Connection between Gravity and Electromagnetism

Abstract A theoretical framework is presented which connect the electro-magnetic field with gravity considering the vacuum as a gravitational aether. The space and time are treated as imaginary and independent concepts. The aim is to explain electrodynamics and gravitational phenomena independent by the space-time system and also to better understand the cause of gravitational attraction.


Introduction
The electromagnetic eld theory initiated by Faraday and Maxwell presume that a special medium called luminiferous aether is the bearer of electric and magnetic elds, aether which was considered at absolute rest in the entire universe. This model of aether and some variants of it were in contradiction with many observed phenomena involving interpretation of electrodynamics in the conditions of relative motion. All this problems open the way to the special relativity which not need any aether, at least at rst sight. But as a result, the new entity formed, the space-time continuum, start to have physical characteristics and consequently can be considered a new form of aether, especially in general relativity and quantum theory where this materialization of space-time continuum became more obvious. In fact a form of space-time aether has been created, which is always at rest relative to any arbitrary chosen reference frame. The problem with this space-time continuum is that it blend the abstract and arbitrary relative concepts of space and time with physical and localized elements like the gravitational eld and mass. This lead to a dicult and contra-intuitive way to view the physical universe. A better and more natural approach is to construct a theory of vacuum independent by the space-time system. From a macroscopic viewpoint the vacuum have physical properties including electromagnetic properties, so is logical to assume that the vacuum is not empty but is a medium, being an alternative name for the gravitational aether.
The space and time are abstract concepts, this mean that they are only the product of our imagination not a real entity, used as a helper system.
In consequence we can imagine them however we want, but completely independent by the physical phenomena. In this article we will use a Galilean system, where velocity is relative, not necessary to the reference frame. This relative velocity can be expressed with respect to the reference frame, when is arbitrary relative, or can be expressed with respect to physical entities when is no longer arbitrary relative. In the case of Newtonian dynamics of which equations are dependent only by accelerations, is possible to use any relative velocity with respect to an inertial frame, however this is only a peculiar case, its rise at the level of fundamental principle of physics (the principle of relativity) is not a necessity. As an example, the friction force experienced by an object which move trough air is dependent by velocity between object and air, air in this case represent the physical entity to which the velocity from friction force expression is relative. Now this is so clear and simple because we can understand and imagine easily the concept of air and its inuence. The case of electromagnetic eld is similar to the previous example, but the place of physical entity is taken by aether. The electromagnetic eld is immobile in the gravitational aether, as was in luminiferous aether and space-time continuum. Consequently the gravitational aether is also the reference for the speed of electromagnetic eld propagation due to electromagnetic eld immobility relative to it.

Gravitational Aether
The most simple and direct explanation for bending of light by gravity, knowing that the light is an electromagnetic wave, can be make if we assume that the gravitational potential change the properties of vacuum, which will produce a gravitational refraction of light. This also will have many other implications like the change of the speed of light and a new way to explain how gravitational attraction appear.
In absence of any ponderable matter the aether will be homogeneous distributed in space, having everywhere the same positive value of gravitational potential which is the aether background gravitational potential. Now if ponderable matter, characterized by its heavy mass, is present in space, it modify the local gravitational potential of aether in accordance with Poisson type equation of gravity where G gravitational constant, ρ m mass density. Assuming a spherical mass distribution (M ) we can express gravitational potential at a distance (R) from the center of mass and outside of it, as follow where Γ 0 background gravitational potential in absence of mass. As we observe, the gravitational potential of aether decrease in vicinity of masses and this in turn modify its electromagnetic properties. The electromagnetic properties of aether are not universal constants but are dependent by local gravitational potential. The electric permittivity of aether depend by gravitational potential as follow where κ and f 1 are undetermined constant and function. The permittivity must increase with proximity to heavy masses, in order to explain the gravitational refraction and the gravitational force. The magnetic permeability must depend by the gravitational potential in a manner similar of permittivity. To account this we consider an electromagnetic wave propagating through the vicinity of a heavy cosmic body, wave direction is deected due to electromagnetic properties variation (gravitational refraction) but suer no reections to disperse some of its energy, because such a phenomenon have been observed on sky (light reections around heavy bodies). Consequently we can assume that electromagnetic waves do not suer reections when traversing zones with dierent aether properties, which can happen only if aether impedance is an universal constant.
As a result the electric permittivity and magnetic permeability become higher and the propagation speed of electromagnetic eld become lower in zones with lower gravitational potential. For determination of constant and function from (3) we will use the equality between inertial and heavy mass, but rst we must express the electromagnetic force due to permittivity variations.

