The EMRP Gravity Theory

© Engineer Xavier Borg - Blaze Labs Research

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Speed of gravity

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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 with 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 speeds not greater than c. In order to understand the speed of gravity one has to analyse the origin, 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, 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.
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 2x10¹⁰c.

The 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 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.

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= √(e_rm_r)

where e_r is the relative permittivity, and m_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. The speed of all electromagnetic radiation in vacuum is the same, approximately 3×10⁸ 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.

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 q₁ and q₂ according to Snell's law:

sinq₁/sinq₂= v₁/v₂ = n₂/n₁

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 sphere

This 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.


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/c².

In order to calculate this critical angle, let q₂ = 90^o and solve for q_crit:

q_crit = sin^-1(n₂/n₁)

When q₁ > q_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/rc²), the refractive index must be 1/(1-2u/rc²)", where u=GM.

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 n₁ equal to the refractive index within the modified vacuum, and n₂ equal to that of free space vacuum; n₂=1, we can apply Snell's law to solve for the radius of such a sphere:

sinq₁/sinq₂= n₂/n₁

sin 0^o/ sin 90^o = n₂/n₁
0 = 1-2u/rc²
2u/rc² = 1
r = 2u/c² or 2GM/c² ..... = 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.

Dispersion of electromagnetic waves in space

Dispersion is the change of index of refraction with wavelength. Generally the index decreases as wavelength increases, blue light traveling more slowly in the material than red light. When the refractive index decreases as wavelength decreases the situation is known as anomalous dispersion, and has been observed at X-ray frequencies and higher. Any refracting medium offers some degree of dispersion including vacuum. Different vacuums at different energy levels, such as the space within a strong gravitational field, have different refractive index and also a different degree of 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 Plancktons of different frequencies, different velocities while travelling in space.

Click on diagram to activate Greg Egan's nice applet,
but read below about its 'shutter' function.

Now that we know about the distribution curve of Planckton energy, about the refractive index of space, and about the presence of anomalous dispersion expected at high frequencies from refractive mediums, we can work out what happens to the Planckton energy as each wave travels at subluminal (less than c) velocities from the universe core to each body in existence. Let's consider our solar system, a space in which we measure the speed of light to be equal to c. The refractive index of space would slow down electromagnetic waves of higher frequencies to subluminal velocities. All waves in the Planckton energy band would be moving at a velocity less than c. The interesting part of this process, is that even though electromagnetic waves do not act upon each other, the resultant radiation pressure does add up at any point in space. In the diagram shown above, the lower white curve is simply the addition of the waves above it. The poynting vector of such a wave packet will thus be detected as an impulse over the target, more like an individual particle push than a continous force. What's even more interesting is that this wave packet does travel at superluminal speeds, even though its constituent waves are classical electromagnetic waves. This is not an artifact, it's a real energy packet travelling at superluminal speeds, with characteristics that would certainly fit the theorised graviton, or the ultramundane particles which Le Sage has described as most certainly they must be of exceeding swiftness and must be carried far more quickly that the light of the Sun and had estimated their speed to be at least 10¹³ times c.


Requirements to generate a superluminal graviton

The variation of speed of light can be characterised by describing the medium's refractive index, n, as a function of frequency f; the speed of a single pure sine wave is then equal to c/n(f). This speed is known as the phase velocity of the medium at the specified frequency. The electric field of a single frequency EM wave in a medium with refractive index n(f) takes the form:

E(x,t) = E0 sin(2.π.f (n(f)x/c - t)) .... (1)

At any given moment, two sine waves of slightly different frequency travelling together through the medium will be in phase with each other at a number of points. These points will move with time, and the speed at which they move can be found by equating the phases of the two waves. Assuming that the waves have frequencies of f and f+Df:

f(n(f)x/c - t) = (f+Df) (n(f+Df) x/c - t)
f(n(f)x/c - t) = (f+Df) ((n(f) + (d/df[n(f)])Df) x/c - t)
x = (c / (n(f) + (f+Df) d/df[n(f)])) t

