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In the present paper , gravitational lensing is described as the electromagnetic influence from gravity waves on light waves. Previous reports have described the dynamic electromagnetic processes of the atom, the photon and gravity. Results from these reports have been compiled into a theoretical model. The theoretical model describes the mechanism which results in gravitational lensing. The study also displays how the electromagnetic characteristics of gravity waves and light waves and the mechanism creating gravitational lensing are measured.

It has been reported that the universe contains a gigantic singularity which generates very low frequency and synchronized TEM (transverse electromagnetic) waves, having extremely high amplitude and energy [

It has also been reported that atoms absorb these TEM waves in the frequency range 0.005 - 0.03 Hz [

Furthermore, it has been reported that atoms also absorb TEM waves with frequency 69.9 Hz [

It has also been reported that excess energy quanta hv in oscillators, contained in a particle, an electron or an atom, is superpositioned on gravity waves absorbed by the oscillator. The re-emitted TEM wave has the superpositioned energy quanta hv and the frequency 69.9 Hz + v [

A large or compact body, e.g. a star, is characterized by its huge mass, i.e. its enormous amount of atoms [

The objective with the present paper is to build on results already presented in reports [

The aim of the study is to present a theoretical model of gravitational lensing.

The theoretical model builds on the observation that atomic oscillators_{69.9}, with natural frequency 69.9 Hz, absorb TEM waves with frequency 69.9 Hz [

The behavior and characteristics of plane TEM waves is independent of their frequency. The field vectors E and B or H (B = µ_{0}H) are linked and perpendicular. The field vector amplitudes relate as E = cB, where c is the speed of light. The electric and magnetic field vector amplitudes E and B decrease with the distance from the source as 1/r. The Poynting vector S describes the TEM energy flow density [

The energy stored in the magnetic field is just equal to that in the magnetic field. The direction of energy flow is reversed for a wave travelling in the opposite direction because the phase of E and H is reversed.

Assume that one source, Source 1, absorbs and re-emits plane TEM_{1} waves, described by its Poynting vector S_{1}(r) at the distance r from Source 1. Another source, Source 2 is positioned at the distance r. Source 2 absorbs TEM waves and re-emits plane TEM_{2} waves uniformly into space. In the direction towards Source 1 plane TEM_{1} and TEM_{2} waves interact because of the force between their synchronized field vectors. This also implies that there is energy transfer from TEM_{1} to TEM_{2} when TEM_{2} propagates towards Source 1. In equilibrium there is energy transfer in both directions, i.e. from TEM_{1} to TEM_{2} vice versa. Note that E and H are always perpendicular and hence can be replaced by S = E·H. Equilibrium is defined by the amount of energy that Source 1 is able to deliver at Source 2, e.g. at the distance r, S_{1}(r), and the amount of energy that Source 2 is able to deliver at Source 1, i.e. S_{2}(r). This results in back reaction force F(r), i.e. radiation reaction [

It is now assumed that each source consists of many oscillators_{69.9} where each atomic oscillator_{69.9} re-emits TEM waves described by its Poynting vector δS(r) and where r denotes the distance from the source and its oscillator_{69.9}. E and H decrease linearly with the distance r implying that δS(r) decreases with the square of the distance; δS(r) = δS(0)/r^{2}. The mutual force of attraction δF(r) between two atomic oscillators_{69.9} with distance r is

It is now assumed that one oscillator_{69.9} acts on p collocated oscillators_{69.9}, belonging to the set P of all oscillators_{69.9} at Source 2, and where each force can be described by δF(r). These oscillators_{69.9} are synchronized resulting in the force

It is now assumed that n collocated oscillators_{69.9}, belonging to the set N of all oscillators_{69.9} at Source 1, act on p collocated oscillators_{69.9}, belonging to the set P of all oscillators_{69.9} at Source 2, resulting in the total force F(r)

δS·δS is a constant described by the intrinsic characteristics of the oscillator_{69.9}, and hence Equation (5) is simplified into

where ξ is a constant.

