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Schumann Resonance and Brain Waves: A Quantum Description

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In this paper for the first time we compared spectra of the brain and Schumann electromagnetic waves. We argue that both modes of electromagnetic radiation: brain waves and Schumann waves can be analyzed with the help of the Planck formula. From our calculation we deduced the temperature of the Schumann and brain waves T= 10-10 K.
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NeuroQuantology | June 2015 | Volume 13 | Issue 2 | Page 196-204
Marciak-Kozlowska and Kozlowski., Schumann resonance and brain waves
eISSN 1303-5150
www.neuroquantology.com
196
Schumann Resonance and Brain Waves:
A Quantum Description
Miroslaw Kozlowski, Janina Marciak-Kozlowska
ABSTRACT
In this paper for the first time w ecom pared spectra of the brain and Schumann electro magnetic waves. We
arguethatboth modes of electromagneticradiation:brain waves and Schumann wavescan be analyzed with
thehelpof the Planckformula. Fromourcalculationwededucedthetemperatureof the Schumann and brain
wavesT=10-10K.
Key Words: brainwaves,Schumannwaves,modelcalculation, Planckformula
DOI Number: 10.14704/nq.2015.13.2.795 NeuroQuantology 2015; 2: 196-204
1. Introduction1
Geospaceis the term that relates to the solar-
terrestrial environment and the relevant space
occupied by Earth and her fields. Schumann
Resonances (SR), global electromagnetic
resonances, excited by lightning, is one of the
natural electromagnetic (EM) fields in our
planetary environment. But resonances can be
excitedbyanyelectromagneticdisturbanceinthe
atmosphere. The fundamental SR mode roughly
corresponds to a wave with a wavelength equal
to the circumference of the Earth. Transverse
resonanceis predominantlya local phenomenon
containing information on the local height and
conductivity of the lower ionosphere and on
nearbythunderstormactivity.Wavesintheultra-
lowfrequency(ULF)rangeULFrange(i.e.,below
Corresponding author:MiroslawKozlowski
Address:MiroslawKozlowski,WarsawUniversity,Warsaw,Poland
andJaninaMarciak-Kozlowska,InstituteofElectronTechnology,
Warsaw,Poland.
e-mailmiroslawkozlowski1@gmail.com
Relevant conflicts of interest/financial disclosures:Theauthors
declarethattheresearchwasconductedintheabsenceofany
commercialorfinancialrelationshipsthatcouldbeconstruedasa
potentialconflictofinterest.
Received:7November2014;Revised:14Feb2015;
Accepted:22May2015
the first Schumann Resonance), will have
wavelengthsmuch largerthanthecircumference
ofthe Earth.ULFwaves,atapproximately1mHz
to1 Hz, playa major rolein propagating energy
throughout the magnetospheric system. At the
lowest end of this frequency band, the
wavelength of ULF waves is comparable to the
entire magnetosphere. In this frequency range,
the global structure of the magnetosphere can
lead to global cavity resonances and waveguide
modes. The structure of these modes is
determined by the gradients in the Alfvén and
fast mode speeds in the magnetosphericsystem.
SR is not the internally-generated resonant
frequency of the planet Earth,which is 10 Hz as
Tesla discovered. It is electromagnetic
oscillations - the Earth’s global electric circuit
consisting of the frequencies that play through
theionosphericcavity(spacebetweentheground
and ionosphere) as waves in a plasma. The
ionosphere is a highly-conductive region of
cosmicplasma(NikolaenkoandHayakwa,2014).
The solar-terrestrial environment is
modulatedbysolarcycleswhichaffecttheglobal
climate and all organisms in the biosphere.
Interference patterns are the transducers of
NeuroQuantology | June 2015 | Volume 13 | Issue 2 | Page 196-204
Marciak-Kozlowska and Kozlowski., Schumann resonance and brain waves
eISSN 1303-5150
www.neuroquantology.com
197
energy, which at its most fundamental is
described as information. Earth functions like a
planet-sized electrical capacitor or condenser,
storing electrical potential (Nikolaenko and
Hayakwa,2014).
The space between Earth and the
ionosphereisadissipativeclosedcavitybetween
50-375 miles that can sustain quasi-standing
waves at wave lengths of planetary dimension.
