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E-Cat SK and long-range particle interactions
Andrea Rossi
Premise
This is a major revision made in December 24 2020 of the original pre-print
Last update: October 21st 2022
Abstract
Some theoretical frameworks that explore the possible formation of dense exotic
electron clusters in the E-Cat SK are presented. Some considerations on the proba-
ble role of Casimir, Aharonov-Bohm, and collective eects in the formation of such
structures are proposed. A relativistic interaction Lagrangian, based on a pure elec-
tromagnetic electron model, that suggests the possible existence of very low entropy
charge aggregates and that highlights the primary role of the electromagnetic potentials
in these clusters, is presented. The formation of these cluster may be associated to a
localized Vacuum polarization generated by a rapid radial charge displacement. The
formation of these dense electron clusters are introduced as a probable precursor for
the formation of proton-electron aggregates at pico-metric scale, stressing the impor-
tance of evaluating the plausibility of special electron-nucleon interactions, as already
suggested in [21]. An observed isotopic dependence of a particular spectral line in the
visible range of E-Cat plasma spectrum seems to conrm the presence of a specic
proton-electron interaction at electron Compton wavelength scale.
keywords:
Aharonov-Bohm eect, Anomalous Heat Eect, Bose-Einstein Condensate,
Casimir eect, charge clusters, collective eects, Darwin Lagrangian, electron model, Elec-
trum Validum, geometric phase coherence, long range interactions, low entropy aggregates,
pico-metric structures, Electron Energy Distribution Function (EEDF), relativistic interac-
tion Lagrangian, vector potential, Zitterbewegung electron model
Introduction
The E-Cat technology poses a serious and interesting challenge to the conceptual founda-
tions of modern physics. Particularly promising, for understanding this technology, is the
exploration of long-range particle interactions. In paragraph
Nuclear Reactions in Distant
Collisions
[49], E. P. Wigner highlights their importance in nuclear transfer reactions:
The
fact that nuclear reactions of the type
Au197 +N14 →Au198 +N13
take place at energies
at which colliding nuclei do not come in contact is an interesting though little-advertised
discovery
. More recently a possible double role of electrons in long range interactions has
been suggested in
Nucleon polarizability and long range strong force from
σI = 2
meson
exchange potential
" [21]:
In other words these two views deals with the electrons' role. One
is as a carrier of the nucleon and the other is as a trigger for a long-range potential of the
nucleon.
1
In this paper we propose that, at a relatively long distance, intermediate between the
atomic and nuclear scale, in the same order of magnitude of electron Compton wavelength,
the eects of magnetic force, the Casimir force and quantum vacuum/virtual particles should
not be dismissed. In particular, in section 1 we show that Coulomb repulsion between elec-
trons at a distance of four reduced Compton wavelengths can be balanced by the Casimir
force in specic geometric congurations. The possible role of Casimir forces in the E-Cat
technology has been rstly proposed by Professor Sven Kullander during our discussions in
2013. In section 2, extending to leptons the N.D. Cook, V. Dallacasa and P. Di Sia nu-
clear force model [13, 14], based on the magnetic attraction between nucleons, and applying
the condition that the four-distance between charges in Minkowski space-time is a light-like
vector, a possible balance of magnetic and Coulomb force is proposed. A relativistic inter-
action Lagrangian that suggests the possibility of these coherent low entropy aggregates is
presented. In section 3, it is hypothesized that a relatively narrow Electron Energy Distri-
bution Function (EEDF) is a pre-condition that may favor the formation of these coherent
aggregates. A mechanism that may allow Zero Point Energy within the E-Cat technology
will be presented in section 4. In section 5 dense electron clusters are introduced as a prob-
able precursor for the formation of proton-electron aggregates at pico-metric scale. In this
last section one spectroscopic signature of these structures is discussed. Section 6 contains
a brief description of the experimental setup, while in section 7 the E-Cat SK performance
is computed.