Gravitational Force
One result of electromagnetic properties spatial variation is the gravitational force. Let consider a small electric charge characterized only by its charge q distributed on the surface of a sphere with radius b, at rest sitting at a distance R from a heavy mass M. The gravitational potential of aether decrease toward the center of mass as described by (2) The energy of electric eld decrease when the charge approach the heavy mass due to increase of ε 0 , the lost energy is converted into work of a force which is the gravitational attraction force. Because neutral bodies are composed from atoms which have internal electric elds result that they are attracted too, actually all bodies which have internal electromagnetic energy experience this attractive force in zones with spatial variable aether properties.
Because permittivity is no longer equal around the outer area of sphere, the charged sphere surface no longer have a constant electric potential and tangential components of electric eld appear. Supposing that electrical charge can move freely on spherical surface, this charge will redistribute over the surface until the surface electric potential will be constant, the electric eld becoming again normal on surface. But the charge density is no longer uniform over the surface of sphere, being denser where permittivity is higher and gravitational potential lower. Because the electric eld is the same over the surface, a net attraction force appear, fueled by the decreasing electric eld energy, representing the gravitational force. When charged sphere go down to lower gravitational potential areas, the outside oriented electric forces over the sphere surface decrease and the inside oriented forces that hold charged surface in equilibrium also must decrease, consequently the gravitational potential must have inuence over this forces and over the radius of charged sphere too. In order to obtain the expected expression for the gravitational force, the charge radius (b) must increase with the decrease of gravitational potential as follow b = α · f 2 (Γ) (7) where α and f 2 are the second undetermined constant and function. To resolve this we consider the charge at rest and make use of the observed fact that inertial mass and heavy mass are equal (not say equivalent because their are the eect of dierent phenomena). Replacing permittivity and radius in The gravitational force where e R is the versor of R = R · e R , and m h0 is the rest heavy mass of charge q. The only way to satisfy (9) is that with which will result and the heavy mass At rest the inertial mass depend only by charge electric eld energy and must be as follow To satisfy the equality m i0 = m h0 , one condition is that inertial mass must be independent of gravitational potential, which lead to f 1 (Γ) = f 2 (Γ) and considering (10) result Also we have the equality the inertial and heavy rest mass become Taking into account (16) and (14), we can write permittivity, permeability and speed of light as follow From equation (20) result that local gravitational potential equal the square of local speed of light.
Above was expressed the electrical part of gravitational force at rest. At near to rest approximation the magnetic eld energy alone have no contribution to gravitational forces. To account for this we can express the magnetic eld energy of a moving charged sphere relative to local aether with a low velocity. The magnetic eld energy produced by this movement is which is independent by gravitational potential. However we use here near to rest approximation for simplicity, we will show later that, when propagation eects are taken into account, the gravitational force, heavy and inertial mass are the eect of the total electromagnetic energy.
From previously described mechanisms, result that gravitational force is not powered by some gravitational eld energy, which not exist, but by body internal electromagnetic energy. The body internal electromagnetic energy also contribute to the phenomenon of inertia. This lead to the possibility that the entire concept of mass may be of electromagnetic nature. Other forms of elementary energy may exist but these may or may not contribute to the eects linked with the concept of mass.

Atomic Radius variation
Because the permittivity change with gravitational potential, this in turn will lead to the change of atomic radius and the dimensions of bodies. The radius of an electron orbit around the nucleus is given by the equilibrium between nucleus attraction force and centrifugal inertial force of electron over itself.
Of course quantum eects have an important inuence at a such small scale.
Let consider for simplicity the Bohr model of atom, the electron orbit radius where Z is the atomic number and Z 0 aether impedance. The m e0 is the rest mass of electron and is independent by gravitational potential for low velocities compared with c. The radius of atom vary with the gravitational potential in a similar way than the radius of our sphere of charge considered previously. The atomic radius and dimensions of bodies increase in lower gravitational potentials.