Electrical conductivity in the atmosphere is
driven largely by cosmic rays that generate a
torsion field. Conductivity increases
exponentially with altitude because the lower
atmosphere buffers collision frequency. The
ionosphere begins about 50 miles out from the
Earth’ssurfaceandextendsoutover180miles.It
consistsofchargedparticles.Thishighlydynamic
region is constantly exposed to harshultraviolet
radiationfromtheSun.Itbreaksdownmolecules
andatoms.Highlychargedionsandfreeelectrons
therefore fill the ionospheric layers creating a
“spectral power station”. Lightning radiates
broadbandEMfieldsthatspreadlaterallyintothe
cavity. Global thunderstorms excite the
Schumann resonances, which can be observed
around 7.8, 14, 20, 26, 33, 39 and 45 Hz
(NikolaenkoandHayakwa,2014).
The resonant spectrum is a superposition
of global lightning discharge. For these resonant
values to change, the planet would have to
changediameter.
The detection of Schumann resonances in
the ionosphere calls for revisions to the existing
models of extremely low frequency wave
propagation in the surface-ionosphere cavity.
Suchfrequencieshavewrappedearth’slifesince
itsinception.Normaldailyvariationranges ± 0.5
Hz. Driven by lightning, this primary SR pulse
calibrates us and enhances our physical and
mental well-being (Nikolaenko and Hayakwa,
2014).
That natural resonance helps us achieve
our optimal brainwave states, but this
atmospheretohumanlinkageisdisruptedbythe
electrosmogoftoday’stechnology.
2. Schumann Waves (SW)
That information is propagated as sequential
seriesofdigitalsignalsalongdistinctpathswhose
lengths are much longer than their widths is a
primary assumption of contemporary neuronal
function.Dispersionratesarewithintherangeof
1–100 m/s with space constants in the order of
about 1 mm. The fastest of these transients
exhibitsaltatorymovementsbetweenspecialized
conductive spaces along the axon barrels. The
ratios and scaling of the spatial and temporal
relationshipsof thesemediatorsof the“language
of the brain” share remarkable similarities to
lightning. Because lightning’s absolute spatial
scale is so large compared to the observer’s
reference point, minute characteristics are
discerned whose equivalence at the level of the
axon are below contemporary resolution.
Quantitativeidentitiesbetweenthesetwoclasses
of phenomena could encourage alternative
interpretations of the electromagnetic (EM)
components of action potentials and reveal
recondite relationships concerning neuronal
function.
The identity between exogenous and
endogenous“electricity”is not really a new idea.
The observation that atmospheric electricity,
lightning, and the electrical fields within living
systems, “nerve conduction,” shared similar
origins was considered as early as the 18th
century by Galvani and Volta. Galvani showed
contractionsinfrogmuscleselicitedfromLeyden
jarsand electricmachineswas thesameas those
evoked during lightning when a long metallic
wirewasconnectedtothenervesandpointedto
the sky. The similarity has been viewed
historically as more of a congruence of quality
than a potential blueprint for quantitative
characteristics. In the present comparison these
features are demonstrated. To facilitate
understandingthecalculationsandreasoningfor
the similarities between action potentials and
lightningwillbearticulatedingreaterdetailthan
the usual narrative discussion in the
neurosciences.
The concept of scale-invariance or
recurrent ratios within measurements of the
physical world assumes an intrinsic repeated
structurewithinthevaryingincrements of space
(Δs) and time (Δt) as well as their relationship.
For example the proportion of matter (protons
and electrons) that occupies the space (volume)
occupied by an atom is about1 part per trillion.
The ratios of the volume of the sun and planets
withinthespaceofthesolarsystemandthestars
within galactic space are the same order of
magnitude.
One temporal example is the equivalent
order of magnitude of the ratio of the electron
orbitaltimeofahydrogenatom toitsprecession
NeuroQuantology | June 2015 | Volume 13 | Issue 2 | Page 196-204
Marciak-Kozlowska and Kozlowski., Schumann resonance and brain waves
eISSN 1303-5150
www.neuroquantology.com
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andthe earth’s rotation to its spin axis gyration.
Comparable “scale-invariance” has been found
within the human brain and for functional EM
fields within the cerebrum and over very large
spaces.
3. Classical description of the Schumann and
brain waves
The brain is a massive source of extremely low
frequency (ELF) signals that get transmitted
throughoutthebodythroughthenervoussystem,
whichissensitivetomagneticfields.Brainwaves
and natural biorhythms can be entrained by
strong external ELF signals, such as stationary
waves at Schumann resonance. Entrainment,
synchronization, and amplification leads toward
coherent large-scale activity, rather than typical
flurries of transient brainwaves. Thus, resonant
standing waves emerge from the brain, which
undertherightconditionsfacilitatesinternaland
external bioinformation transfer, via ELF
electromagnetic waves (Nikolaenko and
Hayakwa, 2014).  These SR waves, exhibit non-
local character and nearly-instant
communication.