1 Charge clusters and the Casimir force
Putho and Piestrup in their paper
Charge connement by Casimir force
[41] propose,
as a possible cause of the high-density charge clustering seen by K. Shoulders [44] and
other researchers, the vacuum pressure hypothesized in 1948 by H. B. G. Casimir and
experimentally veried by S. K. Lamoreaux [32] in 1996. To compensate electron Coulomb
repulsion with vacuum pressure in a spherical shell distribution of
N
electrons, Putho found
a critical value for the sphere radius
RN
:
RN≈~√N
2mec=c√N
2ωe
=re√N
2,
(1)
where
re=c
ωe=λe
2π
is the reduced electron Compton wavelength. This value is derived by
applying the Compton angular frequency
ωe=mec2
/~
as the cuto frequency for electron-
vacuum interactions and assuming a vacuum spectral energy density
ρ(ω) :
ρ(ω) = ~ω3
2π2c3dω.
For a charge cluster of
N= 1011
electrons, the computed cluster size
D
is approximately
D= 2RN≈0.12 µm
, a value not too far from the typical charge cluster size seen by Shoul-
ders. The electron distance
dE
in the spherical shell that minimizes electrostatic potential
can be roughly approximated as
dE≈r4πR2
N
N=√πre≈1.78re≈0.68 ·10−12 m.
(2)
It's interesting to note that this distance is not a function of
N
but a constant value of
the same order of the reduced electron Compton wavelength
re=λe
/2π≈0.38 ·10−12 m.
At this scale the electron should not be modeled as a point-like particle, not even as a rst
2
approximation. Consequently, a more detailed and realistic electron model is preferable to
evaluate the Casimir eect in free electron clusters.
An interesting approach along this direction is proposed by J. Maruani in his paper
The
Dirac Electron and Elementary Interactions
[33]. To compute the Casimir force between
electrons, Maruani suggests applying the Casimir force
FC
formula per unit area
A
for
the
ideal case of perfect plates in perfect vacuum at 0 Kelvin
:
FC(d)
A=π2~c
240d4.
(3)
where
d
is the distance between plates and
c
is the light speed in vacuum. Maruani
considers a Zitterbewegung [26, 25, 23, 8] electron model where the reduced Compton wave-
length is the electron
diameter
. In this case the plate area in (3) becomes
A=π(λe
/4π)2
and the attractive Casimir Force
FC(d)
between electrons can be computed and compared
with the Coulomb repulsion force
Fe(d) :
FC(d) = π~cλ2
e
3840d4,
(4)
Fe(d) = 1
4πε0
e2
d2.
(5)
According to this approach, the Casimir force balances Coulomb repulsion approximately
at a distance
db≈2λe
/2π≈0.77 ·10−12m
, a value close to that of two reduced Compton
wavelengths (see Fig. 1 in [33]).
According to another Zitterbewegung electron model [8, 15, 31], the electron can be
modeled by a current loop, with radius
re
, generated by a charge distribution that rotates
at the speed of light. This current loop is proposed as the origin of the electron's mass,
inertia, angular momentum, spin and magnetic momentum. In this case the area enclosed
by the zbw current is
A=π(λe
/2π)2=πr2
e
, a value four times larger than that used by
Maruani, and consequently the Casimir force may reach a value four times greater than
the one indicated in (4). With this larger area, Coulomb repulsion is balanced at a distance
db≈4λe
/2π≈1.54·10−12 m
, as shown in Fig. 1, where in a logarithmic scale the hypothesized
Casimir force between two electrons is plotted together with Coulomb and a magnetic force
computed considering the electrons as two parallel aligned current loops. We can nd the
idea of an internal rapid motion (Zitterbewegung) at light-speed in electrons in the P.A.M.
Dirac Nobel lecture [16].
2 Charge clusters and magnetic interactions
2.1 Space-charge, vacuum polarization and virtual particles
An important eect in vacuum tubes is the so-called space-charge. This name is related
to the spontaneous formation of an electron cloud around a cathode heated in vacuum. Al-
though well known and exploited since the early years of vacuum tube technology, this eect
lacks a well-dened theory. This statement is supported by the observation that the forma-
tion of a stable space-charge should be prevented by the Coulomb repulsion between free
electrons. L. Nelson in US patent 6465965 proposes, as a rationale for this long-range elec-
trostatic screening, a possible vacuum polarization, generated by the creation-annihilation
of virtual charges pairs as a consequence of the quantum vacuum uctuations predicted by
the Heisenberg uncertainty principle. The lifetime of such particle-antiparticle couples is
3
Figure 1: Trends of Casimir, Coulomb and magnetic forces as a function of distance.
inversely proportional to their mass-energy, but, during their short existence, these may act
as the charges in the solid dielectric of a capacitor that, screening the electric eld, lower the
voltage required to accumulate a charge in capacitor plates. The creation of these virtual
particles is favored by the high density of allowable energy states in vacuum and is hindered
by the relatively low number of permitted states in an ordinary metallic conductor. Ac-
cording to Nelson, this dierence may be exploited to generate a macroscopic voltage and
an energy gain. Alternative hypotheses, based on self-organizing Zitterbewegung electron
phases in vacuum and Lorentz force, are however possible as will be shown in the next
sub-sections.
