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## The EMRP Gravity Theory

© Engineer Xavier Borg - Blaze Labs Research

Speed of gravity

Hot debates are presently going on between scientists, over the issue of speed of gravity, with one side voting for a speed very close or equal to

c, the speed of light, and the other side voting for a superluminal velocity resulting in almost zero aberration of the gravitational forces. It is widely accepted, even if less widely known, that the speed of gravity in Newton's Universal Law is unconditionally infinite. Newton himself assumed instantanous transmission of the gravitational force between two bodies. On the other hand, we have repeated here many times, that the source of gravity is of classical electromagnetic radiation whose components travel at the speed of light. In order to understand the speed of gravity one has to analyse the origin, what we mean by 'speed of light', the kind of energy being transmitted, and the properties of the medium that it's being transmitted through. Once we establish these criteria, we can analyse how fast can such force act at a distance, that is, how fast can Einstein's elastic space time fabric change its shape in relation to a moving mass.

What evidence shows

Superluminal velocities have been detected in laboratories all over the world, and can be easiely explained and also simulated. Quantum entanglement, requires superluminal speeds in order to be explained. Following their creation, a pair of entangled particles A and B having complementary characteristics, fly off into space in the opposite direction. When they are billions of miles apart, and one measures particle A; because B is the opposite, the act of measuring A instantaneously tells B what to be; therefore information would somehow have to travel between A and B faster than the speed of light; hence both Einstein-Podolsky-Rosen paradox and Bell's inequality show that superluminal information is possible.

Events such as gravity pull between planets seem to be transmitted instantaneously, otherwise it can be shown that any two planets will spiral into each other. As shown by Sir Arthur Eddington, this means: "If the Sun attracts Jupiter towards its present position S, and Jupiter attracts the Sun towards its present position J, the two forces are in the same line and balance. But if the Sun attracts Jupiter toward its previous position S', and Jupiter attracts the Sun towards its previous position J', when the force of attraction started out to cross the gulf, then the two forces give a couple. This couple will tend to increase the angular momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observations if the speed is at all comparable with that of light." (Eddington, 1920, p.94).

Evidence of superluminal gravitational speed has been also recently observed by a few other researchers by noting the high stability of earth's orbit about the sun. Light from the sun is not observed to be collinear with the sun's gravitational force. Both solar eclipses in the sun-earth-moon system, and planetery radar ranging data, show that optical and gravitational events do not coindice. Astronomical studies indicate that the earth's acceleration is toward the gravitational centre of the sun even though it is moving around the sun, whereas light from the sun is observed to be aberrated. If the gravitational force between the sun and the earth were aberrated at the same magnitude as light, then gravitational forces tangential to the earth's orbit would result, causing the earth to spiral away from the sun, due to conservation of angular momentum. One might think that such discrepancy might indicate that gravity and light are two seperate entities, and not related at all.

The same argument is true when we observe the binary pulsars. Observation shows that the position, and velocity of each mass is aniticipated between the two masses in much less that the speed of light, setting a lower limit to the speed of gravity at 2x10^{10}c.

Newtonian gravity has two special traits: there is no event horizon and it transmits its force in a manner of

immediate(non local) action at a distance. So, non-locality is assumed in Newtonian gravity. All these events, which indicate the transmission of energy and information at superluminal speeds (or infinite speeds), are somehow all related to the gravitational force. But since there has not been a good scientific explanation of how this could ever be possible, we still learn that gravity forces must travel at the speed of light, and the reason given is that no information can travel faster than the speed of light. As we shall see, infinite speed might not be the case, but this does not exclude the possibility of a finite superluminal speed for gravity. There must be therefore a way for an electromagnetic signal to travel at a velocity much greater than c, and at the same time travel at the speed of light. This statement might seem contradictory, only until we understand what we mean by speed of light.

The refractive index of different vacuums

The refractive index (or index of refraction) of a medium is the inverse ratio of the phase velocity of a wave to the phase velocity in a reference medium. For electromagnetic waves, the vacuum is used as the reference medium, although historically other reference media (e.g. air at a standardized pressure and temperature) have been common. It is usually given the symbol n. In the case of light, it equals:

n= √(ε_{r}μ_{r})

where ε_{r}is the relative permittivity, and μ_{r}is the relative permeability of the transmission medium.

The phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. We learn that the speed of all electromagnetic radiation in vacuum is the same, approximately 3×10^{8}meters per second, and is denoted by c. Therefore, if v is the phase velocity of radiation of a specific frequency in a specific material, the refractive index is given by n=c/v. For vacuum, we assume n=1, so v=c.

This number is typically greater than one: the higher the index of the material, the more the light is slowed down. The ratio of velocities and refractive index relates to the sine function of angles θ

_{1}and θ_{2}according to Snell's law:sin θ _{1}/sin θ_{2}= v_{1}/v_{2}= n_{2}/n_{1}

This diagram shows how the gravitational shadowing of a huge mass corresponds to a spherical gradient of refractive index, which changes the direction of light and electromagnetic waves in general. Thus when light passes next to a heavy body, it bends as if the surrounding space is filled with a denser medium than vacuum. It may come as a big surprise to most of you readers, that the refractive index of vacuum is not necessarily a constant equal to one, and n=1 is an approximate value for open space within our solar system. The refractive index in the neighbourhood of heavy planets or near the sun, may be far off from this value, and certainly will not hold its value outside our solar system.

Animated simulation of gravitational lensing caused by a Schwarzschild black hole going past a background galaxy.

Refractive index of spherical space around a massive objects

generates the same refraction effect of a glass sphereThis concept is exactly analogous to the old concept of the aether, in which the vacuum was considered to have the characteristics of a gas like fluid having its own density. In fact, we see here, that space time, the new term which today replaced the aether term, although not made up of particles, does indeed act like an atmosphere with its own properties like permeability, permitivity and refractive index. These parameters are set up according to the local incoming background radiation reaching the particular location in space from the core of the universe. Where an imbalance or shadowing occurs, a refractive index gradient is generated, and all constants we know of, shift off from their nominal values.

Dispersion of electromagnetic waves in space

Dispersion is the change of index of refraction with wavelength. So, the issue is now getting even more interesting. Not only n is not equal to one in vacuum, but it is also a function of frequency! Generally, at visible wavelengths the index decreases as wavelength increases, blue light traveling slower in the material than red light. In a normal dispersive medium like glass, the refractive index in the visible spectrum increases as the frequency increases. All of us are familiar with the rainbow like colors that appear from a glass prism when sunlight is incident on the prism. Each color travels differently through the prism due to normal dispersion; blue light bends more and travels slower than the red light. The emerging color sequence at the output end is important: red light is farthest from the base of the prism and blue light is the closest, thus the slowest. Most naturally occurring transparent media exhibit normal dispersion in the visible range of the electromagnetic spectrum.

In an anomalous dispersive medium the refractive index decreases as the frequency of light increases, and the region of anomalous dispersion coexists with a strongly absorbing behavior making the medium opaque. Most anomalous dispersive mediums are man made, with one exception, the vacuum! If a prism is made out of a transparent anomalous dispersive material, the sequence of the emerging colors would be reversed, with the blue light being farthest from the base of the prism and the red light closest to it, indicating that the blue light would travel faster than the red light inside such a medium. Experiments have shown that such anomalous dispersion is in fact the norm at X-ray frequencies and higher. It depends on both the wave frequency and target properties. Any refracting medium offers some degree of permeability and hence dispersion including vacuum. Different vacuums at different energy levels, such as the space within a strong gravitational field, have a different refractive index and also a different degree of anomalous dispersion. Such dispersion effect in space is not generally noticed since the effect is much smaller than with a glass prism within the visible spectrum, but nonetheless, must theoretically have a non zero value. This dispersion effect would give cosmic 'light' a value n<1, indicating that the speed of electromagnetic light at these frequencies is much higher than the numerical value of c. Recapitulating, we have got electromagnetic waves, which generate gravitational pressure due to the net magnitude of their poynting vectors, travelling at the speed that a light wave having their frequency would travel, which we may call the speed of light, which is also NOT equal to constant c. The below diagram shows how small is today's known electromagnetic spectrum as compared to the cosmic radiation range. We have evidence that v exceeds c in the upper x-ray region. Extrapolating the curve of velocity vs frequency up to cosmic radiation, indicates that the speed of light at such extreme limits could be many orders of magnitude greater than the 'constant' c value. This should finally close the issue of having almost instantaneous gravitational transmission, and visible light travelling at velocity c, operating in the same medium with exactly the same kind of electromagnetic waves, differing only in their frequency. We must however accept that c is no longer to be expressed as a constant. Einstein clearly had no problem with this, and neither shall we.

