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Findings show that the gravitational deflection of electromagnetic waves in the microwave frequency spectrum are severely impact parameter dependent at the plasma limb of the sun. By definition the impact parameter epsilon is the nearest point of approach of a given ray of light or a ray of microwaves to the center of the gravitating mass M that is enclosed in an analytical Gaussian sphere of radius R. The light bending rule of General Relativity predicts that impact parameters of epsilon$ approximately R for gravitationally bent rays of light and microwaves should occur in empty vacuum space as well as in the plasma limb of the sun, where R is the radius of the analytical Gaussian sphere that encloses the gravitating mass M of the sun. The past century of astrophysical observations show that the bulk of gravitational light bending effects has been observed primarily at the plasma limb of the sun, namely, at impact parameters of epsilon approximately R. With current technical means in Astrophysics, the gravitational light bending effect should be an easily observable effect for impact parameters corresponding to several solar radii above the plasma limb of the sun, namely, at epsilon = 2R, epsilon = 3R, epsilon = 4R, etc., etc., at epsilon = nR, for analytical Gaussian spheres of several solar radii R. The corresponding effects of gravitational deflection should be 1/2, 1/3, 1/4, ..., 1/n times 1.752 arcsec observed at the solar plasma limb. Of course, this assumes the light bending rule of General Relativity applies to all empty vacuum space above the surface of the sun as well as in the plasma limb. Findings show that the plasma atmosphere of the sun represents an indirect interaction between the gravitational gradient field of the sun and the microwaves from the extra galactic radio pulsar sources. A minimum energy path calculation, supporting this argument, leads to a derivation of the very same light bending equation obtained from the assumptions of General Relativity. This result was confirmed by a measurement on the gravitational deflection of microwaves at the Solar plasma limb by Lebach. (1995), who used a very-long-baseline-interferometer (VLBI) technique. The researchers used extra galactic radio pulsar sources to determine the gravitational deflection of the microwaves from these sources at the solar plasma limb, obtaining a results to within 0.9998 +/- 0.0008 times 1.752 arcsec. PACS: 95.30Sf, 04.25.dg, 52/25/Qt. 52.40.Db

Decades of observations of the gravitational deflection of electromagnetic waves at the solar limb show a very strong impact parameter dependency. Apparently, the gravitational deflection effect is an explainable phenomenon, which vary in relation to the solar limb due to an indirect interaction between the gravitational gradient of the sun and the deflected electromagnetic radiation itself. The famous equation of general relativity for the gravitational deflection of light was derived by an application of the conservation of energy.. It was assumed that the propagating wave in the solar plasma limb travel along a minimum-time or a minimum-energy path. Surprisingly, this result was found to be completely frequency independent. To date no clear distinctions can be made between a direct and an indirect interaction gravitation-electromagnetism interaction. The plasma limb of the sun is a representation of an indirect interaction between the gravitational field of the sun and the deflected electromagnetic waves. The minimum time calculation has been confirmed by a number of very-long-baseline interferometer (VLBI) measurements of the microwaves emitted by the extra galactic radio pulsar sources. Lebach et al. (1995). The impact parameter dependency of microwave signals at the solar limb has been experimentally verified showing that the microwave signals deflect precisely at the impact parameter R exactly at the plasma limb of the sun, where R is the solar radius and at an angle of exactly 1.75 arcsec. A gravitational deflection of microwave signals from extragalactic sources at higher impact parameters are yet to be observed or resolved.

