A comprehensive proof that free will exists in the brain, derived from subatomic physics and cellular anatomy:

First, a primer on neuron anatomy and function. The main structures of a neuron are the axon, dendrites and soma. The soma is a cell body housing the nucleus and additional organelles, which looks like a typical cell. At least several dendrites plus their branches sprout from the soma, long and thin protrusions that are also microscopic. The axon projects from the opposite side of the soma and is responsible for longer distance transmission of an electrical signal. Each neuron has only one axon. It is larger in diameter than dendrites but also relatively narrow and can range from microscopic to meters in length. The axon is insulated by a layer of fat called the myelin sheath to increase conductance speed, the source of white matter's color as opposed to the grey matter of dendrites, soma and the interior of axons. Production and positioning of myelin is regulated by glia, either Schwann cells or oligodendrocytes, located around the axons. The synaptic cleft is on the far side of the axon from the soma, where axon and dendrites make connections for transmitting a signal between neurons. Most Na ions are located outside the cell, K ions inside the cell, and Ca ions at the synaptic cleft, maintaining concentration gradients for selective diffusion when ion channels open. Cl channels are located at the junction between dendrites and soma to block signal transmission while the neuron is at rest. Ions are transported perpendicularly through channels in the neuron's outer membrane as a chain reaction that proceeds from dendrites, through the soma, and ultimately to the axons which integrate more distant regions of the body and brain to form a nervous system. The brain makes roughly a hundred trillion connections between eighty billion neurons.

Neuron firing begins with communication transmitted from an axon to dendrites at the synaptic cleft. Na, K and Ca ions as well as a host of more complex molecules such as neurotransmitters are secreted by the axon, flowing around and through the synaptic cleft to stimulate dendrites at the proper moment. This process is called a synapse, and it triggers downstream ion channels to open in sequence, temporarily depolarizing the cell in a voltage change that travels like a blip along the length of a dendrite. This is called an EPSP (excitatory postsynaptic potential). An IPSP (inhibitory postsynaptic potential) from Cl influx through its channels at the base of dendrites can block signal transmission, but if cumulative EPSPs from dendrites are strong enough to overcome Cl blockage and traverse the soma, a signal reaches the axon hillock at the junction of axon and soma. With enough signal strength, ion channels around the axon hillock start letting ions flow through the outer membrane, instigating a longer chain reaction called an action potential. This voltage signal travels along the axon's length to the axon terminal where a synapse is again prompted at the synaptic cleft.

In an axon, numerous Na channels are clustered at the nodes of Ranvier, relatively small interruptions in the myelin sheath that are evenly spaced along the axon's length. Na channels are ''voltage-gated'' for sensitivity to the neuron's electrical signal, which triggers them to open and let Na flow in. Each node of Ranvier is flanked by paranodes, where the myelin sheath attaches to the cell membrane. The paranodes are flanked by juxtaparanodes, where voltage-gated K channels allow K to rush out of the axon when open. The majority of an axon is internodal space, with K leakage channels that let this ion back into the cell. Because a neuron is more porous to K than Na, sodium-potassium pumps are located throughout the cell membrane, helping to restore ion concentrations of the resting potential by a constant ferrying of two K ions into the cell accompanied by three Na ions out of the cell. Dendrites propagate EPSPs by a similar mechanism, with Na channel nodes and strategically located K channels throughout. After depolarization occurs and the electrical blip travels past a given region, the neuron quickly begins to repolarize, resetting ion concentrations to presynaptic levels. Vigor of neuron firing is determined by the frequency of depolarizations rather than voltage intensity, with more rapid rates of pulse stimulating stouter responses downstream. The adage is ''neurons that wire together fire together'', interweaving to form intricate networks and feedback loops.

Many aspects of neuronal function have been well-understood for decades but mysteries remain, for the transport and diffusion of ions alone cannot account for some observations about signal transmission and neuron anatomy. In theory, ions encounter less axial (lengthwise) resistance in axons of larger diameter, which should result in greater degrees of freedom for diffusion and more rapid diffusion rates. Nodes of Ranvier would then be spaced farther apart to keep the signal's voltage change constant upon reaching nodes, but they are actually spaced closer together in larger diameter neurons. Computer simulations have demonstrated that widening nodes of Ranvier slightly to substantially increase the quantity of Na channels does not change the rate of signal transmission with larger amounts of diffusion. Neither can diffusion plausibly explain why voltage-gated K channels are concentrated at the juxtaparanodes. And an action potential travels meters in milliseconds, far exceeding rates of diffusion. Signal transmission in neurons is not the product of collisions between ions, but quantum coherence in solution seems to explicate it.

Most of the solution internal to a neuron is made up of positive ions and water molecules. Water is a polar molecule, its oxygen atom being the negative pole and hydrogen atoms the positive poles, bent somewhat at the fulcrum. A solvation shell forms around each positive ion, with negative poles of water aligned on the shell's inner surface and positive poles facing outward. Thus, the solution contains a complex contour of positive and negative charge, or more precisely less and more electron waveform concentration. Nanoscale electromagnetic pressure to evenly distribute electron density within and between atoms, quantified as momentum and strength of charge, drives a dynamic equilibrium which keeps water molecules and ions in perpetual motion. Trillions upon trillions of haphazard interferences are generated, making decoherence the solution's baseline condition.

