Subelectronic Particles

According to Einstein, electromagnetic (EM) waves represent a flux of quanta of pure energy in the form of massless particles (called in 1923 by Compton photons), moving with the speed of light c. How could such a concept of mysterious massless particles appear?

Introducing for the first time the notion of small portions of energy rushing in empty space with the speed of light, Einstein was forced to accept their rest mass m₀ to be equal to zero, otherwise their relativistic mass m will turn out to be equal to infinity according to the equation . And he had understood that it is unconditionally inadmissible. His quanta of energy have no size in the space being the mathematical formless objects. It transgresses the bounds of science. Indeed, the relativistic relation for lengths of objects, moving along the x-axis, is determined by the equality . Einstein interpreted the length as the length in the state of rest, and the length - as the length in the state of motion. Because of this, the length of an object moving with the speed c in the direction of motion is assumed to be equal to zero. As a result of such an interpretation, a photon is transformed into a fig-leaf of a zero thickness, which, moreover, moves in an allegedly empty space and has the wave properties, looking like (in some sense) an energetic snake-sinusoid. This model of the wave motion is deeply naïve and speculative. Obviously, the concept of mystic photons with unusual properties, nonsensical to real essences, is a result of disregarding of common sense for the sake of fitting such a concept to the theory of relativity and nothing else.

One should realize that a wave motion is the mass process having the binary character. It means that the wave process of any subspace of the Universe runs simultaneously at the two levels: the level of basis and the level of superstructure. The basis level embraces an interaction of particles between themselves in a subspace. This interaction gives rise to its own superstructure – the wave motion of longitudinal-transverse structure – the dynamic collective interaction of particles with the subspace. Here, the basis is the cause and superstructure is the effect. Thus, any wave process is a contradictory complex of basis and superstructure, of cause and effect.

For example, an interaction of atoms between themselves in a string (fixed from both ends) is a process occurring at the level of basis of the string. A disturbance of the equilibrium interaction (caused by an external influence) leads to the expansion of this disturbance along a string, which has the wave character. At that the oscillatory motion with the speed of every atom of the mass m of the string (in the wave of the expansion) and the wavelength itself represent the collective parameters of the wave motion related to the level of superstructure.

The energy of the wave quantum of superstructure generates, at the level of basis, the equal energy of the wave quantum of basis , where c is the basis speed. For instance, the wave motion of a string with the frequency of the fundamental tone and wavelength generates in a surrounding air an acoustic wave of the same frequency, but with the basis (sound) speed in air c and the wavelength different from :
                            .
The similar situation takes place under disturbance of the hydrogen atom, where is the orbital (oscillatory) speed of the electron – superstructure of H-atom. The basis speed, equal to the speed of light c, is the speed of interaction (strictly speaking, of exchange of matter-space-time) of the longitudinal (radial) wave field of the proton with the transversal (cylindrical) wave field of the electron at the fundamental frequency of exchange of the subatomic level . At the same time, c is the basis speed of interaction of any particles of the subatomic level, including elementary particles oscillating (during the wave process) in an outer space with a variable speed of superstructure dependent on the intensity of their disturbance.

During the motion in a transient process, the electron in the hydrogen atom causes the wave perturbation. The myriad of particles of the subelectronic level is involved in this process. They have nothing in common with the mathematical points-photons of zero rest mass and zero rest energy. It is a huge world of particles-satellites of electrons. For them, Earth is in the highest degree the “rarefied” spherical space. These particles called neutrino pierce the Earth just freely as asteroids pierce the space of the solar system and galaxies. Just their directed motion, fluxes, called “magnetic field” surrounds a conductor with a current, a bar magnet, our Earth and fills up interplanetary, interstellar, and intergalactic spaces. It is the cylindrical field-space of the subelectronic level.

Taking into account above, let us consider the wave propagation of EM radiation in outer space of Cosmos filled with subelectronic particles. We will rest on the concept that the propagation of EM waves (including light) proceeds like propagation of any material waves, for example, sound waves in an ideal gas. According to the theory of matter-space-time described in the book “Atomic Structure of Matter-Space” (2001), the oscillatory-wave (or, in other words, superstructure-basis) energy density of a medium is equal to
                            ,
where is the density of a medium, is the oscillatory speed of particles (superimposed onto the speed of their incessant random motion and a drift) involved in the wave process of energy transfer of a disturbance, c is the phase speed of wave propagation of the disturbance in the medium.

