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European Journal of Applied Sciences – Vol. 11, No. 3
Publication Date: June 25, 2023
DOI:10.14738/aivp.113.14932
Smulsky, J. J. (2023). Neutrino is the Brightest Particle of the Fictitious Micro-world. European Journal of Applied Sciences, Vol -
11(3). 616-633.
Services for Science and Education – United Kingdom
Neutrino is the Brightest Particle of the Fictitious Micro-world
Joseph J. Smulsky
Institute of Earth’s Cryosphere, Tyum. SC of SB RAS,
Federal Research Center, Tyumen, Russia
ABSTRACT
During the decay of radioactive radium E, electrons with a continuous spectrum of
velocities are emitted. The average energy measured with a calorimeter is 0.36
MeV. Based on the dependence of mass on velocity accepted in the Theory of
Relativity, W. Pauli calculated the kinetic energy of the electron and obtained a
value of 1.16 MeV. For explaining the excess energy of 0.8 MeV, a new particle,
neutrino, was postulated. In the present study, we show that the experimental laws
of electromagnetism were misinterpreted in the Theory of Relativity. Using the
correct laws, we have derived the right expression for the force exerted on a moving
charged particle. This expression depends on the distance from the acting object
and on the particle velocity. According to the new expression for the interaction
force, the particle mass suffers no change. Therefore, there is no reason to introduce
a neutrino. As a result of the electromagnetic interaction, particles move along
other trajectories that were not known previously. Therefore, the wrong
interpretation of particle motions has led researchers to the introduction of
fictitious particles that now in large quantities inhabit the imaginary microcosm. It
is necessary to reconsider the erroneous postulates on the basis of real interaction
forces. This revision must be started from Rutherford experiments without
invoking the Theory of Relativity and Quantum Mechanics.
Keywords: Neutrino, β-radiation, energy, charges, motion, force, trajectories.
INTRODUCTION
The decay of a number of radioactive elements is accompanied with β-radiation in a continuous
spectrum, i.e. with the emission of electrons with a continuous velocity distribution. This
phenomenon contradicted the concept of the discreteness of energy levels in atoms. In the
1920s, it was deduced from the developing quantum mechanics that the energy spectrum of
particles emitted during the decay of nuclei had to be discrete. The energy of particles must be
corresponding to the difference between energy levels. Therefore, for the followers of quantum
theory the continuous spectrum of emitted electrons was a serious obstacle to all quantum
mechanical constructions [1, 2].
In order to save quantum mechanics, on December 4, 1930 W. Pauli writes a letter to the
participants of the physics conference in Tübingen. In that letter, he puts forward a hypothesis
that β-decay is accompanied by the emission of a neutral particle, which takes away so much of
the decay energy that the sum of the energy of the newly introduced particle and the energy of
the electron remains unchanged. This particle was later given the name neutrino. Initially, this
hypothesis, due to its absurdity, was rejected, but with time it was fitted by the supporters of
quantum mechanics into the modern picture of the microworld.
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Smulsky, J. J. (2023). Neutrino is the Brightest Particle of the Fictitious Micro-world. European Journal of Applied Sciences, Vol - 11(3). 616-633.
URL: http://dx.doi.org/10.14738/aivp.113.14932
CONTINUOUS Β-DECAY SPECTRUM
Apparently, it was A.H. Bucherer who for the first time experimentally identified the continuous
spectrum of electron velocities during the radioactive decay [3]. The central element of the
Bucherer arrangement (Figure 1a) was a flat circular capacitor 8 cm in diameter (Figure 1b).
The spacing between the capacitor plates was defined by 4 quartz flakes with a diameter of 5
mm and a thickness of 0.25075 mm. A 0.5-mm pellet of radioactive radium fluoride was placed
at the center of the capacitor. The capacitor was located in an 8-cm high brass cylindrical box
16 cm in diameter, which was placed in a uniform magnetic field of strength H. Inside the box,
photographic film 2, stretching along the cylindrical surface of the box, was located (Figure 1b).
