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Solitons, as self-reinforcing solitary waves, interact with complex biological phenomena such as cellular self-organisation. Soliton models are able to describe a spectrum of electromagnetism modalities that can be applied to understand the physical principles of biological effects in living cells, as caused by electromagnetic radiation. A bio-soliton model is proposed, that enables to predict which eigen-frequencies of non-thermal electromagnetic waves are life-sustaining and which are, in contrast, detrimental for living cells. The particular effects are exerted by a range of electromagnetic wave frequencies of one-tenth of a Hertz till Peta Hertz, that show a pattern of twelve bands, if positioned on an acoustic frequency scale. The model was substantiated by a meta-analysis of 240 published papers of biological radiation experiments, in which a spectrum of non-thermal electromagnetic waves were exposed to living cells and intact organisms. These data support the concept of coherent quantized electromagnetic states in living organisms and the theories of Davydov, Fr\"ohlich and Pang. A spin-off strategy from our study is discussed in order to design bio-compatibility promoting semi-conducting materials and to counteract potential detrimental effects due to specific types of electromagnetic radiation produced by man-made electromagnetic technologies.
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Electromagnetic Biology and Medicine
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Bio-soliton model that predicts non-thermal
electromagnetic frequency bands, that either
stabilize or destabilize living cells
J. H. Geesink & D. K. F. Meijer
To cite this article: J. H. Geesink & D. K. F. Meijer (2017) Bio-soliton model that predicts
non-thermal electromagnetic frequency bands, that either stabilize or destabilize living cells,
Electromagnetic Biology and Medicine, 36:4, 357-378, DOI: 10.1080/15368378.2017.1389752
To link to this article: https://doi.org/10.1080/15368378.2017.1389752
Published online: 22 Nov 2017.
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ARTICLE
Bio-soliton model that predicts non-thermal electromagnetic frequency bands,
that either stabilize or destabilize living cells
J. H. Geesink and D. K. F. Meijer
Department of biophysics, Groningen, The Netherlands
ABSTRACT
Solitons, as self-reinforcing solitary waves, interact with complex biological phenomena such as
cellular self-organization. A soliton model is able to describe a spectrum of electromagnetism
modalities that can be applied to understand the physical principles of biological effects in living
cells, as caused by endogenous and exogenous electromagnetic fields and is compatible with
quantum coherence. A bio-soliton model is proposed, that enables to predict which eigen-
frequencies of non-thermal electromagnetic waves are life-sustaining and which are, in contrast,
detrimental for living cells. The particular effects are exerted by a range of electromagnetic wave
eigen-frequencies of one-tenth of a Hertz till Peta Hertz that show a pattern of 12 bands, and can
be positioned on an acoustic reference frequency scale. The model was substantiated by a meta-
analysis of 240 published articles of biological electromagnetic experiments, in which a spectrum
of non-thermal electromagnetic waves were exposed to living cells and intact organisms. These
data support the concept of coherent quantized electromagnetic states in living organisms and
the theories of Fröhlich, Davydov and Pang. It is envisioned that a rational control of shape by
soliton-waves and related to a morphogenetic field and parametric resonance provides positional
information and cues to regulate organism-wide systems properties like anatomy, control of
reproduction and repair.
KEYWORDS
Solitons; biology; quantum
dynamics; quantum
coherence; eigen-frequencies;
phonons; excitons; electrons;
photons; coherence;
Bose-Einstein condensates;
toroidal coupling; repair;
Fröhlich; Davydov; Pang;
Belyaev
Introduction
Extensive biophysical research has learned that the typi-
cal discrete frequencies of electromagnetic waves can be
favorable for living cells. An earlier analysis of 180
articles from 1950 to 2015, dealing with effects of elec-
tromagnetic waves on in vitro and in vivo life systems
has been made by Geesink and Meijer (Geesink and
Meijer, 2016), and has shown that discrete eigen-fre-
quencies of electromagnetic waves are able to stabilize
cells, whereas others cause a clear destabilization. In this
article we actualize these preliminary data by a further
analysis of another 74 articles, with special reference to
potential adverse effects of EM radiation, and detected a
striking agreement with the earlier observed frequency
pattern as depicted in Figure 2. On the basis of this
research an obvious question arises: what can we learn
from the existence of such (un)favorable EM (electro-
magnetic) radiation frequencies on living cells, realizing
that the same frequency bands ranging from Hertz to
sub-Terahertz are produced by man-made technology
on a daily basis? Indeed, both living organisms and
man-made technologies are able to generate electromag-
netic pulses, that are transferred and processed at a non-
thermal level. The main difference between both systems
is that living organisms seem to be favorably affected by
coherent patterns of electromagnetic waves, that may
induce a biological order, whereas modern man-
made equipment not yet produces such selective coher-
ent frequency bands. Our previous article (Meijer and
Geesink, 2016)wastitled:Phonon guided Biology,in
the present publication we prefer the term Soliton as a
further differentiation, since the latter term indicates a
phonon/electron coupled quasiparticle formed through
interaction with a lattice phonon cloud (solitons were
also called polarons). Solitons are seen as electrically
longitudinal vibrations that can travel along proteins,
microtubules and DNA similar to semiconducting mate-
rials, inducing an endogenous electromagnetic field and
interfere with local resonant oscillations by excitation of
neighboring molecules and macromolecules. Coherence
is defined as the physical congruence of wave properties
within wave packets and it is a known property of
stationary waves (i.e. temporally and spatially constant)
that enables a type of wave interference, known as con-
structive. Constructive wave interference leads to the
generation of specific resonance patterns promoting
coherent cellular domains and dynamic cell systems are
CONTACT J. H. Geesink hans.geesink@ziggo.nl
ELECTROMAGNETIC BIOLOGY AND MEDICINE
2017, VOL. 36, NO. 4, 357378
https://doi.org/10.1080/15368378.2017.1389752
© 2017 Taylor & Francis
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partially operating via this principle. On this basis an
important question arises: is it possible to increase the
degree of coherency of man-made electromagnetic sig-
nals in order to externally support the health of living
cells? Living cells have been demonstrated to be influ-
enced by selective spectra of frequency bands in the UV,
light, IR, THz and ELF range, as was consistently
reported from many current bio-radiation research
groups. Fröhlich proposed in 1968 (Fröhlich, 1968),
that living cells, for constructive interference, seem to
employ so called acoustic polarons, which can be
described by Bose-Einstein-statistics. The particular
wave-information that affects living cells at Terahertz
frequencies, consists of oscillating charges in a thermal
bath, in which a large numbers of quanta condense into
a single state. The latter is known as a Bose-Einstein
condensate, and induces a physical and non-thermal
interaction between biomolecules. Bose-Einstein con-
densation represents a phenomenon wherein the bosons
(particles/waves in quantum mechanics that follow
BoseEinstein statistics) produce a combination of
waves that merges at the lowest cellular energy level
into a shared quantum state. Such a collection of weak
interacting waves, thereby constitute a discrete set of
available energy states at a thermodynamic equilibrium.
This results in a so called macroscopic wave function,
implying that all the particles/waves in the condensate
take the form of a coherent wave modality. The latter
can take wave dimensions that are many orders of mag-
nitude larger than that of the microscopic objects such as
atoms and molecules, due to the fact that the resulting
overall wave field is highly correlated.
Coherence versus decoherence in cell processes
One of the fundamental questions in developmental
biology is how the vast range of pattern and structure
we observe in nature emerges. Turing (1952) wrote a
article about the chemical basis of morphogenesisin
which he proposed an ingenious new theory (Turing,
1952). Turing hypothesized that the patterns we
observe during embryonic development arise in
response to a spatial pre-pattern in biochemicals,
which he termed morphogens. Cells would then
respond to this pre-pattern by differentiating in a
threshold-dependent way.
Maini (2012) discussed the one-dimensional inter-
vals and two dimensional squares, which concepts are
generalizable to higher dimensions and different geo-
metries. With increasing dimension, the number of
possible patterns and arrangements of these patterns
also increases. For example, in two dimensions, spots
or stripes can be produced, with the spots having the
ability to be arranged in square, diamond, rhombic or
hexagonal patterns. In three-dimension lamellae,
prisms and various other cubic structures, all exist
making prediction even more difficult. In general, typi-
cal Turing models lose robustness with the inclusion of
delays associated with the time scales of gene expres-
sion or the cell cycle, regardless of the inclusion of
customary stabilizing features such as tissue growth.
They emphasize the need for genuine multi-scale mod-
elling coupling sub-cellular dynamics with large-scale
self-organization within developmental biology (Maini
et al., 2012).
We propose a mathematical and physical principle of
morphogenesisbased upon parametric resonance and
coherence. A physical system undergoes a parametric reso-
nance if one of its parameters is modulated periodically
with time (Butikov, 2004). Examples of parametric models
are the ion cyclotron models of Lednev (Engstrom, 1996;
Lednev, 1991) and Blackman (Blackman et al., 1985,1995;
Blanchard and Blackman, 1994).Coherenceornon-ran-
domness of quantum resonances has been discussed by
Einstein and Infield (1961) for the so-called prequantum
modes. And it was Schrödinger who recognized that
coherent interaction of waves is coupled to entanglement
as the characteristic aspect of quantum mechanicsand
suggested that eigenstates,alsocalledpreferred states
are able to survive interaction with the environment.
Coherent resonances can be present, for example, in elec-
trons, photons and water molecules. The preferred loca-
tions receiving resonance transfer in the case of living cells,
are the surrounding domains of ion water clathrates,
nucleic acids and ion-protein complexes. These are present
in and near neurons, ion channels, proteins and DNA.
Water is known to be coherently nano-structured and
coherent affecting bio-molecular processes, including pro-
tein stability, substrate binding to enzymes, as well as
electron and proton transfer (Chaplin, 2000;DelGiudice
et al., 2010;Johnson,2009).
Quantum mechanics explains the interactions of
wave/particles energy at the scale of atoms and suba-
tomic particles. Quantum mechanics assumes that phy-
sical quantities such as energy or momentum are,
under certain conditions, quantized and have only dis-
crete values. Quantum coherence have been shown not
only for micro states, but also for macro processes such
as photosynthesis, magneto-reception in birds, the
human sense of smell as well as the photon effects in
vision, all showing a non-trivial role for quantum
mechanisms throughout biology (Huelga and Plenio,
2013;Lambert et al., 2013; Rozzi et al., 2012).
Thus clear quantum coherence in living systems has
been proposed (Swain, 2006). Apparently, nature makes
use of wave information to induce and stabilize
358 J. H. GEESINK AND D. K. F. MEIJER
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biological order. The stability and life times of these
waves depend upon the extent of thermal decoupling of
the stable state(s) of cells from the heat bath.
Coherent neuronal oscillations correlate with the
basic cognitive functions, mediate local and long-
range neuronal communication and affect synaptic
plasticity. Theoretical modelling, as well as emerging
experimental evidence indicate that the neuronal cytos-
keleton supports highly cooperative energy transport
and information processing based on molecular coher-
ence (Plankar et al., 2012) and morphogenic pathways
are integrated in glands (Fata et al., 2004).
Yet, in order to maintain stability of bio-molecules
in living systems, also external coherent information is
required. For example: whether or not (externally
applied) coherent electromagnetic radiation in the
Terahertz region can effectively pump bio-molecules
in and/or out of the meta-stable state(s) in relation to
collective biochemical reactions, is a question of critical
importance to the existence of associated bio-effects
(Illinger, 1981).
Interestingly, it is also known that the coherent wave
information can be perturbed by de-coherent wave
information and the reversed process can also occur
in a kind of coherence-decoherence state cycling. Shor
(1997) proposed a quantum error correction theorem
for quantum calculations. If degrees of freedom in
quantum computing are de-cohering due to loss of
phase information from the computing system to its
environment, the addition of coherent information to
the system from the outside, turns the de-coherent state
into a re-coherent one again (Shor, 1997). In relation to
this, Kauffman examined data on photosynthetic sys-
tems (Arndt et al., 2009; Lloyd, 2014).
