What about the experiments of Libet and others? How do we reconcile the deterministic, predictive experimental results of neuroscience with the indeterminant, crisscross quantum entanglement description of free will presented here? The short answer was provided by the experiments of J. Haynes, B. Blankertz and M. Schultze-Kraft who had patients play a game against a computer interfaced to read their EEG activity real-time, “Point of No Return in Vetoing Self-Initiated Movements” (2015). Contrary to the conclusion of Libet and others, the team showed that you can still willfully override the RP and outdo prediction by the computer up to a point of no return just prior to action. This suggests that something besides the neurons is functioning here, affirming (although not proving) the argument for free will, because you can consciously veto or cancel an action after prediction by an RP (visit the group’s website here to learn more). However, this does nothing to describe how the crisscross quantum entangled system we have described here could exist in an organism, nor how it interacts with neurons, RP’s, the brain and the rest of the organism. And, frankly, this is a very complex question which we will not resolve here. Rather, our purpose is to describe, at a high-level, a plausible mechanism by which this might happen. Probably, this does not involve simple particles like the electrons we have described, but more likely complex quasiparticles (e.g. the Davydov Soliton – see figure 8). We think this will provide a sliver of insight for future, more detailed, investigations and compelling circumstantial arguments for free will now. Next, we will review some existing theories regarding quantum effects in the brain, what the buttons and sensors we talked about above might be, and how the quantum systems we described might interact with them and reconcile to experimental results.
We have already seen that neurons themselves are too big to persist quantum entanglement (see “The Importance of Quantum Decoherence in Brain Processes” by M. Tegmark (1999)), but scientists have suggested other theories involving much smaller mechanisms that may support quantum entangled states in the brain. One theory involves ion channels (see “Ion Channels: Structure and Function“). These channels allow sodium, calcium, potassium or chloride ions to flow into and out of neuron cells throughout the nervous system. They are only about the diameter of a single ion, even though millions of ions per second pass through them, and regulate very precisely the ratio of sodium to potassium ions they allow through. The ion channels are small enough they are susceptible to quantum effects, but can still influence neuron firing suggesting a conceivable way that quantum effects could be magnified and thereby manifested at a macroscopic level (a button press!). The process of thinking about something, exploring our preferences, could affect these ion channels through weak measurement and result, through amplification, in increased neuron firing rates and cause the formation of the readiness potential (RP) witnessed by Libet prior to motor activation. See, for example, this paper which shows how preference is related to the RP: “The LRP (lateralized readiness potential) is capable of measuring preparatory motor activity underlying the dynamic accumulation of subjective preference in the premotor cortex” (2014). A choice, or button press, occurs when ion channels are affected even more significantly and increase neuron firing rates enough to initiate action. In this paper “The Speed of Free Will” by T. Horowitz, J. Wolfe et. al. (2009), the authors compare the time required for voluntary shifts of attention versus task-driven shifts (i.e. external stimulus). The voluntary shifts occur more slowly suggesting a speed of free will on the order of 100-200 milliseconds. This is consistent with the framework we describe and indicates the time latency for quantum effects to be amplified. Still, the quantum entangled system discussed here would require a vast network of ion channels to all be entangled. How could ion channels in different neurons – vast distances for quantum entanglement – be entangled together?
In quantum networking, if we have a photon source that produces entangled photons (an EPR source) and we send one photon to lab A and another to lab B and then let them interact with qubits in those labs we can entangle the qubits at A with the qubits at B without them ever coming into contact with one another. Even if labs A and B are far apart (many kilometers apart). After the photons interact with the qubits the photons can be measured, discarded, or whatever – the entanglement between the qubits will remain. We know biological decoherence rates are very fast, like picosecond-fast, but if continual absorption of entangled photons from an EPR source by the ion channels cyclically reestablishes entanglement ala’ a biological quantum network, it could allow entanglement to persist. Since biomolecules, such as DNA, can absorb, down convert, and reemit photons on time scales ranging from picoseconds to femtoseconds they may be a possible EPR source (see here for details on internal conversion). Photons that interact with the vibrational frequencies of biomolecules, such as THz, are candidates (see “Observation of coherent delocalized phonon-like modes in DNA under physiological conditions” by M. González-Jiménez et. al. (2016)).
