From the Chalkboard

This is topic # 05,  "Light Bending at the Galactic Core?"

Ein Gedankenexperiment:

Now Solid Evidence!

NO direct gravitational-electromagnetic interaction at the galactic core!

{Posted July 2003}

Let us perform still another Gedankenexperiment. But before that, let us hypothesize that the sum total of the mass M of a star were to collapse down to a miniature dwarf star or something like a black hole.  According to Gauss's Law, the gravitational potential at any Gaussian surface of radius R is a function of the total mass M enclosed.  This effect is theoretically a function of 1/R, where R is the nearest distance of the light ray from the center of the mass M.  The effect has no dependence at all on nearest distance to the surface of the mass as depicted in the following animation. A frequent error in describing light bending effects, as is predicted by General Relativity, is often noticeable in the literature and in many papers written on this subject, often suggesting that the effect is detectable only at the grazing distance from the surface of the mass or, for instance, at the limb of the solar disk.

It should be noted that, with today's astronomical instruments, the solar light bending effect should be very noticeable at distances even greater than that of the grazing distance of the light ray at the surface of the solar mass from the solar center.  From Gauss's surface Law, at the distances of R, 2R, 3R, and 4R from the center of the sun, the gravitational light bending effect on the rays of star light, according to Relativity, should vary theoretically as graphically illustrated below for an enclosed solar mass of M.  Hence, the rays of star light passing by a virtual Gaussian surface at the distance of 2R from the center of the sun should have an effect of one half the quantity of 1.75 arcsec. If we assume the validity of Relativity, then this effect should be easily noticeable in modern astronomy for ALL the stars of the heavens, for the mass located at the galactic core, as well as for the solar mass.

The important point to note here is: The grazing of the light ray at the surface, or tangent to the gravitating mass, as is implied by many theories and taught in many textbooks, should not be required or necessary for the observation of this effect.

Theoretical Light Bending Effect as f(1/R) as is implied by Relativity

IMPORTANT NOTE: The light bending effect implied by Relativity

should diminish continuously as 1/R

In reality, historically, the ONLY observed effect has been one that

grazes the plasma of the solar rim.

The following animation illustrates the historically observed solar grazing effect of star light.

Please note: The referenced http://science.nasa.gov/headlines/y2004/26mar_einstein.htm wherefrom the above image is borrowed, has to do with a topic pertaining to a sought after grand unifying "Theory of Everything", nothing at all to do with this topic.

For a thought process, let us examine a Gaussian surface which encloses a constant mass of M. Supposed we now allow this constant mass to shrink in its size. Collapse in volume.

Shrinking Star of Constant Mass M.

Given such, the light bending effect, according to Gauss's Law, should remain unchanged to the above depicted observer as the grazing distance {nearest distance to the surface of the mass} increases due to the collapsing radius of the mass M.

Let us now take a look at the galactic core of our Milky Way.  To summarize what is apparently taking place at the core, let us first of all examine some  important astrophysical data that will be most helpful in describing the events at the core and will also aid us in performing a Gedankenexperiment on the subject.

Nearly a decade of intense observations by global astronomers and astrophysicists have revealed the following astrophysical data as summarized:

 Parameter Best Value Description Mcore 7.363E+36 Kg Mass of Galactic Core from MPE Galactic Center Research 3.7±1.5 million solar masses determined from rapidly moving stars at the core Reference: Max-Planck-Institut für extraterrestrische Physik: Msun 1.991E+30 Kg Mass of the Sun {for comparison} Rsun 6.960E+08 m Radius of the Sun RSE 1.496E+11 m Mean Earth Orbital Radius about Sun a(Rsun) 274.23 m/s2 Gravitational Acceleration due to Solar Mass at Surface of Sun  (ca 27.98 g's) a(RSE) 5.936E-03 m/s2 Gravitational Acceleration due to Solar Mass at Earth Position  (ca 6.0E-04 g's)

For a hypothetical case, let us assume that the galactic core or the black hole located at the Galactic center were place at the site of the sun and had the radius R=Rsun. What would be the implications for an earth based observer?  The following calculations would apply:

 Parameter Best Value Description 1.647E+04 s Orbital period for Earth with Mass of the Core placed at the Sun would be only Tperiod = 4.58 hours  A year would take only 0.19 days on Earth! 2.20E+04 m/s2 Gravitational Acceleration at the Earth (at distance RSE from Core) would be approximately 2245 g's  Ca 80 times greater than the Gravitational Acceleration at the Sun's Surface! A Light Bending effect grazing the Core Mass using relativistic assumptions for Earth based observer should be more than  106 times the predicted Solar Light Bending effect of the Sun!