The radium pellet emitted β-rays in all possible directions. Those electrons passed through the
narrow slot of the capacitor, where the action of the electric field E due to the capacitor and the
action of the magnetic field H, perpendicular to it, were mutually compensated.
As it is evident from Figure 1b, the negative electron will be acted upon inside the capacitor by
the upward force due to the capacitor and by the downward force due to the magnetic system.
Therefore, only those particles, for which the magnetic and electric forces turn out to be
mutually balanced, will leave the centrally located radioactive source. After leaving the
capacitor, the "compensated electrons" are entering the only one magnetic field, experienced a
deflection in it, reached the photographic film, and produced blackening on the film.
Figure 1. Schematic of the Bucherer experiment [3]:
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a – view along the central axis of the capacitor; b – view on the diametrical section of the
capacitor. 1 – source of β-rays; 2 – photographic film.
The angle φ is reckoned on the film from the direction of the magnetic field H (Figure 1a). In
the direction φ = π/2, the electrons fly out of the capacitor at the lowest velocity. Therefore, in
the magnetic field they acquire the largest deviation (Figure 2). The more the angle φ differs
from π/2, the faster the electrons fly out of the capacitor, and the less they become deflected by
the magnetic field. The larger the angle φ differs from π/2, the faster the electrons escape from
the capacitor and the less they become deflected by the magnetic field. At angle
H
E
= arcsin ,
electrons fly out of the capacitor at a velocity approaching the speed of light c. As it is seen from
Figure 2, such particles are not deflected in the magnetic field. The line obtained on the
photographic film thus represents the spectrum of electron velocities during the decay of
radioactive radium. With the polarity of the fields E and H having been reversed, a line appears
in the upper half-plane. The photographic film also shows a horizontal line produced by γ- radiation and fast electrons. A characteristic feature of the electron spectrum line is that this
line intersects the horizontal line at an acute angle.
Figure 2. Curve of deviation of the electrons with different velocities on the photographic film
in Bucherer's experiments [3].
A study of the continuous spectrum of the β-radiation of radioactive RaE, or bismuth (210Bi83),
was performed in 1927 by C.D. Ellis and W.A. Wooster [4]. At the beginning of their article, the
authors cite the results of a study by Mr. Madgwick of the Cavendish Laboratory, concerning
the energy distribution of emitted electrons. Those measurements were carried out using an
ionization chamber. The distribution curve of electrons exhibits a smooth behavior with a
maximum at 0.30 MeV energy. In this case, the electron energy varies from 0.040 to 1.050 MeV,
with the average value being Wm = 0.39 MeV. The aim of the work by C.D. Ellis and W.A. Wooster
was the determination of the total energy of electrons using a calorimeter. As a result of several
series of experiments, a calorimetric mean electron energy Wcm = 0.35±0.04 MeV was obtained.
That is, the energy that was determined using the calorimeter proved to be coincident within
the experimental error with the mean energy Wm.
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Smulsky, J. J. (2023). Neutrino is the Brightest Particle of the Fictitious Micro-world. European Journal of Applied Sciences, Vol - 11(3). 616-633.
URL: http://dx.doi.org/10.14738/aivp.113.14932
In a later paper by W.W. Buechner and R.J. van de Graaff [5], it was confirmed that the
calorimetrically determined energy of electrons corresponded to their energy spectrum.
Therefore, according to the authors, there were no reasons for the occurrence of additional
energy losses due to emission of any other radiation, including neutrinos.
Thus, those experiments showed a continuous spectrum of β-radiation, with the
calorimetrically measured energy corresponding to this spectrum. As already noted, the
continuous spectrum was in contradictions to quantum-mechanical concepts, and the
measured energies did not agree with the electron energies calculated using the Theory of
Relativity. For example, W. Pauli has calculated the kinetic energy of an electron using the
relativistic formula [2, 6]:
(1/(1 ) 1)
2 2 Wcr
=me
c − − , (1)
➢ where me is the electron mass;
➢ с is the speed of light;
➢ β = v/c is the electron velocity reduced by the speed of light,
➢ and obtained the following value of Wr: Wr = 1.16 MeV.