In photosynthesis, photons are captured by the
chlorophyl molecule that is held by an antenna protein,
by which the chlorophyl molecule maintains quantum
coherence for up to 750 femtoseconds. This is much
longer than the classical prediction, and is viewed as
responsible for the highly efficient energy transfer in
photosynthesis. The particular antenna protein plays a
role in preventing de-coherence, and in inducing re-
coherence in de-cohering parts of the chlorophyll mole-
cule. Kauffman proposed that this raises the possibility
that domains of quantum coherence or partial coher-
ence can also extend across neurons in the brain (Lyle
et al., 1983).
Cellular effects are sensible to low-level sinusoidal-
modulated signals of different frequencies and pulse
modulations. Windowing in many observed biological
interactions in both frequency and amplitude domains
have been found (Arndt et al., 2009; Kauffman, 2010;
Lloyd, 2014; Shor, 1997). Even electromagnetic noise
has an influence on DNA (Lai and Singh, 2005; Lai
1969) and decoherent modulations of signals have a
greater influence on biological properties than unmo-
dulated signals (Davydov, 1977; Fröhlich, 1969,1988;
Hidalgo, 2007).
2. Coherent vibrations in the relation to Bose-
Einstein condensates and suppression of
anharmonicity
When in nature coherent states are induced to be
organized and stabilized at the lowest possible energy
level, then atoms, electrons, photons, bosons and mag-
nons will potentially be ordered in the same way. The
processes that mediate such events in biological systems
are driven by fine tuned molecules, structured at the
nano- and sub-nanoscale. At these small scales, the
local dynamics are governed by the laws of quantum
mechanics, as shown for photosynthesis in which exci-
tons exhibit a wave like character. Hidalgo (2007)
argued that the maximum payoff for a quantum system
is provided by its minimum energy state. The indivi-
dual system components will rearrange themselves to
reach the best possible state for the whole system, being
a sort of microscopic cooperation between quantum
objects. (Hidalgo, 2007).
If energy is fed into these vibrational modes, then a
stationary state will be reached in which the energy
content of the electromagnetic modes is larger than in
the thermal equilibrium. The excess of energy is sup-
posed to be channelled into a macroscopic wave func-
tion, like Bose Einstein condensates, provided the
energy supply exceeds a critical value. Thus, under
these circumstances, a given supply of energy is not
completely thermalized but used in maintaining coher-
ent electromagnetic states in living organisms. Fröhlich
inferred that such orderings principles employ boson-
like quasi-particles in biological processes, similar to
condensed inorganic matter (semiconductors). He
claimed in 1968 that oscillating charges in a thermal
bath, in which a large numbers of quanta condense into
a single state, form a condensed set of oscillators that
can activate a vibrational mode of the lowest possible
frequency at room temperature. Bose-Einstein conden-
sation, in this manner, serves as a method for energy
storage as well as for channelling energy to specific
bioprocesses such as cell division and macromolecule
synthesis. He considered the many boson system to be
consisting of polar vibrations of biopolymers under
excitation (longitudinal phonons due to metabolic
energy pumping) that are embedded in a surrounding
fluid. He derived a set of equations that describe the
time evolution of collections of these vibrational modes
ELECTROMAGNETIC BIOLOGY AND MEDICINE 359
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in various model structures such as proteins or mem-
branes. He also estimated, on the basis of theoretical
arguments, that collective vibrational modes of meta-
bolically active biological systems are in the frequency
range of 0.110 THz (0.11.0 ps), displaying typical
spectral features and that polarons play a crucial role
in such processes (Fröhlich, 1968,1969,1988).
Polarons (also called Solitons, see later) are quasiparti-
cles, produced by coupling of electrons and phonons,
producing collective excitations of surrounding atoms
(see Figure 1). The term polaron was coined by Landau
in 1933 to denote this type of quasiparticle, comprised of a
charged particle coupled to a surrounding polarized lattice
in the presences of photons. Next to polarons, polaritons
play a role, which represent phonons coupled with excitons
(electron hole pair that arise from excitation of electrons by
photons). Fröhlich proposed a Hamiltanion model for
polarons, through which their dynamics can be treated
quantum mechanically as acoustic phonons located in a
BoseEinstein condensate (BEC).
In the same time Davydov discovered the related prin-
cipleoflongitudinalwaveformscalledsolitons (Davydov,
1977). A soliton is defined as a self-reinforcing solitary
wave that travels at constant speed without changing
shape. He proposed that the solitons play a role in the
energy transfer and conformational states of biomolecules.
The Davydov model, describes the interaction of the
amide vibrations of peptide groups with the hydrogen
bonds that stabilize the α-helix of proteins. The excitation
and deformation processes balance each other and
thereby form a soliton. His theory showed how a soliton
could travel along the hydrogen bonded spines of the alfa-
helix protein molecular chains (Davydov, 1977). He stated
that solitons are able to suppress anharmonicity (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 trans-
fer of a molecule to a new conformational state. His
concept of the excitations of atoms and solitons, as the
quanta of collective vibrational motions of atoms and
molecules in living cells, is also known from solid-state
theory. The resulting excitation (excitons) moves through
the protein uninhibited, much the way electrons move in
a superconducting state. The excitons are bound states of
electrons and electron holes present in semiconductors
and liquids, which are attracted to each other by electro-
static Coulomb forces. Excitons interact with the lattice
vibrations, under the action of electromagnetic fields and
show a bound state. A bound state in quantum physics
describes a system where a particle is subject to a potential
such that the particle has a tendency to remain localized
in one or more space regions. The energy spectrum of the
set of bound states is discrete, unlike the continuous
spectrum of free particles and shows typical eigen-frequen-
cies, at which a system tends to oscillate on its own, in the
absence of any driving or damping force. Davydov intro-
duced a mathematical model to show how solitons could
travel along the three spines of hydrogen-bonded chains
of proteins. Davydovs Hamiltonian is formally similar to
the Fröhlich-Holstein Hamiltonian for the interaction of
electrons with a polarizable lattice.
Thirty years later, solitons are a widely observed phy-
sical phenomenon that behave like waves but possess
many features of particles (Lakshmanan, 2011). In biol-
ogy, soliton theory has been applied to explain signal and
energy propagation in bio-membranes as occurs for
example in the nervous system, and to low frequency
collective motions in proteins and DNA. Solitons do not
obey the superposition principle, which makes the wave
structure robust in collisions with other wave structures
(Kuwayama and Ishida, 2013).
Pang recently improved Davydovs model by incor-
porating a change in both the particular Hamiltonian
and the intrinsic wave function of the system, propos-
ing a quasi-coherent two-quantum state (Pang et al.,
2016). A soliton model of charge and energy transport
in biological macromolecules is used by Brizhik to
describe a possible mechanism for electromagnetic
radiation influences on biological systems (Brizhik et
al., 1998). It remains to be established whether solitons
are also involved in higher-level biological phenomena.
3. A quantized acoustic reference scale able to
predict frequencies that stabilize or destabilize
living cells
According to Shapiro (1961) the concept of coherence
in the field of acoustics only means something on an
Figure 1. Artist view of a polaron. A conduction electron in an
ionic crystal or a polar semiconductor repels the negative ions
and attracts the positive ions. A self-induced potential arises,
which acts back on the electron and modifies its physical
properties (Devreese J.T.L., 1979).
360 J. H. GEESINK AND D. K. F. MEIJER
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intuitive level, yet a formal definition has not been
generally agreed upon. He proposed that when the
particular processes can be called highly coherent the
variability of the phase differences between the signals
is small, whereas if the processes are defined as inco-
herent the phase difference has a high degree of varia-
bility (Shapiro, 1961).
Interestingly we found series of coherent quantized
eigen-frequencies located in 12 bands, which could be
depicted on an acoustic reference scale: 256.0, 269.8,
288.0, 303.1, 324.0, 341.2, 364.7, 384.0, 404.5, 432.0,
455.1, and 486.0 Hz, as previously published by
Meijer and Geesink (Geesink and Meijer, 2016). This
not only agreed with the acoustic scale calculated by
Ritz of eigen-frequencies of thin vibrating square mem-
branes, but was also inferred from the basic frequency
G-tone, positioned at 96 Hertz as measured for thin
vibrating membranes by Chladni, both showing stable
and coherent geometry patterns at discrete frequencies
of this acoustic scale, which give rise to self-organiza-
tion. Additional frequency scales for electromagnetic
wave values could be derived from this reference scale
by multiples of 2
n
(n is an integer); see for further
details of the construction of the acoustic reference
scale the appendix in (Geesink and Meijer, 2016).
The mathematician Ritz (1909) found the same inter-
vals by computing eigenstates and eigen-frequencies for
sound frequencies of vibrating thin square plates, such as
discovered in the membrane studies of Chladni, 1787
(Hidalgo, 2007). Instead of trying to solve the partial
differential eigenvalues directly, Ritz used the principle
of energy minimization, from which the essential equa-
tions could subsequently be derived. He succeeded to
calculate the different coherent geometric Chladni pat-
terns and the first 35 overtones of these patterns, which
could be duplicated in subsequent studies by others from
19702013. In this way a quantized acoustic frequency
scale has been calculated based upon 12 scalars with a
qualitatively small variability of phase differences and
describing coherent geometric patterns (Geesink and
Meijer, 2016; Meijer and Geesink, 2016).
We subsequently questioned whether biological sys-
tems are also sensitive to selective coherent electromag-
netic wave frequencies, in which the variability of phase
difference between the signals is small. Therefore, we
performed a meta-analysis to validate published fre-
quency data of biological studies in which cells and
living organisms have been exposed to non-thermal
electromagnetic waves. In total 114 different frequen-
cies employed in 145 independent published studies
covering a broad area of health effects were identified
able to stabilize living cells in vivo and in vitro (called
beneficial effects of EM radiation, see Appendix 3).
All measured beneficial biological data of the applied
frequencies in the Hz, kHz, MHz, GHz and THz range
could be accommodated by the single acoustic refer-
ence scale, ranging from 256 till 486 Hz. All the values
of the beneficial frequenciesare indeed located in 12
distinct quantized frequency bands. The different mea-
sured beneficial biological data fit precisely with the
calculated stabilizing frequencies (see the green circles
and the green triangles in Figure 2) and are positioned
again and again at a typical stabilizing frequency, each
within a mean bandwidth of 0.74% (see the green
ellipses and for the deviations of the individual values
from the theoretical values Appendix 1).
Also 60 different measured frequency-data were
identified in 74 independent published biological stu-
dies, that rather seem to destabilize living cells (called
detrimental effects of EM radiation, see Appendix 3).
The different measured detrimental biological data fit
with the calculated destabilizing frequencies in
between the beneficial frequency bands(see the red
squares and the red triangles in Figure 2) and are
positioned again and again at a typical destabilizing
frequency, each within a mean bandwidth of 0.88%
(see the red ellipses and for the deviations of the indi-
vidual values from the theoretical values Appendix 2).
Figure 2. Calculated normalized EM soliton frequencies that were experimentally applied to living cells systems are found to be
patterned in 12 apparent bands of life-sustaining frequencies (green dots) and detrimental frequencies (in red squares) are
positioned in between the beneficial frequency bands.
ELECTROMAGNETIC BIOLOGY AND MEDICINE 361
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(148 beneficial EM frequencies, positioned in 12
bands (green points) and 77 detrimental EM frequencies
(red squares) in between the life-sustaining bands. Effects
were measured following exposure of living cells in vitro
and in vivo to the indicated (non-thermal) EM radiation
conditions, as derived from 219 separate biological stu-
dies. The reported life sustaining frequencies (in Hz, kHz,
MHz, GHz, THz, PHz) appeared to be positioned in 12
discrete bands, if normalized by multiplying or dividing
by 2
n
(n is an integer) and plotted on a logarithmic
acoustic scale, whereas the adverse frequencies (depicted
in red) are shown to lay in between the beneficial fre-
quency bands. Green points plotted on x-axis represent
life-sustaining frequencies; Points in red represent the
life-destabilizing frequencies. Each point indicated in
the graph is taken from earlier published data and
indicates a typical frequency for (a) biological experi-
ment(s). For clarity, points are evenly distributed along
the Y-axis)
The zones, which are located in between the desig-
nated regions of stabilization and destabilization are
probably transformation zones of geometric standing
wave like patterns as shown by Chladni for acoustic
patterns in membrane vibration experiments (1787),
which have been replicated by independent researchers
in studies from 19702013. The bandwidth of transfor-
mation regions of patterns (the mutual distance of the
ellipses) is estimated at about 0.50% of the applied
algorithmic frequency.
