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The EMRP Gravity Theory

© Engineer Xavier Borg - Blaze Labs Research


Radiation Pressure

James Clerk Maxwell Electromagnetic radiation produces many effects in its interaction with matter. Just to mention a few of them; it ejects photo electrons, induces electrical conduction in photoconductors, produces flourescence in some materials, heats up bodies during absorption, and produces nervous response in our eyes in the visible part of its spectrum. Electromagnetic Radiation Pressure (EMRP), denoted by PRAD is defined as the force per unit area exerted by electromagnetic radiation. The fact that electromagnetic radiation exerts a pressure upon any surface exposed to it was deduced theoretically by the father of electromagnetic theory James Clerk Maxwell in 1871, and later on, proven experimentally by Lebedev in 1900 and by Nichols and Hull in 1901. Solar radiation EMRP is very feeble and acts only on the surface of the target, but can be detected by allowing the radiation to fall upon a delicately poised vane of reflective metal in a Nichols radiometer, not to be confused with Crookes radiometer. EMRP is a real effect that exerts a positive force due to the momentum given up during the interaction of waves with matter (De Broglie standing waves), or using quantum jargon, by photons imparting a recoil on a target. Electromagnetic radiation pressure is proportional to the energy intensity of the EM field, and inversely proportional to the speed of light. It acts in the same direction as the wave propagation direction, that is in the direction of the Poynting vector S. Whilst the electric and magnetic fields oscillate in transverse mode, the Poynting vector oscillates in longitudinal mode. A longitudinal wave is defined as oscillations of energy in the direction of the wave movement. Usually, this term is used to describe acoustical (sound) waves in air that is alternating compression and expansion of air. The longitudinal Poynting vector works exactly in the same way, with two important differences - it can travel through vacuum, and its magnitude is always positive. Unfortunately, the Poynting vector is not introduced to the students at the very first moment they learn about electromagnetic waves, and in most cases, its momentum continues to be treated just as a side effect of the wave/particle duality nature till the end of the most advanced courses. The wave/particle duality is nothing but the electromagnetic properties/poynting vector effects of a simple EM wave. When momentum is exchanged with matter, we say the EM wave is acting as a particle, but momentum does not necessariliy have to be carried by matter.

Electromagnetic Waves


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, different antennas can only transmit or recieve one 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, results in a prefect plane wave. EM waves in the form of a plane wave having a single electic 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 by 90°, then it is said to be circularly polarized. A circular wave whose vector amplitudes are not equalIf is said to be elliptically polarized. The direction of an 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.

Polarization

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.


  • 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 ˝ or Ľ wavelength delay. A quarter wave plate causes linearly polarized light to become perfectly circularly polarized for an angle of orientation of 450.

    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.

    Photon Energy E=hf ... h=Planck constant, f= radiation frequency

    Number of photons or wavelets per second = Power/hf

    Radiation imparted momentum p= QPRh/λ = QPRhf/c = QPRE/c ... QPR= coefficient of radiation pressure, λ= wavelength

    Radiation Pressure PRAD = QPRφE/c = QPR<S>/c .... φE is the mean energy flux density, also called intensity <S>

    Radiation Pressure PRAD = QPR|N|/2c = QPR|ExH|/2c = QPREB/(2μoc)... |N| is peak magnitude of the Poynting vector

    Directional Radiation Pressure PRAD = QPRψT4/c .... ψ is Stephan-Boltzmann constant, T is the absolute temperature

    Force acting upon target = QPRERP/c ... ERP effective radiation power reaching the target

    ERP = <S>A ... <S> is the time averaged intensity and A the surface area

    Force acting upon target = QPRhf x number of photons per second/c ... c=speed of light

    Scattering force Fscat = QPR P/vp= QPR nP/c , n=refractive index, vp= phase velocity, P=power of photon source

    Peak Energy per unit volume of an EM field = u = B2o = εo E2, and E=cB

    Time averaged Intensity <S> = cu/2 .... c=speed of light, u= peak energy per unit volume

    Radiation Pressure PRAD = QPRE B/(2μoc) .... E and B are the amplitudes of the electric and magnetic fields respectively

    Radiation Pressure PRAD = QPRεoE2/2

    Time averaged values are half of peak values because the integral of the Poynting function sin2(x)dx over one wavelength (0-2π) gives half its peak value.

    Average of normal pressure on a 'black' spherical surface in homogeneous radiation energy density ε = ε/3


    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.

    Radiation Pressure Coefficient

    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.

    Across the EM spectrum

    We know that as frequency of the EM field is increased, penetration of the radiation goes deeper and deeper within matter. For example X-rays at 1E17Hz travel through our body, finding slight difficulty to penetrate the bones. Gamma rays at 1E22Hz find no problems to penetrate most materials including various metals. Shielding against such Gamma rays requires thick dense metals such as lead. Higher band EM radiation is referred to as Gamma radiation, but naturally occurring EM radiation in space referred to as cosmic radiation, suggest that Gamma rays' highest frequency limit can be much higher than the known Gamma band. As the frequency of radiation increases further, the wavelength becomes very small in comparison to even the densest metal lattices, shielding becomes much more difficult, and most metals, including the heaviest ones, will not be able to reflect or deviate any of this radiation, loosing a group of mechanisms which usually makes matter effective as an electromagnetic shield. It is known that cosmic-rays are far more penetrating than the gamma rays emitted by cobalt-60. With an energy of 1 MeV, gamma rays penetrate just about 1 centimeter of lead. Cosmic rays with an energy level of about 3000 MeV penetrate nearly 2m of lead. Indeed, for many years, cosmic rays were the only source available for the study of highly energetic rays through matter.

    cosmic ray through lead

    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.

