The Concept of the Graviton Field to Describe Non-Relativistic and Relativistic Mechanics of Substance Objects

In [1] it is proved that "in the framework of real physics, the physical equivalent of philosophical Matter is self-organizing energy, i.e., the movement of self-organizing energy carriers that forms our natural world, in the form of a set of nested organizational levels that combine energy -related connections, characteristic size, structure and properties of energy-informational system formations-material objects." In our natural world, there is a nesting of energy levels consisting of material objects of different levels of organization. Material objects are understood as both substance objects (objects formed from substance) and field objects, which are energy fields formed by various quanta.

Moreover, energy carriers of more organized energy levels are created in the environment of energy carriers of less organized energy levels, and, consequently, the former will be invested in the latter. To deny the nesting of energy levels means to deny the process of development of material objects, since without the nesting of levels after the decay, any material object would slide to the initial level of organization and could not develop [2].

The nesting of energy levels clearly indicates the existence of the energy level of carriers of a unified physical field, in which the more organized levels of energy carriers of all substance objects are nested.

Thus, all the substance objects of our natural World are formed, develop, interact, disintegrate and disappear (annihilate) in the environment of a unified energy field, most often called the gravitonic field. The quanta (energy carriers) of this field are gravitons, which are torus-shaped vortex energy formations that self-move at the speed of light [3]. At the same time, each substance object of our natural World has an inseparable graviton shell that moves with it, and through which it carries out all its interactions (energy-informational exchange) with other substance objects [1].

The paper [4] presents a set of experiments proving the existence and composition of the components of the gravitonic field in our natural World, in which the gravitonic field should have as many components as substance objects have independent fundamental properties (parameters) [5].

At the same time, it should be taken into account that we are talking only about the fundamental parameters of substance objects, which are equally characteristic of any substance objects, both the microcosm and the meso - and macrocosm. This is true, because the properties of substance objects can only manifest themselves when interacting through the medium of the gravitonic field, i.e. through the gravitons of the inseparable gravitonic shells surrounding the substance objects and forming their gravitational mass and electric charge [6].

The unified nature of mass and charge is confirmed by an experiment in which, at the electric field strength E ≈ 10¹⁶ V/m, an electron and a positron with charges e and e+ and with masses equal to m 0 are born from this field [7, 8]. This fact also proves the unity of the electromagnetic and gravitational fields [3].

Therefore, a gravitonic field medium must have two components: a longitudinal gravivariational or mass-variational (often called gravitational) one that affects all substance objects, since they always have a gravitational charge (often called gravitational mass), and a transverse electromagnetic one that affects substance objects that have an electric charge [3, 5].

Physical fields are non-local states of Matter in the form of flowing energy (energy-informational) system media that have no shape and volume and are formed by self-moving energy objects (quanta - energy carriers) that do not have longitudinal inertia, i.e., an inert mass at rest or simply an inert mass in the direction of motion.

Substance objects (substances) are local states of Matter in the form of discrete energy (energy – informational) system formations that have a shape and volume and are formed by material objects (energy - carrier particles) that have a longitudinal inertia, i.e., an inert rest mass or simply an inert mass in the direction of motion [1].

In this paper, based on the concept and properties of the gravitonic field, the main formulas of classical and relativistic mechanics of substance objects are derived, without the use of Lorentz transformations and special relativity theory (SRT).

2.    Modes, properties, parameters and equations of the gravitonic field.

To describe the interaction of substance objects in a gravitonic field, it is necessary to determine the modes, properties and parameters of the gravitonic field and derive the laws of their change in the presence of moving and resting substance objects.

For a quantitative description of the graviton field medium, the standard formula for the density of a continuous medium can be used [8, 9]:

Pg = Pg (Г, t) = mgr • Пдт (Г, t), (2.1)

in general, depending on the coordinates Г = i • X + j • y + к • z and time t , where T g (Г, t) is the concentration of gravitons in the graviton medium; m_gT is the average mass of the graviton.

It should be recalled that the graviton does not have a rest mass, i.e., a mass in the direction of motion (in the direction perpendicular to the plane of its energy torus-like vortices), but it has different inertia in all other directions of motion [3].

However, if we consider the dynamics of a graviton field medium associated with a moving field-forming substance object and its subsequent effect on a field (test) substance object, it is better to use the energy density of the graviton field medium [6]:

Wg = Wg {Г, R(t)} = Wg (Г, t),             (2.2)

in which the dependence of the position R of the field-forming substance object is replaced by the dependence on time using the trajectory formula R = R(t) . If the field-forming substance object is stationary, then the dependence R = R(t) disappears, and the density configuration of the graviton field medium W g (г) is static.

Based on the dimension of physical quantities, the energy density of the gravitonic field W g [J/m³] is equal to its pressure P g [N/m²] on substance objects:

Wg (Г, t) = Pg (Г, t) = TTgT (Г, t) • kB ■ TgT_          (2.3)

because [J/m³] = [№m/m³] = [N/m²]; where к в is the Boltzmann constant; T g _r is the temperature of the gravitons.

As shown in [10, 11], the ratio of the energy density of the gravitonic field medium W g (formulas (2.2) and (2.3)) to its density P g (expression (2.1)) is a constant value equal to the square of the speed of light C² :

W g ^/P g = C².                                        (2.4)

According to [10], the density of the graviton field P g is an indicator of its specific inertia, and inertia is a physical phenomenon of the reaction (resistance) of the medium of the graviton field to the change in the motion of substance objects in it.

In the framework of real physics, we can distinguish two fundamentally different modes of dynamics of a gravitonic field medium -two models of its behavior in the interaction of substance objects [6].

The first mode is the classical one, which implies that the field medium does not have its own dynamics and is based on the model of independent separate (isolated) field graviton shells for substance objects, which is typical for classical physics.

The separation of the field graviton shells of substance objects occurs when there are few substance objects and the distances between them are large, which means that the magnitude of the field connection -the intensity of interactions is also small. Under these conditions, the unified environment of the gravitonic field, which causes interactions between all substance objects as elements of the system at once, is divided between individual substance objects. As a result, each substance object received its own piece of the gravitonic field environment - its independent separate field shell.

Such a separate field shell has limited dynamics, since it is connected with a substance object, and can only move together with it or experience elementary deformation. The field medium in the field shell should have the highest density at the surface of the substance object and decrease as it moves away from it. As a result, the interaction effect should decrease with distance.