The EEG (electroencephalograph)
measures brainwaves of different frequencies
withinthebrain. RhythmicityintheEEGisakey
variable in the coordination of cortical activity.
Electrodes are placed on specific sites on the
scalpto detectandrecordtheelectricalimpulses
within the brain. Frequency is the number of
timesawaverepeatsitselfwithinasecond.Itcan
be compared to the frequencies on a
radio. Amplitude represents the power of
electrical impulses generated by the
brain.Volume orintensityof brainwaveactivity
ismeasuredinmicrovolts.
Raw EEG frequency bands include Gamma
(higher than 30Hz); Beta (14-30Hz); Alpha (7.5-
13Hz); Theta (3.5-7.5Hz); and Delta (less than
4Hz).Theirrangesoverlaponeanotheralongthe
frequency spectrum by 0.5 Hz or more. These
frequencies are linked to behaviors, subjective
feeling states, physiological correlates,
etc. Clinical improvement with EEG biofeedback
is traceable to improved neuroregulation in the
basic functions by appeal to their underlying
rhythmicmechanisms.
Schumann's resonance forms a natural
feedback loop with the human mind/body. Our
brainsandbodiesdevelopedinthebiosphere,the
EM environment conditioned by this cyclic
pulse.Conversely,thispulseactsasa"driver"of
our brains, and can also potentially carry
informationaswell.Functionalprocessesmaybe
altered and new patterns of behavior facilitated
through the brain's web of inhibitory and
excitatoryfeedbacknetworks.
Likesoundwaves,thebrainhasitsownset
of vibrations it uses to communicate with itself
and the rest of the body; EEG equipment
distinguishes these waves by measuring the
speed with which neurons fire in cycles per
second. At their boundaries these waves can
overlap somewhat, merging seamlessly into one
another, so different researchers may give
slightlydifferentreadingsfortherangeof cycles
per second. Rate of cycling determines the type
of activity, kindling wave after wave over the
whole surface of the brain, by igniting more
neurons.
There is a harmonic relationship between
the earth and our mind/bodies. Earth's low
frequency isoelectric field, the magnetic field of
the earth, and the electrostatic field which
emerges from our bodies are closely
interwoven. Our internal rhythms interact with
external rhythms, affecting our balance, REM
patterns, health, and mental focus. SR waves
probably help regulate our bodies' internal
clocks, affecting sleep/dream patterns, arousal
patterns, and hormonal secretion (Başar, 2011;
Başar,2005).
The rhythms and pulsations of the human
brain mirror those of the resonantproperties of
the terrestrial cavity, which functions as a
waveguide.This natural frequency pulsation is
not a fixed number, but an average of global
readings, much like EEG is an average of
brainwave readings. SR actually fluctuates, like
brainwaves, due to geographical location,
lightning,solarflares,atmosphericionizationand
dailycycles(Nunez,1995).
The most important slow rhythm is the
daily rhythm sensed directly as change of light.
Rhythms connected with the daily rhythm are
called circadian (an example is pineal gland
melatonin secretion). Some experiments in the
absenceofnaturallighthaveshownthatthebasic
human"clock"isactuallyslightlylongerthanone
day, and closer to one lunar day (24h and 50
min).Thelunardayhasasimilarperiod(24hand
50min).
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Onaslowerscale,astronginfluenceonthe
Earthisitsgeomagneticfield,whichisinfluenced
by the following periods: the Moon's rotation
(29.5 days); the Earth's rotation (365.25 days);
Sun spots (11 and 22 years); the nutation cycle
(18.6years);the rotationoftheplanets(88days
to 247.7 years); and all the way out to the
galaxy'srotationcycle(250millionyears).
Veryimportantrhythmsarein theorderof
1-2hours,like hormonesecretion,anddominant
nostrilexchange.IntherangeofhumanEEG,we
have the Sun's electromagnetic oscillation of 10
Hz, while the Earth-ionosphere SR system is
resonantat frequenciesinthetheta,alpha,beta1
andbeta2bands.
Different species often have internal
generatorsofenvironmentalrhythms,whichcan
beextremelyprecise,upto10-4.Thefrequencyof
theseoscillatorsis then phase lockedloop (PLL)
synchronized with the natural rhythms.
