Some investigators , ,  have noted that the photon has latent parameters. If it were possible to find them, all (28-34) mathematical relations describing its behaviour would be derived analytically. Let us try to find these parameters.
As the photon model is rather complicated (Fig. 5), it is difficult to find the relations (28-34). But if we take into consideration that the photon has the plane of polarization, the movement of its centre of masses in this plane as well as the movement of the centres of masses of its six electromagnetic fields can be accompanied by rolling of the conventional circumferences, which kinematics and energy parameters will be equal to the corresponding parameters of the photon. The centre of mass M of the photon makes a complete oscillation in the interval of the length of its wave (Fig. 6); that’s why radius (the first latent parameter) of the conventional circumference, which describes the motion of this centre in the interval of the length of one wave, will be determined according to the formula (Fig. 6) , , :
The second conventional circumference will be the kinematics equivalent of the group motion of the centres of mass of six electromagnetic fields of the photon. Its radius (the second latent parameter) is determined from the condition of a turn of the centre of mass of each electromagnetic field of the photon through the angle in the interval of each length of its wave (Fig. 6).
If angular velocity of the conventional circumference, which describes the movement of the centre of mass M of the photon in relation to its geometrical , is (the third latent parameter) and angular velocity of the conventional circumference, which described the motion of the centre of masses of each electromagnetic field, is (the fourth latent parameter) and the linear frequency is , the period of oscillations of the centre of masses of the photon will be determined according to the formulas (Fig. 6):
We have from it:
Binding relation between the wavelength , which describes the centre of mass of the photon and radius of its rotation, shows that the photon has six electromagnetic fields connected with each other according to the circular circuit (Fig. 6).
Kinematical equivalence between the motion of the complicated electromagnetic structure of the photon and the conventional circumferences with radii and gives the opportunity to derive the postulated mathematical relations (28-34), which describe its behaviour. The latent unobserved parameters of the photon take part in the intermediate mathematical conversions and vanish in the final formulas.
As the small conventional circumference of radius moves in the plane of rotation of the photon without sliding, velocity of any of its points will be equal to velocity of its centre and group velocity of the photon. Using relations (36) and (39), we’ll have:
which corresponds to the relation (29).
The same result is given by the relations (37) and (40) of the second conventional circumference of radius .
Now we see that the derivation of the relation (29) not only agrees with the photon model (Fig. 5) and mechanics of its movement, but also explains corpuscular and wave properties of the photon.
When deriving the relations (28), let us pay attention to the fact that kinetic energy of motion of the photon with mass is equivalent to kinetic energy of rolling of the conventional circumferences with the same masses m, which are distributed equally in their length. Total kinetic energy of the conventional circumference will be equal to the sum of kinetic energies of their translational motion and rotation in respect to the geometric centre
We’ll have the same result if we use the second conventional circumference of radius
We’ll reduce the equation (44) to (28)
As it is clear, the latent parameters give the opportunity to derive the main mathematical relations of quantum mechanics, which describe behaviour of the photon, from the laws of classical mechanics. The conventional circumferences allow to determine the group pulse of the photon.
From this one it is easy to obtain the corpuscular version of the Louis de Broglie’s relation
We’ll rewrite this as
In the left part of the equation (51) we have the product of the impulse of the photon and its wave-length , and on the right part we have Planck’s constant . Heisenberg’s uncertainty relation originates from it:
Let us rewrite this inequality in an extended from.
As the photon displays its pulse in the interval of each wave-length, and its size is more than two wave-lengths (Fig. 5), the values and in inequality (53) will be more than 2 each. If we assume that and and substitute these values into inequality (53), we’ll have
Usually the inequality of the uncertainty principles is written as
If we assume that and , we’ll obtain
, or (57)
Thus, the model of the photon restricts accuracy of experimental information being obtained with its help , , . It is explained by the fact that the dimensions of the photon are some what larger than two lengths of their waves. It means that the photon cannot transmit a size of geometrical information, which is less than two lengths of its wave or two radii of rotation as it appears from Heisenberg’s inequality.
If we examine the object with the help of the photon with the specified wavelength, we cannot get geometrical information concerning the object, which would be equal to the wavelength of the photon being used or be less than it. If the photon with smaller wavelength is used in order to get the same information, accuracy of geometrical information will be increased. It restricts physical sense of Heisenberg’s inequality greatly. If this inequality is referred to experimental information being obtained with the help of the photon, it is just only within the framework of one length of its wave or one radius of rotation.