As can be seen from [8, 9], the laws of Coulomb and Newton's universal gravitation are similar and are determined by geometry, because they describe the electrostatic and gravistatic components of a unified graviton field [5]. But the discovery of the true nature of electricity and gravity does not consist in finding the dependence of the force of interaction on distance, which is what official (academic) physics was satisfied with. It consists in understanding the causes of the properties of electric and gravitational charges in substance objects, as well as in identifying the structure of charges and finding factors to control their values.

In a model independent field shells all disturbances graviton field environment are due solely to the motion of the considered substance objects, and the field environment itself turns out to be like a sea in calm weather, when every ship on the water leaves its mark, only slightly perturbing it.

For the classical regime, it is not necessary to consider the dynamics of the gravitonic field medium at all points in space, but only to calculate it at the location of the object under study. In this case, the energy density function of the graviton field medium W g (r, t) is transformed into the field coupling function of substance objects W g (R), which depends only on their relative distance R and has in classical physics the meaning of the potential energy of interaction of substance objects in the graviton field W_p g , therefore [6]:

Wg (Г, t) = Wg (R) = Wpg .                       (2.5)

The second mode - quantum or wave is associated with the assumption of the possibility of the existence of proper perturbations in a 9

graviton field medium and is based on the model of a single field graviton shell for interacting substance objects.

The quantum mode occurs when the gravitonic field environment of a group of substance objects (usually microparticles) located at a small distance from each other is a unified connected system with complex general properties. At short distances, the bonds between substance microparticles are much stronger, and the role of the gravitonic field medium as a carrier of interactions increases markedly. This means that for small distances between substance objects, it is necessary to switch from the model of separate graviton field shells to the model of a single graviton field medium.

Indeed, in a single graviton field medium, the motion of the field medium itself is of paramount importance. And all substance particles begin to move collectively under the influence of this environment. Such a model leads to the emergence of collective effects, the presence of selected stable states forming a discrete spectrum, as well as to a change in the properties of a system of substance particles by a sharp transition from one stable qualitative state to another, which is characteristic of quantum physics.

This is especially true for substance microparticles, which are much more affected by the gravitonic field environment compared to substance macroobjects. The gravitonic field environment in the quantum or wave mode becomes like a raging ocean, when all the ships lose the individuality of their movement and become puppets of the general storm waves.

In the bound state with a group of substance microparticles, the graviton field medium has a certain configuration of its energy density, in which each microparticle occupies its own place or has its own stationary orbit. This corresponds to the formation of a unified system in a stable quality condition. Therefore, it is possible to change the state of a single substance microparticle only under the influence of significant factors, and this change will be associated with the transition (jump) of the entire unified system to another qualitative stable state.

The quantum (or wave) mode is much more diverse and more complex than the classical one. It is necessary to calculate the dynamics of the field environment at all points of the considered area. The density function of the field medium in this case turns out to be very consonant with the wave function (psi-function) [7-9] or the probability density from quantum mechanics. This allows us to arrive naturally at discrete quantum effects for continuous fields and to approach a unified field theory [12].

In relation to the graviton field medium, the term "intensity" is used along with the term "density"(formula (2.1)). In the model of individual field shells (classical mode), the intensity corresponds to the function of the source of the gravitonic field (field-forming charge) and reflects the amount of the field medium that is inseparable connected with a given particle of substance. In other words, the intensity characterizes the magnitude and saturation of the field shell of a particle, and its classical analog is the charge (electric or gravitational).

In the model of a single field shell (quantum mode), the intensity value is a characteristic of the common field shell of interacting substance particles and corresponds in the classical representation to the product of charges (electric or gravitational) of interacting substance particles [6].

The concept of the gravitonic field as an intermediary in the transmission of interactions between substance objects arose as an alternative to the Newtonian mechanism of long-range action, i.e., direct, without any intermediate agent, interaction of substance objects at a distance.

According to the long-range hypothesis, the force between two substance objects, such as particles with electric and / or gravitational charges, occurs only in the presence of both particles. At the same time, the space between the particles is not assigned any role in the transmission of the interaction [8, 9].

It was the mathematical formalism of the long-range hypothesis, which requires the presence of both a field-forming charge and a field (test, investigated) charge, that led to the inconsistency of classical mechanics and electrodynamics at the turn of the XIX - XX centuries. Because of this discrepancy, we had to switch from the real Galilean transformations to the abstract Lorentz transformations and use the formal dependence of mass on velocity and other relativistic corrections [6].

In the framework of real physics, the concept of a gravitonic field implies that the very presence of a field-forming substance particle changes the energy (state) in the space around it.) the corresponding component (electromagnetic or gravivariational) of the existing gravitonic field [5], i.e. creates an energy density gradient (wave perturbation) of the field. The region of the gradient of the energy density of the gravitonic field has the potential ability to manifest the action of a force.

To do this, it is enough to place a second test substance object in this region, for example, a particle with an electric and/or gravitational test charge. The field (test) charge does not interact directly with the field -forming charge (field-forming particle) - the creator of the energy density gradient of the gravitonic field, but with the energy density gradient of the gravitonic field in the region where this test charge is located.

The gravitonic field plays the role of an intermediary: it transmits the action of one electric charge on another or one gravitational mass on another through a wave change in its energy density. Such a mechanism of interaction of substance objects is called short-range interaction [6, 7, 13].

When one substance particle moves in the medium of a gravitonic field, the force acting on it due to the change in the energy density of the field from the second substance particle changes. Therefore, its energy will also change, for example, decrease. Having shifted, the first electrically and/or gravitationally charged substance particle transmits to the corresponding component of the gravitonic field, as a signal about its displacement, the fraction of energy that it has lost.

Consequently, the energy density of the gravitonic field itself changes in the region where the first particle is located. This change in the energy density will begin to propagate along the field from point to point in the form of longitudinal gravivariational (gravitational) waves and transverse electromagnetic (electrovariational) waves [5]. After reaching the second substance particle after a certain time, the waves transfer energy from the first particle to it. From this moment on, the force acting on the second substance particle will begin to change.

