Neuroanatomical organization of a sufficient complexity is thought to be a necessary condition of consciousness [1] wherein neural networks form and the resulting structure dictates the function of the organ [2] . Neurons, composed mainly of water and proteins [3] , communicate by means of electrochemical signalling with direction and magnitude which result in cognitive states and behaviours. However, as the convolutions which constitute the structure of the brain became increasingly complex, so did the intervening negative spaces—including the extracellular environment. Studying consciousness exclusively within cells is problematic when considering that the medium between cells is primarily composed of water with ions [3] and that solutions such as these are able to store and release electromagnetic energy [4] . The implication is that the proteinaceous structure of the brain itself is an epiphenomenon which operates simultaneous to a covert system where neurons express activity from the local environment in an integrated network of aqueous boundary conditions.

That the relatively stable microstructual patterns, at the level of the synapse, function to maintain the temporal consistency of the conditions that correlate with consciousness, is a viable, alternative possibility. Water molecules adjacent to a surface exhibit all of the major properties attributed to the plasma cell membrane. Interfacial water, compared to bulk water, displays about ten times the viscosity. The resulting exclusion zone is associated with a narrow zone of protons. The generated potential difference ranges in the order of 100 mV which is the same order of magnitude as the resting membrane potential traditionally attributed to the disparity in concentration of cations and anions across the membrane space. Within the exclusion zone generated by ordinary water adjacent to a surface, electromagnetic fields can be retained for protracted periods of time [5] .

Water displays universal properties derived from fundamental physical parameters. For example its diffusivity (0.8 × 10⁻⁷ m²∙s⁻¹) is obtained by dividing the magnetic moment of a proton (1.41 × 10⁻²⁶ A∙m²) by the unit charge (1.6 × 10⁻¹⁹ A∙s). When this quotient is multiplied by the typical viscosity of water (1.0 × 10⁻³ kg∙m⁻¹∙s⁻¹) at 20˚C the resulting force is 8.8 × 10⁻¹¹ kg∙m∙s⁻² [5] . When applied across the width of two O-H bonds (1.92 × 10⁻¹⁰ m) the energy is about 1.7 × 10⁻²⁰ J. This value is within the measurement error of the energy for the second shell hydrogen bond that reflects proton mobility in water [6] . We think it is relevant that ~1.7 × 10⁻²⁰ J is within the range of energy associated with effects of a typical neuronal action potential upon a unit charge and the energy required to stack one nucleotide onto an RNA sequence [7] . In other words, the most fundamental increment of energy associated with the neuronal correlate of consciousness and cognition, the action potential, and energy required to add different nucleotides, the determinant of the protein patterns of memory, is the same value as that associated with the movements of protons through water.

The proton is a primary candidate to mediate information within brain space. According to DeCoursey [6] the proton is unique among cations in being interchangeable with the protons that form water. There is a five-fold higher conductivity for H⁺ in water compared to other cations such as K⁺ and there are more proton channels than the sum of channels from all other ions combined. Even when one considers the numbers of free protons within the hydronium atom is about 40 nM (compared to the 110 M of hydrogen in water), the numbers become significant when one appreciates that most of the brain volume is water. During a 100 pA outward H⁺ current between 10⁸ and 10⁹ H⁺ leave the typical cell. The importance and prevalence of protons and proton channels has been attributed to the evolutionary necessity of quickly dissipating the intracellular diminished pH associated with interactions between organic acids.

Shifts in pH along neuronal membranes accompany action potentials and occur as transients with intervals between 10 and 40 ms [8] . Highstein et al. [9] showed that protons act as neurotransmitters with shifts of ~0.2 pH near synaptic clefts. Recently Murugan et al. [10] observed that continuous exposure of spring water with ion concentrations similar to biological fluids to physiologically-patterned magnetic fields produced frequent temporal shifts of small increments in pH whose durations were between 20 and 40 ms. The relevance of this increment, which is the ~40 Hz activity associated with higher functions for cerebral activity such as consciousness, is well known. Llinas and Ribary [11] found that cohesive integrative waves displaying phase modulation moved as recursive phenomena in a rostral to caudal direction every 20 to 25 ms. Several authors have noted the “coincidence” that the time required for bulk velocity action potentials to move through the hippocampal, thalamic, cerebral “circuits” displays durations of approximately 20 to 25 ms. This reiterates our approach that the structure of pathways through which consciousness is mediated are arranged to ensure the specific timing of the circuit to match intrinsic features of water.