When Na rushes into the cell at a node of Ranvier, electron density lessens in that region, drawing nearby electron energy into the vicinity. This electric current moves towards Na increase, but initialization of the current begins adjacent to the node and propagates outward into successively distant regions. Symmetry of the nodal region means that simultaneous propagation in the reverse direction wil halt signal transmission's forward trajectory so the node can more quickly reset upstream. If charge is on average constant the signal slows as it travels because of electron mass' inertia and some spreading, so I have named this mechanism the ''ebb effect''.

Since electromagnetism essentially consists in an extremely diffuse, high velocity field containing relatively small loci of dense wavicle matter that perturb it while shifting around, the initialization of flow from greater to lesser electron density as a current of electrical coherence, drawing electron energy out of increasingly distant regions of solution, includes a companion EM field fluctuation that acts remotely and with effective instantaneity. (As a side note, the nuclear field is similarly instantaneous, for the nucleus possesses at least 99.9 percent of an atom's mass while binding atomic orbitals that have a hundred thousand times the volume into a synchronous unit.) Ion channels are apparently adapted for sensitivity to this EM field perturbation that accompanies the lengthwise voltage effect, a phenomenon observed by in vitro experiments with neural networks. Because the EM field's domain as linked with electron density at a specific region extends to multiple cells, perturbations via coherence currents which alter electron density overlap and form a sort of synchronous grid, integrating the neurons of neural networks via a mechanism of ''phase-locking'' between ion channels and the EM field. Quantum spins of atoms in neuronal solution are not aligned as in an iron bar magnet for instance, and this creates interference canceling magnetic effects even at the cellular scale, making the field exclusively electric at very basic levels of emergence, though internal currents of the ebb effect may be momentarily synchronous enough that a spike in nanoscale magnetism is the trigger for ion channels, propagating at the speed of light. Macroscopic waves of the electric field as induced by phase-locking within tightly coupled feedback loops are what EEG (electroencephalogram) measures, and can range in length from millimeters to more than a dozen centimeters.

The greater a discrepancy between ion concentrations in abutting regions, the stronger the electrical coherence current will be drawn towards more positive concentration, causing initializations to accelerate in the opposite direction and traverse longer distances. Thus, when voltage-gated Na channels at a node of Ranvier open, the electrical signal along with a companion EM field fluctuation accelerate enough to propel through internodal space. When the electrical signal reaches a juxtaparanode, EM field fluctuation perturbs voltage-gated K channels to open and let the ion rush out of an axon. This rapidly increases the discrepancy in electron density between a node of Ranvier and the juxtaparanode, accelerating an electrical signal with enough force to traverse internodal space and reach the next nodal region. The next node has usually not been completely repolarized, so once the signal attains this node's sphere of influence, acceleration is resumed and EM field perturbation reopens voltage-gated sodium channels, a chain reaction that continues down the length of the axon. This mechanism of electrical signal transmission via currents of quantum coherence and the ebb effect, initiated and boosted by voltage-gated ion channels in the neuron's outer membrane, blows through rate barriers of lengthwise diffusion in millisecond communication between neurons.

Microscopic platinum sensors have been inserted into individual neurons, revealing a crystalline structure extending lengthwise just below the axon's membrane, wrapped around a core support framework of microtubules. This crystalline structure probably restricts diffusion into the center of an axon so the ebb effect is not diminished by dilution and ion concentrations remain at efficient levels. Larger diameter axons have more volume surrounding this structure, perhaps necessitating that nodes be closer together so as to compensate for more dilution.

Similar structure in dendrites indicates that they transmit an electrical signal from synapse to soma by the same mechanism. Cl channels block these EPSPs by increasing electron density at the junction between dendrites and soma, which causes the ebb effect to propagate upstream within dendrites as an IPSP, in the same direction as current flow. If EPSPs are strong and coordinated enough to push through counteractive current and reach the soma, this buildup of electron density accelerates rapidly afterwards across the soma's relatively vast expanse due to the biggest charge gradient in a neuron between the base of dendrites and the largest quantity of voltage-gated Na channels at the axon hillock.

The ebb effect has not been verified by experiment, but in theory it would be observable within any solution containing ion concentrations disequilibrated enough to produce charge differentials that cause electric currents to flow. A combination of quantum coherence, the ebb effect, phase-locking and neural networking could be sufficient to model the brain's electrical properties from the intracellular to organwide scale. Macroscopic, ultrasynchronous oscillations within the brain's electric field would correlate with consciousness because magnetic properties of atoms are hypersensitive to this supervenient field, just as electricity from a wall socket drives magnets to run many appliances. If diverse neurons and neural networks engage in a range of breadth and saturation in phase-locked synchrony depending on the chemistry of their ion channels, membranes and circuitry, this might explain the spectrum of low to high arousal, from unconscious to subconscious to maximally attentive states as CEMI (conscious electromagnetic information) theory suggests. EEG readings during thoughts, behaviors and decision-making classified as intentional by both researchers and subjects tend to show that large swaths of the electric field segregate from the global pattern in more serial processing, an unmistakeable sign of functional autonomy. Volitional will is most probably, at the very least, neural structure phase-locked to the brain's electric field in feedback loops, powered by quantum coherence.