# Substantial photon model

Substantial photon model is a theoretical model, which considers the origin, structure, state of matter, and other properties of the photon. To support the substantial model of the photon, the equations of classical electromagnetism and quantum mechanics are used, as well as Infinite Hierarchical Nesting of Matter, electrogravitational vacuum and strong gravitation.

## Photon formation

The cross section of a photon propagating along the axis ${\displaystyle ~OZ}$. The positive charge near the axis ${\displaystyle ~OZ}$ is indicated with + , the negative charges of the lobes are indicated with – . The rotation of the photon matter leads to a helical spatial configuration.

In the model under consideration, a photon emitted from an atom during quantum transition is formed under the action of the atom’s electromagnetic field from relativistic praons, which are constituents of the dynamic electrogravitational vacuum. [1] [2] The properties of praons, including their mass and charge, are derived in the framework of the theory of Infinite Hierarchical Nesting of Matter, taking into account the similarity of matter levels. The praon level of matter is related to the nucleon level of matter in the same way as nucleons are related to stars. This means that all hadrons and leptons of the nucleon level of matter, as well as photons, consist of praons in one or another of their states. The praonic structure of the proton and neutron is described in the articles substantial proton model and substantial neutron model.

According to the substantial model, an electron in the atom represents a disk-shaped object. The electron spin appears when the center of the disk is shifted relative to the atomic nucleus and revolves around the nucleus, in this case a photon is emitted from the atom. In the first approximation, the entire disk is replaced by a point electron located at the center of the disk and revolving around the nucleus. This allows us to calculate the electric and magnetic fields of the revolving electron in the near, far, and wave zones for a hydrogen-like atom. These fields act on the relativistic praons of the vacuum, that pass through the electron disk, and cause them to form the rotating helical structure of the photon. So an internal periodic wave structure is formed inside the photon.

The analysis shows that in the course of emission of a photon, the current revolution frequency of the electron disk and, accordingly, the frequency of the wave inside the forming part of the photon are changing constantly and are equal to each other, reaching a maximum near the lowest energy level. In this case, the photon frequency, found with the help of the photon energy and the Planck constant, turns out to be equal to the average revolution frequency of the electron disk over the entire time of the photon emission.

The photon is emitted along the axis of the electron disk, but some part of the energy in the form of electromagnetic emission leaves the excited atom in other directions. This emission is in phase with the oscillations inside the photon. The latter can explain the results of the Young's interference experiment with low light intensity, when interference between single photons is observed. In this case, each photon passes through a particular slit and the coherent emission from the atom, associated with it, passes through another slit, which as a result gives the interference pattern.

The photon represents a complex lobe structure and has the shape of a long and thin rotating cylinder, the central part of which contains the prevailing positive charge, and the surface part is negatively charged. It is assumed that the strong gravitation acts at the praon level of matter, while the gravitational constant reaches the value ${\displaystyle ~G_{pr}=1.752\cdot 10^{67}}$ m3•s–2•kg–1, which can be obtained from the strong gravitational constant using the similarity relations. In gravitational field with this large gravitational constant, the praons of the photon can form sufficiently rigid structure, so that the photon could fly large cosmic distances without decaying.

In gravitational model of strong interaction, the strong interaction between particles appears as a result of summation of electromagnetic forces, strong gravitation and forces from the gravitational torsion field. The main components are the gravitational attraction force and the spin-spin repulsion force. When the distances between the particles are smaller than the nucleon radius, the balance of forces and formation of such composite objects, as atomic nuclei and neutron stars, are possible. [3] Thus, the praons in photon matter have such proper spin rotation, that the resulting torsion field creates the pressure, which counteracts the action of strong gravitation.