We propose to consider the identified 12 basic
eigen-frequencies of the acoustic wave-function, as
defined by the inferred frequency scale, for an extended
bio-soliton model and related to a morphogenetic field.
This might be a complementation of the earlier models
that were initially derived by Davydov and Fröhlich for
a supposed macroscopic wave function. This proposal
is further supported by the calculated frequency data of
Ritz (1909), the measurements of Chladni (1787)
(Chladni, 1980,1817).
In such an approach, all of the registered beneficial
frequencies for living cells can be integrated in an
extended macroscopic wave functionthat includes
a broad coherent frequency range of 0.1 HertzPHz
(see the Appendix 1 and 2).
A quantized acoustic scale might have been found to
predict frequencies that stabilize or destabilize living
cells and the experimentally applied frequencies turned
out to be very close to theoretically calculated frequen-
cies, which are positioned at typical algorithmic fre-
quencies within a bandwidth.
Conclusion: These observations provide clues for the
existence of a specific pattern of electromagnetic radia-
tion that potentially affect the viability of life systems
and may be involved in the functional structuring and
self-organization of bio-molecules within cells through
organizing them at the lowest possible energy level.
Physical models about biological influences on
cells by electromagnetic waves
Research about electromagnetic pulses on living cells
has been systematically undertaken the past eighty
years. About 25.000 biological/physical reports are
available, of which a part is dealing with non-thermal
biological effects on cells. Influences of electromagnetic
waves causing thermal effects on biological systems are
relatively well understood, and more knowledge about
non-thermal effects of electromagnetic waves have
become available. Seven additional physical principles
have been discovered the past fifty years to describe the
effects of non-ionizing electromagnetic waves on living
cells: 1) ion cyclotron resonance, 2) parametric reso-
nance, 3) electromagnetic fields and electrons, 4) reso-
nant frequencies and polarization, 5) resonant
recognition, 6) radical concentrations and 7) coherence
of waves and quantum coherence.
1) The original hypothesis by Liboff (1985) and the
model of Blackman (1985) describe the role of ion
cyclotron resonances (ICRs) that involve a combined
action of an Extreme Low Frequency (ELF) electromag-
netic field and a static geomagnetic field on the reso-
nance of typical ions (Blackman et al., 1985; Liboff,
1985). The model of Lednev (1991) proposes the ion
parametric resonance hypothesis, which predicts that
when frequencies of a combined dc-ac magnetic field
parametrically equals the cyclotron frequency of an ion,
for example calcium, the affinity of the calcium for
calcium-binding proteins such as calmodulin will be
affected. It is considered that ions bonded to proteins
(Ca
2+
,K
+
, and/or Mg
2+
) behave as isotropic coupled
oscillators (Lednev, 1991,1993). There is not yet con-
sensus about the replication of the biological effects at
the same typical frequency of combined static and
time-varying fields under resonance conditions pre-
dicted by these models (Blanchard and Blackman,
1994; Halgamuge et al., 2009; Hendee et al., 1996;
Zhadhin and Barnes, 2005), but there is much evidence
that ion cyclotron resonances play an important role.
Changes in the Ca
2+
dynamics in neuronal cells at
intermediate RF-field frequencies appear to support
the frequency dependent Ca
2+
spiking activities that
peaked at 800 MHz (Rao et al., 2008).
2) Butikov showed that non-linear parametric reso-
nance is possible at fixed resonance frequencies, but
also inside the zones of instability at frequencies lying
on either side of their resonance values. Parametric
362 J. H. GEESINK AND D. K. F. MEIJER
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excitation for example occurs within ranges of rotary
oscillations of a torsion spring pendulum excited by
periodic variations (Butikov, 2004). Hinrikus showed
that the modulated microwave radiation causes peri-
odic alteration of neurophysiologic parameters and
parametric excitation of brain bioelectric oscillations
(Hinrikus et al., 2016). The experiments with a single-
frequency-modulated microwave radiation demon-
strated that this effect on EEG depended on modulation
frequency (Hinrikus et al., 2008). The theory of para-
metric excitation was demonstrated being appropriate
for interpretation of the modulated microwave effect on
EEG (Hinrikus et al., 2011).
3) Blank pictured the interactions between electro-
magnetic fields and electrons, as particles with the
highest charge/mass ratio, that play a role in relation
to the DNA-molecule, gene activation, Na/K-ATPase,
and cytochrome oxidase (Blank and Findl, 1970).
4) Pall analyzed 26 different calcium channel blocker
studies, and found that a variety of EMFs produce
biological effects by activating voltage-gated calcium
channels (VGCCs). This also makes sense based on a
large number of such effects, being produced by known
downstream effectsof VGCC activation. The appar-
ent direct target of the EMFs is what is called the
voltage sensor, a part of the VGCC structure that pro-
duces its activation to a partial depolarization of the
plasma membrane. When electrical changes activate the
VGCCs, the 4 helixes pull out into the extracellular
space, opening up the channel in the middle of the
structure, allowing calcium ions chelated to 4 different
glutamate side chains, to rush into the cell (Pall, 2013).
5) Belyaev proposed that the millimetre waves (MMW)
with sub-thermal intensity induces rearrangement of
levels in the electron subsystem of DNA and will take
placeinamagneticfield(ZeemanEffect)orinanelec-
trical field (Stark Effect) and circular polarization occurs.
A possibility is that MMW left-handed polarization was
shown to be more effective than right-handed polarization
at certain resonance frequencies and electron tunnelling
could induce electron-conformational transitions which
should involve rearrangement of the ionic framework in
a segment of DNA-protein complex. The strongest micro-
wave effects were observed in stem cells. Stem cells are
most sensitive to microwave exposure and react to more
frequencies than do differentiated cells may be important
for cancer risk assessment and indicate that stem cells are
the most relevant cellular model for validating safe com-
munication signals. Experimental data indicated that non-
thermal biological MMW effects occur depending on
several physical parameters: carrier frequency, modula-
tion, amplitude, polarization, intermittence and static
field (Belyaev, 2015; Belyaev et al., 2010).
6) Cosic introduced the concept of dynamic electro-
magnetic field interactions and that molecules recog-
nize their particular targets and vice versa by the
principle of electromagnetic resonance: the Resonant
Recognition Model (RRM). All molecules have their
own spectrum of vibrational frequencies and DNA
itself can function as an aggregate of EM antennae
that could discern, differentiate, and transform EM
energies to perturbations in protein sequences
(Blackman et al., 1985). Periodicities within the distri-
bution of energies of delocalized electrons along a pro-
tein molecule are crucial to the proteins biological
function, i.e. interaction with its target. The RRM
makes use of the equation of the Electron Ion
Interaction Potential (EIIP), which is coupled to a the-
oretical modulated weak potential experienced by elec-
trons in the vicinity of ions and the cloud of
surrounding electrons. The RRM calculates indirectly
the spectral characteristics of proteins at frequencies of
infrared, visible light and ultraviolet (Cosic, 1997; Cosic
et al., 2015,2016; Pirogova and Cosic, 2001; Veljkovic
et al., 1985; Veljkovic and Slavic, 1972).
7) The models of Barnes and Greenebaum (2014),
and Buchachenko (2015) picture that radical concen-
trations of biomolecules can be influenced by combina-
tions of steady and alternating magnetic fields that
modify the population distribution of the nuclear and
electronic spin states at a relatively low magnetic field
strength in the range of 1microTesla till 100 micro
Tesla (Barnes and Greenebaum, 2014; Buchachenko,
2015). Free radical concentrations have the potential
to lead to biological significant changes. Usselman et
al. found that oscillating magnetic fields at Zeeman
resonance alter relative yields of cellular superoxide
(O
2
) and hydrogen peroxide (H
2
O
2
) ROS products,
indicating coherent singlet-triplet mixing at the point
of reactive oxygen species (ROS) formation. The results
reveal quantum effects in live cell cultures that bridge
atomic and cellular levels by connecting ROS partition-
ing to cellular bioenergetics. The radical pair mechan-
ism hypothesis for ROS-related quantum biology has
been tested by exposing human umbilical vein endothe-
lial cells (HUVECs) to either 50 μT static magnetic
fields and combined with 1.4 MHz, 20 μTrms RF
magnetic fields at Zeeman resonance in experimental
samples (Usselman et al., 2016).
8) Studies of the minute morphology of the skin by
optical coherence tomography showed that the sweat
ducts in human skin are helically shaped tubes, filled
with a conductive aqueous solution. A simulation study
of these structures in millimetre and sub millimetre
wave bands show that the human skin functions as an
array of low-Q helical antennas. Experimental evidence
ELECTROMAGNETIC BIOLOGY AND MEDICINE 363
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is presented that the spectral response in the sub-
Terahertz region is governed by the level of activity of
the perspiration system (Feldman et al., 2008).
9) The Polaron model of Fröhlich (1968) and the
Soliton model of Davydov (1973) are models that
describe effects of coherent states of waves for inani-
mate as well as animate systems and interactions with
electromagnetic waves, electrons, phonons, polarons,
polaritons and magnons with regard to wave stability.
Polarons are similar to solitons, and we will further use
the name soliton. After all John Scott Russell in 1834
was one of the first to observe a soliton: a solitary wave
in the Union Canal in Scotland, which maintained its
shape while it propagates at a constant velocity, see
Figure 3.
Support for a bio-soliton model
Many researchers have contributed to the soliton research
and much progress has been made: Fermi, Pasta and
Ulam (1955), Zabusky and Kruskal (19601970), Porter
(19992012), Fröhlich (19681988), Davydov (1973
1991), Chou (19761994), Luzzi (19822012), Pokorny
(19822015), Gordon (1992), Brizhik (19952017), Pang
(19902017), Heimburg (20052016), Chin (20102013),
Bandyopadhyay (20062017), Lundholm (2015), and
Preto (20122017). The flow of soliton-like energy in a
one dimensional lattice consisting of equal masses con-
nected by nonlinear springs has been calculated (Fermi et
al., 1955). Porter showed later that the energy initially put
into a longwave length mode of a system does not ther-
malize but rather exhibit energy sharing among the few
lowest modes and long-time near recurrences of the initial
state and would not transfer energy into higher harmonic
modes (Porter et al., 2009).
Zabusky and Kruskalz (1965) concluded that the
equation of Korteweg and de Vries (1895) (Korteweg
and De Vries, 1895) admits analytic solutions repre-
senting what they called solitons: propagating pulses or
solitary waves that maintain their shape and can pass
through one another (Chou, 1985) and Figure 4.
Their analyzes showed that the coherence of solitons
can be attributed to a combination of nonlinear and
dispersive effects. Chou found indications for a similar
soliton principle in proteins, in which the conforma-
tional protein adaptation is influenced by low fre-
quency phonons acting as an information system
(Chou and Chen, 1977). More detailed experimental
evidence for the existence of collective excitations of
low-frequency phonons came available for proteins
(Chou, 1985; Chou et al., 1994; Xie et al., 2002) and
for polynucleotides (DNA and RNA) through the
observation of low-frequency oscillations modes in the
Raman and far-infrared spectra of proteins (Fischer et
al., 2002; Painter et al., 1981).
The role of solitonic conduction was also discussed
by Adey in transmembrane signalling across phospho-
lipid-protein energetic domains, established by joint
states of intramembranous proteins and surrounding
phospholipid molecules (Adey, 1992; Adey et al.,
2000). Next to solitons waves kink waves are proposed
that are in active media, and cannot pass through one
another(Gordon and Gordon, 2016).
Figure 3. A: Longitudinal soliton wave, B: Linear and non-linear
soliton wave propagation, C: Union Canal in Scotland as a spot
of the discovery of the solitary wave, D: Optical soliton wave
representation.
Figure 4. A system like the one Fermi, Pasta and Ulam mod-
elled, gives rise to solitons, which propagate in either direction,
exchange positions and eventually return the system to states
that resembles its initial configuration. The motion of the soli-
tons can be seen here by following the lines of colors, which
denote displacements (From Porter, 2009 and image from
Zabusky, Sun and Peng 2006).