This value was in excess of the experimental value of 0.36 MeV by 0.8 MeV. It was proposed to
assign the excess energy of 0.8 MeV to neutrino. It was assumed that during the decay of each
atom, the neutrino, together with the electron, took away the energy of 1.16 MeV. Since no other
particles were detected during the decay of an atom, the properties of neutrino as a particle
without mass, moving at the speed of light and not interacting with the matter, were accepted.
The introduction of such a particle led to many contradictions. For example, since the electrons
had different velocities and energies, neutrinos would also have different energies for the decay
of each atom to be accompanied by the release of the same energy. Meanwhile, all these
contradictions were ignored. The energies of all nuclear reactions have been experimentally
measured. Neutrino energy was added to them, and then this energy was immediately
subtracted as neutrinos disappear without a trace.
THE INFLUENCE OF A MOVING CHARGE ON A STATIONARY CHARGE
Neutrinos and many other particles were invented by theoretical physicists when considering
various microcosm models based on the change of the mass of a moving particle in the Theory
of Relativity (TR):
/(1 )
2
m =m0 − , (2)
where m0 is the mass of the particle, which in the TR is called the rest mass.
The above relativistic expression (1) for the kinetic energy of particle is due to the change of
mass (2). The hypothesis about the change of the mass of two charged particles moving relative
to each other was introduced into the Theory of Relativity to explain the interaction of two
particles.
However, the Theory of Relativity is erroneous [8–10]. The interaction of two charged particles,
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qi and qk (Figure 3), is determined by the force (3), which depends on the velocity
ik υ
and on the
distance
ik r
between them [8, 9, 11]:
( )
3/ 2 2 2
2
[ ]
1
ik ik ik
i k ik ik
ik
r r
q q r
F
−
−
=
, (3)
➢ where
ik r
is the radius-vector drawn from particle qk to particle qi;
➢
ik υ
is the velocity of particle qk relative to particle qi;
➢
1
υ c ik ik
=
is the reduced velocity;
➢
/ 1
с = с
is the speed of light in the medium filling the space between the particles;
➢
and
are the dielectric permeability and magnetic penetrability of the medium;
➢
[ ]
ik ik r
is the vector product of
ik
and
ik r
.
Figure 3. The force
Fik
exerted on the charged particle qi from the side of the charged particle qk,
moving with a velocity
ik υ
relative to the particle qi.
Since the force (3) changes with a change in particle velocity, the change in particle mass
accepted in the TR does not exist. Neither exist all imaginary particles [12].
The Theory of Relativity always treats the interaction of two particles. In reality, not two, but
several particles interact simultaneously. Formula (3) expresses the force exerted by a k–th
particle on an i–th particle. In this case, each of the i–th particles is acted upon by the remaining
k-particles. Therefore, in order to describe the real interaction within the Theory of Relativity,
one has to introduce as many changes of mass, time, and distance related with the particle i as
there exist k–th particles. These changes must occur to the particle i simultaneously. This shows
how absurd the Theory of Relativity is. This is first. Second, this inference also shows that the
calculation of the interactions between charged particles in the Theory of Relativity is incorrect.
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3 12
12
1
I r
r c
H
= (5)
with strength H at the location of the first particle. In Figure 4 this magnetic field is shown with
orange arrows.
The magnetic field is also characterized by the magnetic flux Φ. Since the second particle q2 is
moving, the field H and the flux Φ appear as variable quantities. According to the Faraday law
of induction
dt
dΦ
c
u
1
= −
,
(6)
the alternating magnetic field H at the location of the first particle creates an electric field with
strength E, whose potential difference u is determined by the rate of change of the magnetic
flux Φ. In Figure 4, the electric field with strength E is shown with brown arrows.