## Photon structure

Praons have a charge of the order of ${\displaystyle ~q_{pr}=1.06\cdot 10^{-57}}$ C, an invariant mass of ${\displaystyle ~m_{pr}=1\cdot 10^{-84}}$ kg, and to describe their motion at relativistic speeds, one should use the Lorentz factor, which reaches the value ${\displaystyle ~\gamma =1.9\cdot 10^{11}}$. Such Lorentz factor was found for praons inside a photon with the wavelength ${\displaystyle ~\lambda =1.21567\cdot 10^{-7}}$ m and the angular frequency ${\displaystyle ~\omega =1.54946\cdot 10^{16}}$ s–1, which emerges in the hydrogen atom at the transition of the electron from the second to the first level in the Lyman series. [1] This allows us to turn with the help of Lorentz transformations to the reference frame ${\displaystyle ~K'}$, co-moving with photon, to determine the components of the electromagnetic field and the field of strong gravitation, and to understand motion of praons from the standpoint of a fixed photon. [2]

In the reference frame ${\displaystyle ~K'}$, moving with the photon along the ${\displaystyle ~OZ}$of laboratory reference system ${\displaystyle ~K}$, the role of the angular velocity of rotation of the praons in the planes ${\displaystyle ~X'O'Y'}$ is played by the quantity

${\displaystyle ~\omega '={\frac {\omega (1-V_{z}/c)}{\sqrt {1-V_{z}^{2}/c^{2}}}},}$

where ${\displaystyle ~V_{z}}$ is the photon speed almost equal to the speed of light ${\displaystyle ~c}$.

The angular velocity ${\displaystyle ~\omega '}$ is less than the angular velocity of rotation ${\displaystyle ~\omega }$ of the electron in the atom and the angular frequency of the photon in ${\displaystyle ~K}$, due to the time dilation effect. At the same time, in ${\displaystyle ~K}$ the wavelength of the photon is equal to ${\displaystyle ~\lambda }$, and in ${\displaystyle ~K'}$ it becomes larger and equals to

${\displaystyle ~\lambda '={\frac {\lambda {\sqrt {1-V_{z}^{2}/c^{2}}}}{1-V_{z}/c}},}$

which is due to the effect of reduction of the longitudinal dimensions of the moving bodies in ${\displaystyle ~K}$.

In case of instantaneous motion of the observer along the axis ${\displaystyle ~O'Z'}$ in ${\displaystyle ~K'}$ with changing of ${\displaystyle ~z'}$ there is a displacement of the rotation phase by the value ${\displaystyle ~\Delta \phi =-{\frac {2\pi z'}{\lambda '}}.}$

Thus, in the proper reference frame ${\displaystyle ~K'}$ the photon represents a slowly rotating helical structure with the pitch of the right screw along the axis ${\displaystyle ~O'Z'}$ being equal to ${\displaystyle ~\lambda '}$. In the laboratory reference frame ${\displaystyle ~K}$ the pitch of the photon’s helical structure is equal to the photon’s wavelength ${\displaystyle ~\lambda }$. This leads to the wave pattern of motion of the photon’s matter and, consequently, to the wave electromagnetic field from rotation of the electric charge distributed in the photon’s lobes. In this case the photon has circular polarization.

## Photon properties

Inside each lobe of the photon there should be sufficiently smooth distribution of the charge, from the positive charge at the center – to the prevalence of the negative charge at the edges of the lobes. This should also be accompanied by smooth change of the mass density along the lobes. In this case, the lobes contain not only the negative praons but also a significant number of positive praons, ensuring the electroneutrality of the photon. In this case, the positive praons are matched with protons, the negative praons (praelectrons) with electrons, and neutral praons are the analogues of neutrons.