364 J. H. GEESINK AND D. K. F. MEIJER
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Heimburg and Jackson (2005) argued that electro-
mechanical solitons, with properties similar to those of
an action potential, can travel along the nerve axons.
The compressibilitys of bio-membranes seem to be
nonlinear functions of temperature and pressure in
the vicinity of the melting transition, and show the
possibility of soliton propagation (Heimburg and
Jackson, 2005).
Sinkala (2006) calculated the soliton-mechanism of
electron transport in alfa-helix sections of proteins,
using classical Hamiltonian analysis. He confirmed
that folding and conformation changes of proteins are
mediated by interaction with solitons which propagate
along the molecular chain. In fact, many biological
processes in any living organism are seen to be asso-
ciated with conformational changes, as a result of space
propagation of energy and electrons along protein
molecules (Sinkala, 2006).
One example is the 0.42 eV energy, released under
hydrolysis of ATP molecule, as studied by Davydov
(1973) and Pang (2001) (Davydov, 1973; Pang and
Chen, 2001). A hypothesis is that this energy is trans-
ferred along the alfa-helical protein molecules, while
the oscillation energy of the C = O moieties of the
peptide groups (amide-I vibration) is at 0.21 eV or
1665 cm
1
, which is in resonance with the 0.42 eV of
the ATP process. Interestingly, the energy released
under hydrolysis of ATP molecule, the oscillation
energy of the C = O of the peptide groups and the
different bending modes of interfacial water molecules
fit precisely with the calculated soliton frequencies of
the acoustic wave-function, respectively: 0.415 eV,
0.2073 eV and 16601693 cm
1
.
Salford (2008) suggests that soliton models could be
applied to study the effect of an EMF field on mem-
brane permeability for various molecules such as
calcium and albumin and may be instrumental in the
explanation of how the DNA transcription process is
possibly influenced by microwaves (Salford et al., 2008).
Shrivastava and Schneider (2014) observed two
dimensional solitary acoustic like elastic pulses in lipid
interfaces of biological membranes and elaborated on
the similarity of the observed phenomenon to nerve
pulse propagation and a thermodynamic basis of cell
signalling in general (Shrivastava and Schneider, 2014).
Sahu et al. (2014) have shown that by applying
particular ac electromagnetic signals using specially
designed antenna self-assembly of tubulin protein
molecules could be carried out. Under pumping, the
growth process exhibits a unique organized behavior.
They used 64 combinations of plant, animal and fungi
tubulins and observed a common frequency region,
where protein structures vibrate electromagnetically
and folds mechanically. A ‘‘common frequency point’’
is proposed as a tool to regulate protein complex
related diseases in the future. Of note, the applied
electromagnetic signals match our proposed calculation
of electromagnetic frequency bands that stabilize living
cell conditions (Sahu et al., 2014).
Srobar (2015) and Pokorny (1982) proposed a wave
equation for a Fröhlich system for cellular physiology,
which describes the coherence between individual oscil-
lations, using a number of energy quanta concentrated
in one vibrational mode above the thermal equilibrium
level and suggested an ensemble of interactions char-
acterized with three coupled oscillators, of which the
oscillator eigen-frequencies fall into the MHz and the
THz frequency domains (Pokorny, 1982; Srobar, 2015).
Preto (2016) provided a general classical Hamiltonian
description of a nonlinear open system composed of
many degrees of freedom (biomolecular structure)
excited by an external energy source and it has been
shown that a coherent behavior similar to Fröhlichs
effect is to be expected for a given range of parameter
values (Preto, 2016).
Pang et al (2016) showed that the distributions of the
quantum vibrational energy levels of the protein mole-
cular chain are crucial and used the Davydov theory in
relation to the nonlinear Schrödinger equation to
describe the resonant behavior of proteins (Lloyd,
2014; Sahu et al., 2014).
Pettini (2007) reported that there is a possibility to
reduce and even suppress chaoticity in a magneto-elas-
tic beam system by means of parametric periodic per-
turbations. The experimental parameters are chosen
such that a strange attractor is observed. Then a para-
metric perturbation is added. When its frequency
approaches some resonant value, laminar phases are
observed of increasing duration up to complete
Figure 5. Coherence versus decoherence, and Bose-Einstein
condensation.
ELECTROMAGNETIC BIOLOGY AND MEDICINE 365
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regularization of the motion at exact resonance (Pettini,
2007).
A system of particles or waves can be described in
terms of an energy functionalor Hamiltonian, which
represents the energy of a proposed configuration of
particles or waves. In this system certain preferred
configurations are more likely than others, which are
approached by an eigen-analysis. The Hamiltonians of
the lattice vibration and the soliton wave function of
Davydov have been refined by Pang. The equations
thereby express the features of collective excitation of
phonons and excitons caused by the nonlinear interac-
tion. The interaction domain contains two vibrational
quanta (excitons), while the energy spectra of proteins
at infrared frequencies have been measured. The
DavydovPang model is theoretically plausible and
more appropriate to the alpha-helical proteins contain-
ing amide-I, and show lifetimes of solitons at 300 K
(Srobar, 2015). Pang also confirmed that the soliton
mechanism of energy transport in life systems can be
disturbed by man-made electromagnetic fields. Using
both equations he succeeded to show that external
man-made electric magnetic fields are able to depress
the binding energy of the soliton, decrease its ampli-
tude, and change its wave form. The calculated sup-
pression of the solitons could be experimentally
validated by measuring the infrared spectra of absorp-
tion of collagens activated by external electromagnetic
waves. The stability of the DNA structure was shown to
be dependent on the continuous input of phonon
guided oscillations at which a cloud of entangled elec-
trons surrounding the nucleotides acts as a harmonic
oscillator at room temperature.
Also pigment-protein complexes generate non-equi-
librium vibrational processes that lead to sustenance of
electronic coherence, at physiological temperatures
(Chin et al., 2013). The measured coherence times of
several hundreds of femtoseconds are long enough for
excitation energy transfer and excitonic coherence to
coexist. Based upon this knowledge a semi-classical
model with discrete modes was proposed that protects
oscillatory excitation energy transfer and electronic
coherence against background decoherence.
Solitons are unstable in three dimensions and decay
through snaking instability. Solitonic vortices were pro-
posed to bridge the gap between solitons and vortices,
and have elements of both. Like vortices, their phase
swirls around the defect, but only in a small region of
space. Outside this region, the phase becomes homo-
geneous, like the phase on either side of a soliton. The
3D-soliton can propagate with a constant velocity along
a vortex core without any deformation (Adhikari, 2015;
Chevy, 2014). Vortex solitons at the interface
separating two different photonic lattices square and
hexagonal have been demonstrated numerically. The
conditions for the existence of discrete vortex states at
such interfaces have been considered and a picture of
different scenarios of the vortex solutions behavior
developed (JovićSavićet al., 2015).
Lundholm (2015) found a direct experimental sup-
port for the Fröhlich condensation in the arrangement
of proteins, by detecting Bose-Einstein condensate-like
structures in biological matter at room temperature.
The group used a combined terahertz measuring tech-
nique with a highly sensitive X-ray crystallographic
method to visualize low frequency vibrational modes
in the protein structure of lysozyme. Structural
changes, associated with low-frequency collective vibra-
tions, as induced in lysozyme protein crystals by irra-
diation with non-thermal 0.4 THz radiation, were
detected. The vibrations were sustained for micro- to
milli-seconds, which is 36 orders of magnitude longer
than expected if the structural changes would be due to
a redistribution of vibrations upon terahertz absorption
according to Boltzmanns distribution. The influence of
this non-thermal signal is able to changes locally the
electron density in a long alfa-helix motif, which is
consistent with an observed subtle longitudinal com-
pression of the helix (Lundholm et al., 2015).
How can (de)stabilization of cells take place at a
non-thermal level?
Soliton models are able to describe cellular electromag-
netism, and show underlying physical principles of
endogenous and exogenous biological effects in cells.
Stabilization of cell-states takes place when a proposed
macroscopic wave functionapplied in these models,
is active. Discrete coherent Terahertz frequencies and
much lower and higher frequencies (from some Hertz
to PHz) are coherently coupled, and obey Bose Einstein
condensation, which are able to stabilize living cells at
and near a dynamic equilibrium around room tempera-
ture. The stabilization of cell states will occur at typical
discrete frequencies, described by a particular wave
function, in which each type of cell or bio-molecule
or part of the bio-molecule will have its own eigen-
frequency. Solitons, confined in a harmonic like poten-
tial, can actually reabsorb energy in periodic cycles
(JovićSavićet al., 2015) and the particular stabilizing
eigen-frequencies have a typical band width (Meijer
and Geesink, 2016) and Figure 2.
The calculated and biological verified algorithmic
eigen-frequencies matches with the eigenstates of quan-
tum effects of a selected inorganic silicate mineral, that
contains quantum information and might be able to
366 J. H. GEESINK AND D. K. F. MEIJER
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catalyze the oligomerization of RNA and with pigment
spectra of plants and algae related to photosynthesis
(Geesink and Meijer, 2016).
The knowledge initiated by Davydov and Fröhlich
and the model of Pang showed that the soliton
mechanism of energy transport in life systems can be
disturbed by man-made electromagnetic fields (Pang et
al, 2016). It is postulated that the decay of the macro-
scopic wave functioncan be initiated when the order-
ings principle of the boson-like quasi-particles is
disturbed by a sufficient amount of de-coherent elec-
tromagnetic waves. Such de-coherent waves exhibit fre-
quencies, which do not fit in the range of eigen-
frequencies of electromagnetic waves, and are called
dark solitons, see Figure 6. Dark solitons have already
been observed in optical systems, and in harmonically
confined atomic BoseEinstein condensates. If such a
dark soliton propagates in an inhomogeneous back-
ground, it dissipates coherent energy. Our EM fre-
quency data indicate that destabilizing frequencies
(dark solitons) are located in between the beneficial
frequency bands(see Figure 2), which are positioned
in between some Hertz and Terahertz.
Cellular plasma water is generally supposed to act as
a transfer medium for external electromagnetic waves
to biomolecules. The cellular plasma exhibits a highly
arranged 3-D geometric structure as a liquid crystal
that exhibits surface interactions with macromolecular
structures. The absorption spectrum between 1 THz
and 10 THz of solvated biomolecules is sensitive to
changes in fast fluctuations of the water network.
There is a long range influence on the hydration bond
dynamics of the water around binding sites of proteins,
and water is shown to assist molecular recognition
processes (Meijer and Geesink, 2016; Parker et al.,
2003). Biological watersupports itself by coherent
dipolar excitations and terahertz/femtosecond infrared
interactions and these dynamics extends well beyond
the first solvation shell of water molecules. The reor-
ientation of water molecules around ions and interac-
tion with solvated ions slows down during external
THz-waves, shifting the absorption peak to lower fre-
quencies and thereby reducing the absorption of radia-
tion at THz frequencies (depolarization) (Tielrooij et
al., 2010,2009).
The coherence of liquid water is affected by applied
external electromagnetic waves much weaker than those
allowed according to the kT threshold (Del Giudice et
al., 2010) and the reorientation of water molecules might
take place at energy levels of less than a 100 mW/cm
2
,
which is at a non-thermal energy level.
Fröhlich presented the first explicit hypothesis of the
role of coherence in cancer. He assumed that cancer
transformation pathways include a link with altered
coherent electric vibrations. A cancer cell may escape
from interactions with the surrounding healthy cells
and may perform individual independent activity if
the frequency spectrum is rebuilt and shifted. The fre-
quencies change may be combined with disturbances of
the spatial pattern of the field and the transformed cells
are released from local interactions and prepared to
undergo local invasions and formations of metastases
(Fröhlich, 1978).