Let us recollect the statement of J. Marion: “If some day it is proved that the principle of ambiguity is incorrect, we should anticipate complete alteration of physical theory” . The information obtained by us shows that Heisenberg’s inequality restricts accuracy of experimental information only, it does not restrict accuracy of theoretical information. J.B. Marion’s prophecy makes sense.
5.5. Kinematics of the Photon
Let us begin with the derivation of the equations of centroidal motion of the photon. As centre of mass of the photon moves in the polarization plane and within the framework of the space-matter-time unity axiom, it is necessary to have two parametric equations in order to describe its motion along wave track.
As the centre of mass of the photon moves in relation to an observer and in relation to geometric centre of the model, for the complete description of such motion it is necessary to have two reference systems: stationary reference system and moving reference system .
Amplitude of oscillation A of the centre of mass M of the photon will be equal to radius of its rotation in reference to geometrical centre of the photon. From Fig. 6 we have , , , 
Let us pay attention to a small value of amplitude of oscillation of the centre of mass of the photon in fractions of the length of its wave or radius of rotation .
The equations of centroidal motion M of the photon in relation to moving reference system have the form:
If the photon moves in relation to the stationary reference system with velocity , the equations of such motion will have the form :
Thus, the main property of the equations (61) and (62), which describe motion of the centre of mass of the photon is in the fact that they describe motion of this centre within the framework of the space-matter-time unity axiom. It should be noted that Louis de Broglie’s equation (34) is deprived of this property. If we take into account the relations (39) and (40), we’ll get , , , :
Irregularity of velocity of centre of mass of the photon originates from this formula, in which electrical constant and magnetic constant are introduced easily.
The graph of velocity (65) of the centre of mass of the photon is shown in Fig. 7.
Fig. 7. Graph of velocity of the centre of mass of the photon
As it is clear, velocity of the centre of mass M of the photon is changed in the interval of the wavelength or the oscillation period from to in such a way that its mean remains constant and equal to .
The equations of centroidal motion of one of electromagnetic fields of the photon in relation to moving reference system (Fig. 6) will have the form:
The absolute motion of one electromagnetic field of the photon, i.e. the motion in relation to the stationary reference system , assumes the form:
These equations give the opportunity to determine all kinematic characteristics of the centres of mass of electromagnetic fields of the photon. But for us, it is more interesting to see the track (68), (69) described by these centres in relation to the stationary reference system, i.e. in relation to the observer. It is given in Fig. 8. The form of the track in the area of point is of special interest (Fig. 6). This is the area of location of instantaneous centre of velocities during rolling motion of a large conventional circumference , .
Fig. 8. Track of centroidal motion E1 of one of electromagnetic fields of the photon
A compound track of the centre of mass of each electromagnetic field of the photon (Fig. 8) forms undulatory motion of its centre of mass and straightness of motion of the whole photon. It will become a subject of future investigations of electrodynamics of the photon.
Thus, we have got the equations (61) and (62), which describe the photon motion more precise than Louis de Broglie’s equations (6), (34) and Schroedinger’s equations (7). But if more precise mathematical relations take place for the description of behaviour of some object, they should contain less precise relations and be their consequences. The relations (61) and (62) describing motion of the centre of mass of the photon should fulfil this requirement.
In order to get the wave equation (34), it is necessary to move the process of the description of motion of the centre of masses of the photon outside the space - matter - time unity axiom. For this purpose, it is necessary to take one of the equations (61) and (62), for example, the equation (62). We’d like to draw the attention of the reader to the fact that this operation automatically takes the process of the description of motion of the centre of masses of the photon outside the space - matter - time unity axiom
In order to bring this equation to the form (34), it is necessary to introduce the coordinate x into this equation using the phase difference for this purpose.
Taking into account that and , we have
Let us designate therefore
Now it is clear that the main reason for the theoretical spreading of the de Broglie wave packet is explained by the independence of coordinate x from time and the lack of correspondence of de Broglie’s equation with the space - matter - time unity axiom. Equations (61) and (62) have no such disadvantage.