According to the definition of the field strength E, this quantity is the force of action exerted on
the first particle with its charge being equal to unity, i.e. E = F12/q1. It was shown in [8, 9] that
the Biot-Savart-Laplace law in differential form gives the second Maxwell equation
+
= υ
t
F
c q
H
12
2 4
4
rot , (7)
and the Faraday law gives the first Maxwell equation
t
H
q c
F
= −
2
12 rot . (8)
Eliminating the strength H from these equations, we obtain the following differential equation
for the force exerted by the moving charge q2 on the stationary charge q1:
( )
+
=
−
+
+
grad 1 4 1 1 2
2
1
1
2
1 2
2
2
1
2
1 2
2
2
1 2
2
2
1 2
2
t
υ
c
q
t
F
z c
F
y
F
x
F
, (9)
where ρ is the spatially distributed density of charge q2.
As a result of solving Eq. (9) for a point charge q2, expression (3) for the force was obtained [13,
14]. The solution of equation (9) is a significant achievement in mathematics. This solution was
obtained by the present author in 1968. It should be borne in mind that in this case the indices
in expression (3) are as follows: i = 1, k =2.
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( )
−
−
−
= − − −
2 2 2
2
1
2
2
2
1
1 1
1 1 exp 2
1
p p
p p
p
p
r
R R
υ
, (11)
➢ where
Rp R = r/
is the dimensionless distance from particle q2 to particle q1;
➢
1
υ c p
=
p
is the reduced velocity of particle q1 at pericenter (under pericenter, we
understand the shortest distance between the particles on their trajectory);
➢
Rp
and
p
υ
are the pericenter radius of the orbit and the particle velocity at the
pericenter;
➢
( )
2
1 1 p p = R υ
is the trajectory parameter;
➢
( )
1 2
1 2 1 2
1
m m
q q m m
+
=
is the electromagnetic interaction constant;
➢
m1
and
m2
are the masses of particles q1 and q2, respectively.
The trajectory equation (10) is written in the polar coordinate system (r, φ). At the center of
this system, the particle q2 is located, and the polar angle φ is measured from the pericenter. It
is evident from expressions (10) and (11) that the dimensionless trajectories are determined
by two parameters,
1
and
p
. In the case of attraction, i.e. with a positive charge at the central
particle q2 and a negative charge at the particle q1, for the trajectory parameter we have
1
< 0.
In the case of the inter-particle interaction proceeding according to the Coulomb law, the
trajectories depend on the parameter
1
only [8, 9] and, depending on the magnitude of that
parameter, those trajectories will be either elliptical orbits ( −11 −0.5
) or hyperbolic
trajectories ( −0.5 1 0
). At
1
= -1, the orbit is a circle, and at
1
= -0.5 the trajectory is a
parabola. It should be noted that Coulomb orbits result from equation (10) and formula (11)
with
p
→ 0. Therefore, these expressions appear as generalized equations for the trajectories
of electromagnetically interacting particles, and they are valid both for the Coulomb and
electromagnetic interactions of particles.
Expressions (10) and (11) define a wide spectrum of trajectories [15–17]. In Figure 6, this
spectrum it shown for varied parameters
1
and
p
. For example, at
1
= -0.8 and
p
= 0.3 the
point represents the positively charged particle q2. The negatively charged particle q1 is located
at the right of the horizontal axis at the orbit pericenter, whose dimensionless radius is
Rp
= 1.
The particle moves to the left along a quasi-elliptical orbit and reaches the apocenter, or the
most distant point of the orbit, with dimensionless radius
Ra
= 1.54. In this case, the polar angle
is φa = 3.243, i.e. this angle is greater than π, so that an angular displacement of the apocenter
occurs. During the second half-period, the same angular displacement will occur as well and, as
a result, the pericenter will become shifted over the period by the double angle 2·(φa - π). At
this value of the trajectory parameter,
1
= -0.8, the apocenter radius of the Coulomb orbit is
Ra
= 1.667, and the polar angle is φa = π.