As was mentioned in the previous summary, the fine-structure constant
                            ,
where is the speed of the electron on the Bohr first orbit, reflects the scale correlation of basis and superstructure of wave fields-spaces of objects in the Universe, i.e., conjugate oscillatory-wave processes at different levels of the Universe. In particular, this constant shows the maximal possible oscillatory speed of coupled particles - a lighter particle of superstructure (electron) with respect to the basis speed of its interaction (binding) with the heavier conjugate basis particle (proton) at equilibrium,
                            .
We have talked about this in the aforementioned summary where it was shown that the fundamental dynamic parameters of microworld, the Planck constant h and the fine-structure constant , characterize some of the dynamic parameters of man as well – his perception of sound.

Let us suppose that the same relation for both speeds, oscillatory and wave, is valid for a huge world of particles of the subelectron level filling the interstellar and intergalactic spaces. As was assumed above, these particles are responsible for the transfer of EM (including light) energy. Then, their maximal oscillatory-wave energy density will be equal to the value
                            ,
where is the density of the space consistent of these particles, is the fine-structure constant. Note in this connection that the space of these particles is one of the infinite set of spaces of the Universe embedded in each other.

The energy of quanta of EM radiation, transmitted through the space, depends on the frequency of radiation and is defined by the equation , where is the Planck constant. Obviously, for the transfer of the same energy of the same frequency by the particles behaving like particles of an ideal gas, the Planck’s action h has to be equal to the oscillatory-wave action
                           
of the particles. In this expression is the field mass related with the wave . This mass differs from the equivalent mass estimated from the dynamic energy . The mass is ranged within the values
                           
defined by the frequency band of EM spectrum. Obviously, in the case when , the mass is approximately 137 times as much the mass m of particles, whose dynamic energy at the subatomic level is equal to mc². Thus, because the energy of transmitted quanta , equal to the oscillatory wave energy , is compared to the energy mc² (as it takes place at the estimation of the equivalent mass of photons), we have under the condition the field mass . Let us to come to this relation the other way.

In wave processes, the change of the extension of the wave element of space (along the wave-beam) takes place. Simultaneously, the change of the field mass, , related with the element of space l, occurs. The following relation approximately expresses this peculiarity:
                            .
The is the local change, therefore, . But , hence, we obtain
                            ,
where a is the amplitude of axial displacement. Hence, the axial element of the mass , say “thickening” (we will denote it as ), along the wave-beam of basis is
                            .
In the limiting case, when is equal to c, the field mass and the mass are equal, . One should regard the wave “thickening” as the wave quasiparticle. If its mass turns out to be equal to the electron mass, this particle can be regarded as a quasielectron, or a wave electron, participating only in the wave process of radiation and absorption. Thus, for the wave , the following relation is valid:
                           
and                         .
If is the Bohr velocity, corresponding to the amplitude equal to the Bohr radius, , and is the quasielectron, then, the mass of radiation (field mass) of the unit wave quantum (quantum of mass of radiation) is
                            .
Following contemporary physics, the EM spectrum is within the frequencies from to . As was shown in the paper "Dynamic model of elementary particles and the nature of mass and ‘electric’ charge" (published in "Revista Ciencias Exatas e Naturais", Vol. 3, No 2, 2001 (157-170)), the fundamental frequency of the subatomic level is equal to
                           
(see the summary on E=m₀c²). It is the frequency of the so-called "electrostatic field". This frequency, unrecordable on the human time scale, is also the carrying frequency of EM waves and, accordingly, it is the ultimate frequency of the EM spectrum. Therefore, all observed (detected) electromagnetic waves are just the waves of the frequency modulation of this carrying exafrequency . The fundamental wave radius, corresponding to the fundamental frequency, is
                            .
It is equal to one-half of mean value of the interatomic distance in crystals. This fact shows that the frequency of the field of interaction between atoms in substance is equal to the fundamental carrying frequency of the subatomic level .

Accordingly, for the ultimate value of the EM band of frequencies, we have the following ultimate value of the field mass (under the condition ):
                       
where is the electron mass. As follows from the literature, the same mass is ascribed to a limiting mass of muon neutrino, . The corresponding ultimate quantum of mass of particles of the EM band (equivalent to energy ) is
                        .
The waves of near infrared, visible, and near ultraviolet relate to the frequency band of . For the value near , we arrive at the following field mass
                           
which is multiple to the characteristic value of the metrological spectrum. Masses of all elementary particles take the definite discrete (quantum) values. The mass m_ph is close to the mass of quanta of the visible region, near ultraviolet, and multiple in average (in units of the electron mass) to the fundamental measure in a quarter of the fundamental period
                            ,
, like well-known elementary particles. For instance, in average, g-particle has the mass
                            ,
-quantum - , -mesons have the mass , -mesons - , etc. (details are in the book “Atomic Structure…” (2001)). The g-particle had no luck. It was ascribed to the spectrum of elementary particles under different names: muonic and electronic neutrino and antineutrino, etc. Note also that the average mass of tau neutrino discovered later is estimated about 34 m_e; accordingly, g-quantum can be regarded as consistent of two particles of the mass .

