### The EMRP Gravity Theory

© Engineer Xavier Borg - Blaze Labs Research

Stating that electromagnetic waves are transverse waves is not quite accurate, because we know that EM waves PROPAGATE through space, by means of a longitudinal Poynting vector of magnitude |N| equal to the instantaneous vector cross product of the electric and magnetic fields |ExB|. Also, note that while the electric and magnetic fields alternate their polarity, the Poynting vector varies its amplitude, but not its direction. The reason for momentum transfer between a wave and a material target is solely due to the existence of this vector. The Poynting vector describes the flow of energy (Power) through a surface in terms of electric and magnetic properties and has the dimensions of power per unit area. Radiation pressure in Pascals (N/m2) is equal to the time averaged Poynting vector magnitude <S> divided by the speed of light. Other names for <S> are irradiance and intensity.

Polarized waves and Poynting vector

The polarization of a wave is defined as the trace of the tip of the E-field vector as a function of time seen from behind. In radio frequency applications, antennas can be designed to transmit or recieve a particular type of polarization. For example, straight wires and square wavelengths support linear waves, whilst round waveguides or flat spiral antennas support circular or elliptical waves. Plane and circular polarised EM waves are closely related, and indeed there are occassions in which a combination of circularly polarised waves, result in a perfect plane wave. EM waves in the form of a plane wave having a single electric field vector in space is said to be linearly polarized. If an EM wave is composed of two such plane waves of equal amplitude but out of phase by 90°, then it is said to be circularly polarized. A circular wave whose vector amplitudes are not equal is said to be elliptically polarized. The direction of a circular or elliptical polarised wave is defined by its helicity. Positive helicity or left hand polarization is the case when clockwise motion of the electric field drives the EM energy forward. Negative helicity (or right hand polarization) refers to rotation in the opposite direction. By working out the vector sum of two circular polarised waves of opposite helicities, it can be easily shown that any 2D plane electromagnetic wave can be considered as a vector combination of two 3D circularly polarized waves rotating in opposite directions. Also, it is known that when a linear polarized wave is either deflected or reflected off a material target,its vertical or horizontal polarization will be changed. This means that a receiving antenna which has its polarization properly aligned to the source antenna, will receive a deteriorated signal level once the wave polarization has been changed on its way. So one relevant advantage of having circular polarization is that rotation does not affect it and it remains circular. This feature enables a circularly polarized wave to achieve a greater penetrating power than that of a linear polarized wave having the same power.

Polarization is grouped under four main categories; linear (or plane), circular, elliptical, and unpolarized (natural). Unpolarized waves are simply made up of a mixture of EM waves of different polarization. The effects of the poynting vector of each of these polarization modes are summarised as follows:

• A linear / plane wave results in a target particle being pushed in the direction of the wave progation.

• A circular or elliptical wave results in a target particle experiencing both torque and linear momentum.

• Two opposite circular or elliptical waves hitting a target, give the same result as that of a plane wave.

• A circular wave hitting a chiral target of similar handedness, results in zero momentum transfer.

• A circular wave hitting a chiral target of opposite handedness, results in linear momentum.

• By conservation of momentum, if the target itself can discriminate between different modes of polarization, then, the target can select between linear or angular momentum, even in the case of natural (unpolarized) waves. A chiral material would in fact be able to recover one circular polarization from a plane wave, which is made up of two opposite circular polarization waves. For this case torque would thus be generated by illuminating such target by a plane wave. In optics, wave plates work by delaying one of two orthogonally polarized components of light incident upon them. The materials are asymmetric in that they have a different index of refraction in one direction than the other. The “optical” or fast axis is usually indicated on the wave plate. Light polarized along this axis experience a smaller index of refraction than light polarized perpendicular to this axis. The two orthogonal components of light, one polarized along the optical axis and one polarized perpendicular to that axis, enter the wave plate with a phase difference of zero and emerge with a phase difference of π or π corresponding to either ½ or ¼ wavelength delay. A quarter wave plate causes linearly polarized light to become perfectly circularly polarized for an angle of orientation of 450. Also,all the above mentioned optical activities are known to be valid for all types of radiation and all levels of interaction between EM waves and matter.

For the mathematically inclined readers, here are a few useful equations one can use to calculate radiation pressure effects. Derivation of these relationships may be found in most of the advanced physics textbooks. Note that the SI dimensions for energy density are watt second per metre cubed, which are the same dimensions for pressure.

Do not be intimidated by the speed of light in the denominator of the radiation pressure equation. Radiation pressure can be much higher than the feeble solar EMRP acting on earth. Here is a practical example relating a laser source EMRP to solar radiation (assuming total absorption at the target, QPR=1):

Power incident on the Earth's surface due to radiation from the sun is about 1370 W/m2

Radiation Pressure at Earth's surface is 1370/c = 4.57E-6N/m2 or 4.57 μPa

Flux density from NOVA experiment laser beam is about 1E18W/m2
Radiation Pressure on target is 1E18/c = 3.3E9N/m2 or 3.3 Giga Pascals!!

