Newton’s law of universal gravitation [5] may be expressed as follows:

The gravitational force $F$ between any two particles having masses m₁ and m₂ separated by a distance r is an attraction working along the line joining the particles and has a magnitude

$F=G\cdot \frac{m_1\cdot m_2}{r^2}$

where $G=6.6732\times {10}^{-11}\text{N}\cdot {\text{m}}^2\cdot {\text{kg}}^{-2}$ is a universal constant having the same value for all pairs of particles.

This law expresses the basic fact of gravitation, namely that two masses are interacting “at-a-distance”: they exert forces on one another even though they are not in contact.

According to Newton’s law $F_B$, the force exerted by a particle A, with mass m₁, on a particle B, with mass m, is pointing to the position of A and has a magnitude:

$F_B=\left(G\cdot \frac{m_1}{r^2}\right)\cdot m$

The orientation of this force and the fact that it is directly proportional to the mass of A and inversely proportional to the square of the distance from A to B, implies that particle B must receive information about the presence in space of particle A: particle A must send information to B about its position and about its mass. This conclusion is independent of the position and the mass of B. So we can generalize it and posit that:

A particle manifests itself in space by emitting information about its mass and about its position. We consider that type of information as a substantial element of nature and call it “gravitational information” or “g-information”.

Two-point charges at rest relative to an IRF in vacuum exert an electric force $F$ on one another. Between charges of like sign, this force is repulsive and between charges of unlike sign it is attractive. The precise value of the electric force that one charged particle exerts on another is given by Coulomb’s law [6] :

The magnitude of the electric force $F$ that a particle with charge q₁ exerts on another particle with charge q₂ is directly proportional to the product of their charges and inversely proportional to the square of the distance r between them. The direction of the force is along the line joining the particles.

$F=\frac{1}{4\pi {\epsilon }_0}.\frac{\left|q_1\right|.\left|q_2\right|}{r^2}$

where ${\epsilon }_0=8.85\times {10}^{-12}\text{F}/\text{m}$ is the permittivity constant.

Coulomb’s law expresses the basic fact of electrostatics, namely that two point charges are interacting “at-a-distance”.

According to Coulomb’s law $F_B$, the electric force exerted by a point charge A, with charge q₁, on a point charge B, with charge q, is pointing to the position of A if the signs of the charges are unlike and in the opposite direction if they are like. The magnitude of that force is:

$F_B=\left(\frac{1}{4\pi {\epsilon }_0}\cdot \frac{\left|q_1\right|}{r^2}\right)\cdot \left|q\right|$

The orientation of $F_B$ and the fact that it is directly proportional to the charge of A and inversely proportional to the square of the distance from B to A, implies that particle B must receive information from particle A about its electric charge and about its position. In other words: point charge A must send information to B about its position and about the magnitude and the sign of its charge.

So, we can posit that: a point charge manifests itself in space by emitting information about its charge and about its position. We consider this type of information as a substantial element of nature and call it “electrical information” or “e-information”.

In Figure 4(a) , we consider a particle with rest mass m₀ and (positive) charge q that is moving with constant velocity $v=v\cdot e_z$ along the Z-axis of an IRF O. At the moment t = 0, it passes through the origin O and at the moment t = t through the point P₁. It is evident that:

$O{P}_1=z_{P_1}=v\cdot t$

P is an arbitrary fixed point in O. Its position relative to the moving particle is determined by the time dependent position vector $r=P_{1}P$.

We introduce O', the proper IRF of the particle ( Figure 4(b) ), i.e. the IRF whose origin is anchored to the particle and we assume that t = t' = 0 when its origin O' passes through O. Relative to O', the position of P is determined by the time dependent position vector $r^{\prime }=O^{\prime }P$.