Summarized: living cells make use of coherent fre-
quency signalling, similar to Bose Einstein condensates,
in order to stay stable. If incoming man-made electro-
magnetic signals exhibit a lack of coherency, than these
signals potentially will decrease the coherency of (quan-
tum) wave domains of living cells. A possible way to
deal with such a problem is to lower the energy of the
external man made waves and to add more coherent
frequencies next to potential detrimental frequencies
and by increasing the coherency of the electromagnetic
signals through the use of appropriate semiconductor-
technologies. Coherent Terahertz waves, obeying to the
acoustic wave function, could be produced by appro-
priate semiconducting materials inserted in electromag-
netic man-made devices, while making use of the so
called Terahertz gap, enabling the combination of opti-
cal and electronic coherent information.
How to further constitute an integral bio-
soliton mathematical model
The Fröhlich/Davydov concept 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
Figure 6. Solitons (Polarons) and Dark Solitons, formed by tor-
oidal coupling.
ELECTROMAGNETIC BIOLOGY AND MEDICINE 367
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the system has been expressed in three different
Hamiltonians. Due to this 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 (Pang et al, 2016). According to the
mechanism of bio-energy transport Davydov estab-
lished the theory of bio-energy transport in protein
molecules, in which he gave the Hamiltonian of the
protein molecules:
HD¼jφD
hjβtðÞ
h¼X
n
ε0Bþ
nBnJB
þ
nBnþBnBþ
n

þX
n
P2
n
2Mþ1
2ωunun1
ðÞ
2

þX
n
X1unþ1un1
ðÞ
Bþ
nBn

¼Hex þHph þHint
(1a)
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 interac-
tion in this process, J is the dipole-dipole interaction
energy between neighboring amino acid molecules, m
is the average distance between the neighboring amino
acid molecules. The wave function of the system pro-
posed by Davydov has the form of:
D2tðÞ¼ φDi
jj
βtðÞX
n
φntðÞBþ
n
exp i
hX
n
βntðÞPnπntðÞun

j0i
()
(1b)
Pang has added a new coupling interaction of the
excitons with the displacement of amino acid molecules
into the Hamiltonian and replaced further the
Davydovs wave function of the one-quantum (exciton)
excited state by a quasi-coherent two-quantum state.
The representations in Equations (1a) and (1b) for the
single-channel protein molecules are replaced by:
jΦtðÞi¼jαtð ÞijβtðÞi
¼1
λ1þX
n
αntðÞBþ
nþ1
2! X
n
αntðÞB2
b
!
2
"#
j0iex
exp f i
hX
n
½βntðÞPnπnunj0iph
(2b)
Ritz (1909) had shown that an analytical calculation of
acoustic eigen-frequencies of a thin square vibrating
membrane is possible (Geesink and Meijer, 2016).
Part of the particular calculation of Ritz is presented
below by Gander and Wanner (Gander and Kwok,
2012; Gander and Wanner, 2010).
Calculating
To evaluate JðwsÞ, we thus have to evaluate
ð1
1ð1
1
@ws
@2

¼ð1
1ð1
1
@2Pm;nAmnumðÞunyðÞ
@2
!
2
dxdy
¼Xm;nXm;nAmnApq ð1
1ð1
1
@2umðÞ
@2unyðÞ
@2upðÞ
@2upyðÞdxdy:
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
C1
mnpq:¼
Now c1
mnpq can be computed, since unis known!
Similarly
ð1
1ð1
1
@2ws
@y2

2
dxdy ¼Xm;nXp;qAmnApq c2
mnpq
ð1
1ð1
1
2μ@2ws
@2
@2ws
@y2dxdy ¼Xm;nXp;qAmnApq c3
mnpq
ð1
1ð1
1
1μðÞ
@2ws
@@y

dxdy
¼Xm;nXp;qAmnApq c4
mnpq
ð1
1ð1
1
w2
sdxdy ¼Xm;nA2
mn orthogonality!ðÞ
We found that the calculated eigen-frequencies by
Ritz are fully compatible with the collected beneficial
frequency data for living cells that we inferred from the
(2a)
H¼Hex þHph þHint ¼X
n
ε0Bþ
nBnJB
þ
nBnþBnBþ
n

þX
n
P2
n
2Mþ1
2ωunun1
ðÞ
2

þX
n
X1unþ1un1
ðÞBþ
nBnþX2unþ1un1
ðÞBþ
nþ1BnþBþ
nþ1Bn

(2a)
368 J. H. GEESINK AND D. K. F. MEIJER
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earlier mentioned published biological studies (Meijer
and Geesink, 2016).
In this article we therefore would like to propose a
combination of the knowledge of Pang et al. (2016),
and the frequency scale of Ritz (1909) (Ritz, 1909),
which could be validated by many biological data
from 1966 till now (Figure 2).
Summarizing
The bio-soliton model postulated is based upon the
following considerations:
Soliton interactions with living cell systems have
been earlier modelled by Fröhlich and Davydov,
and later improved by Pang et al.
There is a relation in between the principles of
self-reinforcing waves and parametric resonance.
The pro-lifefrequency bands that we identified
earlier by an acoustic wave function, show 12
apparent basic oscillators that we interpret as
eigenvalues (also known as 12 scalars and mini-
mum energy values) of coherent like vibrations;
lower and higher scalars can be calculated by
octave hierarchy.
Numerically similar eigen-frequencies/eigenvalues
have earlier been calculated by Ritz for coherent
sound patterns of thin membranes.
We postulate that the calculated discrete EM
waves and eigen-frequencies are characteristic for
all types of living cells and represent an arithmetic
code.
Next to living cells, the same eigen-frequencies/
scalars have been found in silicate minerals con-
taining quantum information, as candidate to cat-
alyze RNA.
Cellular plasma water shows a highly arranged 3-
D geometric structure as a liquid crystal, that
exhibits surface interactions with macromolecular
structures and plays a crucial role in cellular
electromagnetism.
The combination of macromolecules and sur-
rounding water molecules can be conceived as
vibrating lattices, sensitive to coherent photon/
phonon/soliton interactions.
Supplying internal and external energy to this
matrix induces coherent vibration domains of
proteins/DNA/H2O, with a distinct spreading
and life-time.
Such coherent domains can adopt minimal energy
levels and can take the form of Bose-Einstein
condensates through energy pumping.
Current quantum biology studies indicate that
long range coherency with sufficient life times
occur at life temperature ranges.
The coherent calculated frequencies fits with mea-
sured eigen-frequencies of quantum effects pre-
sent in pigment spectra of plants/algae, spectra of
proteins among others tubulin proteins, hydrolysis
of ATP molecule and oscillation energy of the
C = O of the peptide groups, resonance of cal-
cium-binding proteins, quantum states of selected
inorganic silicate minerals and a quantum state of
the radical pair mechanism related to ROS.
The life-sustaining frequencies of the acoustic
model can be conceived as solitons having discrete
energies, velocity and typical wave length.
External solitons can interact with endogenous
soliton guided structures in cells through various
mechanisms.
Dark solitons, showing the highest possible deco-
herence can annihilate life-sustaining solitons (by
deconstructive interference) and thereby decrease
stability of macromolecules. Dark solitons are
logarithmic positioned just in between the pro-
posed coherent eigen-frequencies.
Interaction of solitons with BSE condensates and
macromolecular lattices can largely prolong their
life-times.
Interaction of solitons/polarons with BSE conden-
sates requires functional trapping and coupling of
these energies as modelled by toroidal geometry
(see our earlier studies).
Such toroidal geometry can lead to phase-conjuga-
tion, constructive interference or to transmutation
of wave modalities that also can lead to regenera-
tion of pro-life solitons by torus scattering.
Torus mediated coupling of photons, phonons, soli-
tons and BSE condensates is part of a fractal config-
uration operating at various scales of life organisms.
There is a similarity between the toroidal Tonnetz
that is a conceptual lattice diagram representing
tonal space first described by Leonhard Euler in
1739, and the proposed torus.
It is postulated that solitons, as self-reinforcing
solitary waves, show constructive interference
and interact with complex biological phenomena
such as cellular self-organization.
Coherency promoting effects of semiconducting
materials
There is an analogy between resonance phenomena in
biological cells and resonances in (artificial)
ELECTROMAGNETIC BIOLOGY AND MEDICINE 369
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semiconductors, while mathematical models about pho-
non dynamics in semiconducting materials are available
(Vasconcellos et al., 2013,2012). It has been concluded that
the principle of non-equilibrium FröhlichBoseEinstein
Condensation like longitudinal-acoustic vibrations (AC
phonons) in biological fluids and in typical inorganic semi-
conductors is quite similar. Incaseofpolarcrystalline
semiconducting lattices, a macroscopic polarization can
be generated by excitations of external electromagnetic
waves, which subsequently leads to the emission of coher-
ent THz waves. For example, the exciton-polaritons, which
are bosonic quasiparticles, exist inside microcavities of a
semiconductor and consist of a superposition of excitons
and cavity photons. Due to their small effective mass Bose
Einstein condensation (BEC) can be realized at tempera-
tures orders higher than that for ultracold atomic gases.
The lifetime of polaritons in such semiconductors, that
make use of two-dimensional layered materials, are com-
parable to or even shorter than the thermalization time of
10100 ps. This property provides them with an inherently
non-equilibrium Bose-Einstein nature, which accordingly
displays many of the features that would be expected of
Bose-Einstein condensates (BECs).
Materials used in these types of semiconductors are
for example GaAs (Gallium arsenide) and CdTe
(Cadmium telluride), which show exciton-polariton
condensation at cryogenic temperatures in the vicinity
of about 10 K (Byrnes et al., 2014). Typical planar
microcavities for exciton-polaritons are applied consist-
ing of several quantum wells sandwiched by distributed
Bragg reflectors, see Figure 7. The quantum wells are
thin layers (typically of the order of 10 nm) of a
relatively narrow bandgap material (such as GaAs or
CdTe) surrounded by a wider bandgap material (doped
with Al or Mg respectively).
The operating temperature of such coherent semicon-
ductors can be further increased from 10 K to room
temperature by coupling of the polarons and the polar-
itons within nano-minerals exhibiting a 3D toroidal-like
macroscopic geometry (an equilibrium BECswillnotbe
possible in a 2D system). Doped silicate minerals are one
of the possible building block for these semiconductors
containing quantum information (Geesink, 2007). The
principle of EM wave transmutation is incorporated in
the hypothesis that the quantum state properties of such
silicates may have played a role in biological evolution
(Coyne, 1985), in the sense that they may have been
instrumental in the creation of the first living cells
(Ferris, 2005). Hydrous aluminium phyllosilicates are
available with variable amounts of alkali-, alkaline-, tran-
sition-metals and rare earth elements. The silicates are
composed of tetrahedral silicate sheets and octahedral
hydroxide sheets and are characterized by two-
dimensional sheets of corner sharing SiO4 tetrahedral
and/or AlO4 octahedral (see Figure 8). The sheet units
have the chemical composition (Al,Si)3O4. Bonding
between the tetrahedral and octahedral sheets requires
that the tetrahedral sheet becomes corrugated or twisted,
causing a ditrigonal distortion to the hexagonal array, by
which the octahedral sheet is flattened, see Figure 8
(Geesink and Meijer, 2016). This structure enables to
increase the coherency of waves in a surrounding of
potential detrimental EM wave energy and convert this
to more life-sustaining wave modalities.
Conclusions and final discussion
Solitons, as self-reinforcing solitary waves, are pro-
posed to interact with complex biological phenomena
such as cellular self-organization. The supposed
micro-cellular resonances occur at dipolar sites and
bond structures of biopolymers, through perturba-
tionsofthestructureofH-bonding,viaquantum
states of atoms within pockets of non-localized elec-
trons. The soliton mechanism is seen to be based
upon a toroidal mediated electron/phonon coupling
of coherent standing waves, on the basis of twelve
identified coupled oscillators and has a resemblance
with parametric resonances. The models of Davydov,
Fröhlich,Pang,Luzzi,Brizhik,Srobar,Liboff,Lednev,
Figure 7. Exciton-polariton condensation. Typical device struc-
ture supporting exciton-polaritons. Excitons, consisting of a
bound electron-hole pair, exist within the quantum well layers.
These are sandwiched by two distributed Bragg Reflectors
(DBRs), made of alternating layers of semiconductors with dif-
ferent refractive indices. The DBRs form a cavity which strongly
couples a photon and an exciton to form an exciton-polariton.
Polaritons are excited by a pump laser incident from above or
by heat (Byrnes et al., 2014).