Figure 15: A diagram of a quantum network from Centre for Quantum Computation & Communication Technology. EPR sources at either end are sources of entangled qubits where A&B and C&D are entangled. The joint measurement of B & C occurs at the quantum repeater in the middle entangling A & D at a distance.
There has been much study of the electromagnetic field (photons) of the brain (the EM field) – these “brain waves” are what we see in EEG readouts like Libet’s. The source of this field has never been understood, however. There are many theories that relate the brain’s EM field to consciousness, for example the CEMI (Conscious ElectroMagnetic Information) theory. In this theory, the EM field interacts with the ion channels to synchronize neuron firings, but the neuron firings produce changing electric and magnetic fields and therefore reciprocally affect the EM field. Another interesting theory of quantum effects in the brain has been proposed by S. Hameroff and R. Penrose in their Orch-OR (Orchestrated Objective Reduction) theory of consciousness. In this theory, tiny microtubules, which form the cytoskeleton of all cells in the body, but are particularly prevalent in neurons (~ 
This is not without precedent in Biology as the mechanism that transports energy to the reaction center in photosynthesis is proven to be another quasiparticle known as an exciton (an electron-hole pair). Solitons are “propagating pulses or solitary waves that maintain their shape and can pass through one another” (from here). Think of a chain of rogue waves for intuition. Such a system means that no individual electrons are necessarily moving throughout the brain like in a classical electrical system, but rather a composite quasiparticle comprised quantum mechanically of a collective wave function of entangled particles. Other examples of these quasiparticle systems include Cooper pairs in superconductors, magnons (quanta of spin waves), polarons, and phonons (which are known to propagate up and down the double-helix of DNA and thought to direct the replication of DNA in what is known as a transcription bubble). There are all kinds of quasiparticles, a list is here.
Figure 16: Image of the alpha-helix structure ubiquitous in biological systems. Helical structures give rise to nonlinear Hamiltonians
which, in turn, imply the Nonlinear Schrödinger equation. This has quasiparticle solutions – like the Davydov soliton that transports energy along the alpha-helix. The nonlinear Hamiltonian arises from transverse quantum states entangling with longitudinal phonon states. This nonlinearity of entangled particles (in the 3rd person description) is dual to the mind’s eye (in the 1st person, subjective description). This image is from here, image from Voet, Voet & Pratt 2013, Figure 6.7
So, we have an entangled quasiparticle system in the 3rd person that is dual to our feeling of being One in the 1st person, and, moreover, the quantum entangled system interacts with the outside world by pushing buttons and being affected by sensors. The buttons could be neurons via amplification of quantum effects. Sensors, too, could be neurons affecting the quantum system, or something much smaller like the ion channels. To make our bodies do anything or say anything, we need to push these buttons – just like Buddhist scholar Alan Wallace says “the brain is the keyboard of the mind“. Libet’s experiments are measuring the action of the neurons, and the neurons are your keyboard and a critical resource for your mind, but you are not those neurons. And so, when these experiments are conducted they are measuring you through the different ways you interact with the outside world, by pushing the “speak” buttons or the “finger press” buttons. The timing differences these experiments measure are just the timing differences between button presses. These experiments are measuring events correlated with each other in the cascade of neuron firings that produces action, but these events are not the original cause. The reporting of “conscious choice” by subjects is, itself, the reporting of a button press – the button to report the choice. Only when you sufficiently focus your quantum self to fire that neuron(s) does the button get pressed. Only then does a full choice/measurement occur. The decision to override the RP is yet another button press – the negation of the “finger press” button. All deliberate actions start with a button press, but, the original cause originates from your free will, from your mind’s eye, from the crisscross of a quantum entangled system.