The particle is at rest in O'. So according to §.6, ${E^{\prime }}_g$, its g-field relative to O', is completely defined by the vectoral quantity:

${E^{\prime }}_g=-\frac{\frac{\text{d}N}{\text{d}{t}^{\prime }}\cdot s_g}{4\cdot \pi \cdot {r^{\prime }}^2}\cdot e_{r^{\prime }}$

dN is the number of informatons that during the time interval dt' pass through an elementary surface dS' that in O' is perpendicular to $c$, the velocity of these informatons.

By definition, ${E^{\prime }}_g$ is, relative to O', the density of the g-information flow at P and the magnitude of ${E^{\prime }}_g$ is the rate per unit area at which, relative to O', g-information flows through an elementary surface dS' that at P is perpendicular to the velocity $c$ of the informatons that carry that information.

The Lorentz transformation equations [8] provide the key for the mathematical deduction of $E_g$, the g-field at P relative to O, from ${E^{\prime }}_g$, the g-field relative to O'. In §3 of [9] one can find the detailed calculations. They lead to the following result:

$E_g=-\frac{m_0}{4\pi {\eta }_0{r}^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot r=-\frac{m_0}{4\pi {\eta }_0{r}^2}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot e_r$ (6)

It is evident that one, in an analogous manner, can deduce $E$, the electric field at P relative to O, from $E^{\prime }$, the electric field at that point relative to O'.

As earlier mentioned this implies the substitution of the factor ( $-\frac{m_0}{{\eta }_0}$) in formula (6) by the factor ( $\frac{q}{{\epsilon }_0}$). Thus:

$E=\frac{q}{4\pi {\epsilon }_0{r}^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot r=\frac{q}{4\pi {\epsilon }_0{r}^2}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot e_r$ (7)

We conclude: An (electrically charged) mass particle describing a uniform rectilinear movement relative to an inertial reference frame O, creates in the space linked to that frame a time dependent gravitational (electric) field.

1) $E_g$, the g-field at an arbitrary point P, points at any moment to the actual position of the particle2 and its magnitude is:

$E_g=\frac{m_0}{4\pi {\eta }_0{r}^2}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}$

2) If the charge of the particle is negative, $E$, the e-field at P, also points at any moment to the actual position of the particle. If it is positive, $E$ points in the opposite direction. The magnitude of $E$ is:

$E=\frac{\left|q\right|}{4\pi {\epsilon }_0{r}^2}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}$

If the speed of the particle is much smaller than the speed of light, the expressions (6) and (7) reduce to that valid in the case of a particle at rest. This non-relativistic result could directly be obtained if one assumes that the displacement of the mass particle during the time interval that the informatons need to move from the emitter to P can be neglected compared to the distance they travel during that period.

Finally let us note that the fact that the rate at which g- (e-information) that escapes from an enclosed space is completely determined by the rate at which it is generated inside that space (conservation of g/e-information) can be expressed as:

${\displaystyle ∯E_g\cdot \text{d}S}=-\frac{m_0}{{\eta }_0}\text{and}{\displaystyle ∯E\cdot \text{d}S}=\frac{q}{{\epsilon }_0}$

We refer to the situation of §10 ( Figure 3 ). Applying the sine-rule to the triangle P₀P₁P, we obtain:

$\frac{\sin \left(\Delta \theta \right)}{v\cdot \Delta t}=\frac{\sin \theta }{c\cdot \Delta t}$

From which it follows:

$s_{\beta }=s_g\cdot \frac{v}{c}\cdot \sin \theta \text{and}{s}_b=s_e\cdot \frac{v}{c}\cdot \sin \theta$

Thus, taking into account the orientation of the different vectors, the β/b-index of an informaton emitted by an electrically charged point mass moving with constant velocity, can also be expressed as:

$s_{\beta }=\frac{v\times s_g}{c}\text{and}{s}_b=\frac{v\times s_e}{c}$

From the general definitions in §11 of $B_g$ and $B$ it follows that in the particular case of an electrically charged particle moving with constant velocity $v$:

$B_g=\frac{v}{c^2}\times \left(N\cdot s_g\right)=\frac{v\times E_g}{c^2}\text{and}B=\frac{v}{c^2}\times \left(N\cdot s_e\right)=\frac{v\times E}{c^2}$

Taking (6) and (7) into account, we become the β- and the b-induction at P:

$B_g=\frac{{\nu }_0\cdot m_0}{4\pi r^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot \left(r\times v\right)$ (8)

$B=\frac{{\mu }_0\cdot q}{4\pi r^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot \left(v\times r\right)$ (9)

With: ${\nu }_0=\frac{1}{c^2\cdot {\eta }_0}=9.34\times {10}^{-27}\text{m}\cdot {\text{kg}}^{-1}$ and ${\mu }_0=\frac{1}{c^2\cdot {\epsilon }_0}=1.26\times {10}^{-6}\text{H}/\text{m}$

We conclude: An (electrically charged) mass particle describing a uniform rectilinear movement relative to an IRF O, creates in the space linked to that frame a time dependent gravitomagnetic (magnetic) induction field characterized by (8) [(9)], the β-induction (the b-induction).

1) The orientation of $B_g$, the β- or gravitomagnetic induction at an arbitrary point P, is determined by the orientation of the vectoral product $\left(r\times v\right)$ and the magnitude is:

$B_g=\frac{{\nu }_0\cdot m_0}{4\pi r^2}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot v\cdot \sin \theta$

2) If the charge of the particle is negative, the orientation of $B$, the b- or magnetic induction at P, is also at any moment determined by the orientation of the vectoral product $\left(r\times v\right)$. If it is positive, $B$ points in the opposite direction. The magnitude of $B$ is:

$B=\frac{{\mu }_0\cdot \left|q\right|}{4\pi r^2}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot v\cdot \sin \theta$

If the speed of the mass is much smaller than the speed of light, the expressions for the gravitomagnetic and magnetic induction reduce to:

$B_g=\frac{{\nu }_0\cdot m_0}{4\pi r^3}\cdot \left(r\times v\right)\text{and}B=\frac{{\mu }_0.q}{4\pi r^3}\cdot \left(v\times r\right)$

This non-relativistic results (Biot-Savart law) could directly be obtained if one assumes that the displacement of the point mass during the time interval that the informatons need to move from the emitter to P can be neglected compared to the distance they travel during that period.

Finally from the fact that $s_{\beta }$ ( $s_b$) is always perpendicular to both $c$ and $s_g$ ( $s_e$) it follows that:

${\displaystyle ∯B_g\cdot \text{d}S}=0\text{and}{\displaystyle ∯B\cdot \text{d}S}=0$

An electrically charged particle with rest mass m₀ and charge q, moving with constant velocity $v=v\cdot e_z$ along the Z-axis of an IRF, creates and maintains an expanding cloud of informatons that are carriers of g-/β- and e-/b-information.

1) Focusing on the g-/β-information, that cloud manifests itself as a time dependent continuum: the gravitoelectromagnetic field (GEM-field) of the particle. It is characterized by two time dependent vectoral quantities: the “gravitational field” (short: g-field) $E_g$ and the “gravitomagnetic induction” (short: β-induction) $B_g$. With N and n respectively the density of the flow and the density of the cloud of informatons at an arbitrary point P:

$E_g=N\cdot s_g=-\frac{m_0}{4\pi {\eta }_0{r}^3}.\frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot r$

$B_g=n\cdot s_{\beta }=\frac{{\nu }_0\cdot m_0}{4\pi r^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot \left(r\times v\right)$

If $v\ll c$, these expressions reduce to:

$E_g=-\frac{m_0}{4\pi {\eta }_0{r}^3}\cdot r\text{and}{B}_g=\frac{{\nu }_0\cdot m_0}{4\pi r^3}\cdot \left(r\times v\right)$