With the help of the Lorentz transformations, we can recalculate the electromagnetic field components from the photon’s reference frame ${\displaystyle ~K'}$ into the laboratory reference frame ${\displaystyle ~K}$. If some lobe in the photon at a given time point is directed along the axis ${\displaystyle ~OX}$, then the electric field ${\displaystyle ~E_{x}}$ appears in this lobe. In addition, due to the photon’s motion at the velocity ${\displaystyle ~V_{z}\approx c}$, the magnetic field appears in this lobe ${\displaystyle ~B_{y}={\frac {E_{x}V_{z}}{c^{2}}}\approx {\frac {E_{x}}{c}}.}$ This allows us to understand for the photon the relation between the transverse components of the electric and magnetic fields, connected by a coefficient in the form of the speed of light.

The relation between the centripetal force, required to rotate the particle on the surface of a photon, and the electric force, exerted on the particle with the charge ${\displaystyle ~q}$ and the rest mass ${\displaystyle ~m}$, is as follows:

${\displaystyle ~qE_{0}={\frac {\gamma mV^{2}}{R_{0}}}=\gamma m\omega ^{2}R_{0},}$

here ${\displaystyle ~E_{0}}$ is, in the first approximation, a certain averaged electric field inside the photon’s lobes from the viewpoint of the laboratory reference frame ${\displaystyle ~K}$, ${\displaystyle ~R_{0}}$ is the transverse radius of the photon , ${\displaystyle ~V}$ is the particle’s velocity on the photon surface, ${\displaystyle ~\gamma }$ is the Lorentz factor of the photon’s motion in general. The emergence of ${\displaystyle ~\gamma }$ is due to the fact that practically the velocity of the photon’s particles is close to the speed of light and is perpendicular to the centripetal acceleration from the electric force that causes the particles to rotate.

For the photon, it is assumed that half of its energy ${\displaystyle ~W=\hbar \omega }$ is the energy of the particles’ rotation, and the other half of its energy is the total energy of all the fields. Besides, in the reference frame ${\displaystyle ~K}$ the angular momentum of the photon is equal to the Dirac constant and is given by a formula, which corresponds to a rotating cylinder composed of ${\displaystyle ~N}$ particles:

${\displaystyle ~L_{p}=\hbar ={\frac {1}{2}}N\gamma m\omega R_{0}^{2}.}$

As a result, the rotation energy can be estimated as half the photon energy:

${\displaystyle ~W_{r}={\frac {1}{2}}L_{p}\omega ={\frac {1}{2}}\hbar \omega ={\frac {1}{2}}W.}$

Dividing the photon energy ${\displaystyle ~W=\hbar \omega }$ by the photon volume, we obtain the energy density, which can be equated to the double density of the electromagnetic energy inside the photon:

${\displaystyle ~{\frac {\hbar \omega }{\pi R_{0}^{2}c\tau }}=\varepsilon _{0}E_{0}^{2}.}$

Hence, with the known values for the photon’s angular frequency ${\displaystyle ~\omega =1.54946\cdot 10^{16}}$ s–1, with the photon radius ${\displaystyle ~R_{0}=4a_{B}}$, where ${\displaystyle ~a_{B}}$ is the Bohr radius, the photon emission time ${\displaystyle ~\tau =9.8\cdot 10^{-10}}$ s, the electric constant ${\displaystyle ~\varepsilon _{0}}$, the average electric field ${\displaystyle ~E_{0}}$ inside the photon is found. Substituting ${\displaystyle ~E_{0}}$ into the equation of rotation of the charged particle gives:

${\displaystyle ~{\frac {q}{\gamma m}}=R_{0}^{2}{\sqrt {\frac {\pi \varepsilon _{0}c\tau \omega ^{3}}{\hbar }}}=2.4\cdot 10^{16}}$ C/kg.

If we substitute the charge and mass of the praon instead of ${\displaystyle ~q}$ and ${\displaystyle ~m}$, we can estimate the Lorentz factor for the photon: ${\displaystyle ~\gamma =1.9\cdot 10^{11}}$. The highest value ${\displaystyle ~\gamma }$ of the photon is expected in the hydrogen-like atom, which has the nucleus with the largest number of protons, and in electron transitions near the smallest orbits. In this case the largest fields of the atom influence the praons of the emerging photon and transfer their energy to them.