Environmentalsynchronizationsourcesareoften
called “zeitgeber”. The mechanism of optical
synchronization can be shown. The presented
rhythmsshouldinspireabetterunderstandingof
the interaction of internal and external rhythms
duringspecificstatesofconsciousness.
This bioelectrical domain is geared to
thalamocortical generation of rhythmic activity.
In neurofeedback, what is being trained is the
degree of rhythmicity of the thalamocortical
regulatory circuitry. Rhythmicity manages the
entirerangeofactivationandarousalinthebio-
electrical domain. One role advocated for
rhythmicactivityisthatoftimebinding,theneed
for harnessing brain electrical activity which is
spatially distributed while maintaining it as a
single entity. Brainwaves indicate the arousal
dimension, and arousal mediates a number of
conditions. Changes in sympathetic and
parasympathetic arousal "tunes" the nervous
system(Polk,1982).
Deltawaves are the slowest but highest in
amplitude.Theyareabundantindeep,dreamless
sleep, non-REM sleep, trance, and
unconsciousness. Theta waves mean 'slow"
activityconnectedoftenwithcreativity,intuition,
daydreaming or recalling emotions and
sensations. Focus is internal in this state
between waking and sleep. Under stress it may
manifest as distraction, lack of focus. Alpha
waves aid relaxation and overall mental
coordination, calmness, alertness, inner
awareness,mind/bodyintegrationandlearning.
Betaisa'fast'activity,presentwhenweare
alertorevenanxious;problem-solving,judgment,
decision making, processing information, mental
activity, and focus. Gamma appears to relate to
simultaneously processing information from
different brain areas: memory, learning abilities,
integrated thoughts, information-rich task
processing. Gamma rhythms modulate
perception and consciousness, which disappears
with anesthesia. Synchronous activity at about
40Hzappearsinvolvedinbindingsensoryinputs
intothesingle,unitaryobjectsweperceive(Polk,
1982).
The brain responds to inputs at a certain
frequency or frequencies. The computer can
createwaveformpatternsor certainfrequencies
that compare with the mind's neural signals in
terms ofmind patterns. If people can control
their mind patterns, they can enter different
states of being (mental relaxation, study, etc.).
Whathappenswhenthemindisentrainedwitha
sound or vibration that reflects the thought
patterns? When the mind responds to certain
frequenciesandbehavesasaresonator,istherea
harmonicfrequencythatthe mind vibrates to or
can attune to? What does the study of harmonic
resonance - sound or vibration have to do with
thebrain'sfrequencywaves?
Soundwavesareexamplesofperiodicity,of
rhythm. Sound is measured incycles per second
(HertzorHz). Eachcycleofawave isinrealitya
single pulse of sound. The average range of
hearingforthehumanearissomewherebetween
16Hzand20,000Hz. Wecannothear extremely
lowfrequencies(ELFs),butwecanperceivethem
asrhythmic.Actionpotentialsarethecarriersof
the discrete signals along the axon barrel. An
average net potential difference for an action
potential (-70 to +50 mV) is 1.2 × 10-1 V which
would exert on each unit charge of 1.6 × 10-19
Coulomb (A·s) an energy of 1.9 × 10-20 J. If we
assume ~1010 neurons occupy human cerebral
cortices with an average frequency of
propagationof1Hz, the total energy per second
involved with just the effects of all action
potentialswithinbrainspacewouldbeabout10-
10J/s.Thevolume(~1330cc)ofanaveragebrain
is1.3× 10-3m3.Thisresultsinanenergydensity
ofabout10-7J/s·m3.Ontheotherhandthetypical
lightningstroke involves a flow of ~10 Coulomb
(C) of electrons across a potential difference of
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108V resulting in 109J.There are about 70–100
lightning flashes/s worldwide resulting in
(assuming100flashes)thegenerationof1011J/s
or100Gigawattsofpower.Forreferencethereis
4.3 × 1012 J per kiloton (kT) of standard
explosives such that the energygenerated every
approximately 14 min by global electrical
discharges is equivalent to about a 20 kT
(Hiroshima-like)nuclearexplosion.