Thus, according to real physics, the nature of the interaction of substance objects in the environment of a gravitonic field is that each of them perturbs the surrounding field environment-creates an energy density gradient. These perturbations from each substance object propagate in the field gravitonic medium as energy waves and reach other substance objects, distorting the energetically gravitonic medium around them-creating energy density gradients. These energy distortions (energy density gradients) of the field gravitonic medium in the vicinity of each object lead to a change in the nature of its motion, which is interpreted as the action of forces [6].

In the mechanism of interaction transmission based on the principle of short-range interaction, the gravitonic field is a physical reality, and during the entire time of delay of interaction (signal) transmission, it owns the share of energy already given by the first real particle, but not yet received by the second [3].

The principle of short-range interaction is formalized in real physics in the form of the wave equation of the gravitonic field [6]:

d²W g /dt² = С² • ^W g = С² • V 2 W_g , (2.6) where W g = W g (r, t) is the energy density of the gravitonic field; Д is the Laplace operator; V is the symbolic nabla vector; С is the speed of light.

If the graviton field medium is inseparable connected with the moving substance field-forming charge Q = Q(r, t) , then equation (2.6) is supplemented by the source function U (r, t) and takes the form [6]:

^wg — 1/c2 • d2Wg/dt2 = — U(r, t).              (2.7)

The source function is a term that describes the number of graviton field environment, which is an inseparable belongs to a given substance particle. From the expression (2.6), the ratio of the second derivatives of the energy density of the gravitonic field in time and in space is equal to the square of the speed of light, and from the comparison of equations (2.4) and (2.6) it follows:

(d2Wg/dt2)/^Wg = Wg /pg = c2.               (2.8)

The principle of conservation of energy, which is characteristic of the motion of discrete substance objects, in relation to the motion of continuous media was transformed into the principle of preserving the continuity of the medium [7, 8]. For a gravitonic field medium in terms of real physics, it has the following formulation [6]:

"The material graviton field environment, which determines all the interactions and movements of substance objects in our natural World, cannot be born out of nothing and disappear into nowhere, so the change in the density (energy density) of the graviton field environment in a certain region of space, associated with the movement of a substance object, can only occur due to its redistribution to neighboring regions".

In mathematical form, the principle of preserving the continuity of the field medium means that the energy density of the gravitonic field medium W g = W g (r, t) corresponds to the continuity equation [7-9]:

wg/ dt + div(Wg • v) = dWg/дt + V •(Wg -v) = 0,         (2.9)

where V is the symbolic nabla vector.

The gravity field flux density vector j g is related to the velocity of the field-forming substance object v moving in the gravitonic field by the following relation [11]:

j g = dJg/dO = Wg • V,                                   (2.10)

where J g - the flow of energy gravitonic field; о - single area of the control surface; W g = V /_g (V - energy density of the gravitonic medium; W g -energy gravitonic environment volume V .

Taking into account the expression (2.10), the formula (2.9) can be rewritten as:

dWg/dt + divjg = 0,                             (2.11)

where div is a scalar linear differential divergence operator?

In the right-hand side of the continuity equation (2.9), zero is written, because energy is an indestructible quantity. Therefore, the divergence of the vector flux density of energy equal to the rate of change of the energy density of gravitonic environment with the opposite sign, i.e. energy (energy carriers, which serve graviton field quanta) can only be moved across borders some amount of gravitonic field to accumulate it or leave it.

Thus, according to real physics, if energy formations appear or disappear somewhere, it is only with equal and opposite directed energy values.

According to the rules for calculating the divergence [7], taking into account V = const , equation (2.9) can be rewritten as:

dW g /dt + vgrad w_g = dw_g/dt + vVw_g = 0, (2.12) where grad is vector linear gradient differential operator.

3.    Derivation of the formulas of the classical mechanics of motion of substance objects using the concept of the gravitonic field.

According to expression (2.5), for the classical mode of motion and interaction of substance objects in a graviton field, the density function of the graviton field medium W g (r, t) turns into the field coupling function of substance objects W g (R) . This function depends only on their relative distance R and has in classical mechanics the meaning of the potential energy of interaction of substance objects in the gravitonic field W pg .

Substituting W pg instead of W g in the wave equation (2.6), taking into account that d² W pg /dt² = 0 , we can obtain the equation AW pg = 0 , which has the following general solution [6]:

Wpg = const/R. (3.1)

Expression (3.1) describes, in general, the potential field, and is applicable to both the electrostatic and gravistatic components of the graviton field [5].

In the framework of real physics, to obtain the equation of motion of substance objects in a gravitonic field (the field equation of motion), replacing W g with W_pg , take the time derivative of the expression (2.9) and substitute it into the formula (2.6), then it is easy to get:

d2Wpg/dt2 = V • [d(Wpg • v)/dt] = c2 • V2 Wpg = V •

[(1/C2)d(Wpg • V)/d t-VWpg ] = 0. (3.2)

The expression in square brackets is the rotor of a certain function, and the rotor in the potential field is always zero, since the potential field is vortex-free. Therefore, the field equation of motion, which defines the relation of the acceleration a = dv/dt of the motion of the studied field (test) substance object in the gravitonic field environment of the fieldforming substance object, in the classical mode of motion has the following form [6]:

(1/c2) • d(^ • v)/dt = grades = VWpS,     (3.3)

where c is the speed of light.

It is important to note that equation (3.3) is written in a coordinate system in which the origin of coordinates coincides with the position of the field-forming substance object, i.e. in the field system when the field source is stationary.

According to real physics, the values of mass and force do not appear explicitly in the field equation of motion, because these characteristics do not belong to a substance object, but are determined by the gravitonic field environment in its vicinity [6].

The field equation of motion (3.3) indicates that the change in the velocity of a field (test) substance object during interaction is determined by the function of its field connection with the field-forming substance object (the potential energy of interaction W p _g ).

In order to get the expressions for mass and force in a graviton field that are familiar to the equation of motion of substance objects, multiply the right and left sides of equation (3.3) by -1 and enter the usual notation [6]:

d[(-Wpg/c2) • v]/dt = - grad^.                      (3.4)

According to the definition [8, 9], the force F acting on any substance object from the side of the potential physical field is equal to the gradient of the potential energy of this field, taken with the opposite sign, i.e. the force in the gravitonic field is defined as:

F =-grades.

Then the equation (3.4) can be written in the form:

dR-W^/c2) • v]/dt = F, and comparing the expression (3.6) with the equation describing Newton's second law [9]:

dp/dt = m -dv/dt = m^a = F, where m is the inert mass of the substance object; a = dv/dt; v and p are the acceleration, velocity, and momentum of the substance object, respectively.