The calculation shows that ratio of the fluxes of gravitational and electromagnetic energies in the photon turns out to be equal to the ratio of the proton mass to the electron mass. An estimate of the longitudinal magnetic field inside the photon under consideration gives the value ${\displaystyle ~B_{z}=5.4\cdot 10^{-28}}$ T. This means that in the laboratory reference frame ${\displaystyle ~K}$ the magnetic dipole moment of the photon equals ${\displaystyle ~P_{m}=1.8\cdot 10^{-41}}$ A • m2. Comparison with the Bohr magneton ${\displaystyle ~\mu _{B}}$ shows that for this photon ${\displaystyle ~P_{m}=1.9\cdot 10^{-18}\mu _{B}}$.

## Mass

In the special theory of relativity there is a well-known formula, connecting the relativistic energy ${\displaystyle ~W}$, momentum ${\displaystyle ~\mathbf {p} }$ and invariant mass ${\displaystyle ~m}$ (the rest mass) of a particle:

${\displaystyle ~W^{2}=p^{2}c^{2}+m^{2}c^{4}.}$

As a rule, it is believed that the rest mass of the photon is zero, ${\displaystyle ~m=0}$, and then the photon energy depends only on its momentum: ${\displaystyle ~W=\hbar \omega =pc.}$ The latter ratio allows us to find the photon’s momentum using the energy or angular frequency of the photon. In this case the photon must move at the speed of light ${\displaystyle ~c}$.

In the substantial model, the photon energy ${\displaystyle ~W}$ characterizes the rotational energy of the photon’s particles and the energy of the fields inside the photon from the viewpoint of the laboratory reference frame ${\displaystyle ~K}$. However, the photon still moves at the velocity ${\displaystyle ~V_{z}}$, which is very close to the speed of light, due to which the relativistic energy of all the photon’s particles reaches the value ${\displaystyle ~E_{pr}}$. This energy is much greater than ${\displaystyle ~W}$, because the following relation holds true: ${\displaystyle ~{\frac {E_{pr}}{W}}={\frac {2c^{2}}{\omega ^{2}R_{0}^{2}}}.}$ By the order of magnitude, the difference between the energies ${\displaystyle ~E_{pr}}$ and ${\displaystyle ~W}$ is about tens of thousands and more.

The invariant photon mass, which is understood as the invariant mass of the praons that make up the photon, turns out to be equal to the value ${\displaystyle ~m_{ph}={\frac {2\hbar }{\gamma \omega R_{0}^{2}}}.}$ For the photon under consideration ${\displaystyle ~W=1.6\cdot 10^{-18}}$ J or 10.2 eV, ${\displaystyle ~E_{pr}=2.7\cdot 10^{-14}}$ J or 170 keV, ${\displaystyle ~m_{ph}=1.6\cdot 10^{-42}}$ kg or ${\displaystyle ~9\cdot 10^{-7}}$ eV/с2 in energy units. It turns out that the rest mass of the photon’s particles ${\displaystyle ~m_{ph}}$ is not equal to zero, though it is quite low. As a result for the photon one can write:

${\displaystyle ~E_{pr}^{2}=p_{pr}^{2}c^{2}+m_{ph}^{2}c^{4}\approx p_{pr}^{2}c^{2},}$

here ${\displaystyle ~p_{pr}=\gamma m_{ph}V_{z}}$ is the total momentum of the photon particles. As an estimate of the number of praons in the photon, emitted by the hydrogen atom, there is a relation: ${\displaystyle ~{\frac {m_{ph}}{m_{pr}}}=1.6\cdot 10^{42}}$praons.