Values shown are for indicative purposes only

Maxwell Proca equations

One interesting mathematical solution for the existence of dispersion of the value of 'c' across the EM spectrum, is given by Maxwell Proca equations. These are less known than the simpler Maxwell's format, but more complete. Unlike Maxwell, Proca did not assume the photon to be a massless energetic entity and modified Maxwell's original equations to include a very small but non zero rest mass for the photon. From his equations one can immediately notice that for a non zero mass of a photon there will be some very interesting consequences. Indeed, if one applies the spherical wave structure of matter to all energetic entities capable to move in space and time, one can easily imagine photons to be the most basic single shell EM standing wave similar in many ways to a soap bubble floating in air. As discussed in our particle section, what we call mass is simply a standing wave structure, whether it has just one layer, or composed of nested layers as in the case of more complex matter like nucleons and atoms. From this definition, the photon would automatically gain its property of non zero mass, and the common Maxwell's equations would be incomplete. Maxwell's equations would give a constant value for speed of light 'c' across the whole EM spectrum, whilst Proca equations would result in an increasing value for 'c' as one goes higher in the spectrum.

So, one may say that the most direct consequence of a finite photon mass is a frequency dispersion of the speed of light. With a finite photon mass, EM waves would still behave as electric and magnetic fields. They are still described by the third and the fourth Maxwell equations, which state that a moving magnetic field generates an electric field and vice versa. However, in contrast with Maxwell's original equations, EM waves with different frequencies now propagate with different speeds given by:

v = c √[(ω^{2}- m^{2}c^{2})]/ω.....ω=2πf....where c is the speed of light of the upper limit of the EM spectrum (the real upper limit)

High frequency electromagnetic waves move faster than low-frequency ones. This would solve the enigma of the seemingly 'faster than light' speed of gravity and also enigmas with anomalous red shift values currently observed in astronomy. It's not gravity that is faster than 'c', but all photons at the gravitons frequency are faster than 'c'. Thus at such frequency band, gravity and light move at the same speed, where such a speed is much higher than the usual value for 'c'. De Broglie seems to be the first to notice that photon mass would lead to a larger speed of violet light than of red light. He concluded that during an eclipse of a star, the appearing star would propagate its spectrum starting from the violet part and continue to the red part. He also considered radio dispersion, and got his own upper limit for the photon mass using the dispersion of starlight at m <7.8e-43kg. The characteristics of our proposed high speed ultra high frequency cosmic waves would certainly fit the theorised graviton, or the ultramundane particles which Le Sage has described asmost certainly they must be of exceeding swiftness and must be carried far more quickly that the light of the Sunand had estimated their speed to be at least 10^{13}times c. Data of dispersion in the speed of starlight from Crab nebula pulsar gave an upper limit for the photon of m <1E-47kg, whilst the best limit at the time of writing is set by Lakes experiment, based on the Cavendish method, giving m <1.8E-53kg. Plugging in this value for m, and taking the nominal value of 3E8m/s to be true at 700nm (visible light) in the above equation, we get an upper limit for the speed of light c' equal to 1.36E38 x c

Another consequence is the exponential fall off of static fields. For the limit of static fields, we have ,exponential decay of static fields with a range 1/m. This behavior in fact predicts the familiar Yukawa's model for interaction of nucleons through pion exchange. Consequently, flux in no longer conserved, and the familiar equations for the three force fields will thus take the form:

Electrostatic Force F = [KQ_{1}Q_{2}/R^{2}]e^{-AR}.... K = 1/4pie_{o}, Q = charge, R = distance, A = electric flux attenuation constant

Gravitational Force F = [GM_{1}M_{2}/R^{2}]e^{-BR}.... G = gravitational constant, M = mass, R = distance, B = gravitational attenuation constant

Magnetic Force F = [UM_{1}M_{2}/R^{2}]e^{-CR}.... U = μ_{o}/4pi, M = magnetic monopoles strength, R = distance, C = magnetic flux attenuation constant

EMRP predicts existence of black holes and correct value for Schwarzschild radius

A black hole is an object originally predicted by general relativity, with a gravitational field so powerful that even electromagnetic radiation (such as light) cannot escape its pull. EMRP can perfectly explain the phenomena of light being trapped within a gravitational field by the well known optical effect we know as total internal reflection. It all has to do with the so called critical angle.

