Is the Fabric of Reality Guided by a Semi-Harmonic, Toroidal
Meijer D.K.F1* and Geesink J.H2
1Em Professor of Pharmacokinetics and Drug Targeting, University of Groningen, Groningen, the Netherlands
2Ir Previous Project Leader Nanotechnology, DSM, Geleen, the Netherlands
*Corresponding authors address:
Meijer D.K.F, Geesink J.H (2018) Is the Fabric of Reality Guided by a Semi-Harmonic, Toroidal Background Field?. Int J Struct Comput Biol 2(1): 1-15.
Received: August 8, 2018; Accepted: August 28, 2018; Published: August 30, 2018
Citation: Meijer D.K.F, Geesink J.H (2018) Is the Fabric of Reality Guided by a Semi-Harmonic, Toroidal Background Field?. Int J Struct Comput Biol 2(1): 1-14.
In this mini-review we describe our recent work, summarizing
13 publications, integrating their concepts and picturing potential
perspectives. The history of the discovery of the generalized music
(GM)-scale is highlighted in relation to the areas of bio-field research
and quantum biology. The central message is that nature may be
guided by a discrete pattern of electromagnetic frequencies, as
expressed in photon/electron (polariton) and phonon/electron
(polaron or soliton) activities. This guiding is based upon a physical
coherence principle that is coupled to entanglement, acts in a local and
non-local way, and is embedded in a toroidal geometry. We performed
meta-analysis studies on biomedical, cancer and neurological
literature, revealing the discrete EMF frequency pattern in a consistent
manner. This novel biophysical principle exhibits a mathematical
background and was also applied to brain function (consciousness
research) and 3-dimensional protein folding in integrates cells.
Strikingly, this life algorithm could also be detected in various nonanimate
systems. Among others we discovered a very similar pattern
such as energy/frequency distributions in entanglement (EPR)
experiments, frequencies of the currently known elementary particles
in the standard model as well as in frequency patterns of spectral
energy gaps that promote superconducting properties. The latter
aspect provides an interesting bridge between life systems and pure
physical phenomena. Finally some potential applications in quantum
computing and health technology are treated on the basis of a toroidal
Keywords: Quantum biology; Biophysics; Quantum computing;
Macroscopic coherence; Generalized music (GM) scale; Protein
folding; Brain function; Consciousness studies; Solitons; Polarons;
Polaritons; Toroidal modeling; Preventive health technology; Cancer
therapy; EMF and Neurological disorders; EPR experiments; Mass/
energy distribution of elementary particles; Superconductors at high
The Discovery of a Semi-harmonic EM Spectrum in Life
A biophysical basis for spectrum of discrete electromagnetic
field (EMF) frequencies that were shown to affect health and
disease [1, 2, 3, 4], were elaborated and generalized . The
particular EMF pattern was earlier revealed by us through a
meta-analysis of more than 500 biomedical publications that
reported life-sustaining as well as life-decaying EMF frequencies.
The detected Eigen-frequencies could be arithmetically scaled
according to a corresponding music theory, based on an adapted
Pythagorean tuning. The particular semi-harmonic scale exhibits
a core pattern of twelve Eigen frequency functions (Figure 1),
with adjacent self-similar patterns, according to octave hierarchy
[1, 2, 3, 4 and 7]. It should be realized that this frequency pattern
reflects experiments in which the life systems were exposed to
external EMF radiations, as well as influenced by the presence
of endogenous frequencies. We postulated that this coherent
pattern is effective because it mimics internal oscillations within
the organism and its constituting cells, and acts through resonant
communication, as extensively discussed in literature by many
others [see 1-4]. Our studies should be seen in the light of the
rapid expanding areas of Biofield Research, adequately reviewed
in [14-17], as well as that of Quantum Biology [18- 23].
Figure 1: Measured frequency data of living cells systems that are life-sustaining (green points) and detrimental for life (in red squares) versus calculated normalized frequencies. Biological effects measured following exposures or endogenous effects of living cells in vitro and in vivo at frequencies in the bands of Hz, kHz, MHz, GHz, THz, PHz. Green triangles plotted on a logarithmic x-axis represent calculated life-sustaining frequencies; red triangles represent calculated life-destabilizing frequencies. Each point indicated in the graph is taken from published biological data and are a typical
frequency for a biological experiment(s). For clarity, points are randomly distributed along the Y-axis.
The Mathematical Basis for a Generalized Music Algorithm
A more detailed mathematical analysis  shows that the
derived arithmetical scale exhibits a sequence of unique products
of integer powers of 2, 3 and a factor √2. These discrete Eigen
frequency values can be related to supposed bio-resonance of
solitons or polaron quasi-particles in life systems. Bio-solitons
are conceived as self-reinforcing solitary waves that constitute
local fields, being involved in intracellular geometric ordering
and patterning, as well as in intra- and intercellular signaling.