One can obtain a formula for the observed total inert mass m_tot of a substance object in a gravitonic field:

-tot = —Wpg/C2.                                     (3.8)

After substituting the expression for the total inert mass into the formula (3.6), the field equation of motion (3.3) takes on the well-known form of Newton's second law (3.7) [6]:

d[-tot^v]/dt = F.                                          (3.9)

Thus, in the framework of real physics, both the force and the mass of substance objects are determined by the dynamic characteristics of the gravitonic field. The force is determined by the change in the energy density of the gravitonic field medium in space, and the mass is determined by the change in the energy density of the gravitonic field medium in time.

The formula (3.9) is an illustration of the principle of double action, according to which the interaction in the medium of a gravitonic field, on the one hand, is associated with the action of a force on a substance object, and on the other - with a change in inertia (total inert mass) this object [6].

Thus, when a substance object moves in a gravitonic field with a changing potential energy, its inertia, characterized by the total inert mass, will also change [6].

The potential energy of the interaction of the gravitonic field W_p g with a substance object has the gravistatic (gravitational) W g and electrostatic (electric) W_e components, determined by the product of the gravitational g _g and electric g_e charges of the object on the potentials of the gravitational (P g and electric p_e fields in the area of the object, i.e.:

^W = ^g g • ^p g,                                     (3.10)

^W e — ^g e • ^p e .                                         ⁽3.11⁾

According to the provisions of real physics, in the general case for all substance objects on our Earth and with a high probability in the entire Solar System, the potential energy of interaction with the gravitonic field consists of two parts [6]:

• -    the global potential energy W gb , created by the gravistatic (gravitational) field of all substance objects in the Universe;

• -    and the local potential energy W i _c , which is formed in the vicinity of the investigated (test, field) substance object due to local electric and gravistatic (gravitational) fields, i.e.:

Wpg = Wgb + Wlc.                                   (3.12)

Substituting the expression (3.12) into equation (3.4), it is easy to get the most general form of the equation of motion of a substance objects in our natural World:

d[(-{Wgb + Wic/C2) • v]/dt = -gradWgb - gradWic. (3.13)

Important conclusions can be drawn from equation (3.13) [6]:

• 1.    At a constant potential energy of interaction of substance objects W_P g (г) = W_Zc + W_gb = const , they acquire a constant mass characterized by their passive inertia, and their motion is determined only by the action of forces.

• 2.    With a variable potential energy of interaction of substance objects W p _g (г) = var , they acquire a mass that changes during their movement and characterizes their active inertia, which depends both on the action of forces and on the change in mass.

• 3.    For an isolated substance object, the potential energy of interaction W pg (г) = 0 , i.e., the isolated substance object has no mass, and its equation of motion turns into the trivial identity 0 = 0 . In other words, the movement of an isolated substance object is completely devoid of physical meaning. This means that completely isolated substance objects simply do not exist in our natural World.

In addition, it should be emphasized that the equation of motion (3.13) is written in the field system associated with the field-forming substance object. And since there are two field-forming sources that create global and local potential energy, they must rest relative to each other. The source of the local interaction must be stationary relative to the center of mass of the Universe, Galaxy, system of fixed stars, or, in some approximation, relative to the Earth.

As can be seen from equation (3.13), a substance object has two components of the observed total inert mass m_tot : the constant classical inert mass m , determined by the global potential:

m = — Wgb/c2                                     (3.14)

and the variable local field mass m / , determined by the local potential:

m/ = -Wlc/c2,                                       (3.15)

so

mtot = - Wpg/c2 = — Wgb/c2 -WZc/c2 = m + mt     (3.16)

The global potential energy in our Solar System is usually much greater than the local potential energy [6], i.e.:

I W gb | » |W , _C I ,                                           (3.17)

and its gradient is much smaller than the gradient of the local potential energy, i.e.:

| gradWgb | « | gradWZc |,                              (3.18)

or in other words, W gb ~ const within the Solar system.

Taking into account the conditions (3.17) and (3.18), equation (3.13) is modified into the field equation of motion of substance objects in classical mechanics [6]:

d[(-W gb ^/c²) • v]/dt = d^[m • v^]/dt = -gradW_Zc = F, (3.19) for which all the masses are determined exclusively by the global interaction, and all the forces are exclusively local in nature.

For classical mechanics, under the conditions W gb = const and the absence of local fields W_Zc = 0 , a substance object will move in a gravitonic field uniformly and rectilinearly in accordance with the equation of motion:

d[(-Wgb/c2) • v]/dt = d[m • v]/dt = m • dv/dt = 0.   (3.20)

It can be seen from equation (3.20) that the Galilean principle of preserving the uniform and rectilinear motion of a substance object will be valid only if the global potential energy of the interaction W gb = const is strictly constant. Otherwise, even in the absence of any external forces, when a substance object moves from a region of stronger potential energy to a region of weaker potential energy, or vice versa, its speed will change due to a change in the mass value associated with a change in the potential energy value [6].

As can be seen from the comparison of the formulas (3.14) and (3.15), the nature of the classical inert mass is dynamic, completely analogous to the nature of the local field mass, and consists in the fact that each substance object participates in a global interaction with the collective gravitonic (gravitational) field of the Universe, which makes the main contribution to its inertia [6].

The scale of the Earth and even the Solar System is very small compared to the scale of the Universe, so the global interaction potential ( gb in the vicinity of the Earth can be considered constant with high accuracy. So, is constant and the potential energy of interaction of any substance object in the Solar system with the global field W gb , i.e.:

W gb = m g • (Pgb = const ,                         (3.21)

where m g is the gravitational mass of a substance object, which carries the meaning of its gravitational charge and is included in the formula of Newton's law of universal gravitation.

Therefore, although mass is dynamic in nature, it behaves as a constant in all phenomena on Earth. It creates the illusion that mass is an unchanging "innate" property of the substance object itself, and not the result of external influence. The masses of all the bodies (substance objects) on Earth would gradually change if the Solar System were moving towards the center of our Galaxy, or away from it.

Thus, the inert mass m of any substance object is determined by the potential energy W g^ of its interaction with the gravitonic field of the Universe, which, in turn, is the product of the gravitational mass m g of the same object by the potential of the global field ф д^ in a given region of the Universe.