Persinger [12] proposed that the Earth’s quasi-static main magnetic field is a potential medium by which all brains can be unified at a fundamental level. Although speculative and potentially interesting, the solution for the individual brain is particularly relevant. Assuming an average volume of 1350 cc which is ~945 cc (70% water), there would be 55.5 M of water (18 cc per M). This would involve 3.16 × 10²⁵ water molecules. The magnetic energy from the static geomagnetic field, assuming an average of 5 × 10⁻⁵ T, would be in the order of 0.945 × 10⁻⁶ J or 2.9 × 10⁻³² J per water molecule [10] . The equivalent frequency, obtained by dividing Planck’s constant (6.626 × 10⁻³⁴ J∙s) would be ~40 Hz. Even neural correlates of consciousness have been attributed to synchronous gamma activity [13] . The fundamental theta (4 to 8 Hz) frequency of the hippocampal formation, the “gateway to memory”, exhibits superimosed ~40 Hz ripples that may be fundamental to interaction between cerebral cortical and parahippocampal regions [14] .

The extremely-low frequency (ELF) component of the Earth’s electromagnetic radiation spectrum is generated by a resonance phenomenon between its surface and the ionosphere with a fundamental operating frequency of 7.8 Hz [15] . Originally characterized by Schumann [16] , this fundamental and its harmonics (14.1 Hz, 20.3 Hz, 26.4 Hz, and 32.5 Hz) are a result of global lightning discharges where the fundamental mode is determined by the circumference of the Earth. The wave forms and temporal structures associated with the Schumann frequencies are remarkably similar to the classic delta, theta, and alpha patterns attributed to cerebral cortical activity [17] . The magnetic field strength of these resonances is in the order of 1 to 3 pT, which is within the range of the operating magnetic field within the human cerebrum. If the typical 0.2 μV change associated with a single ion channel is applied to a unit charge (1.6 × 10⁻¹⁹ A∙s), the increment of energy is 0.3 × 10⁻²⁵ J. The square root of this value divided by the mass of a proton is ~4.5 m∙s⁻¹ which is the typical velocity of the rostral-caudal waves or bulk velocity of the integrated cerebral electromagnetic fields. Assuming the average circumference of a human skull to be 60 cm, the standing wave would be between 7.5 to 7.8 Hz. Schumann resonance frequencies are thought to influence brain activity as well as blood pressure [18] [19] and other biological processes [17] .

The hippocampal formation and parahippocampal gyrus in particular are thought to be strongly coupled to the Schumann resonance [20] . The observation that the low-frequency oscillations which characterize the typical human electroencephalographic profile overlap significantly with the fundamental Schumann resonance frequency (7.8 Hz) and the paired harmonics might not be coincidental. Layers II and III within the entrorhinal cortices of the parahippocampal gyrus, which provides the bi-directional interactions between the cerebral cortices and hippocampal formation [21] , exhibit a near-continuous subthreshold oscillation of ~8 Hz. The mean amplitude of these oscillations was 2.6 (±0.5) mV.

Geomagnetic storms are associated with altered human cognition and behaviour [22] , suggesting some intrinsic relationship between the brain and the electromagnetic environment. Whereas it is possible that some recondite third factor is influencing both systems, experimental inductions of altered brain function using artificially generated electromagnetic fields indicate that the brain is a magnetoreceptive organ [23] . Though electromagnetic cellular interactions have been studied in detail [24] , the negative brain-space of the extra-cellular environment wherein subtle physical phenomena might be occurring must be further considered as a contributing source of variance.

A negative space brain system might function by absorption and emission of electromagnetic energies as has been demonstrated in paradigms involving spring water [25] , and cell cultures [26] . In both cases, externally applied stimuli were involved, suggesting that non-cerebral sources of electromagnetic energies could potentially interact with the brain by means of interaction with water. The discovery that induced, subtle shifts in pH within the synaptic cleft in C. elegans were sufficient to alter post-synaptic firing indicates the importance of proton-based neurotransmission [27] . Synapses, consisting effectively of parallel plates, operate within parameters sufficient to generate Casimir forces [28] , suggesting that these interfaces are more than just transitional zones through which molecular neurotransmitters traverse. The same authors have calculated that the wavelength equivalent of the energy associated with these forces applied over 10 nm—a value approximating the width of the synaptic cleft and the neuronal membrane—would approximate the width of neutral hydrogen.