To set up our Gedankenexperiment, using the above hypothetical case, a Gussian Surface constructed around the galactic core could be summarized to have the following effects:

 Note:  Any given ray of light that grazes a Gaussian Surface constructed around the Mass of the Galactic Core of radius RSE, the orbital radius of the Earth, will undergo a light bending effect as predicted by   multiplied by a 1/R effect of     The above predicted effect = 8.3 degrees

Expanding this Gaussian Surface to a larger radius, the results would be:

 Note Again: Increasing our Gaussian Surface out to the orbit of Pluto, ca 39.5 AU or 5.6 Light-Hours, above value light bending effect would be that of the above core light bending multiplied by 1/R effect of   The above predicted effect = 0.2 degrees. This equates to 436 times the effect of 1.75 arcsec  for light rays grazing a Gaussian Surface the radius of Pluto's orbit.

Very Important Note: This effect has absolutely no dependence at all on the actual size or radius of the Galactic Core Mass.  The radius of this mass is not known and is not needed for the calculation of the predicted core light bending effects.

Now let us perform our

Gedankenexperiment.

Let an observer on a distant solar system observe the emissions of a star whose light grazes our Super Galactic Core Mass.  Let the light photons have to propagate at least the distance from our present position to the position of the galactic core and pass to within 39.5 astronomical units (5.6 Light-Hours, 0.23 Light-Days) of the center of the core's mass.  Our distant extraterrestrial observer notes the precise position of this star and is plotted on his scope in his own coordinate system.

Our extraterrestrial's coordinate system would note the apparent position of this star if and only if the assumptions of General Relativity were correct, which suggest a direct interaction of electromagnetism and gravitation.  This apparent position would deviate from the actual position of this star by at least 0.2 degrees (720 arcsec), a factor of 436 times that of the 1.75 arcsec of the Solar Light Bending effect as predicted by General Relativity.

Now, our extraterrestrial notes the emissions of yet another star whose light has to graze the galactic core, passing to within 23 Light-Days, a factor of 100 greater impact parameter.  Relativistic light bending effect predicts that this apparent position would deviate this time by 7.2 arcsec from the actual position, a factor of 100 less than the previously noted effect. Even this effect would be extremely significant, and would be apparent when observing distant light sources, whose photons of light happen to graze a supper massive objects as massive as our galactic core.

Now let our extraterrestrial note the photons emitted from the rapidly moving stars whirling about in our galactic core.  Now, the observer notes a region that lies well within tenths of an arcsec.  The observer now decides to plot the path of the stars moving about the galactic core.  If General Relativity were valid, the extraterrestrial observer would plot the apparent paths of the rapidly moving photon emitters and would also note that the geometry of the paths, due to light bending distortions, would not fit properly any of the conic sections.  Their orbits would deviate drastically from that of true Keplar orbits, as 7.2 arcsec is far greater than the tenths of an arcsec field of observation.  From observational evidence, this is actually not the case.  This is also consistent with the fact that there can be no material secondary sources of emission at the surface of a black hole.

Intergalactic and Interstellar Secondary Sources of Emission

The Evidence

It is also evident that the so-called Gravitational Lensing effects at the rim of the sun are direct consequences of the secondary sources of emission as is predicted by this emission theory.  The evidence is clearly seen at the light bending effect most apparent at the solar rim only. This is also evident from the scattering (re-emissions) of the intense X-ray sources.

details http://www.uni-muenchen.de {Search X-Rays sources, Prof Saglia}

The image of the X-Ray Emission being scattered by secondary sources of emission surrounding the X-Ray source is direct proof for the presence of unseen intergalactic and interstellar dark matter. Without the presence of this unseen re-emitting matter, the X-Ray sources would have gone completely unnoticed. See also Chandra X-Ray Space Telescope photo: http://www.chandra.harvard.edu/photo/2006/1e0657/1e0657.jpg {chandra.havard.edu}. Also star Eta Carinae in infrared: http://science.nasa.gov/newhome/headlines/ast08oct99_1.htm

However, being realistic and true to observational evidence, let us assume our extraterrestrial observer did actually note the very same Keplar motions of the rapidly moving stars observed by global astronomers and astrophysicists over the past decade, since the very same laws of nature should universally apply.  {See movie image file: http://www.mpe.mpg.de/www_ir/GC/images/movie2003.gif ; Max-Planck-Institut für extraterrestrische Physik

{See also http://www.mpe.mpg.de/www_ir/GC/intro.html} This is thereby consistent with an indirect interaction of gravitation and photons via secondary sources of emission as is predicted by Extinction Shift Principle.  The proof lies in the everyday features of the cosmology of point light sources.