2) Focusing on the e-/b-information, that cloud manifests itself as a another time dependent continuum: the electromagnetic field (EM-field) of the particle. It is, just like the GEM-field characterized by two time dependent vectoral quantities: the “electric field” (short: e-field) $E$ and the “magnetic induction” (short: b-induction) $B_g$:

$E=N\cdot s_e=\frac{q}{4\pi {\epsilon }_0{r}^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot r$

$B=n\cdot s_b=\frac{{\mu }_0\cdot q}{4\pi r^3}\cdot \frac{1-{\beta }^2}{{\left(1-{\beta }^2\cdot {\sin }^2\theta \right)}^{\frac{3}{2}}}\cdot \left(v\times r\right)$

If $v\ll c$, these expressions reduce to:

$E=\frac{q}{4\pi {\epsilon }_0{r}^3}\cdot r\text{and}B=\frac{{\mu }_0\cdot q}{4\pi r^3}\cdot \left(v\times r\right)$

Let us notice that the role played by the factor ( $-{\nu }_0\cdot m_0$) in the definition of $B_g$ is taken over by the factor ( ${\mu }_0\cdot q$) in the definition of $B$.

One can verify that:

1) $div{E}_{\left(g\right)}=0$

2) $div{B}_{\left(g\right)}=0$

3) $rot{E}_{\left(g\right)}=-\frac{\partial B_{\left(g\right)}}{\partial t}$

4) $rot{B}_{\left(g\right)}=\frac{1}{c^2}\cdot \frac{\partial E_{\left(g\right)}}{\partial t}$

These relations are the laws of Maxwell-Heaviside.

We consider a set of particles with rest masses $m_1,\cdots ,m_i,\cdots ,m_n$ and electric charges $q_1,\cdots ,q_i,\cdots ,q_n$ that move with constant velocities $v_1,\cdots ,v_i,\cdots ,v_n$ relative to an IRF O. It creates and maintains a GEM and an EM field that in O at each point is characterized by the vector pair ( $E_g,B_g$), respectively ( $E,B$).

1) Each particle continuously emits g- (e-)information and contributes with an amount $E_{gi}$ ( $E_i$) to the g- (e)-field at an arbitrary point P. As in §8 we conclude that the effective g- (e-)field $E_g$ ( $E$) at P is:

$E_g={\displaystyle \sum E_{gi}}\text{and}E={\displaystyle \sum E_i}$

2) Because it is moving, each particle emits also β- (b-)information, contributing to the β- (b-)induction at P with an amount $B_{gi}$ ( $B_i$). It is evident that the β–information in the volume element dV at P at each moment t is:

${\displaystyle \sum \left(B_{\left(g\right)i}\cdot \text{d}V\right)}=\left({\displaystyle \sum B_{\left(g\right)i}}\right)\cdot \text{d}V$

Thus, the effective β- (b-)induction $B_{\left(g\right)}$ at P is:

$B_g={\displaystyle \sum B_{gi}}\text{and}B={\displaystyle \sum B_i}$

On the basis of the superposition principle we can conclude that the laws of Maxwell-Heaviside mentioned in §13, a remain valid in the case of the gravitational field of a set of particles describing uniform rectilinear motions.

The term “stationary flow” refers to the movement of an, either or not electrically charged, homogeneous and incompressible fluid that, in an invariable way, flows relative to an IRF. The intensity of a mass flow (charge flow) at an arbitrary point P is characterized by the flow density $J_G$ ( $J_E$). The magnitude of this vectoral quantity at P equals the rate per unit area at which the mass (charge) flows through a surface element that is perpendicular to the flow at P. The orientation of $J_G$ ( $J_E$) corresponds to the direction of that flow. So, the rate at which the flow transports, in the positive sense (defined by the orientation of the surface vectors $\text{d}S$), mass (charge) through an arbitrary surface ΔS, is:

$i_G={\displaystyle {\iint }_{\Delta S}{J}_G\cdot \text{d}S}\text{and}{i}_E={\displaystyle {\iint }_{\Delta S}{J}_E\cdot \text{d}S}$

$i_{G/E}$ is the intensity of the mass/charge flow through ΔS.