The discrete pattern of EM wave frequencies is mathematically
expressed as follows:
(En : Energy distribution, ωref : Reference frequency 1 Hz, ℏ :
Reduced Planck’s constant, n : Series of integers: 0, 0.5, 2, 4, 5, 7,
8, -1, -3, -4,-6, -7, m : series of integers: 0, 1, 2, 3, 4, 5, -1, -2, -3, -4,
-5, p : Series of integers: < -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, > +52)
The complete range of EM frequencies (lying between 0.2 Hz
to 500 Thz, see ref. , on basis of the 12 core frequencies, depicted
in Figure 1, can be easily expanded in lower and higher frequency
values by multiplication or division by a factor 2. This provides
an octave hierarchy of self-similar extensions of the scale. One
informative example is the calculation of the vibration frequency
of water from the known Einstein/Planck equations E= mc^2 and
E=h.v. In the case of the H2O molecule with an M of 18, and knowing
the values of speed of light c and the Planck constant h, a waterspecific
frequency can be calculated in Hz. Multiplying this value
with the octave hierarchy of 2, up to the THz-range (10^12 Hz),
a range can be found where the biophysics of ordering of water
molecules, relevant for life conditions, is at stake (see Figure 3). It
is of interest that the boundaries of this frequency spectrum lie in
the far-infrared EM region that occupies a middle ground between
microwaves and infrared light waves, known as the “terahertz
gap”. It represents the region in the electromagnetic spectrum
where the frequency of electromagnetic radiation becomes too
high to be measured digitally via electronic counters, so must
be measured by proxy using the properties of wavelength and
energy. In quantum many-body systems, several of the relevant
states have an energy difference that matches with the energy of
a THz photon. THz field’s photon energy plays also a role in semiand
superconducting phases because it can be resonant with
several quantum many-body transitions .
Figure 2: Short and long distance guiding of macromolecular structures in the cell by internal EMF wave frequencies (red) and external EMF scattered energies (blue). Discrete molecular vibrations in coherent domains in the cell can obtain a resonant state that is instrumental in intra- and intercellular communication and information processing in time.
Figure 3: Toroidal hypersphere mediated morphogenesis of the integral cell. A: The nested torus structure with an outer surface of the torus (red circle and arrows) represents the event horizon memory space surrounding the cell. B: depicts the 3-D folding of life macromolecules as it occurs
following primary synthesis in the cell. C: shows the fractal attractor structure of H2O around DNA, steered by quantum information of the toroidal
hypersphere memory workspace, D: Shows the dipole radiative EM field of arranged water molecules that bridges the DNA molecule and PCR enzyme
as essential for realization of the PCR activity. The coherency of cytoplasmic domains may be steered by externally applied EM fields in a resonance
state with the various cellular vibratory elements (modified from Montagnier, see ).
The GM-principle is operating in animate and Nonanimate
Additional literature search, revealed very similar frequency
patterns in the color spectrum, for wave resonances of
phyllosilicates, albumin and nucleotides in aqueous solution, as
well as for a candidate RNA-catalyst (see Table 1).
Of note, the calculated standing wave values of soundinduced
vibrations evoked on thin vibrating membranes, as
reported in the previous century by Chladny, also are congruent
with the GM-scale [1, 2]. This collective evidence, thus, points
at a generalized biophysical algorithm underlying complexity
in nature, evidently manifest in both animate and non-animate
modalities. It was therefore coined by us the generalized musical
(GM) principle [reviewed in 5]. The particular semi-harmonic
frequency spectrum may reflect a discrete pilot-wave structure
that can be interpreted as a, so called, hidden variable in Bohm’s
causal interpretation of quantum field theory , as described
by Bohm [47, 48] and as further adequately discussed by Sarfatti
Table 1: Guiding GM- principle in Animate and Non-animate systems
Biomedical research, 500 papers
Energy distribution in EPR-experiments, 40 papers
Cancer research, 219 papers
Energy distribution elementary particles, 40 papers
Neurological studies, 24 papers
Coherence promotion in superconductors, 80 papers
Nucleotide and albumin resonances
Coherent sound induced vibration patterns, 6 papers
RNA synthesis catalysis
Phyllosilicate semi-conductor materials
Brain function and Consciousness? *
Zero point energy of elements?
Protein folding in intact cells?
Super conduction in life systems?
Plasma waves in noble gasses?
*Question mark indicates: preliminary results, under investigation
Brain function and consciousness studies
The GM-biophysical principle was also applied to the areas
of modeling brain function related to human consciousness 
, as treated earlier in major reviews [31-39]. In this study, the
brain was conceived to be embedded in a holographic structured
field that interacts with resonant sensitive structures in the
various cell types in our body. In order to explain earlier reported
ultra-rapid brain responses and effective operation of the metastable
neural system, a field-receptive mental workspace was
proposed to be communicating with the brain. Among others, it
is integrating discrete patterns of Eigen-frequencies of photonic/
solitonic waves, thereby continuously updating a time-symmetric
global memory space of the individual. Its toroidal organization
may allow the coupling of gravitational, dark energy, zero-point
energy field (ZPE) as well as earth magnetic fields energies
(Figure. 4) and may transmit wave information into brain tissue,
that thereby is instrumental in high speed conscious and subconscious
information processing. It was proposed that the
supposed field-receptive workspace, in a mutual interaction with
the whole nervous system, generates self-consciousness and
is conceived as operating from a 4th spatial dimension (hypersphere).