Light bending as theoretically implied by Relativity

The above illustration assumes a tilt of the orbital plane of approximately 15 degrees

relative to the line-of-sight.   The light must pass over the gravitating mass from behind.

It is easily noted that any light grazing the galactic mass of the Milky Way of 3.6 million solar masses, coming to within 5.5 light days (less than 0.12 arcsec), the semi-major axis of the star orbiting about Sagittarius A* with an orbital period 15.2 years, must deflect, according to General Relativity, by an angle of at least 30.7 arcsec.  This is easily demonstrated using simple dimensional analysis and the light bending equation of General Relativity.

IMPORTANT: Do solve this exercise as a Gedankenexperiment! IMPORTANT

A practically forgotten Principle of Reciprocity clearly implies near field distortions,

assuming that any direct interaction of gravitation and photons actually took place!

The Principle of Reciprocity clearly suggests that the observer would definitely see both the nearer and distant stars at the very same image position that happen to coincided with an optical path as is implied by General Relativity.  This is not evident!

The above illustrations clearly imply that the images of the orbiting stars are bound to be greatly distorted,

given the validity of General Relativity, as all these stars would have to be bound to the very same principle of light bending!

The Principle of Reciprocity states that the path of the photons from any near-field star that lies on the optical path of the photons from a distant star, must take the very same optical path as the photons from the distant star to reach the Earth based observer. The photons moving on a give light ray, arriving from a source near Sagittarius A*, from symmetry, must experience at least half the light bending effect as the photons arriving from the distant source.  This assumes the lens is midway between the distant source and the observer.

Important Note: The impact parameter of 1.616 arcsec of the Einstein ring is nearly an order of magnitude greater than the semi-major axis of the orbit of S2. Since the past decade of astrophysical observations made on the Galactic Core, a number of other stars, S1 for instance, have already been observed to have passed well to within this impact parameter of 1.616 arcsec!

Most obviously evident is the lack of lensing or distortions (deviations from the Keplar motion) in the apparent orbital paths of the rapidly moving stars about the Galactic core. Also note: optical lensing effects on the images of S2 as predicted by General Relativity are not seen. {Review again the movie image file.} Also, the countless numbers of wandering stars (wanderers) about the heavens should have already given enormous opportunities for the observation of this effect predicted by Relativity.

Therefore, NO gravitational light bending is predicted at the Galactic Core of the Milky Way as a consequence of direct interaction of electromagnetism and gravitation.

The past decade of astrophysical and astronomical observations made on the Galactic Core of the Milky Way reveals NO definitive evidence of  gravitational light bending as can be revealed from the emissions from the rapidly moving stars around Sagittarius A*.

This emission theory predicts that all future observations will reveal NO light bending as a consequence of direct interaction of electromagnetism and gravitation.

The Extinction Shift Principle does predict the bending of rays of light at the thin shell of the plasma at the surface of the sun and stars as is observed at the sun due to direct re-emissions of the photons of stellar rays grazing the solar plasma.  The very same light bending equation is derived from this emission theory. This effect is due to an indirect interaction via the solar plasma, not a direct interaction between the gravitation and electromagnetism. Beyond the solar plasma, it is predicted by this emission theory, there can be no gravitational light bending in the vacuum media.

As there can be no material secondary sources of emission {no dipole re-emitters} at or above the surface of black holes, i.e., a space void of matter, an ideal vacuum, there can be no bending of the light rays of primary photons at the surface of a black hole as predicted by the Extinction Shift Principle.

The undistorted image of true Keplar orbits about the galactic core along with images of apparent undistorted circulating accretion disks about black holes would be in itself a direct violation of the theoretical light bending effect as is predicted by Relativity.

A quick search will reveal tremendous silence on this topic surrounding Sagittarius A*.