    As you might be thinking already, the radiation pressure exerted by such high frequency radiation, in the top part of the EM spectrum, would be a perfect candidate for the gravity effect, since such radiation would penetrate ANY matter and act all over its constituent particles, not just its surface. The radiation can be visualised as a shower of high energy EM waves imparting impulses of momentum to all bodies in space. It also explains the great difficulty we have to shield anything from such force. The energy of each individual photon is a crucial component of the momentum necessary to create pressure for gravity to be possible. The shadow of incoming high energy EM wave packets can be pictured as the carriers of the gravitational force, the normal role assigned to the theoretical graviton. Hence, gravitons have been theorised due to the lack of knowledge of radiation pressure and radiation shadowing, and that's why they will never be detected. If photons represent the luminance of electromagnetic radiation, then, gravitons represent the shadowing and can be considered as negative energy waves, lack of photons or photon-holes. In a way, its very similar to the way we describe electrons and electron holes in semiconductors.

    The closest source for radiation pressure that comes to ones mind is our star, the Sun. Indeed this has been already proposed in older failed theories as one of the possible sources of such radiation, but we know that the sun is not our source of radiation contributing to gravitational force. We can easily deduce this from the fact that the sun's peak radiation occurs in the visible spectrum band, and at night we do not loose gravity! The most interesting band of radiation is the one on the upper band of the radiation spectrum, where momentum imparted would be the highest, and would enable the gravitational force to act not only through a few metres of metal, but through kilometres of thickness as is evident from measurements beneath the earth's crust. The rays in the upper gamma region are called cosmic radiation. Not all sources for this radiation are known, most are known to come from distant stars, some of which is red shifted, and some which is blue shifted due to relative velocities, the rest presumably comes from sources outside our galaxy, and called extra-galactic cosmic radiation. Such radiation is present day and night (as are the stars), is found everywhere in space and its maximum frequency exceeds by far the maximum frequency which we are able to detect with our present detectors. In fact we can consider the universe as being the biggest upper Gamma band generator. A body surrounded (or better, permeated) by such radiation from all directions, will not feel any force at all, unless such radiation is 'shadowed' by a second mass. Quoting Sir Oliver Lodge, "A fish probably has no means of apprehending the existence of water; it is too deeply immersed in it." Same applies to us that are immersed into this sea of electromagnetic energy, we can only notice it, if it is somehow shadowed from a particular direction. Once shadowed, this radiation pressure will be unbalanced, and the object will be under the effect of a gravity force unbalance between its 'shadowed' and 'illuminated' sides. A similar situation is when a person is being squeezed in a crowd of people all around, in which case he does not move to any particular direction. But if the crowd is pushing only on one side, he will be pushed away, due to the absence of the crowd pushing from the other side. So, such radiation force will thus press the object to the darkest part of the shadow, due to the absence or attenuation of the same radiation force on the dark side. It should be clear by now to see why the so called 'centre of gravity' of the mass is very misleading, as the force is not generated from the centre of mass. The "attracted" object will also cast a shadow on the shadowing object and thus the resultant force between the two objects will depend on the mass of both objects. This is compliant with Newton's law of gravity: F=GmM/r2.

    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.

    Electromagnetic Spectrum



    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?

    solar radiation force vs gravitational force
    Courtesy of Institute for Planetology


    The answer to this is in the relation between particle diameter and wavelength. This is clearly seen from the fact that 0.25um radius particles, that is 0.5um diameter particles result in the best momentum transfer from the 0.5um (500nm) wavelength electromagnetic radiation from the sun, and the sun's peak wavelength happens to be 500nm ! This will result in maximum radiation pressure, which depends on resonance of the wavelength to the physical size of the receiver, exactly analogous to a radio antenna. Those particles having either bigger or smaller diameters, will have a lower coefficient value. If the source had a peak intensity at 1nm, then, maximum radiation pressure would be imparted mostly to those particles with comparable diameters, that is in the range of 1nm. In optics, the radiation pressure for the condition d ~ λ is usually referred to as the Mei- scattering regime and is known as one of the major forms of elastic light scattering (involving negligible energy transfer and maximum momentum transfer). Note that the term elastic derives from kinetic theory, and is used to describe the effect of the momentum transfer. Again, this time in optics, micrometer sized particles having a diameter close to the wavelength have been optically levitated by a single laser beam. So, the dimensions of the actual body or its constituents is very important when considering radiation pressure coefficient. A large body, can have a large surface area, but if its diameter, or atomic diameters are not close to the incident radiation wavelength, it will have a lower radiation pressure coefficient, and thus a lower momentum will be imparted to it. It is well known that the degree of scattering varies as a function of the ratio of the particle diameter to the wavelength of the radiation, along with some other factors including polarization, angle, and coherence. Elastic scattering mechanisms would eliminate the problem of heating up or increase in mass as already proposed by other push gravity theorists, but here we run straight into another problem. It can mathematically be shown that the bouncing back of perfectly elastic collisions will never result in pushing two pieces of matter towards each other. Thus, we find that inelastic collisions, in which the photon must be absorbed by the target without generating heat is a requirement for EMRP.

    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

    planck wavelength 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.

    merging forces



    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 lumičre, 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):

    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.


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