The torus that is envisioned as a basic unit (operator)
of space-time is seen as instrumental in collecting the proposed
pattern of discrete GM-frequencies that provided an algorithm
for coherent life processes. It is postulated that consciousness in
the entire universe arises through, scale invariant, nested toroidal
coupling of various energy fields, that may include quantum error
In the brain of the human species, this takes the form of the
proposed holographic workspace, that collects active information
in a ”brain event horizon”, representing an internal and fully
integral model of the self. This brain-supervening workspace
is equipped to convert integrated coherent wave energies into
attractor type/standing waves that guide the related cortical
template to a higher coordination of reflection and action as
well as network synchronicity, as required for conscious states.
In relation to its scale-invariant global character, support was
found for a universal (cosmic) information matrix. The presence
of a field-receptive resonant workspace, associated with, but not
reducible to, our brain, may provide an interpretation framework
for widely reported, but poorly understood transpersonal
conscious states and algorithmic origin of life[11, 12]. It also
points out the deep connection of mankind with the cosmos and
our major responsibility for the future of our planet.
Figure 4: Modeling of brain/mind relation in a 4+1-dimensional space-time framework (4+1 implies 4 spatial dimensions and one single dimension of time), on the basis of energy trajectories in a nested toroidal geometry. The opposing forces of Dark energy (diverging force) and Gravity (converging force) as well as discrete wave frequencies of electromagnetic fields, are instrumental in the generation and compression of individual life information. The human brain may receive quantum wave information directly derived from the Planck space-time level (left above) through quantum
gravity mediated wave reduction, as well as through resonance with the ZPE field (right above). Our brain can perceive only 3+1 dimensions with a
one-directional arrow of time. The material brain and its 4+1-D supervening field-receptive mental workspace should be seen as an integral whole,
until bodily death of the organism. The 4th spatial dimension allows individual self-consciousness since an extra degree of freedom is required for selfobservation and reflection, while in the mental context the time dimension is symmetrical, allowing to integrate past and future- anticipating events.
The 4th spatial dimensions is also assumed to accommodate the bidirectional flow of information between the domains of self-consciousness and
universal consciousness. Bottom-up information flow from the Planck scale, combined with top-down information conjugation from the ZPE field,
constitute the event horizon of the brain, also integrating gravitational and dark energy related force fields, and supervenes the physical brain. Event
horizons of brain and whole body are depicted in red ellipse and circle respectively.
EM Fields and Neoplastic Diseases
A recent publication of the authors in the Journal of
Cancer Therapy , dealing with EMF and cancer, provides a
comprehensive overview of electromagnetic (EM) frequencies
that influence cancer processes and examines the bio-molecular
and biophysical mechanisms that may play a role in the widespectrum
of tumor etiologies. The study finds discrete bands of
EM frequencies that correlate with cancer suppression as well
as discrete frequency ranges that promote neoplasm formation
(Figure 5). As described in the paper, “carcinogenesis fits in a
frequency pattern of EM waves in which a gradual loss of cellular
organization occurs”. The coherent EM field frequencies are
named such because of their beneficial affect on the biological
system, whereby it appears that their constructive resonance
with macromolecules in the cellular system stabilize and even
reverse abnormal functioning, like that seen in neoplasm’s.
The coherent EM field frequencies stimulate beneficial
solitons/polarons energies, which have been shown to be involved
in macromolecular and cellular signaling and are related to the
mechanism of “Fröhlich condensation”, first hypothesized by
physicist Herbert Fröhlich [1, 14-17]. In this process vibrational
energy is concentrated in the lowest-frequency vibrational mode,
inducing strong quantum coherence of bio-molecules (Figure 2)
similar to the formation of Bose-Einstein condensation as also
related to superconductivity. The coherent EM field frequencies
are thus hypothesized to promote the formation of such strong
quantum coherences, increasing the strength and fidelity of intraand
inter-cellular signaling. In this process coherent oscillating
domains of ordered water molecules in resonance with other
macromolecules are supposed to play a central role [18-23 and
40- 43] and Figure 3.
Figure 5: EMF frequencies, related to cancer-research, that were experimentally applied to living cells systems reported in 219 separate biomedical studies, plotted on a semi-harmonic logarithmic reference GM-scale, are found to be patterned in 12 apparent bands of in total 143 life-sustaining coherent frequencies (green points) and 77 cell-destabilizing non-coherent frequencies (red squares). The latter are clearly positioned between the life-sustaining frequency bands. Each point indicated in the graph represents an individual experiment. For clarity, points are evenly distributed along
the Y-axis, according to the number of experiments within each apparent frequency band.
3-D Functional Protein Folding in Integrate Cells
The Fröhlich/Davydov concept [40-43] on soliton influence
on protein vibration has been elaborated and further improved
by Pang , taking into account that solitons can be largely
stabilized, and their life-time increased due to mutual interaction
of the particles with lattice vibrations. Consequently the total state
of the system has been expressed in three different Hamiltonians.