There is evidence in Psychology that there are two types of memory used by the brain: short-term memory and long-term memory. Short-term memory typically lasts for something on the order of about 18 to 30 seconds, while long-term memory lasts much longer – potentially for the life of the organism. The evidence for these two distinct kinds of memory is based on case studies of patients with a disease called anterograde amnesia as well as certain kinds of “distraction tasks” that seem to affect one or the other types of memory in isolation. Patients with anterograde amnesia tend to have working short-term memories but have difficulty forming long-term ones. In other words, they can retain memories for 30 seconds or so. Such a description of memory naturally fits in with the quantum entangled system we have described above. In such a system, short-term memory is that information which is encoded by collapsing the superposition to an eigenstate of the measurement operation with the chosen/measured eigenvalue – like we described in the 3-electron case above. So, you start in a superposition of states, you choose to think about where to go out for dinner. That choice leaves end “B” in an eigenstate, say, with all the spins pointing up focusing you onto the choice of where to go for dinner. Upon thinking about it, you decide, say, to go to restaurant XYZ. There again, that choice leaves you in an eigenstate – this time at end “A”. So that all states at end “A” have total spin equal to, say, +7/2, which corresponds to restaurant XYZ. Every time you make a choice, you are subjecting yourself to measurement and collapsing your state to an eigenstate of that measurement. You might still be, and probably are, in a vast superposition of states, but all the states have a symmetry to them – an aggregate property of each state, like the total spin, is the same. That is short-term memory, but quantum states are difficult to preserve, even with redundancy and error-correction, so an organism needs to encode this memory in something more stable, more macroscopic. This is where the neurons and long-term memory come in. But, how is this information transferred to long-term memory?
The Hebbian theory of neurons tells us that “neurons that fire together wire together”. Our quantum entangled system, when run through the same measurement conditions repetitively would realize the same outcome over and over. And, if that outcome is amplified to induce neuron firings, then it could cause the same neurons to fire over and over. That is because the quantum superposition is still in an eigenstate. Once a choice/measurement is made, if the same measurement is repeated the system will produce the same result. This may be the feeling of having “your mind set on something” or “your mind made up”. In other words, if the magnetic field generated by end “B” is unchanged and we pass end “A” through it again and again, it will wind up projected onto the same place. For example, if all states of the system have the symmetry that their net spin is +3/2 at end “A” then this will be indicated by their trajectory upon exposure to the same magnetic field from end “B”. The chain of entangled particles will be focused to the same place. Iterated through a loop a number of times, like a broken record playing over and over again, would produce the repetitive firing of the same neurons which then would cause those neurons to wire together – forming a long-term memory of that choice. If you have ever had the experience of, when trying to remember something, you keep “saying it” over and over in your mind, this is possibly the dual description of that experience. You use your mind’s eye to keep playing it repeatedly until it sticks – until the neurons “wire together” per Hebbian principles. Such a model is consistent with the results described in this paper “Delaying Interference Enhances Memory Consolidation in Amnesic Patients” by M. Dewar et. al. (2010), where, if there were no distractions, even patients with amnesia could continually keep the short-term memory “in mind” and give it the extra time needed to wire the neurons together for long-term memory.
So, imagine our quasiparticle system is a system of “brain solitons” propagating around the brain, like a “ticker-tape” of information entangled as One system. Perhaps following a general path like that shown in (figure 17). Inducing the appropriate neurons to fire in synchrony, over and over again, and wire together. One system of particles entangled together but no individual particle is the system. In fact, individual particles may be added, replaced or exchanged over time which is consistent with isotope studies that show that the vast majority of atoms in the body are recycled over time. The critical difference between the ticker-tape of the mind and a classical ticker-tape is that it can be in a vast superposition of states at once. Like zillions of classical ticker-tapes flowing at once and directed by the mind’s eye. All of this is at once described by this quantum mechanically in the 3rd person description, and in the 1st person as what it is like to be you! A mind’s eye, a short-term quantum memory, quantum computing power to enable creative leaps and “aha!” moments, long-term memory storage via neurons – a full-on conscious experience is emerging! However, we must say, as interesting as this depiction is, it clearly is an over-simplification of a very complex process of making choices and storing memory in the brain, and we will not pretend to have all the answers here.