Since a stationary mass (charge) flow is the macroscopic manifestation of moving mass (charge) elements ${\rho }_G\cdot \text{d}V$ ( ${\rho }_E\cdot \text{d}V$), it creates and maintains a GEM- (EM-) field. And since the velocity $v$ of the mass (charge) element at a certain point is time independent, the GEM- (EM-) field of a stationary mass flow will be time independent. It is evident that the rules for a static g-(e-)-field (§9) also apply for this time independent g-(e-)field:

1) $div{E}_g=-\frac{{\rho }_G}{{\eta }_0}$ and $divE=\frac{{\rho }_E}{{\epsilon }_0}$.

2) $rot{E}_g=rotE=0$ what implies: $E_{\left(g\right)}=-grad{V}_{\left(g\right)}$.

It can be proven that the rules for the time independent g- (e-)induction are:

1) $div{B}_g=0$ what implies the existence of a gravitational vector potential function $A_g$ for which $B_g=rot{A}_g$.

2) $rot{B}_g=-{\nu }_0\cdot J_G$ and $rotB={\nu }_0\cdot J_E$.

In this context let us also note that an electric current-carrying conductor is the source of an EM-field that only consists of the magnetic field that is generated by the flow of the conduction electrons. Because a current-carrying conductor is an electrically neutral structure, at an arbitrary point in its vicinity the e-field generated by the negative conduction electrons is equal and opposite to the e-field generated by the positive lattice of the conductor.

We consider a set of mass particles anchored in an IRF O. They create and maintain a gravitational field that at each point of the space linked to O is completely determined by the vector $E_g$. Each particle is “immersed” in a cloud of g-information. At every point, except at its own position, each particle contributes to the construction of that cloud.

Let us consider the particle with rest mass m₀ anchored at P. If the other particles were not there, then m₀ would be at the center of a perfectly spherical cloud of g-information. In reality this is not the case: the emission of g-information by the other particles is responsible for the disturbance of that “characteristic symmetry” of the proper g-field of m₀. Because $E_g$ at P is the density of the flow of g-information send to P by the other particles, it is a measure for the extent to which the characteristic symmetry of the proper g-field of m₀ at P is disturbed.

If it was free to move, the particle could restore the characteristic symmetry of the g-information cloud in its immediate vicinity by accelerating with an amount $a=E_g$. Indeed, accelerating this way has the effect that the extern field disappears in the origin of the reference frame anchored to m₀. In other words, if it accelerates with an amount $a=E_g$, m₀ would become “blind” for the g-information send to its immediate vicinity by the other particles, it would only “see” its proper spherical g-information cloud.

So, from the point of view of a particle at rest at a point P in a gravitational field $E_g$, the characteristic symmetry of the g-information cloud in its immediate vicinity is conserved if it accelerates with an amount $a=E_g$. A particle that is anchored in a gravitational field cannot accelerate. In that case, it tends to move.

The insight is expressed in the following postulate:

A particle anchored at a point in a gravitational field is subjected to a tendency to move in the direction defined by $E_g$, the g-field at that point. Once the anchorage is broken, the particle acquires an acceleration $a$ that equals $E_g$.

If the particles under consideration are electrically charged, they create in addition an electric field $E$ in the space linked to O. The particle with charge q anchored at P reacts on the disturbance by $E$ of the characteristic symmetry of its proper e-field in the same way as it reacts on the disturbance by $E_g$ of the symmetry of its proper g-field: it tends to accelerate with the aim to become blind for the e-field created by the other particles. This insight is expressed in the following postulate:

A particle with rest mass m₀ and electrical charge q anchored at a point in an electric field is subjected to a tendency to move in the direction defined by $E$, the e-field at that point. Once the anchorage is broken, the particle acquires a vectoral acceleration $a$ that equals $\frac{q}{m_0}E$.