Due to these extensions, the solitons obtain life-times that are
more compatible with the ruling biological conditions. This was
expressed in Hamiltonians on quasi-coherent two-quantum state
wave function . According to the mechanism of bio-energy
transport Davydov established the theory of bio-energy transport
in protein molecules, in which he gave the Hamiltonian of the
B is the creation (annihilation) operator for an Amide I
quantum (exciton) in the site n, un is the displacement operator
of amino acid residue at site n, Pn is its conjugate momentum, M
is the mass of an amino acid molecule, w is the elastic constant of
the protein molecular chain, N is a nonlinear coupling parameter
and represents the size of the exciton-phonon interaction in
this process, J is the dipole-dipole interaction energy between
neighbouring amino acid molecules, m is the average distance
between the neighbouring amino acid molecules. The wave
function of the system proposed by Davydov has the form of:
Pang has added a new coupling interaction of the excitons
with the displacement of amino acid molecules into the
Hamiltonian and replaced further the Davydov’s wave function of
the one-quantum (exciton) excited state by a quasi-coherent twoquantum
state. The representations in equations (1a) and (1b)
for the single-channel protein molecules are replaced by:
The important point here is that the soliton transport should be
regarded as a concerted action of both the vibration of the quasiparticle
and that of the protein backbone lattice in interaction.
Recently, the potential long range resonant influence was
further worked out in a study of 3-dimensional protein folding in
the intact cell  that can be largely influenced by the formation
of coherent oscillation domains in the cell water interacting with
the protein backbone (Figure 2 and 3). We argued that the current
geometric and thermodynamic approaches in protein folding
studies do not provide a definite solution to understanding
mechanisms of folding of biological proteins. A major problem
in the understanding of this process is that the protein is first
synthesized as a linear molecule that subsequently must reach
its native configuration in less than 1 sec . Hydrophobicityhydrophilicity
models and random search mechanism cannot
explain folding to the 3-D functional form, as it occurs in the intact
cell. We propose an integral approach, based on the embedding
of proteins in the whole cellular context under the postulate: a
life protein is never alone [11, 12]. In this concept the protein
molecule is influenced by various long and short distance force
fields of nature such as coherent electromagnetic waves (Figure
3) and zero-point energy. This process is pictured as being
influenced by long-distance polaron/soliton vibration patterns
as well as by holographic memory of integrated cell function (see
also Mitchell, ) that is build up for any individual cell. This
approach to protein folding differs from usual quite artificial ones,
in that it takes into account many of the local cellular conditions
in a more holistic frame work.
Potential influence of Discrete EM fields in the Creation
of First Life in Biological Evolution
We found previously that coherent natural and permanently
operating wave pattern phenomena are present in typical
selected clay minerals, that have semi-conductive like properties
[1, 2 and 3]: identical EM field eigenvalues could be measured
by one of us (HG) (Figure 6 and ref.  and ). Of note, these
types of clay minerals are, apart from being present in soil, also
abundantly suspended in the universe, including planet earth (so
called cosmic or extraterrestrial dust) and have been suggested
to provide a semi-conductive medium that produces selective EM
wave patterns following excitation by external energy sources.
It is of interest that such silicates have been reported to be
candidates for the facilitation of oligo-nucleotide synthesis in the
creation of first life in biological evolution [1, 2, 11, 12] and [24,
26]. The selected silicates probably act as quantum replicators,
specifically emitting EM radiation at coherent frequencies in a
surrounding of ordered water molecules. Such silicate quantum
replicators therefore may have been instrumental in the initiation
of first replicating life, cells at the edge of pre-biotic evolution
Figure 6: Example of phyllosilicate semi-conductor, showing layers with tetrahedral and octahedral structures, as present in natural clay material. The material have been shown to act as a semiconductor, that can absorb EM radiation and transmits coherent discrete EM frequency bands. Instrumental in this property are clustered water molecules that provide resonance cavities (left above) and various doped inorganic cations such as Ca2+, Na+, Mg2+ etc.
We propose therefore that a primordial biological principle
(register of rules) was operating, that acts as a “recipe for life”
. This type of a-priory information could have preceded the
development of first life and all known force fields that were
present from the birth of the universe should be taken into
account (as mentioned earlier). Also quantum processes have
probably played an essential role in facilitating the various steps
that gave rise to first life and initiation of the first replicating
cells, in which atomic resonance creates organic shapes and
geometric folding of carbon containing molecules [18, 30, 25, 27].
This in addition to lattice type of organization of dipole water
molecules, together forming life harmonic-like lattice resembling
fluid crystals in which life can be viewed upon as a crystallized
form of quantum oscillations that invites to see the cosmos as a
purpose-driven incubator for life. This entire process was also
depicted as a kind of “biological music” originating from a pre
existing universal law intrinsic to nature, and conceptualized as
a toroidal alternative to random self-organization [11, 12]. Very
likely syntropic (neg-entropic) wave information from the zeropoint
energy field [51, 54, 56], selected in resonance with the
electrome  of the proto-cells played probably a crucial role
in the morphogenesis and building up of functional biochemical
networks during pre-bioses [36, 55].