The relation between the masses of components of a hypothetic coupled system m_ph -particle - electron (m_e) almost coincides with the relation between the masses of a coupling of electron-proton (in the hydrogen atom), m_e and m_p:
                            ,
                            ,
where . Therefore, that is not unbelievable; particles of the mass m_ph can belong to satellites of electrons. The quantum of mass of radiation of these particles (equivalent to mc²) is
                            .
This mass is close to the one of the estimated upper limits of the electron neutrino mass, .

For the frequency , lying close to the mean value of the whole EM spectrum, we obtain the following unit field mass
                       
In this case, the quantum of mass (equivalent to energy mc²) is
                        .
The chosen frequency relates to the extremely high frequency (EHF) band of millimeter waves. It is the region of the cosmic microwave radiation. The mass obtained and taken to estimations is also multiple (in units of the electron mass) to a quarter of the fundamental measure. It practically coincides with one of the plausible masses of neutrinos estimated roughly by the theorists around . Taking into account the multiplicity of elementary particles to the aforementioned fundamental measure of , the expectative value of neutrino mass in units of the electron mass is about
                            .
The fluxes of particles of the discrete spectrum of masses, responsible for the transfer of EM radiation, fill in and drift in cosmic space. Their density has to depend on the carrying frequency of the EM spectrum, basis speed and temperature. As is well known from the experiment, at the illumination of 50 lux and , the number of photons incident on a surface of 1 cm² per one second is . Such an illumination is usual for reading without fatigue of eyes. In this case, the concentration of photons is . Assuming roughly that in outer space of Cosmos an average concentration of particles of the subelectronic level, transmitted EM energy of radiation, is of the same order of magnitude as the aforementioned photons, we obtain for the particles of the mass the following density
                        .
For the particles of the mass , we have
                        .
The modulus of elasticity of such hypothetical field-spaces is turned out to be equal, respectively, to
                       
and                 .
However, the shortest possible wavelength of transfer of disturbance is determined by the shortest possible average distance between oscillating particles, recalling the particles of an ideal gas being in ceaseless random motion. Therefore, it is possible to assume that the approximate average distance between the subelectronic particles in Space should be equal rather to the double value of the fundamental wave radius of the subatomic level. In such a case, for the volume occupied by one particle
                            ,
the density of the field-space of particles, e.g., of the mass in outer space of Cosmos is
                        ,
and the modulus of elasticity of such a field-space is turned out to be equal to
                        .
The modulus obtained exceeds the modulus of elasticity of air, but less than that one of water. Below, for comparison with the above obtained parameters, there are presented analogous estimated parameters of air (T=293 K, P= 1 atm) and sea water (T=288 K) used for the description of propagation of sound in them. The temperature of the medium, consistent of particles of the mass , obviously, could be assumed to be equal to the temperature of the cosmic background radiation equal to 2.7288 K.

Let us estimate the oscillatory speed of -particles assuming that they transmit the quanta of energy of the wide band of EM spectrum of waves. With that, one should not forget that the oscillatory and wave speeds are the speeds of motions superimposed onto the ceaseless random motion and a drift of particles just as it takes place in a gas. The oscillatory-wave action h_ow, equal to Planck’s action h, is
                            .
Hence, for of the visible band (green light), corresponding to the maximal sensitivity of human eye, the oscillatory speed of -particles must be equal to
                        ,
i.e., it exceeds and is close to the basis speed of subatomic level c. For , related to the frequency  of the television band of EM waves, the oscillatory speed is . For ,  of the radio waves band, the oscillatory speed of -particles is , etc.

In conclusion. It is highly plausible that ghostly electron neutrinos are nothing else than ponderable particles of the spectrum of masses of the subelectronic level responsible for the transportation of energy of a huge EM band of wavelengths. Most of the above described particles, including of the mass , rather represent a part of their whole spectrum. Judging by their masses, these particles, identified with electron neutrinos, can be referred to as satellites of electrons. The more so as the ultimate estimated mass of electron neutrinos, known from the literature, does not exceed . In a sense, like fish in an ocean of water, we live in an ocean of neutrinos not feeling it. As concerns mystic massless and formless mathematical points-photons, it is obvious, such objects do not exist in nature; they relate to the realms of fancy.
The present author believes that the hypothesis put forward here could untie many misconceptions of modern physics and astrophysics.

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About the new concept on the wave motion of elementary particles

October 27, 2002