370 J. H. GEESINK AND D. K. F. MEIJER
Downloaded by [84.31.212.213] at 09:35 22 November 2017
Blackman, Barnes, Pokorny, Cosic and Sinkala, dis-
cussed in this article, describe cellular and biomole-
cular electromagnetism. An addition to these models
is proposed, providing a bio-soliton model that is
compatible with quantum coherence and has a fre-
quency predictive value. The proposed extended
model complements the earlier proposed macro-
scopic wave functionof the soliton models of
Davydov, Fröhlich, and Pang with a coherent fre-
quency scale of an acoustic wave function,which
makes use of twelve coupled coherent oscillators, of
which the eigen-frequencies are precisely located in
numerical domains in between Hertz and PHz. The
complementary aspect of the model has been vali-
dated by experimentally observed coherent electro-
magnetic wave frequencies, as has been practised in
240 published biological studies from 1966 till 2016,
in which a spectrum of non-thermal electromagnetic
waves were exposed to living cells and intact organ-
isms. The distinct assembly of identified, life support-
ing EM eigen-frequencies is postulated to represent a
coherent electromagnetic field and touches upon the
phenomenon of Bose-Einstein condensation at life
temperatures. The classical calculation of Ritz con-
cerning acoustic eigen-frequencies, and the experi-
ments of thin vibrating membranes of Chladni are
in line with the observed frequency patterns. The
calculation of distances of the twelve acoustic tones
also complies with a tone scale, of which the position
of seven tones of this scale is calculated according a
diatonic tone scale as proposed by Pythagoras; the
remainder five intermediate tones are calculated
using the Pythagorean calculation for flats developed
during the Renaissance (Meijer and Geesink, 2016).
Measured independent biological radiation data,
which show beneficial effects at typical frequencies
in the broad Hz, kHz, MHz, GHz, THz and PHz
range, are precisely located at eigen-frequencies of
the acoustic wave functionwithameanaccuracy
of 0.4%. The radiation features showing clear detri-
mental effects at typical frequencies are located just
in between these eigen-frequencies of the acoustic
wave function. It is further considered that the par-
ticular acoustic wave functionmay be instrumental
in the self-organization of living cells with their con-
stituting (glyco)-proteins and oligonucleotides (RNA/
DNA), which are electromagnetically organized via
dedicated quantum states related to the supposed
beneficial frequencies. The model and data support
the concept of coherent quantized electromagnetic
states in living organisms. It is postulated further
that detrimental influences of electromagnetic pulses
on living cells are initiated by a critical amount of
decoherency inducing dark-solitons, exhibiting fre-
quencies, which are not compatible with the pro-life
wave characteristics.
Levin (2012) has reviewed the molecular mechan-
isms relevant to morphogenetic fields: large-scale sys-
tems of physical properties are considered to store
patterning information during embryogenesis, regen-
erative repair, and cancer suppression that ultimately
controls anatomy. It is envisioned that a rational con-
trol of shape by soliton-waves provides positional infor-
mation and cues to regulate organism-wide systems
properties like anatomy, control of reproduction and
repair (Levin, 2012).
Tissue and organ development requires the orches-
tration of cell movements, including those of intercon-
nected cell groups, termed collective cell movements;
these properties can be regulated independently in cells,
suggesting that they can be employed in a combinator-
ial manner (Montell, 2008).
According to Bambardekar (2015): The shaping of
tissues and organs relies on the ability of cells to
adhere together and deform in a coordinated man-
ner. It is, therefore, key to understand how cell-gen-
erated forces produce cell shape changes and how
such forces transmit through a group of adhesive
cells in vivo. An approach has been developed using
laser manipulation to impose local forces on cell
contacts in the early Drosophila embryo.
Quantification of local and global shape changes
can both provide direct measurements of the forces
acting at cell contacts and delineate the time-depen-
dent viscoelastic properties of the tissue. The latter
provides an explicit relationship, the so-called consti-
tutive law, between forces and deformations
(Bambardekar et al., 2015).
Figure 8. Example of phyllosilicate-layers, with tetrahedral and
octahedral structures.
ELECTROMAGNETIC BIOLOGY AND MEDICINE 371
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Semiconducting nanomaterials may become available
in the near future to produce discrete stabilizing eigen-
frequencies characteristic of functional cells, that may
prevent possible disturbing influences by de-coherence
induction. In potential, even man-made electromagnetic
technologies could be further improved in this manner by
which anharmonicity is suppressed to obtain a bio-com-
patible status. Such a technology can be based, for
instance, on the principle of toroidal trapping by adding
beneficial modes to man-made electromagnetic signals.
The latter developments can be envisioned on the basis of
the toroidal model as proposed in more detail recently
(Meijer and Geesink, 2016).
Declaration of interest
The authors report no conflicts of interest. The authors alone
are responsible for the content and writing of this article.
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Appendix 1 Frequencies reported in biological
studies, that stabilize cells in vitro or improve in
vivo conditions of cells, versus calculated algo-
rithmic frequencies
Author, year (w;x;y) >z Hz
Author, year of published biological experiment (applied
biological frequency: w; first nearby calculated algorith-
mic frequency: x, difference between applied frequency
and nearby calculated frequency: y %) > applied fre-
quency normalized to the quantized acoustic reference
scale: z Hz
Hz-scale
1) Moore, 1979 (0.3; 0.296; +1.35%) > 307.2 Hz
2) Persinger, 2015 (0.445; 0.444; 0.23%) > 455.7 Hz
3) Persinger, 2015 (0.473; 0.474; 0.21%) > 484.4 Hz
4) Persinger, 2015 (0.482; 0.474; +1.69%) > 493.6 Hz
5) Persinger, 2015 (0.499; 0.500; 0.2%) > 255.5 Hz
6) Kole, 2011 (0.6; 0.0.595; +0.83%) > 307.2 Hz
7) Fröhlich, F., 2014 (0.750; 0.750; 0.00%) > 384.0 Hz
8) Yu L., 2015 (0.952 Hz; 0.949; +0.29%) > 487.4 Hz
9) Mayrovitz, 2004 (1.000; 1.000; 0.00%) > 256 Hz
10) Hartwich, 2009 (1.000; 1.000; 0.00%) > 256 Hz
11) Sanchez-Vives, 2000 (1.000; 1.000; 0.00%) > 256 Hz
12) De Mattei, 2006 (2.000; 2.000; 0.00%) > 256 Hz
13) Ricci, 2010 (2.000; 2.000; 0.00%) > 256 Hz
14) Hartwich, 2009 (2.000; 2.000; 0.00%) > 256 Hz
15) Hartwich, 2009 (3.200; 3.160; +1.27%) > 409.6 Hz
16) Hartwich, 2009 (4.000; 4.000; 0.00%) > 256 Hz
17) Fadel, 2005 (4.500; 4.500; 0.00%) > 288 Hz
18) Selvam, 2007 (5.000; 5.063; 1.24%) > 320 Hz
19) De Mattei, 2009 (5.000; 5.063; 1.24%) > 320 Hz
20) Sancristóbal, 2014 (6.000; 6.000; 0.00%) > 384 Hz
21) Lisi, 2008 (7.000; 7.100; 1.41%) > 448.0 Hz
22) Ross, 2015 (7.500; 7.590; 1.19%) > 480 Hz
23) Leoci, 2014 (8.000; 8.000; 0.00%) > 256 Hz
24) Belyaev, 1998 (9.000; 9.000; 0.00%) > 288.0 Hz
25) Kole, 2011 (9.4; 9.48; - 0.85%) > 300.8 Hz
26) Golgher, 2007 (10.00; 10.10; 1.00%) > 320 Hz
27) Hood, 1989 (10.00; 10.10; 1.00%) > 320 Hz
28) Fröhlich, F., 2014 (10.00; 10.10; 1.00%) > 320 Hz
29) Kole, 2011 (10.7; 10.66; +0.37%) > 342.4 Hz
30) Golgher, 2007 (13.50; 13.50; 0.00%) > 432 Hz
31) Murray, 1985 (15.00; 15.19; 1.25%) > 480 Hz
32) Lei, 2013 (15.00; 15.19; 1.25%) > 480 Hz
33) Ross, 2015 (15.00; 15.19; 1.25%) > 480 Hz
34) Dutta, 1994 (16.00; 16.00; 0.00%) > 256 Hz
35) Belyaev, 2001 (16.00; 16.00; 0.00%) > 256 Hz
36) Mayrovitz, 2004 (16.00; 16.00; 0.00%) > 256 Hz
37) Hartwich, 2009 (17.10; 16.90; +1.18%) > 273.6 Hz
38) Eusebio, 2012 (20.00; 20.20; 0.99%) > 320 Hz
39) Loschinger, 1999 (20.00; 20.25; - 1.25%) > 320 Hz
40) Chen, 2007 (20.00; 20.25; - 1.25%) > 320 Hz
41) Prato, 2013 (30.0; 30.36; - 1.2%) > 480 Hz
42) Cane, 1993 (37.50; 37.90; 1.06%) > 300 Hz
43) Ceccarelli, 2014 (37.50; 37.90; 1.06%) > 300 Hz
44) Singer, 1999 (40.00; 40.50; 1.24%) > 320 Hz
45) Bastos, 2014 (40.50; 40.50; 0.00%) > 324 Hz
46) Golgher, 2007 (40.50; 40.50; 0.00%) > 324 Hz
47) Reite, 1994 (42.70; 42.70; 0.00%) > 341.6 Hz
48) Blackman, 1985 (45.00; 45.60; 1.32%) > 360 Hz
49) Wei, 2008 (48.00; 48.00; 0.00%) > 384 Hz
50) Cheing, 2014 (50.00; 50.60; 1.19%) > 400 Hz
51) Reale, 2014 (50.00; 50.60; 1.19%) > 400 Hz
52) Segatore, 2014 (50.00; 50.60; 1.19%) > 400 Hz
53) Golgher, 2007 (54.00; 54.00; 0.00%) > 432 Hz
54) Blumenfeld, 2015 (60.00; 60.75; 1.24%) > 480 Hz
55) Braun, 1982 (72.00; 72.00; 0.00%) > 288 Hz
56) Tabrah, 1990 (72.00; 72.00; 0.00%) > 288 Hz
57) Luben RA, 1982 (72; 72; 0%) > 288 Hz
58) Varani, 2002 (75.00; 75.78; 1.01%) > 300 Hz
59) De Mattei, 2006 (75.0; 75.78; 1.01%) > 300 Hz
60) Wang, 2016 (75.0; 75.78; 1.01%) > 300 Hz
61) Veronesi, 2014 (75.0; 75.78; 1.01%) > 300 Hz
62) Reed, 1993 (76.00; 75.90; +0.13%) > 303.6 Hz
63) Singer, 1999 (91.00; 91.18; 0.20%) > 364 Hz
64) Singer, 1999 (100.0; 101.1; 1.09%) > 400 Hz
65) Wen, 2011 (100.0; 101.1; 1.09%) > 400 Hz
66) De Mattei, 2006 (110.0; 108.0; +1.85%) > 440 Hz
67) Douglas, 2001 (120.0; 121.5; 1.24%) > 480 Hz