At a higher velocity of the particle,
p
= 0.5, and at the same trajectory parameter
1
= -0.8 (see
Figure 6), we have
Ra
= 1.27 and φa = 3.601, i.e. here the apocenter radius has decreased even
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TRAJECTORIES AT LIGHT SPEED AT THE PERICENTER
On the line S (Figure 6), there are trajectories with a velocity at pericenter tending to the speed
of light, i.e. at
p
→ 1. Here, there is a wide range of trajectories exhibiting very unusual particle
motions [8, 9]. In this case, parameters of the attracting center are such that, as a result of the
Coulomb interaction, the center imparts the infinitely distant particle the speed of light on its
surface. In a similar case with gravitational interaction, the attracting center was called the
Black Hole. According to law (3), in the case of electromagnetic interaction the particles move
freely in such a “black hole”. Therefore, their trajectories for
p
→ 1 were called in [8, 9] intra- hole trajectories, or trajectories inside the “black hole”. Here, under the “black hole” we mean
not some new natural object, but an attracting center with certain proportions of parameters.
Particles can freely enter it and freely leave it. Those trajectories can explain many particle
interaction processes proceeding in nuclei.
The previous trajectories were obtained by numerical integration of equation (10) at the
pericenter (R0 = Rp). With the velocity at pericenter tending to c1, there arises a double
uncertainty at this point. That is why in this case the integration of the equations began at an
intermediate point R0 > Rp, and the integration in our calculations proceeded from this point in
two directions: towards the pericenter and towards the remote points of the trajectory. For
each trajectory, at the starting point R0 the radial velocity
r 0
υ
and the transversal velocity
t0
υ ,
perpendicular to the radial velocity, were specified so that the particle velocity at pericenter
p
υ
tended to the speed of light c1. With variation of governing parameters, the whole spectrum of
trajectories was obtained in [8, 9]. Here, we will analyze only some of those trajectories [10].
Figure 7 shows the trajectories for the trajectory parameter
1
= -0.498 and for the reduced
transversal velocity βt0 = 0.93. The properties of the trajectory equation (10) determine the
equality R0/Rp = 1/βt0. The trajectories in Figure 7 differ in radial velocity. For trajectory 1, at a
low reduced radial velocity of βr0 = 0.1, the apocenter angle is φa° = 59.8°, so that the particle
makes in one period a little less than a third of a revolution around the other particle. In three
periods, the particle makes almost a complete revolution, without 1.2°. At the pericenter points,
the particle moves almost at the speed of light, while at the apocenter points its velocity
decreases, and the particle slightly gets away from the center by a distance of Ra/Rp = 1.103, as
a result, the particle moves with small jumps from the circle of radius Rp.
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Smulsky, J. J. (2023). Neutrino is the Brightest Particle of the Fictitious Micro-world. European Journal of Applied Sciences, Vol - 11(3). 616-633.
URL: http://dx.doi.org/10.14738/aivp.113.14932
[19]. Carezani, R.L., Neutrinos at Fermi Lab. 1997. 3.
https://www.naturalphilosophy.org/pdf/abstracts/abstracts_6241.pdf [Accessed: 2023-05-12].
[20]. Carezani, R.L., Super-Kamiokande: Super-Proof for Neutrino Non-existence. 1997. 8.
https://www.naturalphilosophy.org/pdf/abstracts/abstracts_6243.pdf [Accessed: 2023-05-12].
[21]. Smulsky J.J. Future Space Problems and Their Solutions. New York: Nova Science Publishers; 2018. 269
p. ISBN: 978-1-53613-739-2. http://www.ikz.ru/~smulski/Papers/InfFSPS.pdf [Accessed: 2023-05-12].