It is not difficult to show that equation (72) is reduced easily to Schroedinger’s equation (9) , , , . For this purpose, let us get frequency and wavelength from the formulas (28) and (30).
Let us introduce a new designation of the function (72) and substitute values (73) and (74) into it.
When is fixed, bias is a harmonic function of time; when is fixed, it is a function of coordinate .
If we differentiate the equation (75) twice according to , we’ll find
If behaviour of the electron in the atom is described with the help of the relation (76), it should be taken into consideration that its kinetic energy and pulse are connected with the relation
If we substitute the result (78) into the equation (76), we’ll have
It is known that full energy of the electron (123) is equal to the sum of kinetic energy and potential energy , i.e.
If we take it into consideration, the equation (79) get the form of Schroedinger’s differential equation (9)
It appears from the above-mentioned facts that the result of the solution of the equation (81) is function (72) operating outside the framework of the space-matter-time unity axiom.
Thus, we have derived all the basic mathematical models of quantum mechanics postulated earlier and describing behaviour of the photon. We have shown that Louis de Broglie’s equation (34) and Schroedinger’s equation (9) operate outside the framework of the space-matter-time unity axiom.
Thus, we let all mathematical formulas alone, which are used for the photon behaviour description for a long time. In this sense, we have nothing new, we have only confirmed trustworthiness of these formulas and supplemented them with the equations (61) and (62), which describe centroidal motion of the photon within the framework of the space-matter-time unity axiom.
5.6. On the Way to Electrodynamics of the Photon
It results from this that mass of the photon is formed by its electromagnetic field , , , , . That’s why the interaction between these fields provokes the internal Newton and electromagnetic forces. The forces localize the photon in space and provide its motion with constant velocity. That’s why the main task of future electrodynamics of the photon is to find these forces. As the equations of motion of the centre of mass of the photon and the centres of masses of its electromagnetic fields are known , , , , it is not difficult to determine the Newton’s forces. For example, in order to determine the Newton’s forces influencing the centre of masses of the photon, it is necessary to know tangential and normal acceleration of its centre of mass . Tangential acceleration of motion of the centres of masses of the photon will be equal to
Maximal value of tangential acceleration is equal to .
Tangential force influencing the centre of masses of the photon will be equal to
Normal acceleration of the centre of masses of the photon
Normal or centrifugal force influencing the centre of masses of the photon
Full acceleration of the centre of masses of the photon
Let us note that maximal value of overall acceleration is equal to .
If we take into consideration that , resulting force influencing the centre of mass of the photon will be defined in the following way
Obviously, it is enough to think that the way to electrodynamics of the photon is opened, but it will be not easy. Certainly, the photon model provokes a large number of the new questions and requires the new answers for numerous results of the experiments, in which behaviour of the photon is registered. Nearly ten answers for such questions are available in the books , , . We give a part of them here. But prior to it, we’d like to attract the attention of the readers to the essence of dimensionality of Planck’s constant.
In SI system this dimensionality corresponds to the following equal notions of modern physics and mechanics: angular momentum, moment of momentum and spin. It results from this that the law of conservation of angular momentum governs persistence of Planck’s constant. It runs as follows: if the sum of external forces influencing a rotating body is equal to zero, angular momentum h (momentum of momentum, spin) of this body remains constant al the time.
5.7. Analysis of Experimental Results
1. Why do the photons fail to exist in rest?
Because the centre of photon masses M (Fig. 5) never coincides with its geometrical centre . This lack of coincidence will create asymmetry between the electromagnetic forced of the photon and forms the state of unstable equilibrium, which causes its movement.
2. Why do the photons possess the properties of a wave and of a particle at the same time?
As the electromagnetic fields are closed along the round contour, the photon obtains the properties of a particle, and the oscillations of the centre of mass M of this particle relative to the geometrical centre impart the wave properties to it (Fig. 5). As the photon surface is not a spherical one, but it has a complicated curvilinear form, interacting with the objects, which form diffraction and interference pictures they will be distributed on the screen not at random, but in accordance with the surface form and the interaction laws, which result from this.