68) Buhl, 2003 (150.0; 151.6; 1.06%) > 300 Hz
69) Cheron, 2004 (160.0; 162.0; 1.24%) > 320 Hz
70) Chrobak, 2000 (200.0; 202.2; 1.09%) > 400 Hz
71) Schmitz, 2001 (200.0; 202.2; 1.09%) > 400 Hz
72) Kole, 2011 (242.6; 242.9; - 0.12%) > 485.2 Hz
73) Kole, 2011 (274; 269.6; +1.6%) > 274 Hz
74) Mayrovitz, 2004 (300.0; 303.1; 1.02%) > 300 Hz
75) Foffani, 2003 (300.0; 303.1; 1.02%) > 300 Hz
KHz-scale
76) Pohl, 1986; (33.00; 32.76; +0.73%) > 257.8 Hz
77) Conner-Kerr, 2015 (35.00; 34.50; +1.45%) > 273.4 Hz
78) Pitt, 2003 (70; 69.0; +1.5%) > 273.4 Hz
79) Hernández-Bule, 2014 (448.0; 442.4; +1.27%) > 437.5 Hz
MHz-scale
80) Kyung Shin Kang, 2013 (0.500; 0.498; +0.40%) > 488.3 Hz
81) Kyung Shin Kang, 2013 (1.000; 0.995; +0.50%) > 488.3 Hz
82) Takebe, 2013 (1.000; 0.995; +0.50%) > 488.3 Hz
83) Bandyopadhyay, 2014 (1.000; 0.995; +0.50%) > 488.3 Hz
84) Usselman, 2016 (1.4, 1.398, 0.18%) > 341.8 Hz
85) Kyung Shin Kang, 2013 (1.500; 1.490; +0.67%) > 366.2 Hz
86) Takebe, 2013 (3.000; 2.990; +0.33%) > 366.2 Hz
87) Bandyopadhyay, 2014 (3.770; 3.730; +1.07%) > 460.2 Hz
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88) Zou, 2007 (5.000; 4.970; 0.60%) >305.2 Hz
89) Pokorny, 2009 (8.000; 7.960; 0.50%) > 488.28 Hz
90 Bandyopadhyay, 2014 (20.00; 19.90; 0.50%) > 305.2 Hz
91) Stolfa, 2007 (21.20; 21.24; 0.19%) > 323.5 Hz
92) Hinrikus, 2016 (mod. 450; 453.0; 0.66%); (40 Hz; 40.5 Hz;
1.2%)
GHz-scale
93) Beneduci, 2005 (46.00; 45.79; +0.46%) > 342.7 Hz
94) Fröhlich, ref. G. Schmidl, (46.00; 45.79; +0.46%) >
342.7 Hz
95) Beneduci, 2005 (51.05; 51.54; 0.95%) > 380.4 Hz
96) Fröhlich, ref. G. Schmidl (61.20; 61.09; +0.18%) >
456.0 Hz
97) Radzievsky AA. 2004 (61.22; 61.09; + 0.22%) > 456.1 Hz
98) Kalantaryan, 2010 (64.50; 65.23; 1.12%) > 480.6 Hz
99) Beneduci, 2005 (65.00; 65.23; 0.35%) > 484.3 Hz
THz-scale
100) Sukhova, 2007 (0.129; 0.1305; 1.15%) > 480.6 Hz
101) Fedorov, 2011 (2.300; 2.316; 0.69%) > 267.8 Hz
102) Kirichuk, 2013 (3.680; 3.710; 0.81%) > 428.4 Hz
Optical Nms scale
103) Finkel, 2013 (9.3 nm; 9.36 nm; 0.64%) > 458.1 Hz
104) Hamblin, 2012 (254; 252.8; +0.48%) > 268.4 Hz
105) Osman and Valadon, 1977 (370; 374; 1.1%) > 368.5 Hz
106) 106) De Sousa, 2013 (395; 399.5; 1.13%) > 345.1 Hz
107) Gungormus, 2009 (404; 399.5; +1.13%) > 337.5 Hz
108) Rezende, 2007 (415; 420.8; 1.38%) >328.5 Hz
109) Hawkins, 2007 (415; 420.8; 1.38%) >328.5 Hz
110) Bowmaker & Dartnall, 1980 (420.0; 420.8; 0.19%) >
324.6 Hz
111) Hussein, 2011 (445; 449.8; 1.07%) > 306.4 Hz
112) Carotenoid (450; 449.8; +0.1%) >303.0 Hz
113) Reddy, 2003, (452; 449.8; +0.49%) > 301.6 Hz
114) Silveira, 2011 (452; 449.8; +0.49%) > 301.6 Hz
115) Pereira, 2002 (452; 449.8; +0.49%) > 301.6 Hz
116) Chlorophyll b (453; 449.8; +0.7%) > 308.2 Hz
117) Fushimi, 2012 (456; 449.8; + 1.38%) > 299.0 Hz
118) Adamskaya, 2011 (470; 473.4; 0.7%) > 290.1 Hz
119) Cheon, 2013 (470; 473.4; 0.7%) > 290.1 Hz
120) Palacios, 1997 (503.96; 505.6; 0.32%) > 270.5 Hz
121) Palacios, 1997 (505.86; 505.6; +0.05%) > 269.5 Hz
122) Meyer, 2010 (525; 532.5; 1.4%) > 259.7 Hz
123) De Sousa, 2010 (530; 532.5; 0.47%) > 257.3 Hz
124) Weng, 2011 (532; 532.5; 0.09%) > 256.3 Hz
125) Fukuzaki, 2015 (532 nm, 532.5; 0.1%) > 256.3 Hz
126) Bowmaker & Dartnall, 1980 (534; 532.5; 0.28%) >
255.3 Hz
127) Phycoerythrin (565; 561.0; +0.7%) >482.6 Hz
128) Bowmaker & Dartnall, 1980 (564; 561.0; 0.54%)>
483.4 Hz
129) Weiss, 2005 (590; 599.1; 1.52%) > 462.1 Hz
130) Vojisavljevic, 2007 (596; 599.1; - 0.52%) > 457.6 Hz
131) Komine, 2010 (627; 631.3; 0.68%) > 434.9 Hz
132) Tada, 2009 (629; 631.3; 0.36%) > 433.5 Hz
133) Adamskaya, 2011 (629; 631.3; 0.36%) > 433.5 Hz
134) Karu 2004 (630, 631.3; 0.21%) > 432.8 Hz
135) Huang, 2007 (630; 631.3; 0.21%) > 432.8 Hz
136) 129) Yu, 1997 (630; 631.3; 0.21%) > 432.8 Hz
137) Rabelo, 2006 (632.8; 631.3; +0.24%) >430.9 Hz
138) Carvalho, 2006 (632.8; 631.3; +0.24%) > 430.9 Hz
139) Fahimipour, 2013 (632.8; 631.3; +0.24%) > 430.9 Hz
140) Fushimi, 2012 (638; 631.3: +1.06%) > 427.4 Hz
141) Lacjaková, 2010 (670; 674.0; +0.59%) > 407.0 Hz
142) Lanzafame, 2007 (670; 674.0; +0.59%) > 407.0 Hz
143) Reis, 2008 (670; 674.0; +0.59%) > 407.0 Hz
144) Moore, 2005 (675; 674.0; +0.15%) > 403.9 Hz
145) Chlorophyll a (675; 674.0; +0.14%) > 403.9 Hz
146) Sousa, 2010 (700; 710.1; 1.42%) > 389.5 Hz
147) Choi, 2012 (710; 710.1; 0.01%) > 384.0 Hz
148) Vojisavljevic, 2007 (829; 841.6; - 1.50%) > 328.9 Hz
149) Biscar, 1976 (855.0; 841.6; +1.6%) > 328.9 Hz
150) Hu, 2014 (4300; 4260.0; +0.93%) > 253.6 Hz
Appendix 2 Frequencies reported in biological
studies, that destabilize cells in vitro or in vivo,
versus calculated algorithmic frequencies
Number) Author, year of published biological experiment
(applied biological frequency: w; first nearby calculated
algorithmic frequency: x, difference in between applied fre-
quency and nearby calculated frequency: y %) > applied
frequency normalized to the quantized acoustic reference
scale: z Hz
Hz-scale
1) Puharich (6.600; 6.540; +0.92%) > 422.4 Hz
2) Pfluger, 1996 (16.7, 16.43; +1.64%) > 267.2 Hz
3) Ghione, 1996 (37; 37.0; 0.1%) > 296.0 Hz
4) Ahmed, 2013 (200; 197.2; +1.4%) > 400 Hz
5) Ahmed, 2013 (250; 249.5; +0.2%) > 250 Hz
7) Ahmed, 2013 (350; 353; 0.86%) > 350 Hz
8) Ahmed, 2013 (400; 394.3; +1.4%) > 400 Hz
9) Ahmed, 2013 (500; 499; +0.2%) > 250 Hz
KHz-scale
10) Sausbier, 2004 (5, 5.018; 0.36%) > 312.5 Hz
MHz-scale
11) Brown-Woodman, 1988 (27.12; 27.41; - 1.1%) > 413.82 Hz
12) Tofani, 1986 (27.12; 27.41; - 1.1%) > 413.82 Hz
13) Bawin, 1973 (147; 146.2; +0.55%) > 280.38 Hz
14) Jauchem and Frei 1997 (350; 348.8; 0.3%) > 333.78 Hz
15) Sanders, 1980, (591; 584.9; +1.1%) > 281.8 Hz
16) De Pomerai, 2000, Daniells, 1998 (750; 740.3; +1.3%) >
357.6 Hz
17) Maskey, 2014, (835; 826.9; + 0.98%) > 398.21 Hz
18) Donnellan, 1997 (835; 826.9; +0.98%) > 398.2 Hz
19) Adey, 2006 (836; 826.9; + 1.1%) > 398.6 Hz
20) Mashevich, 2003 (830; 826.9; +0.38%); 395.8 Hz
21) Luukkonen, 2009 (872; 877.12; 0.58%) > 415.8 Hz
22) Hao, 2012 (916; 930.28; 1.5%) > 436.8 Hz
23) Johnson and Guy, 1972 (918; 930.3; 1.3%) > 437.7 Hz
24) Zmyslony, 2004 (930; 930.3; 0.03%) > 443.5 Hz
25) Maes, 1997 (935.2; 930.3; +0.5%) > 445.9 Hz
26) Jauchem and Frei 2000 (1000; 986.9; +1.3%) > 476.8 Hz
27) De Pomerai, 2003 (1000; 986.9; +1.3%) > 476.81 Hz
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28) Lu, 1992 (1250; 1239.8; +0.82%) > 298.0 Hz
29) Oscar and Hawkins, 1977 (1300; 1315.4; 1.1%) >
310.0 Hz
30) Wake, 2007 (1500; 1480.6; +1.3%) > 357.6 Hz
31) Schirmacher, 1999 (1750; 1754.2; - 0.24%) > 417.2 Hz
32) Iyama, 2004 (2000; 1973.8; +1.3%) > 476.8 Hz
33) Senavirathna, 2014 (2000; 1973.8; +1.3%) > 476.8 Hz
34) Aydogan, 2015 (2100; 2093.0; +0.33%) > 250.3 Hz
35) Grin AN, 1974, 2375; 2339.5; +1.5% > 283.1 Hz
36) Shandalal, 1979 (2375; 2339.5; +1.5%) > 283.1 Hz
37) Lai et al, 1987, 1988 (2450; 2479.7; 1.2%) > 292.1 Hz
38) Deshmukh, 2015 (2450; 2479.7; 1.2%) > 292.1 Hz
39) Switzer and Mitchell, 1977 (2450; 2479.7; 1.2%) >
292.1 Hz
40) Kesari KK, 2010 (2450; 2479.7; 1.2%) > 292.1 Hz
41) Shokri S. 2015 (2450; 2479.7; 1.2%) > 292.1 Hz
42) FigueiredoI, 2004 (2500; 2479.7; +0.8%) > 298.0 Hz
43) Bin, 2014 (2576; 2630.7; - 2.1%) > 307.1 Hz
44) Thomas et al. 1982 (2800; 2790.1; +0.35%) > 333.8 Hz
45) Albert EN, 1977 (2800; 2790.1; +0.35%) > 333.8 Hz
46) Frei and Jauchem, 1989 (2800; 2790.1; +0.35%) >
333.78 Hz
47) Gandhi, CR., 1989 (2800; 2790.1; +0.35%) > 333.8 Hz
48) Siekierzynski, 1972 (2950; 2961.1; - 0.38%) > 351.7 Hz
49) Pu, 1997 (3000; 2961.1; +1.3%) > 357.61 Hz
50) Grodon, 1970 (3000; 2961.1; +1.3%) > 357.61 Hz
51) Tolgskaya, 1973 (3000; 2961.1; +1.3%) > 357.6 Hz
52) DÁndrea et al, 1994 (5600; 5580.2; +0.35%) > 333.8 Hz
53) Jensh, 1984 (6000; 5922.2; +1.3%) > 357.6 Hz
54) Copty. 2006 (8500; 8371.8; +1.5%) > 253.31 Hz
55) Goldstein and Sisko, 1974 (9300, 9358; 0.6%) > 277.2
56) Zhang Y, 2014, (9417; 9358.1; +0.63%) > 280.7 Hz
57) Zhang, 2014 (9410; 9358.1; +0.56%); 280.4 Hz
GHz-scale
58) Sharma, 2014 (10.0; 9.92; +0.8%); 298.0 Hz
59) Jauchem and Frei 2000 (10.0; 9.92; +0.8%) > 298.0 Hz
60) FigueiredoI, (2004, 10.5; 10.53; 0.2%) > 312.9 Hz
61) Porcelli, (10.40; 10.52; 1.16%) > 309.9 Hz
62) Paulraj, 2012 (16.50; 16.74; 1.46%); 245.9 Hz
63) Millenbaugh NJ, 2008 (35; 35.29; - 0.82%) > 260.8 Hz
64) Roza K. 2010 (35; 35.29; - 0.82%) > 260.8 Hz
65) Shock, 1995 (35; 35.29; - 0.82%) > 260.8 Hz
66) Kesari KK, 2009 (50; 50.25, 0.50%) > 372.5 Hz
67) Tafforeau M, 2004 (105; 105.85; - 0.80%) > 391.2 Hz
THz-scale
68) Kirchuk, 2008 (0.24; 0.238; 0.78%) > 447.0 Hz
69) Webb and Dodds, 1968 (0.136, 0.134; + 1.54%) >
253.3 Hz
70) Wilmink, 2010 (2.52; 2.54; - 0.78%) > 293.4 Hz
71) Homenko, 2009 (0.1; 0.1; 0.5%) > 372.5 Hz
Optic nms scale
72) Kitchel E., 2000 (435; 434.7; 0.1%) > 313.4 Hz
73) Glazer-Hockstein, 2006, Algvere PV, 2006, Marshall J,
2006, Tomany S.C, 2004, 2008,
Smick K, 2013 (435.0; 435.1; 0.02%) > 313.4 Hz
74) Ham, 1980 (441.0; 435.1; 1.4%) > 309.1 Hz
75) Hu, J., 2014 (466.0; 461.4; +1.0%) > 292.5 Hz
76) Ueda, T., 2009 (465.0; 461.4; + 0.8%) > 293.2 Hz
77) Moore, P, 2005 (810; 820.2; 1.2%) > 336.6 Hz
Appendix 3 The different beneficial and detri-
mental health effects reported in biological
studies caused by electromagnetic fields
114 different frequencies of electromagnetic waves in 145
independent published biological studies could be found,
which show beneficial effects on cells in vivo and in vitro.