In any case, the long-range interaction between the electrons in the space charge is a
phenomenon that deserves to be seriously studied and investigated [47].
2.2 Lorentz force and Zitterbewegung phase coherence
According to [8, 10, 31], the electron is associated with a magnetic ux
ΦM=h
/e
equal to the
ratio of the Planck constant
h
and the elementary charge
e
. Consequently, the possible role
of a magnetic attraction in charge connement cannot be dismissed
a priori
. As shown in
Fig. 1, the magnetic force between two electrons, if naively modeled as two parallel aligned
current loops, cannot compensate for the Coulomb repulsion. However, at this point, it
is important to remember that the Zitterbewegung current is generated by an elementary
charge
e
that rotates at light-speed
c
along a circumference equal to the electron Compton
wavelength [8, 31] and, consequently, that a rotation phase coherence between charges in the
same light cone may greatly enhance the magnetic attraction.
In this case, the force can be computed as the Lorentz force
FL
acting on an elementary
charge moving at the speed of light. Its value can balance the Coulomb repulsion:
FL(d) = ecB (d) = µo
4π·e2c2
d2=1
4π0·e2
d2,
(6)
where
B(d) = µoec
4πd2
(7)
4
is the magnetic ux density generated by another elementary charge that moves in parallel
at light-speed
c
at a distance vector
~
d
orthogonal to the charge velocity vector.
A similar approach has been suggested by Norman Cook, Paolo Di Sia and Valerio
Dallacasa [13, 14, 11], as the possible magnetic origin of the strong nuclear force. The
condition that the charges must be in the same light-cone [34] can be satised if the electron
distance
d
is an integer multiple of Compton wavelength while the rotating charges have the
same Zitterbewegung phase:
d=nλe
(8)
The very restrictive conditions under which eq. 6 can be applied may be created only
in very peculiar environments. A possible solution has been suggested in [15] where the
spin value
±~
/2
is interpreted as the component of the electron's angular momentum
~
parallel to an external magnetic eld while the electron, like a tiny gyroscope, is subjected to
Larmor precession. This particular, semi-classical, interpretation of spin does not exclude the
possibility that the electron's angular momentum may be aligned, in particular conditions,
to the external magnetic eld, so that electrons behave as elementary particles with whole
spin
~
. In this case electron clusters may form Bose-Einstein condensates where electron
Zitterbewegung phases are synchronized and electron distances respect equation (8). In this
highly ordered, low entropy, hypothetical structure the Coulomb repulsion is balanced by
the magnetic force
FL
in agreement with (6). In section 2.3 we will propose a Lagrangian for
N interacting charged particles that suggests the possible existence of these coherent states.
In [15]
a fundamental connection
between Aharonov-Bohm equations and an electron
model is proposed, starting from a geometric interpretation of the electron wave-function
complex phase [24, 23, 25]. This approach suggests the possibility of eciently creating
electron condensates exploiting the Aharonov-Bohm eect, a phenomenon that shows the
dependence of the electron wave-function phase from electromagnetic potentials [1]. In [15] it
is hypothesized that a voltage pulse with a very short, critical rise time may favor the creation
of coherent and dense electron clusters:
The conjecture is based on the possibility that, as a
consequence of Aharonov-Bohm eect, a rapid, collective and simultaneous variation of the
Zitterbewegung phase catalyzes the creation of coherent systems
.