A characteristic hallmark of life is its homochirality: all
biomolecules are usually of one hand, e.g. on Earth life uses
only L-amino acids for protein synthesis and not their D mirror
images. Chirality is a Lorentz invariant quantity and a left-chiral
particle is not transformed into a right-chiral particle by parity
transformations. All fundamental interactions of elementary
particles, with the exception of the weak interaction, are
symmetric under parity. The weak interaction is chiral and thus
provides a means for probing chirality in physics . Adsorption
to the chiral surface of phyllosilicates (see Figure.6) is a possible
mechanism not only to generate frequencies described by the
GM-scale, but also to induce a specific chiral character since
parity-violating weak interactions in these crystalline, enantioselective
and possibly pre-biotic, catalysts has been found .
The GM-principle and Quantum Entanglement Research
In view of the current interest in coherent states and
entanglement in quantum biology, we subsequently performed
meta-analyses of 40 papers in physics that deal with the influence
of electromagnetic frequencies on the promotion of entangled
states in, so called, EPR experiments . Einstein, Podolsky and
Rosen originated the EPR-correlation thought experiment for
quantum-entangled particles, in which particles are supposed
to react as one body. The meta-analyses of the EPR-experiments
learned that the applied frequencies are located at discrete
coherent configurations. As predicted all analyzed EPR-data of the
independent studies fit precisely in the derived scale of coherent
frequency data and turned out to be virtually congruent with the
above mentioned semi-harmonic EM-scale for living organisms.
This implies that the same discrete coherent frequency pattern
of EM quantum waves, that determine local and non-local states,
is also applicable to biological order and may indicate that
quantum entanglement is a prerequisite for life. The study may
indicate that the implicate order of pilot-wave steering system,
earlier postulated by David Bohm [47,48] is composed of discrete
entangled EM wave modalities, related to a pervading zero-point
energy information field [36, 51, 54, 55, 56].
The GM-Principle and Elementary Particles Energies
of the Standard Model
In a follow-up study, the model was further applied to the data
of a meta-analysis of earlier measured discrete mass/energies
and related frequencies of 37 different elementary particles, as
well as zero-point energies of elements .
A clear fit with the GM-frequency pattern was found (Figure
7), indicating that a semi-harmonic background underlies the
quantum field theory of subatomic particles. This confirms the
idea that an ontological basis of the Standard Model is at stake.
These data may also indicate that the GM-scale is frequencylocked
with zero-point oscillations, and thereby evidently
implies involvement of entangled states. The present theory
thereby combines quantum mechanics and classical periodic
systems, obeys to locality and refers back to the “hidden variable
theory of Bohm” [47, 48, 54]. The pattern of electromagnetic
field eigenvalues, within a broad range of discrete frequencies,
as revealed in the present studies, points at a de Broglie/Bohm
type of causal interpretation of quantum mechanics, implying an
integral resonant pilot-wave/particle modality 
Figure 7: Normalized frequencies of masses of Elementary Particles positioned at the GM-scale and added normalized color spectrum. Green triangles plotted on a logarithmic x-axis represent normalized coherent-frequencies. Green points: data of Einstein-Podolsky-Rosen experiments (1972-
2017). Blue points represent calculated normalized frequencies of masses, (for clarity, points are distributed along the Y-axis)
It is important to note that in our life studies a regular pattern
of both coherent and decoherent frequencies were found (see
Figure 1). The coherent part of the GM-scale was defined by us as
semi-harmonic since it is not only be based on integer numbers,
as in classic harmonics, but also on rational numbers and an
irrational number according to an adapted Pythagorean scale,
that suggest a toroidal (rotational) aspect in the mathematical
background. Importantly, only coherent and no decoherent
values were detected in the purely physical studies on EPR
entanglement and elementary particle studies as well as in the
superconductor studies (see section on page 10). What could be
the reasons that the decoherence aspect seems absent in the latter
studies? Needless to say in the case of EPR and superconductors
studies, this is likely to be due the selection of materials that
have been made by the investigators in relation to an optimal
function related to coherence and entanglement, yet in principle,
not excluding decoherent frequency values. Apparently such
an argument does not hold for the standard model study that
clearly lacks decoherent values in the distribution of elementary
particles mass/energies (see Figure 7). Combinations of coherent
and decoherent states according to the GM-scale can be found
in all kind of atoms/molecules, and it may be that decoherent
states are created through interactions in complex structures
as an implicit feature . We have earlier speculated that the
combination of coherent and decoherent wave frequencies in
the life systems could reflect a potential regulatory mechanism
. Alternatively they could be related to entropy-forced repair
mechanisms to remove corrupted cells from the organism by, for
instance, the crucial process of cell apoptosis [4, 5].
Importantly, it has been postulated that the balance of
coherent and decoherent states may be more dynamic than
earlier thought and that creation of a coherent or decoherent
state by collapse of the wave function could in principle be a
reversible process. Consequently, it would be justified to think in
terms of dynamic states of coherence/decoherence in a cycling
mode [20, 21], see Figure 8). Life would thereby always operate
at the edge of chaos in a so called poised realm that allows the
choice between two states in equilibrium, and thereby enabling
fast responses essential for the cell ecology and survival. Also, for
instance wave/particle duality may occur in a domain in which
wave and particle modes are present at the same time. In fact,
such a poised condition could be conceived as a thermodynamic
balance between entropic and syntropic (neg-entropic) aspects
of reality. In fully physical systems such opposing conditions
would have a more implicit character as for instance in wave/
particle duality, matter/antimatter annihilation and forces such
as gravity and dark energy. All this would imply a general aspect
of symmetry and/or duality in nature that even could explain
other poorly understood phenomena such as life and death,
conscious versus non-conscious aspects of brain function [2, 6
and Figure 8].