Recorded history of astronomical observations clearly shows that the rays of star light are gravitationally lensed solely the plasma rim of the sun, not in the plasma-free space for impact parameters of light rays above the plasma rim. Although the plasma atmosphere of the sun has a thickness of only a fraction of a solar radius, the gravitational light bending effect as predicted by the light bending rule of General Relativity should be easily detectable above plasma rim in the plasma-free space for several solar radii with current technical means. Findings show the solar plasma atmosphere represents an indirect interaction involving an interfering plasma medium between the gravitational field of the sun and the rays of the stars light. Calculations supporting this argument lead to the very same light bending equation obtained by General Relativity, derived from classical assumptions of a minimum energy path of a light ray in a plasma atmosphere exposed to the gravitational gradient field of the sun. This result is confirmed by cited researchers who used a very-long-baseline-interferometer (VLBI) measurement on extra galactic radio sources to determine the gravitational deflection of microwaves at the solar plasma rim, obtaining a result to within 0.9998 +/- 0.0008 times that of General Relativity. Moreover, there is a clear lack of lensing among the countless numbers of stars, where likely candidates for gravitational lenses and point-like light sources are by good chance co-linearly aligned with the earth based observer. With this condition well at hand and by assuming the validity of the light bending rule of General Relativity, the sky should be filled with images of Einstein rings. Findings convincingly show the failed observation of Einstein rings in the star-filled skies are fundamentally due to the larger impact parameters requiring the light to pass above the stellar atmosphere of the lensing stars due to the astronomical distances.

Findings show that the rays of star light are lensed primarily in the plasma rim of the sun and hardly
in the vacuum space just slightly above the rim. The thin plasma atmosphere of
the sun represents a clear example of an indirect interaction involving an
interfering plasma medium between the gravitational field of the sun and the
rays of light from the stars.  Since the
lower boundary of this vacuum space is only a fraction of a solar radius above
the solar plasma rim, it is exposed to virtually the same gravitational field.
The thin plasma atmosphere of the sun appears to represent an indirect
interaction involving an interfering plasma medium between the
gravitational field of the sun and the rays of star light. An application of
Gauss' law clearly shows that, if the light bending rule of General Relativity
were valid, then a light bending effect due to the gravitational field of the
sun should be easily detectable with current technical mean in Astrophysics at
analytical Gaussian spherical surfaces of several solar radii. More
importantly, the very same light bending equation obtained by General
Relativity was derived from classical assumptions of a minimum energy path of a
light ray in the plasma rim, exposed to the gravitational gradient field of the
sun. An intense search of the star filled skies reveals a clear lack of lensing
among the countless numbers of stars, where there are many candidates for
gravitational lensing according to the assumptions of General Relativity.
Assuming the validity of the light bending rule of General Relativity, the sky
should be filled with images of Einstein rings. Moreover, events taking place
at the center of our galaxy, a region known as Sagittarius A*, thought to
contain a super massive black hole, is considered a most likely candidate for
an observation of gravitational lensing. A lack of evidence for gravitational
lensing is clearly revealed in the time resolved images of the rapidly moving
stellar objects orbiting about Sagittarius A*.

First noticed by Irvin L. Shapiro in 1964, the transit time required for a microwave signal to propagate through space, arrive at a satellite orbiting Venus or Mercury, required a measurable time delay for the reply signal to propagate back to the earth to be received at the antenna of the observatory. The time delay was noticeably affected by the relative position of the sun. Controlled measurements conducted by Shapiro determined that the time-tagged microwave signals had measurable effects that varied as a function of the impact parameter of the microwave beam relative to the sun. The delays were observed to be in the 100's of microseconds when the impact parameter of the microwave beam was at a minimum. After repeated measurements, varying time delays were recorded and were referred to as the Shapiro delay. These measurements permitted a precise determination of the electron density profile of the solar wind as a function of the radial distance r from the sun. The electron density profile of solar wind is found to behave very nearly as an inverse square of r, namely as r^-2, with electron density profile models ranging from r^-2.05 to r^-2.08, and with effects that engulf the outmost planets of the solar system. The bulk of all the Shapiro delay measurements were done using microwave frequencies from 500 MHz to 8.8MHz (with wavelengths from 80cm to 3.5cm). Significant findings of this research reveal that, for all microwave signals propagating in the solar wind atmosphere of the solar system, the waves are subjected to a frequency dependent plasma index of refraction n that exceeds unity, i.e., n > 1.0000000000. For optical, IR and UV wavelengths, the plasma index of refraction is practically n = 1.0000000000 and these wavelengths are virtually unaffected by the widespread atmosphere of the expanding solar wind described by the electron density profile. As a consequence, the Shapiro delay is a very good measurement of a frequency dependent transit-time effect and can not be a space-time effect of General Relativity that is independent of frequency.