2.3 Darwin Lagrangian
In his work
Magnetic energy, superconductivity, and dark matter
[17] Prof. Essén empha-
sizes the importance of long-range magnetic interactions in systems where a large number
of charged particles are involved. He proposes, as a possible useful tool in modeling such
interactions, a Darwin Lagrangian
LD
, that relates the electromagnetic potentials with the
kinetic energy:
LD=
N
X
a=1 hma
2v2
a−ea
2φa(ra) + ea
2cva·Aa(ra)i
(9)
Aa(ra) =
N
X
b6=a
eb[vb+ (vb·ruab)ruab ]
2crab
φa(ra) =
N
X
b6=a
eb
rab
5
rab =|ra−rb|
ruab =ra−rb
|ra−rb|
In these equations the letters
a
and
b
are used as indexes of the massive charged particles,
ra
are their spatial coordinates,
ea
their charge value,
va
their velocity,
ma
their mass,
Aa(ra)
and
φ(ra)
are respectively the vector and electric potential at
ra
and
N
is the total number
of the interacting particles. Gaussian unit system has been used.
The Darwin Lagrangian can be conceptually simplied recognizing that the mechanical
momentum
pa
of a massive charged elementary particle has a pure electromagnetic origin:
pa=mava=ea
cAazp
In this last equation
Aazp
is the component of the vector potential
Aaz
, generated by
the Zitterbewegung current, parallel to the particle's velocity vector
va
. This means that we
can write a kinetic energy term that is only a function of the magnetic vector potential:
ma
2v2
a=p2
a
2ma
p2
a
2ma
=e2
aA2
azp
2c2ma
ma=eaAaz
c2
p2
a
2ma
=eaA2
azp
2Aaz
For non-relativistic speed we can write:
Aazp
Aaz 'va
c
(10)
Being that
va
and
Aazp
are parallel vectors it's possible to substitute the product of their
modules with the dot product:
ma
2v2
a=eavaAazp
2c=ea
2cva·Aazp
(11)
consequently we can encapsulate the kinetic energy terms inside the vector potential
ones:
Aat (ra) = Aazp +Aa(ra)
(12)
LD=
N
X
a=1 h−ea
2φa(ra) + ea
2cva·Aat (ra)i
(13)
Equation 13 is a rewriting of eq. 9 that clearly shows a more fundamental role of the
electromagnetic potentials, considering that all the kinetic energy terms can be expressed as
a function of the magnetic vector potential.
6
2.4 Zitterbewegung Lagrangian
The component
Aazp
in eq. 12, for non-relativistic speeds, is a tiny fraction of the Zitter-
bewegung generated vector potential
Aaz
as shown in eq. 10. This observation suggests the
possibility to write a new Lagrangian that does not exclude the role of
Aaz.
Accepting an appropriate, pure electromagnetic, Zitterbewegung model for the electrons
[15, 31], the rst step along this path starts with substituting the concept of massive charged
particles with the more fundamental idea of mass-less elementary charges
e
moving at
the speed of light with a mechanical momentum proportional to the dot product of their
velocity and the vector potential value [31]. This choice implies a possible active role of the
vector potential, associated with the rest-mass energy, in the magnetic interactions. The
interactions occur only between charges that are in the same light-cone. This means that
their distance in Minkowski space-time must be a light-like (nilpotent) vector (eq. 23). Using
natural units, where
~=c= 1,
this relativistic interaction Lagrangian has a very simple
form:
Lz=
N
X
a=1
[eaca·Aa(ra)−eaφa(ra)]
(14)
To conrm the validity of 14 we must demonstrate that it satises the classical Lagrangian
denition:
L=T−U
(15)
T=
N
X
a=1
eaca·Aa(ra)
U=
N
X
a=1
eaφa(ra)
Now, according to the Ehrenberg-Siday-Aharonov-Bohm equations, the Zitterbewegung
geometric phase is ruled by the vector potential (eq. 16) and by the electric potential (eq.
17):
dϕaM =eaAa(ra)·dl
dl=cadt
dϕaM =eaAa(ra)·cadt
(16)
dϕaE =eaφa(ra)dt
(17)
Dividing eq. 16 for
dt
we obtain the value of the Zitterbewegung frequency of the charge
ea,
a value equal to the relativistic mass-energy of the particle
a
:
ωzbw =dϕaM
dt =ma
7
T=
N
X
a=1
ma
These observations conrm that eq. 14 respects the classical Lagrangian denition, con-
sidering that the kinetic energy of the electron's mass-less charge is exactly equal to its
relativistic mass.