Figure 8: Hypothetical cycling of quantum coherent and decoherent states (left). Dynamic duality may play a general role in the fabric of reality (right). Middle: 3D/4D poised domain that allows choice between two quantum states in equilibrium in which all of the depicted processes may operate on the brink of 3D and 4D spacetime. Middle below: 3-D Torus can perform 3D to 4-D rotations, that can be compared by closed movement on a
Möbius strip (inside is outside), which may imply restoration of non-duality. Right: Other well known dual processes in Nature.
In fact, there are many suggestions in literature on the
principles of recurrent information flux and all kind of cyclic
processes in nature [6, 65]. A crucial element in these processes
could be a sort of connective information flux instrumented by
bosonic energies such as wave fields of photons and phonons
(depending on the medium at stake). Zero-point energy could
be a prominent information domain since the electromagnetic
photon part can become polarized at accelerated movement
of fermionic charge and in this process is known to obtain a
rotational character. Quasi-particles that bear both bosonic
and fermionic elements, could play a crucial role in information
transfer and may have guiding potential [3-5]. Especially the
topological organization of photon/phonon and electron quanta
flux, as for instance in the present torus model, would be an
attractive multi-cyclic mode. Of note, the torus, including its
knots, is seen as an attractive model for the physical description
of various elementary particles up to very large structures in the
It is further considered that the intervals of this GM-scale can
be described by a 3D toroidal space, according to the knowledge
of a 12-basic coherent scales, and can be modeled, in principle,
by a torus geometry, as described by Amiot .For example:
the circle of “fifths” of the GM-scale can be positioned at rotoids
(composed motions of rotations), that circles or spiralizes each
sub-unit of the nested tori, together with inscribed triads, majorthird
and minor-third relations, see Figure 9.
Figure 9: The cycle of interrelated biophysical and physical observations of the 13 reviewed papers of the present authors (depicted in black in the figure as ref. number in list 1), with the various aspects dealt with.
Potential cyclic/spiral/toroidal and periodic character
of particles in space-time
Elementary cycles theory (ECT) of Dolce , postulates
that every elementary “particle” of nature is characterized by
persistent intrinsic space-time periodicity. In ECT the Planck
energy spectrum is interpreted as an harmonic like spectrum of
a mass-less periodic modalities of fundamental time periodicity
T (quantized energy: En= nhω = nh/T, discretized angular
frequencies: nω, and time periodicity T = h/E)
According to‘t Hooft [44, 45], it is assumed that a theory
describing our world starts with postulating the existence of
sub-systems that, in a first approximation, evolve independently,
and then are assumed to interact. It is suspected that our world
can be understood by starting from a pre-quantized classical or
“ontological” system. If time would be assumed to be discrete,
the Hamiltonian eigenvalues would turn out to be periodic.
Both theories favor a quasi-classical and quantum ontological
interpretation of quantum physics, as in a primary form earlier
suggested by David Bohm [47, 48] as discussed by us in [9, 10].
Solitons/polarons, as quasi particles, are a widely observed
physical phenomenon that behave like solitary waves, but
possess many features of particles. They are able to suppress an
harmonicity (the deviation of a system from being a harmonic
oscillator) by the excitation of high quantum levels, a process
that facilitates the crossing of potential barriers and the transfer
of a molecule to a new conformational state [4, 11, 12]. Particle
attributes and particle conformation in space are linked, and
knots can be scheduled as solitons (polarons), while toroidal
solitons can be depicted as braids and framing. When particles
within fields, move around following classical laws, than these
classical laws could resemble classical field theories such as the
Navier Stokes equations and the existence of vortex and toroidal
solutions [50, 58]
Also high-frequency quasi-periodic oscillations measured in
a torus orbiting in the vicinity of a black hole probably obey to
the Eigen frequencies of the proposed algorithm. According to
Rezzolla , the torus, in fact, can be thought of as a cavity in
which the p modes effectively behave as trapped sound waves.
If the sound speed in the cavity were constant, the frequencies
of these standing waves would be in an exact integer ratio. In
reality the sound speed is not constant but the Eigen frequencies
found are in a sequence very close to 1:2:3:4. So cyclic energy
trajectories and periodicity in quantum physics may be envisioned
as recurrent spiral movements on a torus see Figure. 9.
It is further proposed that Life Systems resemble typical
coherent resonances of atomic cascade transitions of materials
used to show Einstein-Podolsky-Rosen’s argument, and Bell’s
theorem that should be placed by a local realistic process in
space-time. Potentially, these informational frequencies are
linked with the zero point energy field, through resonances
leading to phase-locked cellular information attractors [36, 55],
that are functionally separated by non-coherent wave activity .