Together, these findings have suggested that classical mechanisms, although essential and highly reliable, do not accommodate the variety of processes observed involving neuronal signalling. Additionally, these works indicate that the proton is of central importance with regards to the functioning of the nervous system. We hypothesized that perhaps an external force or zeitgeber is ordering neural activity wherein the sum of the cellular units are necessary although insufficient to produce the resulting function in much the same way a radio receiver is necessary but insufficient in radio transmission. Whereas brain structure would be essential to brain function, the output of the brain would not be explained by cellular structures alone. As neurons would be receptive to this extra-cerebral force, it follows that the energies involved in such a process are subject to experimental measurement and quantification. Here, we present an experimental detection of what is potentially extra-cerebral information which could explain a subset of brain function normally ascribed to synchronous cellular activity.

There was a moderate, positive correlation between intra-skeletal and human spectral densities within the narrow subset of gamma from 30 - 50 Hz, r = 0.60, p < 0.001 corresponding to an effect size of 36% (Figure 4). It was determined that the layer which contributed to this significant relationship was that of the cortex, r = 0.55, p < 0.001. Extra-skeletal spectral densities (Figure 5) as well as the scalp layer of the three-shell model did not show this relationship.

Correlational analyses performed for cases associated with Schumann frequency bands revealed a moderate, positive relationship between human and intra-skeletal spectral densities within the fundamental of ~8 Hz (r = 0.59, p < 0.005) as well as the first harmonic or 14 Hz, r = 0.53, p < 0.01. When performing the analysis separately upon the two conductive layers of the three-shell model, spectral densities of the cortex moderately correlated with human spectral densities for the fundamental Schumann frequency (r = 0.59, p < 0.005); however, the scalp layer was not significantly correlated (r = 0.30, p > 0.05). Extra-skeletal spectral densities did not correlate with those of the human sample within the first three frequency bands; however, within the frequency band corresponding to the fourth harmonic (33 Hz), extra-skeletal and human spectral densities were moderately correlated, r = 0.58, p < 0.005. The cortex layer spectral densities were also correlated with human spectral densities within the frequency band corresponding to the fourth harmonic (r = 0.52, p = 0.01). This relationship was not observed for the spectral densities derived from the electrical activity of the scalp layer alone or in combination with the cortex layer.

ED containing high (r = 0.50, p < 0.001) and medium (r = 0.48, p < 0.001) proton concentrations showed moderate, positive correlations with human spectral densities between 30 - 50 Hz which were not apparent for the low concentration conditions, r = −0.01, p > 0.05. The observed correlations were not significantly different, zF = −0.16, p > 0.05. Figure 6 shows that the spectral characteristics emergent of the high hydrogen ion concentration condition (black) displays peaks of increased oscillatory activity within frequency bands associated with the Schumann resonance. The low hydrogen ion condition (red) displayed relatively equal contributions of power under most frequency bands (i.e. increased noise) with the exception of the 10 - 13 Hz range.

Examining the simulated cortex layer only for each proton concentration condition for the typical waking, human electroencephalographic bandwidth (4 - 50 Hz) revealed a moderate positive correlation between spectral densities of the high hydrogen ion concentration cortex condition and human spectral densities (r = 0.60, p < 0.001). Figure 7 shows spectral densities associated with the high hydrogen ion concentration cortex condition with human spectral densities. This relationship, although observed, was significantly diminished for the low and medium hydrogen ion concentration cortex conditions, zF > 1.96, p < 0.01. There was also a significant difference between the correlation coefficient illustrated in Figure 8 and the significant but weak correlations between human spectral densities and those of the ED sphere (r = 0.38, p < 0.001) and ED disk (r = 0.41, p < 0.001), zF > 1.96, p < 0.001. Figure 8 and Figure 9 show the ED that were shaped as a sphere or a disk paired with human spectral densities. These results suggest that the intrinsic oscillatory activity of the cortex layer within the “high” hydrogen ion concentration condition was more strongly associated with human spectral densities than any other condition.

The “spontaneous” spectral densities for an electro-conductive medium (ED) occupying the approximate volume of the human cerebral cortices and containing “high” (pH = 2.47) or “medium” (pH = 2.52) proton concentrations showed a significant overlap with human spectral densities which were not present for the “low” (pH = 2.66) concentration condition. Other geometries, such as a flat disk or solid spherical shape did not display these significant cross-correlations with actual human cerebral cortical spectral densities.