The vector potential
Aa(ra)
is the sum of the self-interaction term
eaca
αrea
with an interac-
tion term:
Aa(ra) = eaca
αrea
+X
b6=a
eb[cb+ (cb·ruab)ruab ]
rab
(18)
φa(ra) = ea
αrea
+X
b6=a
eb
rab
(19)
Lz=
N
X
a=1 (1
rea
+X
b6=a
αca·cb+α(cb·ruab) (ca·ruab )
rab −"1
rea
+X
b6=a
α
rab #)
(20)
Lz=
N
X
a=1 X
b6=a
α[ca·cb+ (cb·ruab) (ca·ruab )−1]
rab
(21)
rab =ra−rb
rab =|ra−rb|
ruab =rab
rab
ca·cb= cos (ϑab1)
ca·ruab = cos (ϑab2)
cb·ruab = cos (ϑab3)
ϑab1=ϑab2−ϑab3
Lz=
N
X
a=1 X
b6=a
α[cos (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]
rab
Lzab =α[cos (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]
rab
8
In these latter equations
ra
is the generic spatial position of the mass-less charge
ea
,
ca
its unit velocity vector
(c2
a= 1)
,
α=e2
a
the ne structure constant
(α−1≈137.036)
,
rea
the
Zitterbewegung radius,
rab
is the Euclidean distance between the mass-less charges and
tab
their time distance.
ruab
is a unit vector that has the same direction of
rab
. The inverse of
the Zitterbewegung radius in natural units is equal to the value of the relativistic mass of
the charged particle
(mea =r−1
ea )
. The product
αrea
is the charge radius.
The phase space trajectory of the N charges is determined by the stationary Action
condition
δ(S)=0
S=ˆ4T
Lzdt.
According to eq. 21 the Action has the following simple form
S=
N
X
a=1 X
b6=aˆ4T
α[cos (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]
rab
dt
(22)
S=
N
X
a=1 X
b6=aˆ4T
Lzabdt
δ(Lzab) = 0 =⇒δ(S) = 0
δ(Lzab (rab, ϑab2, ϑab3)) = ∂Lz
∂rab
δrab +∂Lz
∂ϑab2
δϑab2+∂Lz
∂ϑab3
δϑab3= 0
∂Lz
∂rab
=−α[cos (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]
r2
ab
∂Lz
∂ϑab2
=α[−sin (ϑab2−ϑab3)−sin (ϑab2) cos (ϑab3)]
rab
∂Lz
∂ϑab3
=α[sin (ϑab2−ϑab3)−cos (ϑab2) sin (ϑab3)]
rab
r2
ab −c2t2
ab = 0
(23)
From these equations we can see that the
coherence condition
(eq. 24) satises the
principle of stationary Action
(ϑab1= 2πn)∩ϑab2=π
2+πm=⇒δ(S) = 0 (n, m ∈Z).
(24)
When these coherence conditions are satised the Coulomb repulsion is balanced by the
Lorentz force as already shown in par. 2.2. This may explain the high density of the electron
clusters studied by Kenneth Shoulders [44][46][45].
9
2.5 Entropy of the coherent clusters
Although the formation of charge cluster coherent states is compatible with the condition of
stationary Action (eq. 22), its probability is heavily hindered by the extremely low entropy of
such states. The order of magnitude of the entropy ratio between non-coherent and coherent
congurations is approximately equal to the number N of interacting particles, considering
that the coherent state can be described by a single wave-function, as in BEC condensate.
The Darwin Lagrangian may be used for non coherent states of N interacting electrons
observed at time scales larger than the Zitterbewegung period
(tz'8.1·10−21s)
. In this case
the average value of the component of the vector potential orthogonal to electron velocity
vanishes and does not play a role in magnetic interactions, but is hidden in the kinetic energy
term, being the value of its module multiplied by the elementary charge equal to the electron
rest mass in natural units.
3 Coherent clusters and EEDF
The Zitterbewegung angular frequency
ωzbw
is exactly equal the electron relativistic mass-
energy
m
in natural units:
ωzbw =m
The relativistic mass-energy
m
is the sum of the rest mass
m0
and the kinetic energy
Ek
m=m0+Ek
The collective phase-lock in the charge clusters requires monochromatic electrons [3] or
a very narrow distribution of Zitterbewegung frequency and consequently an environment
with a narrow Electron Energy Distribution Function (EEDF) may favor the creation of
these coherent structures. The EEDF in a gas mixture plasma discharge is a function of the
pressure and gas composition [6] [19], consequently an appropriate choice of these parameters
[37], narrowing the EEDF, may favor the formation of these aggregates.