Reflection, Absorption and Transmission

When an electromagnetic wave approaches a surface, it may be either absorbed (absorption coefficient=1 for complete absorption) or reflected (reflection coefficient=1 for complete reflection) or just passes straight through (transmission coefficient=1 for complete transmission). Conservation of energy demands that the sum of these coefficients is equal to unity. In the first two cases, momentum 'p' is transferred from the photon to the object whose surface is struck. In this way, a force (dp/dt) is exerted on the struck object, giving rise to EMRP. If the electromagnetic radiation is completely absorbed, the struck object acquires both momentum and electromagnetic energy of the photon. If the electromagnetic wave is totally reflected, so that it rebounds with the same magnitude of momentum, but oppositely directed, conservation of momentum demands that the momentum transferred to the struck object is twice the magnitude of the momentum of the incoming wave. If it keeps on going straight through, no momentum or energy is exchanged. Generally, if a beam of EM waves strikes a surface, some waves will be reflected, some will be absorbed and some keep going straight through, depending on the target's properties AND frequency. As I shall explain later, an object may be totally transparent to one frequency, and still show total absorption or reflection at different frequencies.

The radiation pressure coefficient QPR is equal to the ratio of the momentum acquired by the target to the electromagnetic momentum of the wave before impact. Therefore, as shown in the above diagram, the radiation pressure coefficient for cases where by a beam of EM radiation is incident upon a surface, falls somewhere in the range between zero when all waves go straight through to a maximum theoretical value of 2, when all incident waves are reflected. For perfect reflective surfaces the momentum imparted will be twice as much, that is, p=2E/c. Elastic scattering mechanisms give QPR=2. Visible light EM radiation acts upon each particle on the surface of an object, because most of the radiation is reflected back by its reflective surface. Most of the visible spectrum EM waves do not make it past the top surface of the target due to their wavelength size as compared with the internal atomic structure of the target. So, in the visible spectrum region, the radiation pressure acts mainly on the surface area of the target.

In fact, cosmic waves have far greater penetrating power than the man-made gamma radiation, and can even pass through a thickness of two metres of lead. The highest frequency possible, that is, the shortest wavelength limit is equal to the dimension of the unit element making up space-time itself, equal to Planck length, radiating at a frequency of 7.4E42Hz.

This shadowing effect can easily describe the high/low tides of sea level, depending upon the shadowing position of the moon. Shadows do obey the inverse square law, and is easily mathematically proven. For totally black shadows, the force at a distance R is directly proportional to the objects projected shadow area: Projected area= Original Area/ R2. Also shadow density and source intensity obey the same inverse distance square law because of the variation of the solid angle that one object subtends on the other as we vary the distance. So now, we are able to understand what generates the force of attraction between our Earth and the sun. Suppose that high frequency wave packets are reaching the earth radially all over its surface. When they are absorbed by the Earth's material bulk, they give an impulse to the earth, however, since there are as many going one way as the opposite way, the impulses all balance out. Now, if we take into account the sun as the most massive object in earth's vicinity, then the wave packets coming toward the earth from the sun's direction will be mostly absorbed by the sun's material bulk, so fewer wave packets will reach the earth from the sun's direction than are coming from the opposite side. Therefore, the earth will feel a net force pushing it towards the sun, which is inversely proportional to the distance between the two.

Back scattering and Radiation Pressure Coefficient

Below is a plot of the relationship between the solar radiation pressure and the force due to gravity acting on various dust particle sizes in Earth's magnetosphere. Particle's density is around 2g/cm3. The curve peaks to unity for particles of radius 0.2um to 0.4um. For this size of particles, the gravitational force and solar radiation pressure are equal. For bigger particles, the gravitational force FG is approximately 100 times stronger than the light pressure force FL from solar radiation.

The dashed line shows the dependence of solar radiation pressure on particle radius. The radiation pressure has a significant effect for particles in the range 0.2 to 0.4 micron. The plot is obviously showing us something very important. Why does the peak value for solar radiation pressure act for 0.25um particles? Why does solar radiation pressure impart more momentum on this size range of particles and less momentum on greater and smaller sized particles?

Courtesy of Institute for Planetology

For a perfectly absorbed wave or photon by a resonant spherical target of diameter d = λ, we have QPR=1

Force per photon imparted on such target F = <S>/c * Area
Area is the cross section of target = pi*d2/4 = pi * λ2/4, so,
Force per photon imparted on target F = <S>/c* pi * λ2/4 ... where λ = c/f, so
Force per photon imparted on target F = <S>*c * pi/(4f2), so for waves of the same intensity but different frequency, we get:
Force per photon imparted on resonant target F ∝ 1/f2