A particle with rest mass m₀, anchored at a point P in a gravitational field, experiences an action because of that field, an action that is compensated by the anchorage.

1) That action is proportional to the extent to which the characteristic symmetry of the proper gravitational field of m₀ in the immediate vicinity of P is disturbed by the extern g-field, thus to $E_g$ at P.

2) It depends also on the magnitude of m₀. Indeed, the g-information cloud created and maintained by m₀ is more compact as m₀ is greater. That implies that the disturbing effect on the characteristic symmetry around m₀ by the extern g-field $E_g$ is smaller when m₀ is greater. Thus, to impose the acceleration $a=E_g$, the action of the gravitational field on m₀ must be greater as m₀ is greater.

We can conclude that the action that tends to accelerate a particle anchored in a gravitational field must be proportional to $E_g$, the g-field to which the particle is exposed, and to m₀, the rest mass of the particle. We represent that action by $F_G$ and we call this vectoral quantity “the force developed by the g-field on the particle” or the gravitational force. We define it as follows:

$F_G=m_0\cdot E_g$ (10)

If an electrically charged particle is anchored in an electric field $E$, it is, for similar reasons as in the case of gravitation, subject to an additional action that proportional is to the e-field $E$ and to q, the charge of the particle. That action is represented by $F_E$. It is “the force developed by the e-field on the particle” or the electric force. It is defined as:

$F_E=q\cdot E$ (11)

From (10) and (11) it follows:

$E_g=\frac{F_G}{m_0}\text{and}E=\frac{F_E}{q}$

So, according to the conclusions of §14.a, the acceleration $a$ imposed to a mass particle by a gravitational or an electric force $F$ is:

$a=\frac{F}{m_0}$

As shown in [9] Newton’s law of universal gravitation can be easily derived from what precedes and the same applies to the law of Coulomb.

Finally, let us compare the magnitude F_E of the electric force and the magnitude of the gravitational force F_G between two identical mass particles with rest mass m₀ and charge q:

$\frac{F_E}{F_G}=\frac{{\eta }_0}{{\epsilon }_0}\cdot {\left(\frac{q}{m_0}\right)}^2=1.34\times {10}^{20}\cdot {\left(\frac{q}{m_0}\right)}^2$

In the concrete case of two spheres with a mass of 1 kg and charged with 1 μC this means that the electric force is 1.34 × 10⁸ times bigger than the gravitational force, what implies that F_G is masked by F_E.

We consider a number of mass particles moving relative to an IRF O. They create and maintain a GEM field that at each point of the space linked to O is defined by the vectors $E_g$ and $B_g$. Each particle is “immersed” in a cloud of informatons carrying both g- and β-information. At each point, except at its own position, each particle contributes to the construction of that cloud.

Let us consider the particle with rest mass m₀ that, at the moment t, goes with velocity $v$ through the point P.

1) If the other particles were not there ${E^{\prime }}_g$, the g-field in the immediate vicinity of m₀, would, according to §12.a, be symmetric relative to the carrier line of the velocity $v$ of m₀. In reality that symmetry is disturbed by the g-information that the other particles send to P. $E_g$, the instantaneous value of the g-field at P, is a measure for the extent to which this occurs.

2) If the other particles were not there ${B^{\prime }}_g$, the β-induction in the immediate vicinity of m₀, would, according to §12.b, “rotate” around the carrier line of the vector $v$. This implies that the pseudo-gravitational-field ${E^{″}}_g=v\times {B^{\prime }}_g$ defined by the vector product of $v$ with the β-induction that characterizes the proper β-field of m₀, would also be symmetric relative to that carrier line. In reality, this symmetry is disturbed by the β-information send to P by the other particles. The vector product $\left(v\times B_g\right)$ is a measure for the extent to which this occurs.

So, the characteristic symmetry of the cloud of g-/β-information around a moving particle (the proper GEM field) is in the immediate vicinity of that particle disturbed by $E_g$ regarding the proper g-field and by ( $v\times B_g$) regarding the proper β-induction.