Most of this energy from lightning
dischargesiswithinanarrowshellofabout2km
within the biosphere. The volume of this shell,
assuming a radius of 6,378 km for the earth,
would be about 1 × 1018 m3. This means the
energydensitywouldbe1011J/s·1018m3 or 10-7
J/s·m3 (10-7 W/m3). This energy density is
remarkably similar to that generated by action
potentials within the brain. When applied across
the3–5mmthicknessofthecerebralcortices,the
valueisequivalentto10-10W/m2whichiswithin
therangeof powerofphotonemissionsnear the
skull when subjects engage in specific
imaginationandwhichisstronglycorrelatedwith
the power of electroencephalographic (EEG)
activity.
4. Scaled densities
About 5 C is distributed within a lightning
channel with an average current of 100 A.
Althoughthewidthofaleaderchannelisabout1
m the current flows through a channel with a
radius of about 1 cm. With this cross-sectional
area the density is 10 × 101 A divided by3.14 ×
10-4m2or3.2×105A/m2.Areasonableradiusfor
anaxonis1μm.Howevertheactuallocationsof
the major movements of ions that affect the
transmission of EM field-mediated information
alongtheaxonarewithinthemembranewhichis
about10nminwidth.Thecross-sectionalareaof
thissmall annulusaroundtheaxonwouldbe2×
10-14 m2. Given the average current of 10-9 A
(from the approximately 103 ion channels each
with 1 pA capacities around the ring or
circumferenceoftheaxon),thiswouldmeanthat
the cross-sectional current “density” would be
~105A/m2.
Consequently even though the current is
much larger in a lightning stroke because of its
absolutesizebyafactorof 1010, the “minuscule”
axon potential current is comparable per cross-
sectionalarea.Therangeinthewidthsofnormal
axons would affect the coefficients rather than
the order of magnitude. It may also be relevant
that the actual charge and current per lightning
stroke also displays a comparable range in the
coefficient of variation. Such a large relative
magnitude of potential across neuronal
membranes is not a new concept. For example,
the 90 mV potential differences across a 10 nm
membrane is equivalent to 9 × 107 V/m. Most
lightning (90%) is between clouds. The leader
moves in discrete jumps of 50 m at about 1.2 ×
105 m/s to 1.5 × 105 m/s. This conspicuous
conductionoflighteninghasaratioof[1.2× 105
m/s]/50 m or 2.4 × 103 Hz (about 2 kHz or 0.5
ms) which is remarkably similar to the absolute
refractory period of the action potential. In
comparisontheactionpotential moves along the
myelinated axon in discrete steps of 1 mm
comparedtotheapproximately2μmwidthofthe
nodesofRanvier.
The wave shape characteristics of action
potentials and lightning flashes are similar. All
lightning pulses were the same polarity; most
were single peak but about one-third were
multiple-peaked.Althoughthemeanwidthof the
initialpeakwas25μs(SD:13μs),theratioofthe
overshootdurationto the initial peak was 5.7 μs
(SD: 2.1). This ratio is within the range of the
typical relative refractory to absolute refractory
period in the average axon. More recent
measurements of artificially triggered lightening
revealed comparable peak widths. Interestingly,
theinitial-stagedischargetimewas about 20 ms
andthetimebetweenstrokesrangedfrom 18 to
210ms (mean87ms).Thisintervaliswithin the
range of the global rostral–caudal propagating,
coherentwavesoverthecerebralcorticesandthe
microstates that determine a percept and
consciousness (Nikolaenko and Hayakawa,
2014).
Although the velocity of a leader exceeds
the 10 m/s values exhibited by non-myelinated
axons by a factor of 1.2–1.5 × 104, the scaled
valuesforthemassmediatingthemovementsof
chargesaresimilar.Forexample,themassofNa+,
the major mediator of the action potential,is  30
Daltons or 48×10-27 kg while the mass of an
electron is 9.8×10-31 kg. The difference is in the
order of 104. The coefficients converge more
closely when the range of hydration states
(accompanying H2O molecules) associated with
theionsareincluded.Astheleaderapproachesto
about 10 m above the ground it creates an
electric field sufficient to initiate discharges
rising from the ground (streams). When contact
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is made between the upward and downward
fieldsa heavysurgeofcurrentoccurswithin1–5
ms. This surge produces the luminosity that
progresses up the path produced by the step
leader at ~108 m/s. About 40–50 ms after the
returnstroke,anotherregionofluminosity,about
50 m long, moves from the cloud to the ground
(dartleader).Itdoesnotforkorbranch.Thereis
an average of three to four strokes with a
maximum around 20. The approximately 10 m
interface or boundary where the exchange of
energy between the atmosphere and ground
occursis about3×10-3thelength ofthepathway.