4 Energy from the Vacuum
In his book An Introduction To A Realistic Quantum Physics [38, 39], Giuliano Preparata
denes the Vacuum as
the template of physical reality
that
does not precede creation but
is, actually, a fundamental piece of it
.
Following this point of view some authors [2] claim that the keys to understand the emer-
gence of matter-energy from Vacuum are the magnetic vector potential and the Aharonov-
Bohm eect, completely reversing the widely accepted idea that considers the vector potential
only as an useful math tool. In their work
Aharonov-Bohm eect as the basis of electromag-
netic energy inherent in the vacuum
[2] the authors, starting from this concept, deduce that
devices can be manufactured in principle to take an unlimited amount of electromagnetic
energy from the vacuum as dened by the Aharonov-Bohm eect, without violating Noether's
Theorem
.
Within this conceptual framework Putho has explored [9][40] the idea that, in principle,
it's possible to extract energy and heat from electromagnetic zero-point radiation via the use
of Vacuum pressure. A device that may reach this goal has been proposed in the US patent
US7379286 [22], where the authors consider the possibility of a local energy extraction that
is
replenished globally from and by the electromagnetic quantum vacuum
.
10
The idea that Vacuum is structured and that can be exploited to localize energy extracted
from the environment needs a clear denition of this structure and its relation with energy
and matter. The rst step starts with recognizing the electromagnetic potentials as the
Vacuum structure and consequently as the fundamental entities of the physical reality.
The second one requires an encoding of their relations with both the energy density and the
energy ux in the space-time continuum. Calling
the four-gradient and
γt
the unit vector
along the time axis of the Minkowski space-time, we can dene a scalar eld
S
that is the
four-divergence of the electromagnetic four-potential
A
:
A=A+γtφ
·A=S
Now, the derivatives of the four-potential can be viewed as an operator that rotates in
the four dimensions of space-time the unit vector
γt,
giving raise to a four-vector that has
the time component equal to the Vacuum energy density
U
and the three space components
equal to the energy density ux vector
P
[31]:
1
8πAγtg
A=Uγt+P
P=−1
4π(E×B− SE)
(25)
As we can see the vector
P
is the sum of two vectors: the rst one is the Poynting vector
while the second one is a vector equal to the product of the scalar eld
S
and the electric
eld
E.
In mainstream literature, as a consequence of the widespread application of the
Lorenz gauge
(·A= 0)
, the scalar eld S and the vector
SE
are generally ignored, but
nevertheless their signicance has been highlighted by many authors [42, 48, 7, 36, 28, 29,
35, 50, 51, 43].
Combining the Gauss law (eq. 26) with the component
SE
/4π
of the generalized Poynting
vector
P
, there emerges a non-null divergence of an energy ux density that clearly implies
the presence of a power source or a power sink where both charge density
ρ
and scalar eld
S
are not vanishing. In this case the time derivative of the energy density U is equal to the
product of the charge density
ρ
and the scalar eld
S
4πρ =∇ · E
(26)
ρS=1
4π∇ · ES
dU
dt =ρS
(27)
This time derivative of the energy density can be interpreted as a power ux that is a
consequence of a non-null derivative of the electric potential
φ
:
dU
dt =ρdφ
dt
Integrating over a volume that contains a single electron the eq. 27 becomes:
11
eS =edφ
dt
(28)
Now, combining eq. 28 with the dierential form of the electric Aharonov-Bohm equation
(eq. 29), we can see that the presence of a scalar eld implies a variation
δωzbw
of the
electron's Zitterbewegung frequency
ωzbw
and the appearance of a force
fS
:
eφ =dϕ
dt
(29)
δωzbw =dϕ
dt
eS=deφ
dt
eS=d2ϕ
dt2
eS=dωzbw
dt
(30)
φ=ˆSdt
(31)
fS=−e∇φ
Experimental data suggest that an intense impulsive current with a radial/cylindrical
symmetry and a critical rise time creates a Scalar eld that generates radial forces that,
conning the charges, create the conditions for the formation of the coherent aggregates
discussed in the previous sections. This radial charge displacement can be generated by an
appropriate electrode geometry [4, 20, 12] or by the pinch eect generated by short and
intense current impulses [46]. Eq. 30 describes an energy-mass change, the sign of which
depends on the sign of the product
eS.