Findings show that important fundamental principles of mathematical Physics are consistently misapplied to concepts of gravitational lensing or just simply ignored. The thin plasma atmosphere of the sun represents a clear example of an indirect interaction involving an interfering plasma medium between the gravitational field of the sun and the rays of light from the stars. There is convincing observational evidence that a direct interaction between light and gravitation in empty vacuum space simply does not occur. Historically, all evidence of light bending has been observed predominantly near the thin plasma rim of the sun; not in the empty vacuum space far above the thin plasma rim. An application of Gauss' law clearly shows that, if the light bending rule of General Relativity were valid, then a light bending effect due to the gravitational field of the sun should be easily detectable with current technical mean in Astrophysics at analytical Gaussian spherical surfaces of solar radii, namely, 2R, 3R, 4R, 5R, ..., respectively, where R is one solar radius. An effect of at least one half, one third, one forth, one fifth, etc., respectively, of the observed light bending noted at the solar rim within currently technical means should be easily observable effects. We note that a gravitational bending effect on the rays of starlight is yet to be observed by modern astronomical means at these distances just slightly above the plasma rim of the sun; a clear violation of the light bending rule of General Relativity. Moreover, the events taking place at the center of our galaxy, under intense observations by the astrophysicists since 1992, present convincing evidence that a direct interaction between light and gravitation simply does not take place. This highly studied region, known as Sagittarius A*, is thought to contain a super massive black hole, a most likely candidate for gravitational lensing. The past two decades of intense observations in this region have revealed not a shred of evidence for any gravitational lensing according to the light bending rule of General Relativity. The evidence is clearly revealed in the time resolved images of the rapidly moving stellar objects orbiting about Sagittarius A*.

A frame transfer model introduced here shows that the kinetic energy is totally conserved and accounted for in the ideal inelastic collision as well as in the elastic collision. The kinetic energy transfer between colliding masses in the ideal inelastic collision case is found to be totally consistent with the law of conservation of energy which states that energy can be neither created nor annihilated. In all inelastic collisions, the two colliding masses move jointly at precisely their center-of-mass velocity, a velocity which is unchanging in a closed system of unbound masses. For this reason, a properly formulated energy transfer model is chosen to be one that goes from the initial frame of the moving mass to that of the center-of-mass frame.

Strong astrophysical evidence supported by important fundamentals of Mathematical Physics suggests that a direct interaction between gravitation and electromagnetism does not take place in the empty vacuum space far beyond the solar plasma rim. A fundamental principle of Mathematical Physics, namely, that of the analytical Gaussian spherical surface law, applicable directly to gravitation as well as to electromagnetism, reveals serious flaws in the conventional understanding of gravitational lensing of the sun. The gravitational light bending effect predicted by General Relativity observed at the solar rim should theoretically be an easily detectable effect at distances of multiple solar radii beyond the solar rim. At analytical Gaussian spherical surfaces of radii 2R, 3R, 4R and 5R, respectively, each assumed to be concentric to the center of the sun, the light bending effects of at least one half, one third, one forth and one fifth of the observed light bending effect noted at the solar rim at radius R should be easily detectable effects within currently technical means. Applying Gauss's surface law directly to the enclosed gravitating solar mass, the gravitational effect on a given ray of light depends solely on the mass M enclosed. The evidence clearly shows that a gravitational bending effect on the rays of starlight is yet to be observed by modern Astronomy at distances beyond the solar plasma rim. Furthermore, the time resolved images of the rapidly moving stellar objects orbiting about Sagittarius A*, a region at the galactic core believed to be a super massive black hole, have not revealed any evidence of gravitational light bending. This is a region under intense observations by the Astrophysicists since 1992. A clear lack of observational evidence for optical lensing due to gravitation is apparent when examining the undistorted images of the stars moving along pure Keplar paths about Sagittarius A*. Astrophysical observations reveal that the stellar object s16 has a velocity approaching 3 % of the velocity of light when passing to within a periastron distance corresponding to 60 astronomical units from the black hole thus giving solid evidence that the space in this region has to be, without a doubt, an extremely good vacuum. The space in the immediate vicinity of a black hole is by definition an extremely good vacuum. The presence of any material media near the galactic core mass would conceivably perturb the motion of the stellar object s16 moving with fractional light velocities and would cause it to rapidly disintegrate. To date no sign of gravitational lensing has been observed in this region. {Refereed Paper: Astronomische Nachrichten,  V328, N2, (2007), pp. 186 -191.}