Forcortical axons with lengthsbetween 1 and 5
mm, this would be equivalent to a length of
between 3 and 15 μm whichis  withinthe range
of the length of the terminalendings or boutons
withinwhichthedigitalinformationoftheaction
potentialistransformedtochemicalequivalents.
The surge of current lasting for 1–5 msis
withintherangeofthetimeinvolvedwithrelease
of the contents of the synaptic vesicles. The
energy transfer mediated by the mass of
molecules released from the vesicles into the
synaptic space would be analogous to this
relatively large increment of current. The
occurrencesofsubsequentsurges fromthecloud
to the ground after an interval of 40–50 ms or
about20timesafterthefirstsurgeiscomparable
to the first and second surges of vesicular
releases.
The billions of action potentials and their
correlatespersecondwithinthecerebralcortices
generate emergent phenomena inferred by EEG
measurements that include microstates and
transientcoherenceofactivityoverareas(tensof
mm2totensofcm2)ofthehumanbrain’scortical
surface. Between the earth’s surface and the
lower ionosphere there is a shell of optimum
conduction within which the results of focal
energies in one area are generated throughout
thevolume.Cloud-to-groundlightningdischarges
from global thunderstorm activity are the main
excitation sources within the earth-ionospheric
cavity. These omnipresent pulses propagate for
megameterswithoutappreciableattenuationand
behave as a “cortical manifold” for distributing
tissue-level energies throughout the biosphere.
The fundamental frequency (1/s = Hz) is the
velocity divided by the circumference. Assuming
the speed of light of 3 × 108 m/s and the
circumferenceoftheearthas40,000km(4×107
m)thenaturalfrequencyis7.8Hz.Harmonicsfor
this values, often described as the Schumann
resonancescanbe obtained bytakingthesquare
root of [(n(n + 1))/2] multiplied by the base
frequency (7.8 Hz), where n is the progressive
series of integers 1, 2, 3,…, etc. Those that have
beenmeasuredhavepeaksaround8,14, 20,and
26Hz.
AsdescribedbyNunez(1995)inhisclassic
chapter on “Towards a physics of the neocortex”
comparable solutions exist for the human brain.
The probability density function for myelinated
cortico-cortical propagation peaks at about 6–9
m/s with the half-width of the distribution is
estimatedtobebetween3and4.5m/s.Published
estimates of the neocortical surface areas range
from 1,600 to 4,000 cm2. The effective cortical
radius after flat-mapping is between 11 and 18
cm. As a result the non-dispersive brain waves
frommode n=1wouldbebetween7and18Hz.
Subtleshiftsinpeakpowerinthisfrequencyvary
with head size, defined by the cube root of the
product of three linear measures. As the size
increased over a normal range of volunteers the
peakfrequencydecreasedfrom10.6to9.8Hz.
The EM signals associated with lightning
are propagated through a medium. The simplest
calculation of a time constant is the product of
the resistance (in Ohms) and capacitance in
Farads(F).Forfreespaceresistanceis3.70×102
Ohms [(kg·m2)/(A2·s3)] and capacitance is 8.8 ×
10-12 F/m [(A2·s4)/(kg·m2)]/m or 32.56 × 10-10
S/m. When multiplied by the circumference of
the earth, the time constant is 130 ms or about
7.7Hz;this is within the naturalvariationof the
fundamentalSchumannresonance.
Cerebral tissue is also a medium. The
permeability (inductance/m) of cortical gray
matter at 1 kHz is about 10-2 Henrys, while the
permittivity of gray matter is 2 × 10-1 F/m.
Applicationofthe formula f = 1/(2π(LC)-1/2),the
equation for resonance frequency of a closed
circuit, results in a value of about 7 Hz. The
convergenceofafundamentalcerebralresonance
with the Schumann solutions indicates that
higher order harmonics may exist within EM
fields within cerebral space and be associated
with specific functions. There are often strong
correlations between fluctuations in power
values measured by quantitative EEG across
traditional frequency bands. That resonance
could occur between fields within cerebral
volumes and the Schumann phenomena may
havesignificantimplicationsforthebiosciences.