If it is free to move, the particle m₀ could restore the characteristic symmetry in its immediate vicinity by accelerating, relative to its proper IRF O', with an amount $a^{\prime }=E_g+\left(v\times B_g\right)$. In that manner, it would become “blind” for the disturbance of the symmetry of its proper GEM field in its direct vicinity.

These insights form the basis of the following postulate.

A particle with rest mass m₀, moving with velocity $v$ in a GEM-field ( $E_g,B_g$), tends to become blind for the influence of that field on the symmetry of its proper GEM-field. If it is free to move, it will acquire an acceleration $a^{\prime }$ relative to its

proper IRF that equals $E_g+\left(v\times B_g\right)$.

If the particles under consideration are electrically charged, they create in addition an EM field in the space linked to O. The particle with charge q that, at the moment t, goes through P with velocity $v$, reacts on the disturbance of the characteristic symmetry of its proper EM-field in the same way as it reacts on the disturbance of the symmetry of its proper GEM-field: it accelerates with the aim to become blind for the EM-field created by the other particles. This insight is expressed in the following postulate:

A particle with charge q, moving with velocity $v$ in an EM-field ( $E,B$) tends to become blind for the influence of that field on the symmetry of its proper EM field. If it is free to move, it will acquire an acceleration $a^{\prime }$ relative to its proper IRF that equals $\frac{q}{m_0}\cdot \left[E+\left(v\times B\right)\right]$.

The action of the GEM field ( $E_g,B_g$) [the EM field ( $E,B$)] on a particle with rest mass m₀ and charge q that is moving with velocity $v$ relative to the IRF O is called the gravitational force $F_G$ [the electromagnetic force or Lorentzforce $F_{EM}$] on that particle. In extension of §14.b we define $F_G$ and $F_{EM}$ as:

$F_G=m_0\cdot \left[E_g+\left(v\times B_g\right)\right]\text{and}{F}_{EM}=q\cdot \left[E+\left(v\times B\right)\right]$

According §15.a, if it is free to move the effect of $F_G$ ( $F_{EM}$) on that particle is that it will be accelerated relative to its proper IRF O' with an amount $a^{\prime }$:

$a^{\prime }=E_g+\left(v\times B_g\right)\text{and}{a}^{\prime }=\frac{q}{m_0}\cdot \left[E+\left(v\times B\right)\right]$

Using the appropriate transformation formulas [8] , $a^{\prime }$, the acceleration relative to its proper IRF O', can be expressed in function of the characteristics of the motion of the particle relative to IRF O. In §10 of [9] it is shown that:

$a^{\prime }=\frac{\text{d}}{\text{d}t}\left[\frac{v}{\sqrt{1-{\beta }^2}}\right]\text{with}\beta =\frac{v}{c}$

We can conclude that the effect on the movement of the particle on as well $F_G$ as $F_{EM}$ is described by:

$F=\frac{\text{d}p}{\text{d}t}\text{with}p=m\cdot v$

$p$ is the linear momentum of the particle relative to the IRF O. It depends on its relativistic mass m:

$m=\frac{m_0}{\sqrt{1-{\beta }^2}}$

In §2 of [9] it is shown that m determines the rate at which the particle emits informatons when the time is read on the clock of its proper IRF. The relativistic mass m of a particle is a measure for its inertia i.e. its resistance to changes in its state of motion, while its rest mass m₀ is a measure for its power to gravitate.

Two particles with rest masses m₁ and m₂ ( Figure 5 ) are anchored in the IRF O' that is moving relative to IRF O with constant velocity $v=v\cdot {\bar{e}}_z$.