Powerpoint presentation

You can search continually the known cosmic sky with the most modern instruments without ever finding direct evidence for gravitational lensing in the optical region of the spectrum as suggested by the light bending rule of General Relativity. With modern instruments, the evidence should be clearly revealed. The cosmic sky should be filled with visible lensing effects on the light emitted from background sources, everywhere coinciding with the presence of point-like super massive bodies in the foreground. We shall now look at both the observational evidence and the conventional wisdom.

Astronomische Nachrichten,  V328, N2, (2007), pp. 186-191.

For decades now some very important fundament principles of mathematical Physics have been incorrectly applied to the theory of gravitational lensing or just simply ignored. From astrophysical observations it is apparent that the current understanding of the effects that gravitation should have on light is fundamentally incorrect. Astrophysical observations pertaining to lensing are consistent with effects due to an indirect interaction involving an interfering media, not a direct interaction taking place in vacuum space. It is however theoretically possible that current technical means may not permit a distinction to be made between an indirect and a direct interaction between gravitation and light. The thin plasma atmosphere of the sun represents an indirect interaction between the gravitational field of the sun and the rays of light from the stars. There is convincing observational evidence that a direct interaction between light and gravitation is yet to be observed.  Historically, the observed evidence of light bending occured predominantly near the plasma rim of the sun, not in the vacuum space far above the rim. The events taking place at the site of Sagittarius A* presents convincing observational evidence that a direct interaction between rays of light and gravitation in vacuum space simply does not take place. This is clearly revealed in the time resolved images of the rapidly moving stellar objects orbiting about Sagittarius A*,  a region at the galactic core believed to be a super massive black hole.  This is a region that has been under intense observations by the Astrophysicists since 1992.  A clear lack of observational evidence for optical lensing due to gravitation is apparent when examining the undistorted images of the stars moving along Keplar paths about Sagittarius A*. The space in the immediate vicinity of a black hole is by definition an extremely good vacuum. The evidence for this is clearly seen in the highly elliptical orbital paths of the rapidly moving stars orbiting about the galactic core mass.  The presence of any material media near the galactic core mass would conceivably perturb the motion of the stellar object s16 moving with fractional light velocities, thus causing it to rapidly disintegrate. Astrophysical observations reveal that s16 has a velocity approaching 3 % of the velocity of light when passing to within a periastron distance corresponding to 60 astronomical units from the black hole thus giving solid evidence that the space in this region has to be, without a doubt, an extremely good vacuum. It follows from this that a direct interaction between the light emitted from the orbiting stars and the gravitation of this super massive galactic core at the site of Sagisttarius A* is yet to be observed.

The extinction shift principle, the most recent emission theory, leads directly to the solutions of both gravitation and electromagnetism. It has been found that the formulas of both general relativity and special relativity are derivable from a direct application of Galilean transformations of velocities in Euclidean space geometry. The transformations are applied to both the gravitation and the electromagnetism of a theoretically ideal vacuum. The mathematical illustrations show that, as a consequence of Galilean transformations, direct measurement or observation of the primary wave is not possible and neither the primary wavelength nor the velocity of the primary wave is measurable, consistent with all observations. The extinguished primary wave is replaced at interference by a secondary wave that is re-emitted by its secondary source with an extinction-shifted wavelength. The lens, window, or mirror of the measuring apparatus becomes the secondary source. For this reason this effect is coined here as the extinction shift principle. It is herewith mathematically illustrated that this theory is applicable to gravitation as well as electromagnetism.