As a result, the inert mass of any substance object on the Earth is proportional to its gravitational mass (gravitational charge), i.e. [6]:

m = — W^/c2 = -mg • рдь/с2 = k-mg       (3.22)

where k is the coefficient of proportionality between the two types of mass.

This is the nature of the "mass equivalence principle" observed in terrestrial conditions. For all real objects on the Earth, the appearance of equality of the inert and gravitational mass is created. This is due to the fact that the inert mass of such an object is determined by the interaction with the gravitational field of the Universe, and the magnitude of this interaction is determined by the gravitational mass of this object. As a result, there is proportionality between the two types of mass, which, with the proper choice of constants, can be converted into equality.

Thus, according to real physics, the equivalence of inert and gravitational mass is not a fundamental principle [6].

It should be noted that the introduction of any additional local interaction, such as an electric one, which adds a local field component to the classical inert mass of a substance object, destroys the equality and even proportionality between the two types of mass.

In other regions of the Universe, the potential of the global field ф д^ differs from its value characteristic of the Earth. Therefore, the ratio between the inert and gravitational mass types of the same substance object in other parts of the Galaxy is not the same as on Earth.

This means that the principle of mass equivalence is another local rule, unfairly elevated by official (academic) science to the rank of a fundamental principle [6].

4.    Derivation of formulas for relativistic mechanics of motion of substance objects using the concept of the gravitonic field.

In the framework of real physics, the second modification of the field equation of motion of a graviton medium (3.13) is based on taking into account the local interaction potential W ; _c in the mass value at a constant global potential W b = const [6]:

d[(-Ж + wgb}/c2) • v]/dt = —gradWzc.     (4.1)

In this case, the substance object has two components of the observed total inert mass m_tot : the constant classical inert mass m , determined by the global potential, and the variable local field mass m ^ , determined by the local potential (formulas (3.14) – (3.15)).

Therefore, in equation (4.1), the mass can no longer be taken out from under the sign of the derivative, and the equation takes the form [6]: d(m_t ot • v)^/dt = d[(m - Wz^c²) • v]^/dt = —gradW zc = F ,(4.2) that is, the force F no longer leads to a change in the velocity of a substance object, but to a change in its momentum.

If we expand the derivative of the product in equation (4.2), we can obtain the expression:

mtot • dv/dt = -VWtc — v • dmtot/dt = —VWzc + (1/c2) • v • dWZc/dt,(4.3)

where F =-gradW_Z c = -VW_t c and V is the symbolic nabla vector (formula (3.5)).

For the classical mode of interaction of substance objects in a gravitonic field, the potential energy of interaction depends only on the distance R between them (equation (2.5)). Therefore, the relation dW z _c/dt = v • VW z _c [9,14] is fulfilled, taking into account which equation (4.3) takes the form [6]:

mtot • dv/dt = F — (1/c2) • v • (v • F) = F • (1 — v2/c2) +

(1/c2) •v x (F x v),        (4.4)

where X is the sign of the vector product.

Equation (4.4) is the field equation of motion of substance objects in a graviton field environment for the relativistic case when their velocity approaches the speed of light in magnitude, i.e. v ^ c .

Thus, the presence of a variable additive to the mass of a substance object, determined by the local interaction potential, leads to corrections to the force having the order v²/c² . If the force is parallel to the velocity F || v , then it changes the latter in magnitude, and equation (4.4) turns into the expression:

mtot • dv/dt = F • (1 — v2/c2)(4.5)

that is, there is an effect of reducing the force or increasing the inertia of a substance object:

[mtot/(1 — v2/c2)] • dv/dt = F.

If the force is perpendicular to the velocity F 1 v , and changes only its direction, and not the absolute value, then the equation of motion takes the usual classical form:

mtot • dv/dt = F.

The relativistic dependence of mass on velocity leads to exactly the same expressions as those obtained in formulas (4.6) and (4.7). Indeed, if instead of the formula for the field mass, we introduce a formal relativistic dependence [9]:

m tot (v) = ^ 0 ^/(1 - v^2/c²)^1/2, (4.8) where m o is the rest mass, then by differentiating the expression d[m tot (v) • v]/dt it is easy to obtain for F || v and for F 1 v expressions similar to formulas (4.6) and (4.7), respectively.

Consequently, the field equation of motion, taking into account the variable addition to the mass (4.4), is completely equivalent to the relativistic equation of motion with a velocity-dependent mass [9]:

d[m0^v/(1 — v2/c2)1/2 ]/dt = F. (4.9)

Thus, it is proved that relativistic physics is a consequence of real physics , i.e. the physics of motion and interaction of substance objects in the energetic material environment of the gravitonic field. At the same time, all the calculations performed were carried out exclusively within the framework of Euclidean geometry, and did not require the introduction of space contraction, time dilation, or their unification into space-time. And the special theory of relativity (SRT) is a mathematical formalism introduced in physics by A. Einstein, after he removed from it the concept of "ether" or the gravitonic field in terms of this work [6].

The rest mass of a substance particle m₀ plays an important role in the special theory of relativity (SRT) and, according to equation (3.16), consists of two parts:

• -    the classical inert mass m , determined by the global potential energy of the interaction W g^, and constant under terrestrial conditions;

• -    and an additional local field mass m_a d , determined by the local potential energy of the interaction W i _c at the point where the particle velocity v is zero.

This additional local field mass m_a d is also constant, since it is only the value of the local field mass m ^ at one of the points in the trajectory of the substance particle with v = 0 , i.e.:

mo = m + mad = m — Wlc/c2 | v=o (4.10)

Therefore, the rest mass of the substance particle m₀ , in contrast to the classical mass m , although constant for a single motion, depends on the value of the potential energy of the local field W i _c at the rest point of the particle v = 0 , corresponding to this particular motion.

The dependence of the rest mass of a substance particle on the potential energy of the local field Wic at one of the points of its trajectory with v = 0 is extremely important, because it means that the same substance particle under different physical conditions (at different values of Wic) will have a different rest mass.

At low values of W i _c , the field additive in the rest mass of the substance particle is negligible, but the stronger the fields in which the substance particle motion is studied, the higher the rest mass will result in a relativistic calculation [6].