In a previous study Equation (6) was called the law of gravity between two clusters, at distance r containing n respectively p oscillators_{69.9} [_{69.9}, an electron, an atom, a mass, a planet or a black hole.

Equation (6) can be illustrated with gravity between the earth and the sun. The earth contains n atomic oscillators_{69.9} creating a force n·δF(r) on every atomic oscillator_{69.9} in the sun. The sun contains p oscillators_{69.9}, thus the total force of attraction is n·p·δF(r) and that is equal to Equation (6). The earth’s mass m_{1} is proportional to the number of atomic oscillators_{69.9} on earth, i.e. m_{1}~n, and the sun’s mass m_{2}~p. Equation (6) is then approximately equal to the Newtonian geometric law of gravity, where F_{G} is the gravitational force:

S_{1}(r) and S_{2}(r) in Equation (6) depend on the distance between the singularity and S_{1}(r) respectively S_{2}(r). Thus ξ in Equation (7) increases at decreasing distance to the singularity.

Gravity is illustrated in

The theory of photon energy transport in space can be illustrated with light waves. It has been shown [_{69.9} in an electron or atomic nucleus, see _{69.9} absorb and re-emit gravity waves with frequency 69.9 Hz. Accelerating or decelerating an electron or an atomic nucleus implies that they gain energy, i.e. each of their intrinsic oscillators_{69.9} increases its energy and this excess energy can be described by one or many

energy quanta hv. In this case the oscillator_{69.9} 4 in the electron or atom contains one energy quantum hv at a time, where h is Planck constant or quantum of action.

The energy quantum hν is discrete and limited in time. The energy quantum hν is superpositioned on a reemitted TEM wave. This TEM wave contains the superpositioned energy quantum hv and the frequency 69.9 Hz and instant frequency ν. Hence, the re-emitted wave is a gravity wave with superpositioned electromagnetic energy. The superpositioned electromagnetic energy quantum hv with frequency v is the photon. In a continuous process the sum of many photons and their energy quanta hν, superpositioned on re-emitted gravity waves, result in light waves.

The light wave’s amplitude is proportional to the number of photons per time unit, which is proportional to the number of involved energy quanta hv, which in its turn is proportional to the number of involved oscillators_{69.9} and which is proportional to the inertial mass. This light wave has the frequency 69.9 Hz + v.

The light wave can be absorbed in matter 5 and where the superpositioned energy quanta hν are absorbed, resulting in that the light wave is converted back to the original gravity wave with frequency 69.9 Hz.

The energy contained in a TEM wave is proportional to its frequency ν. From this follows that the superpositioned energy and the photon energy δE is:

The TEM wave’s superpositioned energy and momentum are related as δE = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0 [

where k is the wave vector (where the wave number k = |k| = 2πν/c), and ħ = h/2π is the reduced Planck constant. Since p points in the direction of the TEM wave propagation, the magnitude of the momentum is:

The photon also carries spin angular momentum that does not depend on its frequency v. The magnitude of its spin is and the component measured along its direction of motion, its helicity, is ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon [

Thus the photon contained in the light wave is not a particle; however, discrete electromagnetic energy quantum hν, with frequency v, superpositioned on a low frequency TEM wave, i.e. a gravity wave. From this follows that the photon is strictly mass less, has zero charge and propagates with the speed of the low frequency TEM wave, i.e. with the speed of light in free space.

The theoretical model encompasses a compact or large body like the sun, comprising enormous amount of atoms. It radiates vast amount of gravity waves (TEM waves) with frequency 69.9 Hz and where the energy flow density is described by the Poynting vector S. Furthermore, the theoretical model comprises light, where the photon energy hv is superpositioned on gravity waves with frequency 69.9 Hz, resulting in a new TEM wave (i.e. the light wave) with the frequency 69.9 Hz + v. The light wave energy is high due to its high frequency v; however, its low frequency component with frequency 69.9 Hz has low energy flow density and is described by its Poynting vector S.

