The Synapse as a Quantum Nano Computer

There are at least 100 trillion synapses in the human brain. For comparison, there are about 1 billion "hosts" (Unique devices) on the internet. So there are 100,000 synapses in one brain for all the computers in the world. I compare synapses to "hosts" (computers) rather than "bits" for reasons that will become clear.

In theory, a synapse is either "open" (permitting a signal from the "upstream" neuron to pass to the "downstream" neuron) or "closed" (resting or somehow blocking the signal). Call this state variable S=1 or 0 for open or 0 for closed. So one might naively think of the synapse as a "bit" in a computer analog. Every neuron in the brain is only a few synapses away from any other neuron, so one might think that the brain could be like a 100 billion x 100 billion matrix with the synapse "bit" telling whether the signal passes from neuron i to neuron j. That would be a pretty big matrix, but it would still fail to capture the "state" of the brain. The image leaves out the quantum nature of the "bits", encouraging us to think there is some kind of huge function that could "compute" the next matrix from the last one (erasing free will in the process).

The state of a synapse changes about 5 to 50 times per second. During that time, the synapse "re-computes" its status using a massively complex series of chemical reactions. On this scale, quantum effects are everywhere. It is quite proper to consider the state of the synapse using a Schroedinger wave function. This function (perfectly real but known really only to God) gives the probability of the next state (say, in 20 milliseconds) given the state "now". Both states would involve a mind-boggling array of "inputs" including the state of billions of individual active molecules. The most interesting thing about the "state" of protein molecules (the ones that really count here) are its shape and potential energy. Both of these are well into the influence of quantum effects. You can't really say what the shape of a protein is. It's a superposition. Molecules don't have energy, positions or momentum in the sense that macro objects do.

The quantum variable we are interested in is S. The wave function gives the probability for S being between 0 (closed) and open (1) at some specific time. The wave function "collapses" to either 0 or 1 in any particular instant. The synapse conducts or it doesn't. This cannot be "computed" (predicted), or mathematically modeled even in principle, because:

• It depends on billions of inputs, themselves quantum states (superpositions)
• even classically (ignoring quantum mechanics), the synapse would be characterized by thousands of non-linear equations - unsolvable in principle

One interesting thing about the "synapse" computer is that its state depends on its previous state in fundamental ways - you might say "designed in" ways. In particular, the state is "sticky", meaning that a synapse that passes a signal once is likely to do so again. That's how brains learn. Synapses also send signals "upstream" to the parent neuron, ultimately influencing DNA expression which determines the proteins available for the quantum calculation we are talking about.

Another interesting thing is that the synapse "system" described here can never be described formally as an isolated system in any particular case. That's because we can never say what is and is not part of the system. The synapse requires the constant supply of energy (in the form of glucose or ATP). The whole thing is bathed in active molecules that come and go, such as hormones, neurotransmitters, and enzymes that catalyze the reactions. The list goes on. The problem here is that the Schrodinger Wave equation needs to refer to the same system on each side of the equation, so it can never quite apply as I have sketched above. The effect of this is to add even more indeterminacy to the situation, but not so much as to undermine the usefulness of the approximation.

If we are to consider the synapse as a chemical computer, we should note that individual steps in molecular reactions occur in the picosecond range. The synapse is performing millions of these calculations in parallel and the reaction times depend on classical considerations such as concentration, temperature and so forth. At the scale of the synapse (20 nanometers), it's worth asking if classical parameters matter or whether quantum effects dominate. When considering the effective speed of a calculation, perhaps we should take into consideration the relevance of the outcome. Relevance is exactly what a synapse is calculating. 

There are complications. For example, we cannot assume that passing a signal through the synapse will, somehow, influence the downstream neuron. Ultimately, that depends on many factors, most notably the availability of ions and ATP along the way and how this signal is combined in the neuron's calculations.  The point is that the "matrix" model of neurons influencing or not influencing each other in some kind of binary way just can't work. Your brain is not a computer. It's a network of 100 trillion quantum computers, each performing calculations that cannot be simulated in a computer, even in principle. It's a "thing" of its own, unlike anything else in the world.

Synapses are, of course, just part of the story. Neurons are living things in their own right. They influence each other in many ways besides through axons and dendrites. There are hundreds of different types of neurons. The more you know about the brain the less it resembles some kind of computer.

At least in the human brain, it does not seem plausible that 100 trillion quantum calculations will somehow "average out" to produce predictable ideas and behavior. In fact, our experience is that humans are wonderfully unpredictable and creative. At the very least, there is no reason whatsoever to regard human behavior as being the result of a massive number of determinative mechanical effects. At every instant, we are all surfing on a Schrodinger wave. What's next is anybody's guess.

What's more, our brains influence each other, forming a meta-network of their own. But I'll stop there.