The group velocity v_g equates to x/t, and for two frequency components that have almost the same frequency, that is as Df->0, we get:

v_g = x/t = c / (n(f) + f*d/df[n(f)]) ...(2)

For the condition d/df[n(f)] < (1-n(f))/f , we get v_g > c

The group velocity describes the speed of a wave packet that relies on 2 or more different frequencies remaining in phase. For example, a pulse of finite width will contain a range of frequencies, and the centre of the pulse will occur where they are all in phase, so such a pluse will move with this velocity. when the refractive index falls with increasing frequency ,that is, whenever d/df[n(f)] is negative, the situation is known as anomalous dispersion. If d/df[n(f)] < (1-n(f))/f , it can reduce the denominator in Equation (2) to less than one, yielding an electromagnetic pulse velocity greater than c. This packet is thus able to transmit its poynting vector pressure impulse at speeds much faster than the speed of light, even though the 'sea' in which it travels is made up of subluminal EM waves. So what happens when a third body gets in the way? Some people make the mistake of analysing this situation by introducing a kind of independent shutter in the middle of the path of the EM waves to work out such event. The big mistake is that this shutter, if it should correctly simulate a third material body, is made up of the incoming planckton radiation itself, so a third body must be simulated by looping these EM waves in a complete circle to form its own De Broglie matter waves, before continuing their journey. This would result in a time dilation effect over the straight line path time denoted by t, in the above equations. The more matter there is, the more loops have to be done. It is analogous to someone moving a rope up and down to generate waves. The crest of the waves will travel at a certain speed along the rope, but if one just pulls the rope horizontally, the tension would travel much faster than the waves. So, intruducing a third body would effect this tension, it would in fact make the rope go slack. If Dt is the extra time taken by each wave to go around the third body position, then the group velocity calculated over the complete straight path length x, will no longer be equal to x/t but to v_g'=x/(t+Dt) < v_g, hence the superluminal graviton reaching its final target from this shadowed region, will effectively have a lower REAL group velocity than others which come from a less shadowed region. The APPARENT group velocity however, remains the same, since the graviton will reach the target in the same time as before. I have already explained in my unified theory foundations section, how one can derive Lorentz factor by considering such changes in the path velocity within a refractive medium. So, by the introduction of a third body, we have both a real and apparent change in velocity of the constituent EM waves, which travel at the speed of light, and a real but no apparent change in superluminal velocity of the graviton packet. Now, it happens that we percieve only what is apparent, and might be tempted to say that the real change in graviton speed is only an artifact, because it seems to perform the extra loop in zero time, but what is an artifact for us, might not be an artifact to the masses involved. We already know that some physicists, attempting to unify gravity with the other fundamental forces, have come to a startling prediction: every fundamental matter particle should have a massive "shadow" force carrier particle, and every force carrier should have a massive "shadow" matter particle. This relationship between matter particles and force carriers is called supersymmetry. Such startling predictions are due to the fact that matter itself has both real and imaginary components of mass, and will not only react to what is apparent, but also to what is real. I have discussed this matter in my Variable Phase Model of the nucleus, which basically shows that mass has both components. Thus the forces acting on the target body, will be effected by the loop delay, even though the delay cannot be seen in the apparent group velocity. This imbalance of graviton pressure is equivalent to the radiation imbalance I have already explained. Such imbalance is creating the force of gravity, and gravitational information IS travelling at superluminal velocities, even though the actual individual electromagnetic radiation waves composing the medium are subluminal.

So, in EMRP theory, gravity is mediated by the shadowing effect of radiation pressure of paired photons coming from the extragalactic radiation in Planck's frequency region. These pairs of photons are compliant with the hypothetic properties of the graviton. To this day, we learn that the gravitational interaction is carried by gravitons. Although the graviton has yet to be observed, some of its hypothesized properties are known. It is a massless particle having no electrical charge. Its spin is twice that of a single photon; in technical terms, its spin is 2 hbar instead of 1 hbar, where hbar is Planck's constant divided by 2 pi. So, as explained above, the definition of the hypothetic graviton would in fact result in an entity that can travel faster than the speed of light.