Indeed, in the absence of local external fields W = 0) , the rest mass of the electron m_0e is determined only by the potential energy of the global interaction ( W ^b ) and is equal to the classical inert mass m , given in all reference books. But if an electron is born and begins its movement in the region of a very strong local field, as a result of the calculation according to relativistic formulas, its rest mass will be much larger than the classical one.

The application of the formulas of classical relativistic mechanics (SRT) to the calculation of the experimental results leads to the fact that under different conditions the same substance particle has a different rest mass. As a result, instead of one substance particle, whole groups of them appear, differing only in the magnitude of the rest mass and the lifetime.

For example, mesons are born at particle accelerators with a local field energy of hundreds of MeV, which is two orders of magnitude higher than the energy of 0.511 MeV, which causes the rest mass of an ordinary electron m_e o [9]. As a result, the rest masses of the mesons are also hundreds of times greater than the rest mass of the electron.

Thus, according to real physics, the rest mass does not characterize the substance particle itself, but only the initial conditions of motion in which this particle participates at a given moment, and, therefore, cannot serve as an unambiguous identifier of the observed particles. This requires a serious revision of the entire system of currently known elementary particles [6].

It should be noted that testing the conclusion of real physics about the dependence of the rest mass of a substance particle on the potential energy of the local field at the rest point of its trajectory requires much simpler and cheaper experiments than those conducted at the Large Hadron Collider. Indeed, it is only necessary to register the resulting substance particles at different values of the electric field potential in the registration region during the interaction reaction of identical particles [15].

The expression (4.10) allows us to clearly and simply understand the mass defect effect – an experimentally established phenomenon, which consists in the fact that the mass of the decaying nucleus is always less than the total mass of the decay products, and in this phenomenon an energy is released equal to the mass difference (defect) multiplied by the square of the speed of light [8, 9].

If we consider the mass of the nucleus as a whole, it is determined exclusively by external fields and, above all, by the global interaction. When the mass of each individual nucleon is determined during the decay of the nucleus, it increases due to the internal interactions of the nucleons.

The value of this additional mass m_a a can be determined by the formula for the second term in expression (4.10), in which the local potential energy of interaction W [ _C is replaced by the potential energy of interaction (binding) of nucleons in the nucleus W_nuc , i.e.:

^m ad = - ^Wiuc ^/c ■                         (4.1¹)

In the process of nuclear decay, the potential binding energy W_nuc is converted into the kinetic energy of the decay products W_k in accordance with the law of conservation of energy W_k = -W_nuc . That is why there is a well-known connection between the mass defect m_a a caused by local fields inside the nucleus and the energy of the nuclear decay reaction W_k [9]:

Wk = -Wnuc = maa^c2.                (4.12)

Equation (4.12) creates the illusion that part of the mass of substance has been converted into energy. But what actually happens is the following.

The interaction between substance objects (bodies, particles) determines a certain amount of inertia for each of them. However, this inertia manifests itself only when these objects move relative to each other. If we consider the movement of these objects as a single system, then everything changes.

In the framework of real physics, the total mass of a system of substance objects will be determined only by external interactions for this system. And all internal interactions do not affect the mass of a substance object in any way [6], which is always a system (composite) material (energy-informational) formation.

Indeed, the property of mass is associated with the presence of changes in the medium of the gravitonic field, with which each substance object is connected through its inseparable field shell. If a substance object moves as a whole, then its field shell remains on average unchanged, although it may experience fluctuations. In other words, the movement of a substance object as a whole (as a system) neutralizes the contribution to its mass of all internal (within the system) interactions.

If a substance object begins to disintegrate into its component parts, then with the relative movement of its parts, additional inertia will begin to manifest itself, associated with internal interactions between them. The components of any stable substance object are connected by 23

internal forces of attraction. These forces cause an additional positive mass to all the constituent parts of this substance object.

Thus, according to real physics , the mass of any substance object as a whole will always be less than the algebraic sum of the masses of its constituent parts due to the additional inertia caused by internal interactions. This additional inertia is called the internal or latent mass [6].

The example given in [16] can serve as a clear confirmation of this position, which is the cornerstone of the level approach , in addition to the mass defect effect observed during the decay of nuclei.

If the whole solid (substance system) of a volume divided into many separate substance particles, each of which has a small enough volume, the sum of the volumes of this set of substance particles will be less than the volume of the initial whole body, but the density and weight of separate small particles will increase. The volume of a single particle of substance is less than the fraction of the volume that falls on the same particle when it is part of a whole solid, i.e., a volume defect occurs.

The contraction of a substance particle, the decrease in its volume, and the increase in its density and mass is due to the energy of the system's decay (the energy released when the parts of a solid body connected by internal forces of attraction break apart).

In modern official physics, there is a scientific position that as a result of the annihilation phenomenon, a substance particle and an antiparticle destroy each other, and their entire mass is converted into energy. However, according to real physics , in the process of annihilation, two substance particles with opposite properties form a bound state (a new system, a new object), in which their interaction with the surrounding external substance World is compensated.

As a result, this pair ceases to interact with external substance objects, and, consequently, loses all inertia that could be caused by external fields for each particle separately. And their interaction with each other is internal and also does not create any total inertia. It is clear that it becomes practically impossible to register such a new object, so the illusion is created that as a result of annihilation, the particles simply disappear. Certain external influences, such as intense fluctuations in the gravitonic field medium, known as gamma quanta ( y -quanta), can again break this pair, which is interpreted as the "birth" of particles [6].

5.    Derivation of formulas for energy, momentum, angular momentum, and force in

a gravitonic field for the classical and relativistic cases.

In classical physics, when moving substance objects (systems), the laws of conservation of their energy, momentum, and angular momentum are fulfilled, i.e. these quantities are integrals of the equation of motion in general form. Moreover, the law of conservation of energy determines the uniformity of time, and the laws of conservation of momentum and angular momentum determine the uniformity and isotropy of space, respectively [8, 9].