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Theclassicalalthougharbitrarydivisionof
EEG activity into delta, theta, alpha, and beta
activity with a myriad of complexes and
transients have been considered both emergent
and reflective of “distant” fields of neuronal
activity. As shown by Koenig et al. (1981) all of
thefundamentalfrequenciesandpatternsofEEG
activity are measured within the Schumann
(earth–ionospheric) cavity or as local electric
field configurations during thunderstorms. In
addition, biofrequency (1–100 Hz) pulses of
about0.5ms whosecarrierfrequenciesdiminish
from100kHz toabout10kHzatdistances more
than 1000 km from the source display
magnitudes in the nanoTesla (nT) to picoTesla
(pT)range.
Within the range of 7 –40 Hz the electric
field components associated with the EM fields
generated through the ionospheric–earth cavity
are about mV/m, while the magnetic field
components are between 1 and 10 pT. For
comparison the magnetic field intensities within
galaxies are in the order of 10-10 T with upper
limits of 10-13 T for extragalactic fields. In a
mannersimilarto the changing, averaged power
outputs of neuronal activity within the cerebral
volumethat can vary in response to fluctuations
in subtle external energy, the Schumann values
alsodisplaydiscretealterations.
The long-term averages for the Schumann
frequency, damping, and amplitude change as a
function of solar proton events (SPE). They
increase the Schumann resonance frequency
from a reference value of ~7.8 Hz by between
0.04and0.14Hzdependingupontheintensityof
the proton flux. The amplitude of the resonance
increased by several 10% from a mean value of
about 1.0 pT. Electric fields within the mV/m
range and magnetic fields within the pT range
also define the operating intensities overly
spatially distributed cerebral functions. The
strong correlations between variable power
densitieswithinthe ionosphere–earthcavityand
powerchangeswithinquantitativeEEGmeasures
as well as the quantum-like properties of
interhemispheric interactions indicate that
physical connectivity may be pervasive. Phase
modulation has been considered the most
optimalmeanstopropagatethemostinformation
overdistance.Phaseshiftcanbeobtainedbytime
divided by the square root of v2/c2. Because the
EM fields associated with lightening generated
within the earth–ionospheric cavity are within
the 10–100 kHz (“atmospherics” or “sferics”)
range,theΔc/c(c,velocityoflight)is0.05forthis
range.Thismeansthatthephaseshiftforevery1
sis1/0.9897sor16ms.Thismagnitudeofphase
shiftisremarkablysimilar to phase comparisons
associated with the presence of the continuous
“40 Hz-oscillations” over the entire cerebral
cortical mantle. An approximately 12 ms phase
shift between the rostral and caudal pole of the
brainhas been reported (Pollk, 1982 search for
the “missing” equivalents between lightning and
actionpotentials could be revealingin a manner
similar to the search for Mendeleyev’s missing
elements in the Periodic Table. There is no
traditionalequivalentofthe“returnstroke”atthe
synapse, although back propagation might be
considered a conceptual candidate. However,
backpropagationinfluences the dendrites ofthe
neuronfromwhich theactionpotentialhasbeen
propagated. Its variable effect dependsupon the
extent by which the neuron’s action potential
penetratesintoitsowndistaldendrites.
Whenasteppedleaderapproacheswithina
fewtensofmetersabovetheground,itismetby
a positively charged return stroke towards the
cloud. Within a synaptic scenario, this would be
equivalent to a “return field” transiently
generatedfromthepost-synapticregiontowards
thepresynapticmembranejustbeforethearrival
of the action potential. If the quantitative scale-
invariant relationships between lightning and
action potentials can be generalized in this
context, then impulse magnetic flux densities
from the post-synaptic membrane must emerge
and cross the synapse into the presynaptic
membraneduringthefewmillisecondsbeforethe
helicalEMfield(theactionpotential)reachesthe
synapse. In other words, a comparison with
lightning would predict that sub-threshold,
electrotonic-like shifts in voltage (approximately
theLandauerprinciplelimit:ln2kT,orabout10-
21J)shouldbeapparentatthesynapseinadvance
of the arrival of the major action potential. It is
morelikelywehavenotmeasuredthisequivalent
ratherthanafrankdeviationfromNewton’sthird
law: for every force there is an equal and
oppositeforce.Itiswellknowntherepolarization
of the (heart) atria after its depolarization (P)
during electrocardiographic measurements is
masked by the QRS component of the massive
depolarizationoftheventricles.