Condition for Radiation Pressure Coefficient to equate to gravity

The only way in which known radiation pressure (such as solar radiation pressure) acts differently than gravity, is that is acts with different force magnitudes depending on particle size, and that it gets easily attenuated, reflected or scattered at the surface of the target. On the other hand, we know that gravity is indifferent to the actual target size, and acts equally throughout the entire volume of the target, with no noticeable attenuation. So, in order for radiation pressure to equate to the effects of gravity, we should find a condition for radiation pressure coefficient to be the same for all matter, so that the net force will depend on mass, that is the number of elementary targets within a particle or material body. Most scientist agree that all matter, boils down to different structures made up of the same constituent particle (whatever it might be). Such building block of matter, must have the same energy and size for all existing matter. In such a case, there would exist a particular frequency or close harmonics, having their wavelength equal to this particles' diameter, so that the waves would be absorbed by such building block particles which happen to be in the way of the travelling wave. Since the number of such particles is directly proportional to the number of atoms constituting the whole target, and hence proportional to its total atomic mass, the net effect of radiation pressure over the body would be EXACTLY equal, and behave EXACTLY the same as the interaction between matter and the so called gravity. So, the question is : How big are these constituents, and what frequency range are we talking about? Unfortunately, we tend to think of units, such as energy and the electromagnetic frequency spectrum, as having no boundary limits, which in theory they could, but as with all discrete units in the quantum world, everything has a limit, and in the case of our universe they are set by the properties of free space. These natural limits set the boundary between existence and non existence, that is the boundary of the observed reality itself. The upper energy levels and frequency limits in the universe can be thus worked out from Planck's Length or wavelength λp. Shorter wavelengths than Planck length have no effect on matter, nor can they be generated by any interaction with matter, in other words, they cannot exist in our reality, or at least in the reality we are aware of.

Applying Planck units for a single travelling EM wave, travelling at the speed of light c, we have:

Minimum EM wavelength limit = λp = 4.051E-35 m
Minimum building block particle diameter = 4.051E-35m

Maximum universal cosmic radiation frequency limit = c/ λp = 7.4E42 Hz
Maximum universal quantum energy limit EQ = hf = hc/ λp = 4.904 GJ

Here on, I shall define a Planckton as the most elementary building blocks of matter, whose minimum diameter is equal to 4.051E-35m. Plancktons are thus the matter units which interact with the electromagnetic radiation generating gravity. Planck frequency is also the frequency at which unification of all other forces occurs, and the natural energy in electron volts would be E/e = hf*2 α/e = h*7.4E42*2/(137.036*1.602E-19) = 4.44665E17 Gev equivalent to 5.18E30 Kelvin. At such a high value, the resulting radiation pressure would be more than enough to account for the measured gravity.

The Nature of EMRP waves

Recapitulating from the above discussions, we can describe the general nature of our proposed EMRP waves. Such waves are transverse electromagnetic radiation having a longitudinal poynting force vector, like visible light and like x-rays, but of much shorter wavelength. The wavelength of this radiation is much shorter than that presently assigned to hard gamma rays, nonetheless, their basic properties are qualitatively similar. Their optical properties is what makes EMRP waves behave so different from the rest of the electromagnetic spectrum. This should not come as a surprise, for we know the same is true for other different parts of the known spectrum, such as infra red giving rise to heat, and x-rays used in radiography. The index of refraction n for a pure substance radiated by an incoming wave is given by:

n = 1 - δ = 1 - 1/2π re N λ2

where re is the classical electron radius, N is the number of electrons per cubic meter, and λ is the wavelength in meters.

Given the proposed frequency of EMRP waves, in Planck's frequency region, n would be virtually equal to unity for even the densest matter on earth. Since EM waves travel in a straight line, and can only be scattered, reflected or refracted by a boundary offering a different refractive index than that of the surrounding at their particular frequency, this means that EMRP waves cannot be deviated from their straight path by any known material. This rules out most of the optical effects we are used to observe for visible light, but one - absorption. Unlike other optical characteristics, absorption is independent of the refractive index, and would result in a QPR=1 inelastic collision. The effect of absorption is to reduce the intensity of the radiation as it penetrates through matter. Intensity is defined as the flux of energy which crosses a unit surface normal to the travelling direction of the wave per second and is proportional to the square of the amplitude of the vibration. Intensity can be measured by determining the number of photons recieved by the target per unit solid angle. For extremely high frequency, this measurement can only be done by measuring the momentum transfer upon the target. In 1729, Pierre Bouguer, a French scientist, published his work Essai d'optique sur la gradation de la lumière, in which we find one of his great discoveries relating to light, namely Bouguer's law. This law expresses the relationship between the absorption of radiant energy and the absorbing medium: In a medium of uniform transparency the light remaining in a collimated beam is an exponential function of the length of the path in the medium. We can express the absorption as the ratio of I, the intensity of the transmitted radiation to Io, the intensity of the incident radiation, as a function of shield thickness x and material density ρ, according to Bouguer law (also known as Beer-Lambert, or Bouguer Lambert Law):

I/Io = e(-μρx)... where μ is known as the mass absorption coefficient.

For a given target, the coefficient μ decreases with frequency, thus even though absorption seems to be the only obvious characteristic left for us to successfully detect the EM properties of EMRP, it is still a great challenge to succeed in measuring the minute absorption of matter (resulting in a minute change in weight) at such high frequencies.