This process is a consequence of a Vacuum polarization
caused by the presence of the Scalar eld
S.
This implies the possibility of a long range
interaction that consists in a mass-energy transfer from positive charged particles to negative
ones or vice-versa. This mass-transfer obviously does not violate the principle of energy
conservation and apparently does not lead to the instability of the nuclei of the positive ions
present in the plasma, even if some authors claim the possibility that Scalar elds may alter
the nucleus dynamic [27]. The tiny energy lost by the nuclei can be replenished by their
interaction with the active Vacuum.
The hypothesis that a mass-transfer mechanism may be the cause of the anomalous heat
seen in the E-Cat QX has been presented in a previous paper [21], inside however a dierent
theoretical framework.
To evaluate the power generated in a device as the E-Cat-QX, assuming that the thermal
energy is generated by the electron transition from a coherent to an incoherent state and
assuming an electron distance in the coherent state that is equal to the electron Compton
wavelength
(λe≈2.43 ·10−12m)
, we get a power output in the order of several tens of watts:
I= 0.25A
12
dne
dt =I
e= 1.56 ·1018ne
/s
Ee=1
4πε0
e2
λe
wout =Ee
dne
dt '150w
5 Neutral pico-metric aggregates
Coherent charge clusters may form, in presence of protons, compact neutral aggregates at
a pico-metric
(10−12 m)
scale, intermediate between the atomic
(10−10 m)
and nuclear size
(10−15 m)
, formed by a coherent chain of bosonic electrons with protons located in the center
of their Zitterbewegung orbits [15]. A critical, cathode-temperature-dependent, threshold of
electron density is an important precondition for the creation of such structures.
The existence of electron-proton and electron-deuteron structures at this scale has been
already experimentally veried and studied [5, 52, 18]. In [30] Holmlid recognizes the electron
Zitterbewegung as the underlying rationale for such aggregates:
This electron spin motion
may be interpreted as a motion of the charge with orbit radius
rq=~
/2mec≈0.192
pm and
with the velocity of light c (`zitterbewegung')
. It's important to note that this radius value,
as proposed by Holmlid, Maruani and Hestenes [23], is one half the zbw radius value
re
in [8,
31], and that the choice of such value
(rq=re
/2)
implies that no distinction is made between
electron intrinsic angular momentum and spin, excluding consequently the possibility of
existence of bosonic electrons with spin=
~
.
An interesting aspect of the electron-proton interactions proposed in [15] is given by
the possibility to experimentally verify the existence of some specic spectral signatures.
According to [15] the electron's charge can orbit around a proton at a distance of about
re= 0.38 pm
. The intense magnetic ux density
Bzbw
generated by the rotating charge at
the center of the Zitterbewegung current loop is [8]
Bzbw = 32.21 ·106T.
Now, the proton magnetogyric ratio
gH
is
gH= 267.52 ·106rad ·s−1·T−1
and consequently the Nuclear Magnetic Resonance frequency is
νNMR =gHBzbw
2π= 1.3714 ·1015 Hz
and the relative precession frequency
νp
is
νp=νNMR
/2= 6.8571 ·1014 Hz.
This frequency corresponds to a wavelength in the visible spectrum
λp=c
νp
= 4.372 ·10−7m
13
The presence of this line in the E-Cat plasma spectrum is a possible indication of the
existence of this type of pico-metric aggregate. A stronger and reliable clue in this direction
comes from observing that the amplitude of this spectral line is a clear function of the hydro-
gen isotope present in the plasma: the line is strongly reduced when deuterium is used in the
charge instead of protium. This consideration is supported by the observation that a deuteron
has a much smaller magnetogyric ratio than proton
(gD= 41.066 ·106rad ·s−1·T−1)
. Con-
sequently, considering the strong chemical similarity of deuterium and protium, this large
macroscopic dierence in spectral emission under the same conditions reveals its nuclear
origin.