The fact that a critical number of protons were required strongly indicates the moderate strength correlation between spectral densities observed from passive measurement of the ED and those of actual human brains was not an artefact of the QEEG or our procedures. If procedural artefacts were present then the moderate strength correlations should have been evident when all concentrations of protons were employed. However, the significant correlations were only evident for the pH values < 2.53.

The direct application of these results and this model to actual brain function may appear to be limited by the marked discrepancy in pH. The typical levels of pH in intracellular space during neuronal activity are around 7.0 with shifts of about 0.2 pH units. On the other hand the pH levels within our ED simulation was much more acidic, about pH = 2.5. The most parsimonious solution to this apparent discrepancy involves the numbers of H⁺ within the functional volume. The ionic source of the resting membrane potential for plasma cell membranes for soma around 10 μm in width is about the width of a Bohr radius or 5.6 × 10⁻⁹ cm [31] . The shell (assuming a sphere) occupied by this additional volume is 1.8 × 10⁻¹⁴ cc. The numbers of H⁺ (M = 10^−pH) within this volume with a pH = 2.5 would be 3.16 × 10⁻³ M multiplied by 9.8 × 10⁻¹⁶ cc (1.8 × 10⁻¹⁴ cc divided by 18 cc per M) or 31 × 10⁻¹⁹ M. When multiplied by Avogadro’s constant, the numbers of H⁺ would be about 1.9 × 10⁶ molecules.

On the other hand, the volume occupied by a shell that extends 1 μm from the cell, where experimental pH levels are typically taken, would involve a volume of 3.8 × 10⁻¹⁰ cc or 2.1 × 10⁻¹¹ cc (3.82 × 10⁻¹⁰ divided by 18 cc per M). For a pH of 7 the numbers of H⁺ would be the same order of magnitude (about 10⁶) as that calculated for the more acidic pH within a single layer of charges. Interesting this is the estimated numbers of charges required to maintain the resting plasma membrane potential [7] . This convergence suggests that the functional concentration of H⁺ along the proximal surface that markedly influences the resting cell membrane potential is much more acidic than typically assumed and more typical of what we employed in the ED model. The primary difference between the ED “cerebral cortex” and the natural human cerebral cortex is that the thin shell of protons would line an extraordinarily complex surface structure along the membrane of neuronal soma, dendrites and axons within the ~3 mm thick cortical shell.

The convergent of numbers of H⁺ for the measured neuronal environment when the single layer of charge along the plasma cell membrane is considered has significant implication for mechanisms of consciousness. According to Bordag et al. [32] only the surface layer of atoms or charges can be considered a continuum. It is this continuum that interacts with an electromagnetic field. The Casimir effect, which emerges in space-times with nontrivial topology (such the cerebral cortex) is the interaction between a pair of parallel conducting plates due the disturbance of the vacuum of the electromagnetic field. Bordag et al. [32] describes this process as a pure quantum effect. This connects the Casimir effect to the existence of Zero Point Fluctuations and the forces coupled with Gravity [33] .

That gravity is relevant to consciousness is illustrated by the solution for the potential energy for a human brain’s mass. Gravitational energy is classically defined as G∙kg²∙m⁻¹, where G is the Newtonian Gravitational Constant (6.67 × 10⁻¹¹ m³∙kg⁻¹∙s⁻²), kg is the mass of the human brain (assume 1.5 kg) and m is the average length (assume 12 cm). The resulting energy is 1.25 × 10⁻⁹ J. Assuming an increment of energy of ~2 × 10⁻²⁰ J for the effects of an action potential (120 mV) upon a unit charge (1.6 × 10⁻¹⁹ A∙s) with the average frequency of 10 Hz, the gravitational energy would have the potential to be equivalent to about 10¹⁰ neurons, which is with the order of magnitude of functioning cells within the human cerebral cortices [7] .

For the entire volume, we suggest the value of ~10²¹ units represents a critical threshold—a necessary condition—at which point Schumann-type oscillations are present in the spectral profile of the ED. Assuming the hydron isotope of a proton (H⁺) with an associated mass of 1.67 × 10⁻⁷ kg, the mass equivalency of ~10²¹ protons is 1.5 × 10⁻⁶ kg. Because the typical cell is 1 nanogram or 10⁻¹² kg, the number of cells associated with this mass-equivalency of the hydron threshold is ~1.5 × 10⁶ cells or between 1 and 2 million. This is the approximate number of cells which constitute the hippocampus [34] , a body which is linked to Schumann activity [20] . The value of 10⁶ - 10⁷ neurons also constitutes the typical discrete cluster of cells associated with a “thought” [35] .