The experiments are in the areas of: neuro-stimulation, brain
stimulation, spinal cord stimulation, self-assembly via tunnel-
ling current of microtubulins, transcranial magnetic stimula-
tion, reduction of Parkinson, anti-proliferative effects on
tumor cells, inhibition of tumor growth, reduced and repres-
sion of tumor growth, rhythmic neuronal synchronization,
improvement of memory, improvement of attention, wound
healing, decrease of inflammatory cells, increase of bone
growth, reduction of diabetic peripheral neuropathy, increase
of fibroblast proliferation, stimulation of angiogenesis, gran-
ulation of tissue formation and synthesis of collagen, promo-
tion of proliferation of human mesenchymal stem cells,
entorhinal-hippocampal interactions, regeneration of cells
and others (references of the biological studies can be
obtained upon request, authors and publication year have
been mentioned in Appendix 1).
60 different measured frequencies of electromagnetic waves
could be found in literature, that destabilize living cells in 74
independent biological studies reporting detrimental effects
of EM radiation on cells in vivo and in vitro. The experi-
ments in these studies are in the areas of: tumor growth,
influence on teratogenic potential, DNA single-strand breaks,
gene expression, chromosomal instability, inhibition of cell
growth, influences on sperm parameters, influence on sleep-
ing, influence on the permeability of the blood-brain barrier,
influence on behavior, cognitive impairment, learning and
memory alterations, maculopathy, influence on specific
brain rhythms, alter of protein conformation, effects on
blood pressure, cardiovascular responses, phototoxic effects
on human eye health, and on the retina, influence on alkaline
phosphatase activity and antigen-antibody interaction, cardi-
ovascular effects and others (references can be obtained upon
request, authors and publication year have been mentioned
in Appendix 2).
Appendix 4 Some soliton frequencies accord-
ing to the algorithm, cell stabilizing
12 Hz: 1.0, 1.06, 1.13, 1.18, 1.27, 1.33, 1.43, 1.5, 1.58, 1.69,
1.78, 1.90 Hz
24 Hz: 2.0, 2.11, 2.25, 2.37, 2.53, 2.67, 2.85, 3.0, 3.16, 3.38,
3.56, 3.80 Hz
48 Hz: 4.0, 4.22, 4.5, 4.74, 5.06, 5.33, 5.70, 6.0, 6.32, 6.75,
7.11, 7.59 Hz
3261 Hz: 32.0, 33.7, 36.0, 37.9, 40.5, 42.7, 45.6, 48.0, 50.56,
54.0, 56.9, 60.75 Hz
64122 Hz: 64, 67.5, 72, 75.8, 81, 85.3, 91.18, 96, 101.1, 108.0,
113.8, 121.5 Hz
255487 Hz: 256, 269.8, 288, 303.1, 324, 341.2, 364.7, 384,
404.5, 432, 455.1, 486 Hz
16.331.2 kHz: 16.38, 17.25, 18.43, 19.40, 20.74, 21.84, 23.34,
24.58, 25.91, 27.65, 29.13, 31.10 KHz
16.732 MHz: 16.77, 17.66, 18.87, 19.86, 21.24, 22.36, 23.90,
25.17, 26.53, 28.31, 29.83, 31.85 Mhz
ELECTROMAGNETIC BIOLOGY AND MEDICINE 377
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4.28.2 GHz: 4.293, 4.520, 4.831, 5.085, 5.437, 5.724, 6.119,
6.443, 6.792, 7.247, 7.636, 8.154 GHz.
1.1535 THz: 281.5, 296.5, 316.7, 333.3, 356.2, 375.2, 401.0,
422.2, 444.8, 474.9, 500.4, 534.4 THz.
140.8, 148.3, 158.4, 166.7, 178.1, 187.6, 200.5, 211.1, 222.4,
237.5, 250.2, 267.2 THz
70.38, 74.13, 79.18, 83.33, 89.05, 93.80, 100.25, 105.6, 111.2,
118.7, 125.1, 133.6 THz
35.19, 37.06, 39.59, 41.66, 44.53, 46.90, 50.124, 52.78, 55.60,
59.36, 62.55, 66.80 THz
17.59, 18.53, 19.79, 20.83, 22.26, 23.45, 25.06, 26.39, 27.80,
29.68, 31.28, 33.40 THz
8.80, 9.266, 9.897, 10.42, 11.13, 11.73, 12.53, 13.19, 13.90,
14.84, 15.64, 16.70 THz
4.40, 4.633, 4.948, 5.208, 5.566, 5.863, 6.266, 6.597, 6.950,
7.420, 7.819, 8.350 Thz
2.20, 2.316, 2.474, 2.604, 2.783, 2.931, 3.133, 3.298, 3.475,
3.710, 3.909, 4.175 THz
1.10, 1.158, 1.237, 1.302, 1.391, 1.466, 1.566, 1.649, 1.738,
1.855, 1.955, 2.088 Thz
532.5, 505.6, 473.4, 449.8, 420.8, 399.5, 373.80, 710.1, 674.0,
631.3, 599.1, 561.0 nm.
Appendix 5: algorithm frequencies at an
acoustic reference scale
12 typical frequencies could be defined:
256.00, 269.79, 288.00, 303.16, 324.00, 341.21, 364.73, 384.00,
404.51, 432.00, 455.08, 486.00 Hz.
All higher and lower coherent frequencies can be calculated
by multiplying or dividing each typical frequency by 2.
378 J. H. GEESINK AND D. K. F. MEIJER
Downloaded by [84.31.212.213] at 09:35 22 November 2017
... Numerous observable consequences of zero-point electromagnetic (ZPEM) field have been found in atomic physics that establish its presence, ranging from the isotope effect, line width of spectra, changes in low temperature behaviour, the Lamb shift and the Casimir effect. A proposed theory of quantum biophysics has shown that quantum coherent assembled waves exist for living biomolecules and cells (Geesink, 2017a), EPR-experiments (2018b), superconduction (2019a), and sub-atomic particles (Geesink, 2018f). The postulate of an acting resonating energy field can be further substantiated by the fact that energies of diatomic molecules have a significant term of the vibrational zero-point energy (ZPE) to correct the total energy of the molecules (Irikura, 2005(Irikura, , 2007. ...
... Even the pattern of destabilizing and unhealthy biological effects fit with a quantum behaviour that is described by two quantum equations. The stabilising and destabilising electromagnetic field effects (Geesink, 2016a(Geesink, , 2017a2018a;2018b), were observed in a widespread health and a disease window and related therapeutic measures and see figure 9. It has been proposed that conformational states of living cells have typical spatial arrangements of atoms, that are characteristic for building, homeostasis, decay and apoptosis. ...
... The patterned arrangements of EMF frequencies can be described by electromagnetic wave patterns positioned on a "tone-scale", on the basis of an underlying quantum wave equation. The proposed equation shows a discrete distribution of energy: En= ħ ωref 2 n+p 3 m , that supports quantum entanglement and is in line with the earlier published models of Davydov and Fröhlich (Geesink 2017a(Geesink , 2017b(Geesink , 2018a. The overall results show the presence of a molecular code-script, which supplies information to realize biological order in life cells and substantiates collective Bose-Einstein type of coherent wave behaviour. ...
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A new biomarker is proposed, that shows a diagnostic capability to classify a measure of healthy and unhealthy behaviour by analysing the pattern of brain waves related to discrete frequencies and amplitudes. Discrete frequencies fit in a coherent or in a decoherent frequency pattern and has been substantiated by a quantum physical model about phase-synchronisation of the spectral lines of EEG (Electroencephalography) and MEG (Magnetoencephalography). Phase-synchronisation and spatio-spectral eigenmodes have been shown for our brains and is related to a discrete distribution of energy: En= ħ ωref 2 n+p 3 m. The model shows that the overall resonating spatio-spectral states of living cells and molecules including brain cells can be described by a sum of quantum coherent and decoherent frequencies. Healthy states are quantum coherent and approach a global quantum coherence of 1.0, while unhealthy states are decoherent and cause a decrease of coherence. The proposed model of spatio-spectral eigenmodes has been substantiated by analysing the many measured frequency patterns of EEG's and MEG's, and electromagnetic exposures of brain cells, glands and neurons. The EEG-and MEG studies of healthy persons show a global quantum coherence of 0.90-1.00. Unhealthy subjects show a decrease of coherence, and an increase of decoherence. ADHD subjects show a decrease of coherence from 1.0 to 0.83. During epileptic seizure, the coherence of participants is reduced from 0.94 to 0.75. Depressed patients have a lower coherence than healthy persons: 0.77-0.88, autistic persons show a lower coherence of 0.50 till 0.75, patients with severe psychiatric disorders show a coherence of about 0.59, and participants during anaesthesia show a level of 0.25. Repetitive transcranial magnetic stimulation (rTMS) has been reported to modify brain oscillations and the periodic electromagnetic force generated during rTMS can result in local entrainment of biologically relevant rhythms, mimicking frequency specific oscillatory activities. Potential differential effects occur at typical frequencies: 0.50, 0.75, 1, 5, 6, 8, 9, 10, 12, 15, 17, 20, 25, 40 Hz, that are equal or approach the proposed algorithm, and fit with the eigenstates (eigenfrequencies) described by the proposed equation of coherence. The coherent and decoherent (chaos-like) frequencies can be aligned at a frequency scale and are arranged according to an alternating ordering positioned at a toroidal geometry, while transition frequencies are located just in between the coherent and decoherent frequency zones. The overall results show a presence of an informational quantum code and a molecular code-script, which supplies information to realize biological order in life cells and substantiates a collective Bose-Einstein type of behaviour. Typical nano/submicron minerals can copy healthy behaviour of living cells.
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