When light moves from a dense to a less dense medium, such as from the space region near a massive body into space further away, Snell's law cannot be used to calculate the refracted angle when the resolved sine value is higher than 1. At this point, light is reflected in the incident medium, known as internal reflection. At the limit, just before the ray totally internally reflects, the light refracts at the critical angle; that is it travels directly along the spherical surface between the two refractive media. When the critical angle is exceeded then the resulting sine value according the Snell's law will not invert since sin^{-1}(x) for x>1 gives no solution, and thus the refracted angle can no longer be calculated by Snell's law, due to the absence of a refracted outgoing ray. This invisible 'dividing spherical shell' which electromagnetic waves trace at the critical angle would define the border in space beyond which electromagnetic energy will be unavoidably internally reflected and spiralled further inside the black hole. This border is known as the event horizon, because like the earth's horizon nothing can be seen beyond it. The radius of the event horizon of a non-rotating black hole is known as the Schwarzschild radius equal to 2GM/c^{2}.

In order to calculate this critical angle, let θ_{2}= 90^{o}and solve for θ_{crit}:

θ_{crit}= sin^{-1}(n_{2}/n_{1})

When θ_{1}> θ_{crit}, no refracted ray appears, and the incident ray undergoes total internal reflection from the interface medium. In a refractive medium having spherical gradients of increasing refractive index towards its core, this would mean that the light rays, will be trapped inside the medium and spiral within it. You can now clearly understand, that since EMRP unifies gravity with electromagnetism, all the rest of the gravitational phenomena can be easiely understood and predicted with our present knowledge of optical physics. Quoting Eddington:"We can thus imitate the gravitational effect on light precisely, if we imagine the space around the Sun filled with a refracting medium which gives the appropriate velocity of light. To give the velocity c(1-2u/rc, where u=GM.^{2}), the refractive index must be 1/(1-2u/rc^{2})"

If we solve for the limiting case where a light wave approaching the spherical shell from inside at an angle of 90, escapes to the outside tangentially to the shell and take n

_{1}equal to the refractive index within the modified vacuum, and n_{2}equal to that of free space vacuum; n_{2}=1, we can apply Snell's law to solve for the radius of such a sphere:

sin θ_{1}/sin θ_{2}= n_{2}/n_{1}

sin 0^{o}/ sin 90^{o}= n_{2}/n_{1}

0 = 1-2u/rc^{2}

2u/rc^{2}= 1

r = 2u/c^{2}or 2GM/c^{2}.....= Schwarzschild radius

Precession of the perihelion of Mercury

A long-standing problem in the study of the Solar System was that the orbit of Mercury did not behave as required by Newton's equations. Mercury is the closest planet to the sun. As this planet orbits the Sun, it follows an ellipse as all other planets, but it was found that the point of closest approach of Mercury to the sun does not always occur at the same place but that it slowly moves around the sun. This rotation of the orbit is called a precession. Such effect is not peculiar to Mercury, all the planetary orbits precess. In the diagram shown here, the amount of the advance is greatly exaggerated. The actual advance is only 43 seconds of arc per century. The same phenomenon is more dramatically seen in the binary pulsar PSR 1913+16 where the periastron advances by about 4.2 degrees per year.

Quoting Eddington (1920) in 'Space, Time and Gravitation':"The phenomenon of refraction is in fact caused by a slowing of the wave-front in passing into a region of smaller velocity."

Quoting Einstein :"Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium ... this medium turns out to be equivalent to the gravitational field."

As Mercury orbits in its elliptical motion, it is slowed most at its perihelion, where such optical medium is densest, and is slowed less near aphelion, where this optical medium is sparsest. Such imbalance between refractive index at perihelion and aphelion rotates the ellipse forward, resulting in the advance of perihelion. Le Sage push gravity theories have always had problems to show how gravitons may be effected by the change in density of the refractive index, since in such theories there have never been a direct relation between electromagnetic waves and the ultramundane particles required by these theories. It is due to this missing link that researchers like Tom Van Flandern have been forced to assume the existence of two seperate mediums, the graviton medium and the light carrying medium. We also find the mention of two seperate mediums for gravity and optics in Newton's work. However as you will see in the following paragraph, there is a very direct relation between the two, and that a change in refractive index properties will directly effect the speed of the graviton.

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