A light wave passing the sun can be described by the light wave’s TEM wave and its 69.9 Hz component, where this component’s energy flow density is described by the Poynting vector S_{1}. Gravity waves, radiated from sun are described by their TEM waves with frequency 69.9 Hz and the Pointing vector S_{2}. Synchronized TEM waves of equal frequency propagating in opposite direction or at an angel result in a mutual force of attraction where this force F is

and where η is a constant. The constant η depends on the mass distribution of the large body and the light wave’s energy, i.e. its frequency v.

This results in that the light wave is bent towards the gravity waves and towards the compact or large body, and which results in gravitational lensing [

The energy in the light wave is high due to its high frequency v and S_{1} is very small. Hence, S_{2} must be very large in order to deflect the light wave. Consequently, gravitational lensing occurs primarily close to compact or large bodies. Gravitational lensing is illustrated in

The strength of the present theory is that there exists a method to measure relevant parameters [

characteristics such as direction of origin, amplitude, phase, frequencies and field vector behavior [

It is proposed that all energy in the universe originates from a singularity, and is distributed throughout the universe by low frequency TEM waves, having a broad spectrum of frequencies. The atom in itself is fully passive. At this stage the atom’s physical view is of little interest. However, the atom’s functional view is crucial; the atom consist of forced damped oscillators with different natural frequencies. They absorb TEM waves originating from the singularity. The atomic oscillators are assembled in different configurations, and where the number of oscillators and their mix of natural frequencies result in different types of electromagnetic energies and forces, according to electromagnetic theory [

The platform of modern physics is elementary particle physics described in the Standard Model [

The present study describes gravity, photon and gravitational lensing by their electromagnetic processes. It is a cumbersome task to explain these electromagnetic processes by means of (poorly defined) particles. Consequently, according to the Standard Model, the atom must contain some unknown phenomena which create force of attraction (i.e. strong force, nuclear binding energy, gravity). It also implies that there exists an intrinsic mechanism which can store enormous amount of nuclear energy forever, with no loss. It also implies that the atom can radiate energy, fields and particles (graviton) without losing energy or mass and without any change in its parameters. These are amazing properties. The consequence of the Standard Model is that the universe must contain a large number of different particles which supersede electromagnetism. However, the drawback of the Standard Model is that these particles and their relationship are poorly defined. The Standard Model falls short in explaining e.g. strong force, binding energy, photon, gravity, gravitational mass as well as a number of astrophysical phenomena (e.g. gravitational lensing, gravitational red & blue shift, frame dragging, light conservation in black holes, expanding space).

The present paper describes gravitational lensing. Gravity is caused by TEM waves with frequency 69.9 Hz. Light photons consist of energy quantum hv, superpositioned on gravity waves with frequency 69.9 Hz. There is a mutual force of attraction between gravity waves and the light’s gravity wave component. This force bends light waves towards the gravity wave, i.e. towards the compact or large body. The theoretical model is simplified. For instance gravity waves generated from a large body, like the sun, originate from different parts of the body, i.e. its mass distribution relative to the light wave. Close to the body Equation (5) and Equation (6) provide only approximate values. Close to the body Equation (12) and the Poynting vector S_{2} provide only approximate values. At close distance an exact Equation (12) must include the integral of S_{2}(r), where r is the distance to different parts in the large body. Hence, a light wave passing close to a large body experiences a spectrum of forces according to Equation (12) which may produce multiple images. Likewise, the light wave’s energy depends on its frequency v; hence, light waves containing a spectrum of frequencies v result in multiple images. The paper does not elaborate on the difference between the strong and the weak gravitational lensing; however, it may be the result of the light wave’s distance to the body and the body’s size relative to this distance. The objective with the present paper is to describe the general principle of gravitational lensing. A complete model should include the influence from the light wave’s spectrum, the body’s mass distribution and the light wave’s distance to the body.