The energy ${\displaystyle ~E_{pr}}$ is not transferred to the praons from the electrons in the photon emission from the atom, but they had this energy at the time of interaction of the praons’ fluxes with the electron. Despite the fact that the rest mass ${\displaystyle ~m_{ph}}$of the photon particles is big enough, it cannot be directly found in experiments. This is due to the fact that during interaction of the photon with the matter, the photon’s angular momentum of the order of ${\displaystyle ~\hbar }$ is transferred to the matter, as well as the corresponding energy and momentum. However, the main part of the photon energy, involved in the relativistic motion of praons, is carried away with them at the moment of the photon decay and its scattering into separate praons.

It can be assumed that the velocities ${\displaystyle ~V}$ of the fluxes of praons in the vacuum field are of the order of the speed of light, ${\displaystyle ~V\leq c}$. At the same time, the photons are moving at the velocity ${\displaystyle ~V_{z}}$, and we should have ${\displaystyle ~V_{z}\leq V}$. Some difference between ${\displaystyle ~V_{z}}$ and ${\displaystyle ~V}$ is explained by the fact that the praons in the photon do not only move along the axis ${\displaystyle ~OZ}$, which is perpendicular to the plane of the electron disk at the moment of the photon emission, but they also rotate around this axis by some spirals. Rotation of the praons depends on the photon frequency and energy, which should influence the velocity of the photons ${\displaystyle ~V_{z}}$ and lead to some initial velocity dispersion of the photons of different frequencies. In the article,[4] assuming a non-zero photon mass, the modeling used in atomic spectroscopy for the line shapes and their intensities was considered. It was concluded that massive photons should have velocity dispersion, as well as possible longitudinal polarization state.

It is convenient to assume that the speed of light is the limiting value for the motion of photons and particles. In transition to the lower levels of matter (to nucleons, praons, etc.) the Lorentz factor increases in the particles that make up the photons of the respective matter level, while their velocities must not exceed the speed of light. Thus the theory of relativity is applied in the theory of infinite nesting of particles.

It is known that the photon in the form of a gamma-quantum, with the energy ${\displaystyle ~W}$ exceeding twice the rest energy of an electron, when interacting with an atomic nucleus or a heavy charged particle can create an electron-positron pair in the process of pair production. Since photons, hadrons and leptons are assumed to be composed of praons and contain particles with charges of different signs, the matter and energy of the photon can be transformed into the matter and energy of a pair of oppositely charged particles. The charge separation in the photon’s matter can occur due to the action of the strong electric and magnetic fields near the nucleons.

Being the particles of electrogravitational vacuum, relativistic praons permeate the matter and act on the matter’s charged particles according to the modernized Le Sage’s theory, so that an electric force emerges between the charges and Coulomb’s law becomes valid. [5] [1] Thus, the concept of praons allows us not only to understand the photon structure and to find its mass, but also to give a general explanation of the main electromagnetic phenomena.

## References

1. Fedosin S.G. The charged component of the vacuum field as the source of electric force in the modernized Le Sage’s model. Journal of Fundamental and Applied Sciences, Vol. 8, No. 3, pp. 971-1020 (2016). http://dx.doi.org/10.4314/jfas.v8i3.18, https://dx.doi.org/10.5281/zenodo.845357.
2. Fedosin S.G. The substantial model of the photon. Journal of Fundamental and Applied Sciences, Vol. 9, No. 1, pp. 411-467 (2017). http://dx.doi.org/10.4314/jfas.v9i1.25.
3. Sergey Fedosin, The physical theories and infinite hierarchical nesting of matter, Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN 978-3-659-57301-9. (2014).
4. Joël Rosato. Retaining hypothetical photon mass in atomic spectroscopy models. The European Physical Journal D. Vol. 73, art. 7 (2019). https://doi.org/10.1140/epjd/e2018-90427-9.
5. Fedosin S.G. The Force Vacuum Field as an Alternative to the Ether and Quantum Vacuum. WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991‒8747 / 2224‒3429, Volume 10, Art. #3, pp. 31-38 (2015). http://dx.doi.org/10.5281/zenodo.888979.