Figure 17: Flow of quantum information as a quantum “ticker-tape: in the brain takes the form of a propagating quasi-particle. Such a quasiparticle could take the form of a “brain-soliton” resulting from a nonlinear Schrödinger equation – the mind’s eye. Communication between the hemisphere’s may take place through the corpus callosum and explain why split-brain patients (who have it severed) exhibit traits of two wills. Brain picture from public domain pics here.
In this article “The Great Cerebral Commissure” (1964) by Nobel Laureate R. Sperry, the author talks about “split brains” and their effect on brain functioning. Specifically, the corpus callosum is a massive structure of nerve fibers that connects the two halves of the cerebral cortex. In some cases when patients suffer from epileptic seizures, surgical procedures have been performed to cut the corpus callosum forming split brains. This was effective at halting the seizures, and, at first it appeared as though patients recovered completely from this procedure with no ill-effects. This caused many physicians to wonder what was the purpose of the corpus callosum. Later, Sperry’s experiments on animals took a deeper dive and showed that “it was as though each hemisphere were a separate mental domain operating with complete disregard – indeed, with a complete lack of awareness – of what went on in the other”. This lead Sperry and colleagues to conclude that the “corpus callosum has the important function of allowing the two hemispheres to share learning and memory”. In humans, what seems to happen is one of the hemispheres turns out to be dominant and takes control of the person’s functioning. Tests that isolate the hemispheres show: “(upon) discussing such responses afterward, the patient typically has no recollection of having pointed with his left hand; the dominant hemisphere seems completely ignorant of what went on in the other one.” Sperry went on to say, in regard to experiments on monkeys, “one hemisphere or the other takes command and governs the monkey’s behavior. This dominance may shift from time to time, each hemisphere taking its turn at control, but it would appear that no serious conflict disrupts any given movement.” Perhaps Sperry’s split brain research suggests a flow of brain solitons we described above in (figure 17) in a healthy brain. When the corpus callosum is cut, however, the flow of short-term memories in the quantum ticket-tape between the two halves is disrupted as shown in (figure 18). The patient recovers, but the new topological flow of solitons shifts to the dominant half only. In this article “The split brain: A tale of two halves” by D. Wolman (2012) the author says “the brain isn’t like a computer, with specific sections of hardware charged with specific tasks. It’s more like a network of computers connected by very big, busy broadband cables. The connectivity between active brain regions is turning out to be just as important, if not more so, than the operation of the distinct parts.” The quantum entangled self, the ticker-tape, is, perhaps, the “broadband connection” unifying the brain’s regions. Neurons in the non-dominant half still function and can perform tasks, but the mind’s eye, and the Oneness of the organism persists only in the dominant half. You may have felt a small fraction of this effect, for example, if you ever had the experience of aiming a bow & arrow. While both eyes are passing visual information to your brain, your mind sees and aims subconsciously only with your dominant eye.
Figure 18: Possible flow of the quantum “ticker-tape” of information, “brain solitons”, after patients have their corpus callosum severed. R. Sperry observed that one half at a time becomes dominant, takes control of the mind, and carries on unaware of the actions undertaken by the other half of the brain.
You can get a better feel for the relationship between the quantum entangled mind’s eye and the functioning of neurons by examining vividly the common everyday experience of driving an automobile. You’ve probably had the experience where, while driving, your mind drifted onto something else. Your brain still steers the car, and operates the gas and brake as if on auto-pilot (this phenomenon is so widespread the phrase “highway hypnosis” has been coined). Usually it does so reasonably well. When operating in this mode, depending how deep in thought you are, you might drive right past an important exit without even noticing. All the visual images still fire the same neurons in the visual cortex, it’s just that without your focus nothing is done with that information. The quantum brain-soliton ticker tape doesn’t take that information where it needs to go to initiate action unless you are focusing it there! On the other hand, if you encounter something out of the ordinary that sets off a “red alert”, such as an accident, construction, or your co-pilot says “you missed our exit!”, then suddenly your mind’s eye is called to attention. These “alert sensors” could be neurons that can affect the state of yourself at end “B” causing end “A” to be focused on the present situation requiring attention. The two-way relationship between your macroscopic self, the neurons, and your quantum self is illustrated well in this situation.