6 Experimental Setup
The plausibility of these hypotheses is supported by a series of experiments made with the
E-cat SK. The E-cat SK has been put in a position that allows the lens of a spectrometer
to exactly view the plasma in a dark room: an ohmmeter measures the resistance across
the circuit that gives energy to the E-Cat; the control panel is connected to a
220 V
outlet,
while the two cables connected with the plasma electrodes start from the control panel.
A frequency meter, a laser, and a tesla-meter have been connected with the plasma for
auxiliary measurements and a Van de Graa electron accelerator
(200 kV )
has been used for
the examination of the plasma electric charge. Other instruments used in the experimental
setup are: a voltage generator/modulator; two oscilloscopes, one for the power source and
one for monitoring the energy consumed by the E-Cat; Omega thermocouples to measure
the delta T of the cooling air; IR thermometer; a frequency generator; a Geiger counter and
bubbles columns to measure emissions of ionizing radiations and neutrons.
7 Evaluation of E-Cat SK performance
The performance of the E-Cat SK is summarized in the following calculations. The plasma
temperature can be calculated applying the Wien equation. Calling
b
the Wien displacement
law constant and
λmax
the observed peak wavelength of the radiation we have
Tk=b
λmax
Tk=2.898 ·10−3
0.3575 ·10−6= 8106 K.
Power emission and the average energy produced in one hour can be computed applying
the Stefan-Boltzmann law
Wout =σεT 4
kA≈22 kW
Eout = 22 k W h
where
σ= 5.67 ·10−8W m−2K−4
,
ε= 0.9
(assuming a non-perfect black body) and
A≈10−4m2
(the length of the cylindrical shaped plasma core is
l≈1cm
, while its diameter
is
d≈0.3cm
).
This value must be compared with the calorimetric measurements, considering that the
spectrum of the radiations has not a full Maxwellian curve. The E-Cat has been installed
14
in a laboratory of an industry in the State of Tennessee, in the USA, to keep warm a room
that has a surface of 3000 sq.ft (about 300 sq.m.) and a height of 15 ft (about 5 m).
The temperature outside when we made the measurements was about 32
°
F (0
°
C) and the
temperature in the room was about 61
°
F (16
°
C). To keep this temperature it was used before
a heater of about 20-22 kW.
In detail:
Fan ow rate: 5500
m3
/h'
6700
kg
/h
delta T = 16
°
C
Cp air = 0.17
W = 6700 x 0.17 x 16 = 18224
Kcal
/h
= 20.5
kW h
/h
We also made a test with an air ow of 330
m3
/h
and obtained a deltaT of 312
°
C.
Every 60 days of continued operation the E-Cat SK produces- as we can nd with a simple
extrapolation- 30000 kWh of heat, approximately the equivalent of 2600 kg of heating oil,
therefore avoiding, at the same time, the emission of more than 8000 kg of
CO2
. Now, calling
Einp
the energy consumed by the control panel in one hour
Einp = 380 W h
we can compute the average coecient of performance (COP), as the ratio of output and
input energies
COP =Eout
Einp ≈54
Conclusions
In this paper, three dierent, not mutually exclusive Ansätze, for long-range particle inter-
actions in E-Cat SK have been proposed. The rst one is based on the possible role of the
Casimir force in dense electron aggregates: two dierent approaches, one of which is based
on Zitterbewegung electron models, both indicate that Coulomb repulsion between electrons
may be balanced at a pico-metric scale. The second one, in analogy with the Norman Cook
idea of magnetic origin of strong force [13, 11], deals with the Lorentz forces in coherent
systems, where electron Zitterbewegung phases are synchronized and electron charges are in
the same light cone. A relativistic interaction Lagrangian for a set of elementary charged
particles that suggests the possible existence of these coherent states has been proposed. An
hypothesis that peculiar discharge geometries and dynamics create a Vacuum polarization
that favors the formation of these low entropy structure, has been presented. The third one
is based on the possible electrostatic screening eect of virtual particle pairs created by the
uctuations of quantum vacuum.
As a consequence of these relatively long-range interactions, the possible formation of
dense aggregates at pico-metric scale has been proposed. An E-Cat plasma spectral signa-
ture, isotopic dependent, in the visible range of a proton-electron pico-metric structure has
been reported.
R.P.Y∞X
Acknowledgments
I acknowledge, for interesting discussions and collaborations on the subject, Carl Oscar
Gullström and Giorgio Vassallo.
15
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