Asindicated,thescale-invariantsimilarities
between lightening and action potentials evoke
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the possibility of mutual interaction. In addition
to comparable values for magnetic and electric
fields, the power density for Schumann
resonances within the 8–21 Hz range is in the
orderof10-10W/m2/Hz.Thisisthesameorderof
magnitude as the power density of photon
emissions from the human brain during
imaginationandthecorrelatedchangesinpower
measures from quantitative EEG. Laboratory
experimentswhoexposedvolunteersforabout1
ks to simulated lightening-related sferics by
generating 10 kHz signatures (amplitude 50 nT,
pulserepetition:7–20Hz;pulseduration0.5ms),
demonstratedthatprotractedchangeswithinthe
alpha band and experiences similar to those
attributed to natural phenomena were reliably
elicited. The similarities in quantitative
characteristics between action potentials and
lightening presented in this paper might be
expected if the intrinsic organizations of matter
and energy are reflected within different spatial
and temporal levels of observation. Perhaps by
careful quantification and observation of the
larger phenomena, such as lightning, processes
can be discerned that will point the direction of
focusforwhatwehavenotyetmeasured.
5. Quantum description of Schumann and
brain waves
Inordertoputforwardtheclassicaltheoryofthe
brainandSchumannwaveswequantizetheboth
fields.  In the model (Marciak-Kozlowska and
Kozlowski,2013)weassumed(i)the brainisthe
thermal source in local  equilibrium with
temperature T.(ii) The spectrum of the brain
wavesisquantizedaccordingtoformula
E
(1)
where E is the  photon energy in eV, =Planck
constant,2 ,
 
-isthefrequencyinHz.(iii).
The energies of the photons are the maximum
values of energies of waves. In this paper we
extendedthemodelforSchumannwavestoofor
the emission of black body brain and Schumann
wavesweproposethe wellknowformulaforthe
blackbodyradiation.
In thermodynamics we consider Planck
typeformula for probabilitydEforthe emission
oftheparticle(photonsas wellasparticleswith
m≠0) with energy (E,E+dE )by the source with
temperatureTisequalto:
N (E)dE= AE2 e (-E/kT) dE (2)
whereA=normalizationconstant,E=totalenergy
oftheparticle,k=Boltzmannconstant=1.3x10-
23JK-1.KisforKelvindegree.Howeverinmany
applicationsinnuclear and elementary particles
physics kT is recalculated inunits of energy. To
thataimwenotethatfor1K,kTisequalk1K=K
x1.310-23JxK-1=1.310-23JouleorkTfor1Kis
equivalentto1.3 10-23 Joule= 1.3 10-23/(1.6 10-
19) eV =  0.8 10-4 eV. For comparison measured
and calculated energy densities we applied the
formula:
2
( )
2E
T
Watt
m eV
dP BE e
dE
 
 
(3)
where dP dE  denotes radiation surface energy
density for waves with frequency   E, E +dE
where, B is the normalization constant T is the
temperatureofthewavesourceineV.
In Figures 1-3 we present the results for
brain waves and in Figures 4-6 for Schumann
waves. As can be easily seen the agreement of
calculatedandmeasuredspectraisverygood.
Figure 1. Energy density spectrum for brain waves,
measured.
Figure 2. Energy density spectrum for brain waves,
calculated.
NeuroQuantology | June 2015 | Volume 13 | Issue 2 | Page 196-204
Marciak-Kozlowska and Kozlowski., Schumann resonance and brain waves
eISSN 1303-5150
www.neuroquantology.com
204
Figure 3.Comparison energydensityspectrum of thebrain
waves calculated and measured. The line is the result of
calculations.
Figure 4. Energy density spectrum for Schumann waves,
measured(NikolaenkoandHayakawa,2014).
Figure 5. Energy density spectrum for Schumann waves,
calculated.
As can be easily seen (Figures 1-6) we obtained
thegoodagreementofthemodelcalculationsand
measured energy density profiles. We conclude
that both radiations are emitted from source
which is in -equilibrium thermodynamic state
(Planck-type formula).  It is quite interesting
conclusion for Universe is also in equilibrium
state.ThebrainwavesandSchumannwavesare
described by the same Planck formula but with
different temperatures Temperature of CBR is
much higher (1010 times) for that CBR do not
interactedwithSchumannandbrainwaves.

Figure 6. Comparison theoretical to measured
energy density for Schumann waves. The blue
lineistheresultofcalculations.
6. Conclusions
In this paper we argue that both modes of
electromagnetic radiation: brain waves and
Schumann waves can be analyzed with thehelp
ofthePlanck type formula. From ourcalculation
we deduced the temperature of the source and
the shape of the energy density. We obtained
the good agreement with the measured
energyspectra.
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