Another illustrative example you may have encountered is the experience of looking at an image, and, for a few seconds, you have no idea what you are looking at. It may mean the neurons by themselves aren’t able to recognize the image. It seems the mind’s eye has to get involved somehow to recognize the image – to adjust the timing of neuron firings, to bus the information on the ticker tape to other regions of the brain, or place them in context to achieve recognition. This is called “top-down reasoning“. When humans only have a split second to look at an image and do not have time to invoke top-down reasoning, they can recognize images only about on par with the best machine learning models. These machine learning models, interestingly, use so-called deep learning neural nets which use a neural network structure patterned after the structure of neurons in the visual cortex. However, on hard images that don’t offer instantaneous recognition, humans, if allowed time to think about, can use top-down reasoning to recognize images better than machines. This is the basis for modern “CAPTCHA’s” – Completely Automated Public Turing test to tell Computers and Humans Apart. No computer machine learning models have such functioning, and so far, it has not been understood what is involved to produce it. Also, it is an unsolved question how the brain came up with the neurological structure of the visual cortex, especially since the problem of finding the right structure seems to involve a highly non-linear problem (e.g. discovery of “max pooling” configurations). Quite possibly, in early development, it is the quantum entangled aspects of the organism that are engaging to solve such difficult, probably NP, problems. Training methods in artificial neural networks that use gradient descent type approaches (i.e. non-quantum) tend to get stuck in local optima. But, invoking quantum computing power may provide an exponential speedup on learning problems of this kind and enable a global solution to be found (see this video “Quantum Machine Learning” which shows how quantum algorithms can be applied to neural networks by Seth Lloyd (2016)).
From an evolutionary perspective, this paper “Towards a scientific concept of free will as a biological trait: spontaneous actions and decision-making in invertebrates” by B. Brembs (2010) describes how animal species have been shown to randomize their behavior to gain an evolutionary advantage. Their behavior is shown to be self-initiated, that is, given the same environment, the same external conditions, animals will deliberately inject variability into their behavior. This is in direct conflict with behaviorist models where environmental conditioning alone determines behavior, but strongly agrees with the indeterminant quantum system described here. Animals go even further, actually increasing the variability of their actions when faced with uncertain situations – seeking to deliberately explore the unknown. A model is described in which animals amplify small random differences in internal conditions to generate this variability: “a neuronal amplification process was recently observed directly in the barrel cortex of rodents, opening up the intriguing perspective of a physiological mechanism dedicated to generating neural (and by consequence, behavioral) variability” from “Sensitivity to perturbations in vivo implies high noise and suggest rate coding in cortex” by M. London et al (2010) hat tip B. Brembs. The paper by Brembs gets everything right short of recognizing two things: (1) while these small differences are indeed random when looked at externally and objectively, the randomness follows quantum probabilities that are dual to the preferences of the organism. Even in an organism as simple as a fly, there is a little ‘self’ in there. Not necessarily offering the same experience as in human consciousness, but free will and a mind’s eye are indeed present: “(flies)…can actively shift their focus of attention restricting their behavioral responses to parts of the visual field.” (from here and here, hat tip B. Brembs). Recognizing this will resolve the conundrum specifically called out in “Downward Causation and the Neurobiology of Free Will” by C. Koch (2009): “for surely my actions should be caused because I want them to happen for one or more reasons rather that they happen by chance” (hat tip B. Brembs). The resolution involves recognizing that “want” and “chance” are dual versions of the same thing! Second (2), while it is tempting, and dogmatic, in evolutionary biology to chalk everything up to “that must have been selected for during X billion years of evolution”, we have pointed out in “What if the Miracle Behind Evolution is Quantum Mechanics?“, that this hypothesis class does, in fact, have infinite capacity, i.e. VC-dimension. That means it can explain anything! Behavioral unpredictability was not selected for by natural selection in evolution as an advantageous trait, it was present in life from the very beginning – all the way back to when life was nothing more than a complex molecule who’s only remarkable property was that it vibrated fast enough to sustain growing quantum entanglement!
Figure 19: Drawing by Santiago Ramón y Cajal (1899) of neurons in the pigeon cerebellum via Wikipedia.
