an everyday scale, are large enough so that only classical physics applies.  Thus they claim we have no real choice, no free will.  We will show that, when examined in detail, it does not seem possible to justify their “classical” argument.

2. The Brain and Quantum Mechanics. 

From a quantum point of view, the brain is extremely complicated, so complicated that there is  no hope of doing any exact calculations.  We can, however, do an approximate calculation which shows that quantum mechanics cannot be neglected in the brain.  That is, we can show that, for an appropriate time scale, the brain wave function contains many branches, many possible futures, and presumably many potential thoughts.

3. The Brain and Thoughts.  

Before doing this, however, we need to sketch how the brain works.  For our purposes, it consists of long nerve cells called neurons.  Each neuron has a long branch on one end that receives electrochemical signals from other neurons, a cell body in the middle, and a second long branch on the other end that passes electrochemical signals on to other neurons.  If the receiving end of a neuron receives enough input from other neurons, an electrochemical wave runs the length of the cell.  In that case, the neuron is said to be “firing.”  Each thought (or emotion or perception or initiation of a bodily action) corresponds to a particular set of firing neurons.  So from a materialist’s point of view, we essentially are our pattern of firing neurons.

There is very little doubt that, once initiated, the electrochemical pulse that moves from one end of the neuron to the other is a classical, deterministic event.  The materialist is likely to conclude from this that the whole action of the brain, and therefore of the individual, is deterministic.  One cannot make this judgment, however, until one looks at the process of the initiation of a pulse.

4. The Synapses, Controllers of the Flow of Thoughts.

The juncture between two neurons is called the synapse.  Each of the perhaps 100 billion neurons in the brain is connected to about 1,000 other neurons.  At the synapse, a firing neuron either passes a neurochemical signal to the next neuron, or it does not pass a signal, with the passing or not passing depending on the complex neurochemistry of the synapse.  If, within a millisecond, a certain number of signals are passed on to a neuron, then that neuron will fire.  Otherwise it will not fire.  Thus what happens at the various synapses—signal passed on or not passed on—is the sole determinant of the firing pattern of the neurons in the brain.  The synapses are the control points for our flow of thoughts.

5. Smallness of the Synapse. Quantum Effects. 

The synaptic gap, the gap between one neuron and the next, is quite small, 3.5 nanometers, which is about 35 (hydrogen) atoms.  The sizes of the adjacent parts of the synapse, where much of the neurochemistry goes on, are also small, on the order of 3,500 atoms wide.  Now one of the peculiar effects of quantum mechanics is that if the volume where an atom might be located (the place where the wave function is non-zero) is initially small, it will spread out in time.  One can use Heisenberg’s uncertainty principle to show that a calcium ion, for example, will spread out to the size of the synapses (not just the synaptic gap) in about .1 milliseconds (see 8 below).  Neural processes in the brain occur on a time scale of a millisecond, ten times slower than the spread of a calcium ion over the whole synapse. 

6. Calcium Ions and States of the Synapse.

To see the consequences of this, we must explain why we used calcium ions as an example.  The reason is that in the complex neurochemistry of the synapse, these ions help to determine whether or not a signal will be passed from the firing neuron to the next neuron.  Because the calcium ion quantum mechanically spreads relatively quickly, the wave function of the synapse in one millisecond’s time will be a combination of passing on the signal to the next neuron and not passing on the signal.  So even though we can never hope to do the quantum mechanics of the brain exactly, we can see from this general argument that there is no justification for saying the brain is a strictly classical, deterministic system.  Once initiated, a pulse is classically deterministic (a single future).  But the initiation process for a pulse at the synapses is not deterministic; on the time scale of neural processes, there will be two possible futures at each synapse—sending a signal to the next neuron, or not sending one. 

7. The Brain Wave Function Contains
Many Thoughts Simultaneously.

The cumulative effect from the many synapses is that the wave function for the brain will be a combination of many, many possible firing patterns, each corresponding to a thought or action.  Whether, or how, “we” actually make a choice (see section IIIE) are separate questions.  But quantum mechanics tells us the choice is there.

8. Spreading Wave Packet for Calcium.

Heisenberg Uncertainty principle

Gaussian Wave Packet

If instead we do a somewhat more “exact” analysis and use a spreading Gaussian wave packet for the calcium ion, then the spread of the wave packet is given by

with  the initial spread of the wave packet.  So if we take  (we guess that the initial wave packet is spread over a distance of 50 atoms), then  sec. 

 Results

In either case, the time for the spread is smaller than the  sec. appropriate for thoughts.  That is, on the time scale of thoughts, quantum effects are important at the synapse.  Therefore it is difficult to argue that the brain is classical and deterministic.

References.

See Mind, Matter and Quantum Mechanics (Springer Verlag, New York, 1993) by Henry P. Stapp for the original work on this idea.