3. Why do the photons move rectilinearly?
The linear movement of the photons takes place simultaneously with rotary motion and translational motion; as a result, angular momentum is formed, which keeps the photon on the straight-line trajectory. It should be noted that angular momentum of the photon is its spin directed along the axis of its rotation. This fact follows from dimensionality of Planck’s constant and from the data analysis results of experimental spectroscopy. It contradicts Maxwell’s theory, according to which the photon spin is directed along the photon movement trajectory. It is a natural contradiction, because Maxwell’s theory operates outside the framework of the space-matter-time unity axiom.
4. Why are the photons polarized?
They rotate in one plane, and the centrifugal forces of inertia influencing the centres of the masses of electromagnetic fields of the photon increase their radial dimensions and reduce the dimensions, which are perpendicular to the plane of rotation. Due to it the photons acquire a form, which is different from the spherical one and resemble the flat one.
5. Why do the photons possess no charge?
They consist of even quantity of direction different electrical and magnetic fields, which make the total charge of the photon equal to zero.
6. Why is angle of incidence of the photon equal to angle of reflection despite of the rotation plane orientation (photon polarization)?
When the photon contacts the reflecting plane, the photon is partially deformed and acquires the form, which is almost a spherical one. But this is not all. The calculations demonstrate that at the moment of reflection the photon has no transversal component of a pulse. Thus, as the form of the photon is almost a spherical one at the moment of reflection and there is only a longitudinal pulse, the conditions are formed when the angle of incidence of the photon is equal to the angle of reflection despite of the orientation of its plane of rotation in the moment of reflection.
7. Does the photon have velocity of light after reflection or creation or does it move with acceleration at the beginning?
When reflected or born, the photon moves with accelerations as the processes of creation and reflection are the transient processes, during which it obtains the limit velocity after a definite quantity of oscillations.
8. Does the photon lose energy during transient process?
Yes, it does mainly transferring it to an object, with which it interacts. Compton effect proves it. Due to it the wavelength of the reflected photon is increased. As it is clear from the relations , it is possible only when its mass m and oscillation frequency v is reduced. The photon energy reduction is equal to the reduction of its mass, and the reduction of mass leads to the reduction of density of electromagnetic fields and the reduction of electromagnetic forces, which compress the photon; due to it, the photon rotation radius is increased. Equality between the electromagnetic forces and centrifugal forces of inertia influencing the centres of masses of electromagnetic fields is restored due to the reduction of angular momentum of rotation of the centre of mass of the photon, and, consequently, the linear frequency of its oscillations. It is the essence of the process of “reddening” of the photons in Compton effect and in Doppler effect. The same phenomenon takes place when the photon is born. Infrared and ultraviolet displacement of spectral lines in the astrophysical observations is its proof.
9. What is the nature of radio wave band of the scale of electromagnetic radiation?
A radio wave band of radiation is a flux of photons, and a modelled radio wave is a flux of photon pulses (Fig. 4).
10. Why is the propagation distance of a surface radio wave is increased with the increase of its length?
Due to the increase of the length of the radio wave, the number of the photons, which form this wavelength (Fig. 4), is increased, and the possibility of delivery of information by such wave is increased, despite of the fact that a part of the photons is disseminated by the environment, and a part of them is absorbed. If the wavelength is reduced, the number of the photons, which carry it, is reduced, and the possibility of delivery of information to the receiver is reduced.
11. In which way does a radio wave with the length measured in kilometres transmit the information to an aerial of the receiver, which sizes can have only several centimetres or less?
It is possible to transmit the information by a radio wave, which length is measured in kilometres, to the aerial of the receiver by many factors of magnitude less than the length of radio wave due to the fact that a set of single photons carries the wave. That’s why in order to stimulate the atomic electrons of the aerial of the receiver in the given sequence only several photons (Fig. 4) from this set (waves) are enough to reach it.
12. Why does relic emission possess the largest intensity in millimetre range?
It is due to the fact that in this range there exists a wavelength of the largest infrared photon as far as the dimensions are concerned, but the least one as far as mass is concerned and all photons lose their mass gradually during their life and numerous collisions and are converted into infrared photon with minimal mass (energy). The wavelength of these photons is in millimetre range. It seems that relic emission is an emission of obsolete photons.
13. What electromagnetic emissions are in close vicinity with relic emission?
The emissions, which wavelength is greater than the wavelength of relic emission, belong to a microwave range; the emissions with smaller wavelength belong to an infrared range.