Entrainment of Aether
One important problem related with the gravitational aether is its movement state. In absence of any ponderable matter, the homogeneous dis- How accelerated movement of masses aect the aether entrainment is another open question, the aether will be entrained with accelerated movement or will suer time variations of its potential.
The aether entrainment is inuenced by direction and magnitude of gravitational acceleration, higher the inuence of a body to the gravitational acceleration in one point, lower the movement of aether from that point relative to body, higher the entrainment exerted by that body. Following we will analyze two simple cases of particular interest.
First is the case of a massive body (like a star or planet) far away from other massive bodies, which impose the value of g-acceleration in its vicinity, other bodies having only negligible inuence because of their very low mass or very large distances. In this case the aether is, with a negligible error, total entrained by this massive body. Very small objects with negligible inuence over g-acceleration, moving in proximity of it, will experience an aether wind due to their own movement relative to the massive body.
Second case is that of rotation of a massive body around an axis of symmetry. In this case the rotational movement produce no modication over the gravitational potential in its proximity because the moving is along an equipotential surface, consequently the aether remain unaected. As a result, this body itself and any object that rotate with it experience an aether wind due to body rotation around its own axis. However the rotation is an accelerated motion and because of this the aether around the rotating body may suer some inuences due to this acceleration.
The consequence of aether entrainment over electromagnetic eld which is immobile relative to aether, consist in the advection of the eld by the aether, leading to induction of new eld components.

Electromagnetic Field and Aether
The where u is the velocity between aether and the inductive eld frame. Similarly, but using condition (28), the equation (31) can be expressed in local form as follow where v is the velocity of charge relative to aether and u is the velocity between aether and the inductive eld frame. Regardless of how is eld mathematically expressed, the native state (physical state) of the eld is always that of the frame of local aether. Consequently the physical cause which induce the elds, due to movement through aether, is represented by time variations of elds produced by eld advection. However is very common in analysis of many electrodynamics problems to express the eld in the frame of its source which may not coincide with that of aether, in these cases we must include u velocity components from induction equations.
The electromagnetic force represent the measure of electromagnetic energy exchange associated with a system, with the change of system position.
In this case the electromagnetic force can be expressed as where U em is the electromagnetic energy of system and r is the position of system. While the energetic derivation of electromagnetic force can be a very handy method in some cases, in other cases is more useful to express the electromagnetic force by eld-charge interaction. The force that act over a small electric charge q in an electromagnetic eld is where v is the velocity between charge and aether, magnetic eld being immobile in aether. We have two components, one produced by electric eld and one produced by the presence of magnetic eld also known as Lorentz and magnetic eld where θ is the angle between the direction of movement and the direction of position vector. The spherical charge at rest, in movement must change the shape until tangential forces (electric and magnetic) at surface are canceled, which will happen when the charge take the form of an oblate spheroid on the direction of motion. The longitudinal radius (on motion direction) become γ times shorter than the transversal radius which remain unaected.
Now if we integrate the momentum density over the volume around the we obtain the eld momentum in a similar way result electric eld energy We must make distinction between the eld propagation momentum and the charge movement momentum (inertial momentum), the eld momentum being equal with the inertial momentum only in the case of free elds (electromagnetic wave elds) which form a balanced electromagnetic system.
The elds created by a charge form an unbalanced system, additional stress (Poincare stress) is required to balance the system. Consequently we assume that when this stress is taken into account the 4/3 factor must disappear.
With this we can write the charge momentum relative to aether as If we have the case of total aether entrainment by the body then v = 0 also magnetic eld is zero and eld momentum is zero. To satisfy the charge momentum conservation when the aether is entrained the charge momentum relative to an arbitrary reference must be From (42) can be observed that the total energy (not only electric eld energy like in near to rest approximation) is sensitive to gravitational potential variations, so that the inertial and heavy mass are equals at any velocity and In the case of an electromagnetic wave, the wave elds form a selfbalanced system, the Poincare stress is zero, total inertial momentum density relative to any reference is given only by eld momentum density and is completely independent by aether movement. This mean that a body that move through aether and interact with a wave eld, this eld will always have the same inertial momentum relative to the body independent by the body movement relative to aether.

Mass Dilation
Let consider the movement through aether in the general case, considering a charged particle like in 2.1 moving with constant velocity v through aether.
We consider the case of low enough acceleration such that the acceleration component of eld is negligible compared with the velocity component. The total momentum of moving charge relative to any reference (44) will be Dierent transversal and longitudinal inertial mass are associated with the force of inertia, for transversal mass when acceleration is perpendicular on the movement direc- longitudinal mass when acceleration is parallel with the movement direction this show the mass dilation but only with velocity v relative to aether. In the case of longitudinal mass the aether velocity u also have a small inuence but only in the presence of a movement relative to aether as well.