We pursued the idea that hydrogen ion matrices composed of a minimum of ~10²¹ units are intrinsic receptive structures associated with the Schumann resonance. The volume of the human neocortex is ~5 × 10² ml on average with considerable variability within and between sexes [36] . Converting to grams, ~60% of the mass is water or 3 × 10² g. This mass can be further reduced to its hydrogen component which is 11% by proportional mass or a total of 33 g. If the molar mass of H₂O is 18 g/M, this volume represents 1.83 M that, when multiplied by Avagadro’s number gives 1 × 10²⁴ units within the human cerebral cortex of available hydrogen to dissociate. If the ED and the cerebral cortex are responding in the same way due to microstructural similarity in hydron content, the suggestion would be that a critical threshold of hydron units is needed to resonate with the ionosphere and express the Schumann pattern.

Spectral densities associated with the intra-skeletal condition optimally correlated with human baseline brain activity. This was primarily due to the cortex layer of the model, which suggests an intrinsic role of the shape of the skull in the representation of Schumann patterns in QEEG profiles. Nunez [37] has presented works which demonstrate that the bulk velocity of action potentials within the cerebral cortices (4.5 m∙s⁻¹) applied over a skull with a 60 cm circumference would generate a standing wave of approximately 7.5 Hz—value approximating the fundamental Schumann resonance frequency. A recent quantitative analysis of Earth-Brain interactions has revealed multiple convergences which suggest a profound relationship between the two structures [5] . Where neurons contained within the skull provide structure, the chemical and geometrical orientation of the space surrounding neurons are the primary interfaces for phenomena which precede the action potential. In the absence of neurons, the lattice of the dough might provide a similar network of structures along which signals might propagate in the presence of an external electromagnetic stimulus.

In this study, synchronous gamma oscillations within the 40 Hz range were measured in a three-shell realistic head model which was constructed to simulate the basic organization of the human cortex, scalp, and skull. As a neural correlate of consciousness, the expression of synchronous gamma in an intra-skeletal organization of ED does not indicate that the experimental apparatus was conscious. The only suggestion here is that a neural correlate of consciousness which operated within parameters similar to that observed in humans was disembodied from any neuronal substrate in a geometrical and chemical approximation of the components of the brain measured by the QEEG. These distinct, physiologically-patterned oscillations were not present in the same material shaped as a sphere or disk placed outside of the skull.

One theoretical solution involves a transmission theory of brain activity whereby an external signal is filtered by the brain and intermediate tissues [38] . Coherent oscillations across spaces which do not accommodate typical structural connections would be accommodated as receptive fields and would respond similarly to the application of the external stimulus. These responses, although simultaneous and independent, would be coherent and perhaps vulnerable to intra-cerebral resonance phenomena. Synchronous activity across brain-space is intrinsically linked to the binding problem [39] . If the three-shell model is operating as an antenna and receiving signals from the environment, this project lends experimental validity to the metaphor of consciousness and other brain functions as transmitted information.

Kuhn [40] argued that paradigm shifts are necessary and are brought about by a growing sense that existing models, albeit once optimally useful in pursuit of further knowledge, have malfunctioned in some fundamental way. In order to accommodate the observations that consciousness has avoided the traditional neuroscientific line of inquiry involving localization of function in brain-space, the idea of extra-cerebral signals and the information contained within them must be seriously considered as a potential source for the neural correlates of consciousness.

Here we present results indicating oscillatory electrical activity in a non-human model of the human head displays spectral densities that correlate with those of human subjects obtained over the scalp using QEEG technology. Quantification suggests a central role of the proton in relation to the physical dimensions of the cell. Further experiments are required which would parcel out the environmental contributions to the neural correlates of consciousness and other functions typically ascribed to the brain. In particular, the capacity for this preparation to show simulations of “memory”, that is the representation of previous stimuli no longer present, and learning, the more or less permanent change in responsiveness due to experience, should be demonstrable.

The authors would like to thank Professor Kevin Saroka for his insights and technical assistance.