The latter could explain the function of interwoven “coherent”
and “non-coherent” EM/quantum values and the presence of
trajectories corresponding with initial vibrational energies of
molecules and atoms equal to their measured vibrational zeropoint
energy [50, 51, 55].
GM-scale and Superconductors, Applications in
Quantum Computing and Health Technology
Finally the GM-algorithm was recently applied to the
phenomenon of superconductivity, in the light of the current
interest in Quantum Biology [18-23], a discipline that revealed
that even at life temperatures; cells can operate in a coherent
superconductor-like mode . High Tc superconductors are
composite materials made of multiple structural modules of units
and their electronic structure has a multiple Fermi surface and
multiple gaps in the superconducting phase. It is known that a
fractal network of dopants can lead to a macroscopic quantum
potential that facilitates macroscopic quantum coherence, see
Turner . By a meta-analysis of superconductor research
with regard to coherence time promoting EM frequencies, it was
clearly shown that these frequencies perfectly fit the GM-scale.
This highlights the relevance of this biophysical principle for
information processing in non-animate systems (see Table 1)
and, interestingly, again provides a biophysical bridge between
animate systems and non-animated materials. The knowledge
of decoherence- preventing EM frequencies can potentially be
used in superconducting materials that are currently elaborated
for quantum computing. In this area, again the toroidal geometry
seems to be relevant. It is of interest that decoupling of qbits from
the environment may be realized through a toroidal pole setting,
see Zagosking . Only coherence sources inside the toroidal
section of the qubit may limit the qubit decoherence time and
this decoherence can be further reduced by applying multi-doped
systems that obey to a coherent GM-scale. Toroidal multipoles
are fundamental electromagnetic excitations different from those
associated with the familiar charge and magnetic multipoles and
have been held responsible for parity violation in nuclear and
The Connecting Principle: Dual (Nested) Torus
Operators Create Information Flux via a Wormhole
The collective data forwarded in our publications consistently
present quite a diverse number of physical modalities that is also
expressed in life systems: scale invariance/fractality, toroidal
geometry, coherence/entanglement conditions as well as
superconductivity, zero-point energy, elementary particles and a
supposed pilot wave domain. Yet this spectrum of elements can
be clearly connected through the assumption of an underlying
information matrix [63-65]. The latter may be directly derived
from the information flux in the nested torus with its central
channel or, in more cosmological terms, its entangling wormhole
structure . We postulate an entangled torus/wormhole web,
providing a fundamental connective principle that underlies the
fabric of reality , that bears a electrometric signature exhibiting
harmonic like features.
The particular torus/wormhole matrix, inferred from our
work, is supported by the work of Susskind  and Haramein
, who independently postulated that both space and time
can be understood from the entangling properties of Einstein-
Rosen bridges, in the so called ER= EPR framework (see for the
time aspect also Moreva ). This scale invariant concept is not
only based on macro-information systems such as linked black
holes, but even on micro-events like elementary particle pairs
that pop up in space and disappear again in the zero-point energy
context. It has been suggested that the matter/antimatter parts
of such pairs are connected through a wormhole-like structure
. The latter is pictured as a string in the 3D setting that is
holographically conceived as a wormhole modality in a world
of 4-spatial dimensions. Pair periodicity is often expressed as
quantum fluctuations in the zero-point energy field. This occurs
from the level of the electromagnetic Planck scale up to life cells,
our planet, galactic systems and even the circular (rebound)
character of the whole universe .
A very similar construction with a fractal character is likely to
be present in biological systems including the extremely complex
and dynamic information workspaces of the human brain. In
this respect we argued that, apart from the classical neuronal
transmission system, an additional information guiding principle
of quasi-particles such as polarons (solitons) is required to
explain the super fast brain responses and the phenomenon of
(self)-consciousness [6, 64]. The superconducting property
of bio-photons in cell structures such as plasma-membranes,
mitochondria, microtubuli, and coils of DNA, all associated with
structured water layers [40, 42, 43], may be instrumental in the
coherent synchronization of oscillatory neuronal networks in
the brain, as suggested by us . Super conducting properties
have also been described recently in warm and wet conditions in
the field of quantum biology, for instance in olfaction, magnetic
navigation of animals and, in particular, in photosynthesis
It is of interest that toroidal wormholes may support
electromagnetic and magnetic flux  and the same time can
scatter electromagnetic waves . Stable dual torus/wormhole
structure and transparency require an energy field as well as a
cavity with refractive indexes for efficient traversable conditions
. This latter aspect was also proposed for superluminal
photon flux in neuronal micro-tubuli . We speculate that
the coherent set of discrete EM frequencies revealed by us is
instrumental in creation of such super-radiance conditions.
This, by superposing the particular frequencies on the manifest
torus/wormhole density, explaining the congruent EM frequency
patterns that, according to our studies, promote entanglement
 and superconductivity , as well as energy distribution of
elementary particles . The latter were earlier described as
toroidal knots .