One of the integrals of the equation of motion of a substance object in a gravitonic field, which determines its energy, is quite simple to obtain. It is necessary to multiply the field equation of motion (3.3) by the velocity V , taking into account the equality V • gradlW g = d^ g /dt :

(v^/c²) • d(W pg • v )^/dt = v • gradW pg = dW_pg^/dt, (5.1) and integrate the resulting expression (5.1). This expression can be written as a complete differential [14]:

d[Wpg • (1 - v2/c2)1/2 ]/dt = 0. (5.2)

Therefore, in the process of motion of any substance object in the gravitonic field, the value in square brackets in the formula (5.2) remains constant, which should be defined as its total energy or simply the energy W [6]:

W = Wpg^ (1 - v2/c2y2 = const. (5.3)

From the analysis of expression (5.3), it can be seen that in real physics , the energy W of a substance object in a graviton field is proportional to the potential energy of interaction of substance object in a graviton field W pg or, in the general case, the field coupling function of substance object W g (r, t) (formula (2.5)).

The energy of a substance object in a gravitonic field cannot be divided into kinetic energy (energy of motion) and potential energy (energy of interaction), because the mass of a substance object depends on the value W pg . In the absence of interactions W pg = 0 , the total energy of the substance object is identically equal to zero, i.e. W = 0 . This once again confirms the conclusion that there are no isolated substance objects in our natural World.

In addition, it follows from formula (5.3) that in the field medium of a gravitonic field, the speed of relative motion of substance objects cannot exceed the speed of propagation of transverse perturbations of the medium itself in the form of electromagnetic waves, i.e., the speed of light

• C . Moreover, the rest point v = 0 corresponds to the minimum absolute value of the potential energy of the interaction W Pg .

An increase in the velocity of a substance object leads to a decrease in the value of the root expression in formula (5.3), and to preserve the value of the energy W , an increase in the absolute value of the potential interaction energy W pg is required. In the field of infinite function values W pg substance object can accelerate to the speed limit C , whereas in the domain of small modulo values of the function W pg , smaller module constants of the energy W , the movement of the substance object may never occur, because of (5.3) it follows that v = c • (1 — W² [W ^g )^1/2 [6].

Taking into account the formula (3.12), the expression (5.3) can be written as:

i

W = (Wgb + Wic) • (1 — v2/c2)2 = const,               (5.4)

where W gb and W i _c are, respectively, the global and local potential energies of the interaction of a substance object with a gravitonic field.

For classical mechanics W gb = const , W gb » W i _c and v « c , so the following decomposition of the radical (1 — v²/C²)¹ / ² ~ 1 — v²/2c² , then the expression (5.4) can be written as:

W ~ (Wgb + Wic) • ( 1 — v2/2c2) = Wgb + Wic — [(Wgb + Wic) • v2 ]/2c2.                (5.5)

Introducing for a substance object the classical inert mass m = — W gb /С²»— (W gb + W l _C )/C² , as well as some classical energy W_c i , which, given that W gb = const , simply shifts the energy level by a constant value:

Wci = W — Wgb = const                      (5.6)

from the formula (5.5), it is easy to get the expression [6]:

Wci = (m • v2 )/2 + Wic = const.                 (5.7)

The separation of energy into kinetic and potential became possible due to the fact that in the classical approximation, the mass of substance objects are due to the global interaction, and the forces are due to local fields. Expression (5.7) also shows that the introduced field coupling function W i _c really coincides with the classical concept of potential energy.

For relativistic mechanics , due to the fact that the velocities of substance objects become sufficiently large, it is impossible to decompose the radical (1 — v²/c²)¹ / ² in a series, but it is necessary to introduce some auxiliary quantity, called the rest mass m₀ , of the substance object and defined by the expression (4.10). Then equation (5.4) can be rewritten in the form [6]:

W = (Wgb + Wic) • (1 — v2/c2)1/2 = —mo • c2 = const (5.8) or

[mo • c2/(1 — v2/c2)2] + Wic = —Wgb = const.         (5.9)

By introducing the relativistic energy W_r i , as well as extracting the kinetic energy by adding to both parts of equation (5.9) the value —m o • c² , we can obtain:

WH = W — Wgb = [mo • c2/(1 — v2/c2)1/2j — mo • c2 + Wlc .(5.10)

For relativistic mechanics taking into account equation (4.8), the kinetic energy W_r ik is determined by the formula:

Wrik = [mo • c2/(1 — v2/c2)2] — mo • c2 = mtot(v) • c2 — mo • c2,

(5.11) which at v « c becomes an expression for the kinetic energy in the classical approximation:

W cik = m o • v^2/2 .                                 (5.12)

The expression for the momentum p of a substance object in a gravitonic field environment directly follows from the field equation of motion (3.6) [6]:

dp/dt = d[(—Wpg/c2) • vj/dt = F,                     (5.13)

P = —WPg^v/c2 = —(Wgb + Wic)^v/c2.             (5.14)

Like energy, the momentum of a substance object characterizes its motion in a gravitonic field, and its physical meaning is that the action of forces on a substance object leads to a change in its momentum. If there are no forces acting on a substance object at all, or the action of all forces is compensated, then the momentum of the substance object is preserved.

For the classical mechanics W gb = const , W gb » W i _c и v « c , and from (5.14) it is easy to get the familiar expression for the momentum of a substance object p_c i :

P ci = m-v .                                             (5.15)

In the relativistic mechanics , the value of the momentum of the substance object p_r i will be, according to the formulas (5.9) and (4.8), equal to:

pri = [mo • c2/(1 — v2/c2)1/2j •(v/c2) = mo • v/(1 — v2/c2)1/2 = mtot(v) • v.                      (5.16)

From expressions (5.3) and (5.14), it is easy to obtain in relativistic mechanics the relationship between the energy and momentum of a substance object in a gravitonic field [6]:

W2 = Wp2g • (1 — v2/c2) = Wp2g • (1 — p2 • c2/Wp2g) = Wp2g — p2

(5.17)

or

W2 + p2 • с2 = Wpg. (5.18)

The expression (5.18) is an analog of the relativistic connection in the special theory of relativity (SRT) [9], which is determined by the equations [17, 18]:

W2 — p2 • с2 = m2 • с4, (5.19) p = vW/с2. (5.20)

But in equations (5.19) – (5.20), according to official (academic) science, the rest mass of a substance object m₀ is considered to be the equivalent of the classical inert mass m [18].

And this, as follows from real physics , which describes the theory of motion of substance objects in a gravitonic field, is not so at all, so we should rewrite the expression (5.19) taking into account the rest mass:

W2 = p2 • с2 + m2 • с4. (5.21)

The comparison of expressions (5.18) and (5.21) clearly shows the difference between the real field and abstract relativistic approaches to the concept of energy. In real physics, based on the gravitonic field, the total energy of a substance object W is a constant that characterizes its motion, which, according to the formula (5.8), can be expressed in terms of the mass of the object at rest W = -m₀ • с² = const . Therefore, the total energy in the field coupling equation (5.18) actually corresponds to the term m 2 • с⁴ in the relativistic equation (5.21).