Length Contraction
Now we can extend analysis to atomic radius to prove that all bodies composed from atoms suer longitudinal contraction when move through aether.
First let express the electric eld of nucleus transversal on atom motion di- the centripetal force that act over electron become where l 0 is the length at rest of the clock arm where light propagate. If the clock move trough aether we have two cases: when the clock arm is transversal on movement direction and when the arm is parallel with movement direction. When the arm is transversal the light are forced to propagate over a larger distance through aether due to clock movement, the time base When the arm is parallel the light propagate onward and backward through moving aether over a contracted arm length, the time base become The where ∆t 0 is the time base where potential is Γ 0 .

Interpretation of phenomena
Some eects and experiments will be analyzed in the context of gravitational aether.

5.1
Aether properties variations Speed of light, electric permittivity and magnetic permeability of vacuum are no longer an universal constant, but are dependent by gravitational potential as show in equation (18,19,20). This lead to a series of eects like gravitational refraction of electromagnetic waves when they pass close enough to a massive object. The speed of light decrease gradually toward the center of mass due to permittivity and permeability increase and this make the light to refract following a curved path around the mass. The eect is very small around masses like sun and earth due to very high value of background gravitational potential.
Another eect produced by the aether properties variations is the slowing down of electromagnetic processes and clocks in lower gravitational potentials. This in turn will produce the gravitational red shift of light emitted from a source localized in a lower gravitational potential if that light is received in an area with higher gravitational potential.

Aether Wind experiments
In normal conditions the aether on earth surface is almost completely entrained with earth orbital movement because the earth has the dominant gravitational inuence on its surface, but is not entrained with the earth rotation around its own axis because this rotation not change equipotential surfaces around the earth. The Michelson-Morley experiment and other experiments like it, give a null result because the aether is entrained by earth, even if the experimental device of this kind move relative to earth, the result is also null due to length contraction of apparatus and slow down processes.
Trouton-Noble experiment with suspended charged capacitor also give a null result due to aether entrainment.
In Sagnac type of experiments the movement of apparatus relative to aether is detected. The Sagnac eect appear because the rotation of apparatus relative to earth and aether combined with the fact that light propagate with speed c relative to aether, make the two beams of light to propagate over dierent distances until they reach the receiver. The same eect appear in the case of Michelson-Gale-Pearson experiment where the device rotate with the earth, aether being unaected by the earth rotation.

Aberration of Light
Star light aberration is produced because the light receiver is immersed in earth aetherosphere and move with it, the angular deviation of light beam when enter in earth aetherosphere is just an electromagnetic eect. In gure 1 is a depiction of this eect. The transition from solar system aether (zone 1) to earth aether (zone 2) is gradual with the increasing of earth gravitational inuence, however for simplicity a step transition is considered instead, the earth aether moving with velocity u relative to solar system aether.
The angle of aberration is in the direction opposed to aether movement. While the light propagate in that direction is also advected with the aether and at any moment the light is located in the extension of zone 1 direction of propagation (dashed line).
However an observer located in zone 2 and moving with the local aether will see the light coming at angle. If we presume that the zone 2 is just a band of moving aether between two zone 1 aether, an observer located in the zone 1

5.4
Fizeau experiment Fizeau water tube experiment, in this experiment the mass of the moving water is too small to have any inuence over the aether at earth surface, so the aether is immobile relative to apparatus which is immobile relative to earth. The moving water which is a dielectric inuence the propagation speed of electromagnetic wave, the inner mechanism of this inuence is depicted in gure 2. precisely the term D × u from induction equation (33), because u = −v, become v × P , the ε 0 E term from the expression of electric displacement being immobile relative to aether. And third this additional magnetic eld induced by moving dipole also produce an additional Lorentz force over the charges that always oppose to electric forces. We will use the following notations: ε = ε 0 ε r , µ = µ 0 , Z, c n electromagnetic properties of water at rest; ε v , µ v , Z v , c v electromagnetic properties of water in movement. The speed of electromagnetic eld propagation is relative to aether and apparatus. In water at rest we have the polarization P = ε 0 (ε r − 1) E in this case we also have E H = Z when water move in the particular case from gure 2 we have The moving water impedance is