Future research and applications
Living cells make use of coherent frequency signaling, similar
to Bose Einstein condensates, in order to stay stable [15-17,
40-43]. If incoming man-made electromagnetic signals indeed
exhibit de-coherent EM radiation, than these signals, potentially,
will decrease the coherency of (quantum) wave domains of living
cells. A possible way to deal with such a problem is either to
lower the energy density of the external man made de-coherent
waves and/or to convert them to more coherent frequencies.
We envision innovative methods for increasing the coherency
of the electromagnetic signals through the use of appropriate
semiconductor and superconductor technologies. Coherent
terahertz waves, obeying to the GM-function, could be produced
by appropriate semi-conductive and superconducting materials,
inserted in electromagnetic man-made devices. This by making
use of the knowledge with regard to the earlier mentioned
Terahertz gap, through enabling the combination of supplied
optical and electronic coherent information. Beneficial EM wave
technology may therefore find applications by further improving
health during the increasing use of EM-information/data in our
society as well as in the design of therapeutic instrumentation for
various chronic diseases and ageing processes [5, 8, 13].
What can finally be concluded from the spectrum of data from
our publication? First of all it should be clear that these concepts
are based on the notion that nature is quantized according to
the principles of quantum mechanics. If we assume that also
electromagnetic fields have a quantized character, it follows
that EM frequencies can only occur at discrete eigenvalues:
to be defined as standing waves at typical frequencies. Such
standing waves are able to interact and can produce constructive
interference patterns that have a discrete character composed
of eigenvalues. In order to understand their distribution pattern
a semi-harmonic type of a mathematical relation is proposed.
This relation is known from music theory, and called an adapted
Pythagorean tuning [7, 46]. There are many examples of this
kind of approach in physics, for example in defining a color
spectrum with distinct frequencies, spin quantum states,
Racah-coefficienten, Zeeman-states, LS-values, JJ-couplings, and
quantum orbital moments among others. They all approach a
distribution pattern of standing waves on the basis of whole
numbers 1, 2, 3, 4 and (ir) rational numbers like 1/2, 3/2, 4/3,
5/2, 7/2, 9/2, √2, providing a semi-harmonic scale.
Any physical system that deals with quantized electromagnetic
aspects and thus is based on standing waves and constructive
wave interference can therefore be predicted to show such a
discrete pattern of EM frequencies. In our papers on EM fieldpromoting
effects on the degree of entanglement, and the EM field
frequencies that may overcome superconductor gaps as well as
the mass/energy derived frequencies for the known elementary
particles, demonstrated, albeit retrospectively realized, the
predicted fit with a coherent GM-scale. The most striking element,
however, is our primary observation, that life systems as studied
in the 500 biomedical reports show this distinct EM frequency
pattern. This strongly suggests that coherence, entanglement
and superconductivity may be prerequisites for life. In fact,
superconductor features have been demonstrated in current
quantum biology: in olfaction, long distance magnetic navigation
of various animal species and in particular in photosynthesis [19,
23]. It should be realized also that life material is build up from
elementary particles and that essential macromolecules such as
proteins and DNA have an inherent vibrational property that can
show coherent features. In cells this is likely to be supported by
coherent domains of structured layers of water [12, 13 and 40-
43]. The latter aspect was suggested by us also be instrumental
on the process of 3D- folding of proteins to their functional
structure, as supported by many other studies reviewed in [14-
Also the major influence of coherent (preventive) and
non-coherent (pathology inducing) EM fields on cancer and
neurological disorders highlight the current interest in biofield
research and health technology. The various interrelated aspects
of our studies are depicted in Fig.10, in a circular mode, going
from the initial life algorithm study to the proposed semiharmonic
scale, the earlier mentioned Chladny patterns [1,
2] and subsequently the follow-up studies on entanglement,
superconductors and elementary particles, to be finalized in
the creation of photon energies, phononic lattice vibrations, the
involvement of quasi particles and finally closing the circle with
the study on protein folding and EM field effects on tumor growth
and neurological disorders.
Finally, we want to stress that dynamics of the biophysical
processes at stake (harmonics/music, entanglement, superconductor
conditions and elementary particles (knot theory), all can be
modeled by toroidal geometry, as in many other related studies.
We consider the torus as a versatile space-time operator for
the handling and integration of information fluxes, in which the
physical information is projected in a holographic manner in a
3-D/4-D context and the syntropic life information is projected
in a scattering event horizon . Such field-sensitive toroidal
workspaces have been postulated as a key element for the
creation of scale invariant consciousness in the universe . It
remains to be shown whether an implicate order, as proposed by
Bohm, finds it physical expression in an information/geometric
domain described either as a liquid crystal matrix, zero-point
energy fluctuations or quantum foam at the level of the Planck
scale or even beyond this domain (see Figure 10). The reviewed
studies may contribute to a better understanding of the bio-fields
that operated in the evolutionary organization of complexity,
on the brink of inanimate and animate structures, and still
are instrumental in the ongoing fabric of human and cosmic
Figure 10: The cycle of interrelated biophysical and physical observations of the 13 reviewed papers of the present authors (depicted in black in the figure as ref. number in list 1), with the various aspects dealt with.
We are indebted to drs. Trudi Sonderkamp for critically reading
our manuscript and adequate suggestions for improvement.
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