According to §13.a, the components of the gravitational field created and maintained by m₁ at the position of m₂ are, in magnitude, determined by:

$\begin{array}{l}{E}_{g2}=\frac{m_1}{4\pi {\eta }_0{R}^2}\cdot \frac{1}{\sqrt{1-{\beta }^2}}\\ B_{g2}=\frac{m_1}{4\pi {\eta }_0{R}^2}\cdot \frac{1}{\sqrt{1-{\beta }^2}}\cdot \frac{v}{c^2}\end{array}$

$E_{g2}$ points to the position of m₁ and $B_{g2}$ points in the direction of the X-axis.

And according to the force law $F_{12}$, the magnitude of the force exerted by the gravitational field ( $E_{g2},B_{g2}$) on m₂, this is the attraction force of m₁ on m₂ is:

$F_{12}=m_2\cdot \left(E_{g2}-v\cdot B_{g2}\right)$

After substitution:

$F_{12}=\frac{1}{4\pi {\eta }_0}\cdot \frac{m_1{m}_2}{R^2}\cdot \sqrt{1-{\beta }^2}={F^{\prime }}_{12}\cdot \sqrt{1-{\beta }^2}$

with

${F^{\prime }}_{12}=\frac{1}{4\pi {\eta }_0}\cdot \frac{m_1{m}_2}{R^2}$

the magnitude of the force that m₁, according Newtons universal law of gravitation, in the IRF O', where both particles are at rest, exerts on m₂.

In the same way, we find:

$F_{21}=\frac{1}{4\pi {\eta }_0}\cdot \frac{m_1{m}_2}{R^2}\cdot \sqrt{1-{\beta }^2}={F^{\prime }}_{12}\cdot \sqrt{1-{\beta }^2}$

We conclude that the moving masses attract each other with a force:

$F=F_{12}=F_{21}=F^{\prime }\cdot \sqrt{1-{\beta }^2}$

This result perfectly agrees with that based on S.R.T. Indeed, relative to O' the particles are at rest. According to Newton’s law of universal gravitation, they exert on each other equal but opposite forces:

$F^{\prime }={F^{\prime }}_{12}={F^{\prime }}_{21}=\frac{1}{4\cdot \pi \cdot {\eta }_0}\cdot \frac{m_1\cdot m_2}{R^2}$

Relative to O both masses are moving with constant speed $v$ in the direction of the Z-axis. From the transformation equations between an inertial frame O and another inertial frame O', in which a point mass experiencing a force F' is instantaneously at rest, we can immediately deduce the force F that the point masses exert on each other in O [8] :

$F=F_{12}=F_{21}=F^{\prime }\cdot \sqrt{1-{\left(\frac{v}{c}\right)}^2}=F^{\prime }\cdot \sqrt{1-{\beta }^2}$

If the particles under consideration are electrically charged, there is in addition an EM force. A reasoning analogous to the preceding shows the magnitude of the force that two mass particles with charges q₁ and q₂ exert on one another is:

$F_{12}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{\left|q_1\right|\cdot \left|q_2\right|}{R^2}\cdot \sqrt{1-{\beta }^2}={F^{\prime }}_{12}\cdot \sqrt{1-{\beta }^2}$

with ${F^{\prime }}_{12}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{\left|q_1\right|\cdot \left|q_2\right|}{R^2}$ the “Coulomb force”. Between charges of like sign these force is repulsive and between charges of unlike sign it is attractive.

From the above we can conclude that the component of the gravitational (electromagnetic) force due to the β- (b-) induction is β-times smaller than that due to the g- (e-)field. This implies that, for speeds much smaller than the speed of light, the effects of the β/b-information are masked. This is not the case for EM fields generated by an electric current-carrying conductor where the source of the field is the flow of (negative) conduction electrons that are moving in a fixed positive lattice. Because the conductor as such is an electrically neutral structure, at an arbitrary point in its vicinity the e-field generated by the negative conduction electrons is equal and opposite to the e-field generated by the positive lattice what implies that there is only a magnetic induction field.

Finally, we mention that it can be shown that the β-information emitted by moving gravitating objects is responsible for deviations (as the advance of Mercury Perihelion) of the real orbits of planets with respect to these predicted by the classical theory of gravitation [10] .