In the special theory of relativity (SRT), the use of the value m_tot(v) • с² (formula (5.11)) leads to the substitution of two concepts of energy. The kinetic energy of motion begins to be interpreted as the total energy, which increases with the speed of movement of a substance object. In this case, the potential energy, which should compensate for the change in kinetic energy and make the total energy unchanged, generally falls out of sight. This substitution of concepts led to the fact that in SRT, the total energy of a moving substance object turned from a constant that characterizes the movement into a measure of the energy content of the substance object itself [6].

In real physics, according to the formula (5.3), the mass property of a substance object is a consequence of the existence of a gravitonic field medium and is determined by the potential energy that characterizes this medium. In SRT, from the relation W o = m o •с² , it follows that the presence of a certain mass m₀ means the existence of a certain energy W_o .

Thus, there is a basis for replacing mass with energy, and energy with mass, and there is no obvious physical mechanism behind this relationship that causes such a connection. And the logical emptiness just serves as a reason for completely ridiculous interpretations of this relation. For example, the possibility of any energy, even if it is not associated with substance objects, to match a certain mass [6].

In order to obtain the last integral of the equation of motion of a substance object in a gravitonic field – the angular momentum, it is necessary to perform a vector multiplication of the field equation of motion (3.3) by the distance R between the interacting substance objects:

R x d(Wpg -v/c2 )/dt = R x gradWpg,          (5.22)

where X is the sign of the vector product.

The right-hand side of equation (5.22) is zero, because the potential energy in the gravitonic field has the form W pg = const/R (formula (3.1)), and the gradient of this value is co-directed with the vector R . The lefthand side of equation (5.22) can be transformed using the product derivative formula [14]:

R x d(Wpg ■ v/c2 )/dt = d (Wpg ■ R x v/c2 )/dt — dR/dt x (Wpg ■ v/c2) = 0.          (5.23)

The second term in equation (5.23) is zero, because dR/dt = V . As a result, during the movement of substance objects in the gravitonic field, a constant value remains, which is called the angular momentum and is determined by the expression:

M = —(Wpg • R x V)/c2 = — [(Wgb + Wtc) • R x V ]/c2 = R x p = const           (5.24)

If we assume that Wi g = k/R , where к = const , then the law of conservation of angular momentum in the medium of the gravitonic field takes the form:

M = — (k ■ R x v)/R ■ c2) = — (k/c2) ■ eR x v = — (k/c2) ■ vT = const ,               (5.25)

where e_R is the unit vector in the direction R ; v_T is the tangential component of the velocity of the substance object.

Thus, in real physics , the law of conservation of angular momentum in the motion of substance objects in a gravitonic field is transformed into the law of conservation of the rotational velocity v_T of a substance object [6].

For classical mechanics , W gb = const , W g, >> W z _c and v « c , and from (5.24) it is easy to get a familiar expression for the angular momentum of a substance object M_c z :

McZ = m ■ R x v = R x pcZ.                       (5.26)

In relativistic mechanics , the value of the angular momentum M_r z will, according to formulas (5.9) and (4.8), be equal to:

MrZ = [mo/(1 - v^c2)2] • R x V = mtot(v) • R x v = R x prZ.

(5.27)

From formulas (3.5) and (3.7) it is possible to express the force F acting on any substance object from the gravitonic field, not only through the potential energy gradient of the gravitonic field W> S ’ but also through the momentum flux p_g of the gravitonic field:

F = -gradWpa = -VWpg = dpy/dt. (5.28)

In [19], it is proved that the equations (5.28) are valid for any substance objects of our natural World, regardless of the reference systems and coordinate representations. In this case, the plus sign before the gradient symbol reflects the internal force acting from the side of the substance object on the environment of the gravitonic field, and the minus sign is characteristic of the equivalent external force acting from the side of the gravitonic field on the substance object. Equation (5.28) generalizes Newton's second law (expressions (3.7)), applicable to abstract material points, to real substance objects characterized by continuous spatially distributed physical parameters.

From equations (2.10), (3.3), and (5.28) , we can obtain a formula that relates the energy flow of the gravitonic field J y in the selected volume of a substance object to the energy gradient of the gravitonic field in this volume gradW_pa :

d(Wps • v)/dt = dJ5/dt = -c2 • gradW^y. (5.29)

Equations (5.28) and (5.29) are governed by an arbitrarily allocated volume of any substance object of our natural World (any physical system), containing energy of any forms and types. The energy flux density of the gravitonic field (the energy carriers are the quanta of the gravitonic field – gravitons [3]) in the unit volume of a substance object is directed in the direction opposite to the gradient of its density.

6.    Conclusion.

In the framework of real physics, based on the concept of the existence of a gravitonic field in our natural World, all the basic formulas of non-relativistic and relativistic mechanics of substance objects are obtained without the use of Lorentz transformations and special relativity theory.

It is proved that both the force and the mass do not belong to substance objects, but are determined by the dynamic characteristics of the gravitonic field. The force is determined by the change in the energy density of the graviton field medium in space, and the mass is determined by the change in the energy density of the graviton field medium in time.

It is shown that the equivalence of the inert and gravitational mass is not a fundamental principle, since the introduction of any additional local interaction, for example, an electric one, which adds a local field component to the classical inert mass of a real object, destroys equality and even proportionality between the masses.

It is revealed that the rest mass does not characterize the substance particle itself, but only the initial conditions of motion in which the particle participates at the moment, and, therefore, cannot serve as an unambiguous identifier of the observed particles. This requires a serious revision of the entire system of currently known elementary particles.

It is shown that any force in our natural world is caused by the presence of the energy gradient of the gravitational field in the substance object under consideration. In the absence of external influences, a free substance object can be at rest or move uniformly and rectilinearly only when the energy gradient in its entire volume is zero. Any external force acting on a substance object is characterized by its corresponding energy gradient inside this object.

Thus, an arbitrary substance object, both free and under the influence of an external force, moving with acceleration, has in its volume the energy gradient of the gravitonic field corresponding to this acceleration.