**The
Gravitational Force May Be the
Result of Gamma Ray Energy Exchange
**

Kevin
Fruechte

*Abstract
*

The
following analysis investigates the possibility of there being an exchange of
electron rotational kinetic energy between atoms and molecules, and how it may
relate to the gravitational force. A
conventional, measured value of the gravitational constant is used to find the
wavelength of a graviton which is determined to be 3.97 x 10^{-15} m, on
the order of twice the diameter of the electron.
The calculation reduces to 4hf/3 = G, units added in the body of the
paper, where Planck’s constant, h, is a known physical value, and the
frequency, f, is determined from the wavelength of the photon.
Certain astronomical data is presented as being supportive of the theory;
and a neutron test is suggested that has the possibility of verifying the
proposed lack of gravitational effect on those particles when isolated from
other nucleons. Additionally, since
the resultant energy of the graviton using a conventional value of G is within
0.5 MeV of one third the mass equivalent energy of the proton, the formula is
used to propose a value of G that brings these energies together.

*Background
*

Approximately
ninety years ago, scientists were beginning to accept a model of the atom
proposed by Niels Bohr, which is basically the same model, with quantum electron
orbitals, still used today. Though
it is a matter of opinion, one aspect of that model that has never been fully
brought to coincide with the other aspects is that when an electron is seen as a
charged particle, with mass, it must give off radiation when it accelerates.
Tipler states it this way:

“For
simplicity he chose a circular orbit. Although
mechanical stability is achieved because the coulomb attractive force provides
the centripetal force necessary for the electron to remain in orbit, such an
atom is unstable electrically according to classical theory because the electron
must accelerate when moving in a circle and therefore radiate electromagnetic
energy of frequency equal to that of its motion.
According to classical electromagnetic theory, such an atom would quickly
collapse, the electron spiraling into the nucleus as it radiates away its
energy. Bohr “solved” this
difficulty, modifying the laws of electromagnetism by *postulating*
that the electron could move in certain orbits without radiating.
He called these stable orbits *stationary
states*.” [1]

(Italics
and internal quotation marks are Tipler’s)

There
are many publications that document the difficulty that was encountered with the
acceptance of the Bohr model in the first half of the 20^{th} century.
One recent one is a book on Albert Einstein published in 2005, in which
Andrew Robinson gives us this account:

“There
were two major weaknesses though. First,
the model offered no convincing explanation for the stability of atoms.
According to Maxwell’s equations electrons, being accelerated charged
objects, must radiate energy and quickly spiral into the nucleus.
Bohr’s quantum postulate forbade such an atomic collapse by simple
fiat.

**…** In the end, Bohr’s model of the
atom blended classical and quantum physics imaginatively, even brilliantly (as a
Nobel prize soon confirmed), but without fully satisfying anyone.” [2]

Without
going further into the history, there are several other references that can be
found to indicate that the early effort to reconcile the accepted atomic model
with classical and relativistic theory went on long and hard.
In light of that, it is my intention to re-open the discussion and
therefore I present the following.

*Energy Exchange
*

By
using the diameter of the electron that Rutherford referred to, 2 x 10^{-15}
meter [3], as the wavelength of a generated electromagnetic wave, and the energy
of that wave being calculated as hc/λ, a photon energy of 9.93 x 10^{-11
} J is obtained.
Noticing that this number is on the order of the gravitational constant,
it becomes worthwhile to proceed with an analysis that assumes that the
gravitational force is the result of photon energy exchange between electrons.

Proceeding
with a calculation therefore, where the energy is generated from a certain mass
in proportion to its volume, using a sphere for simplicity, is multiplied by a
factor of 2 for plane polarization, is distributed evenly over its surface area,
and is multiplied by 2 again when there is another mass involved, we can find
the actual wavelength by equating to a conventional value of the universal
Gravitational constant G = 6.672 x 10^{-11 }N-m^{2}/kg^{2}.

The
calculation is done as follows:

[(6.626
x 10^{-34} J-s) (2.998 x 10^{8} m/s) / λ] x [(4πr^{3}/3)
/ (4πr^{2} )] x 2 x (2 kg^{-2}) = 6.672 x 10^{-11 }N-m^{2}/kg^{2}

The
result for the wavelength we will use then is
λ = 3.970 x 10^{-15} m, and the photon energy 5.004 x 10^{-11
} J.

The
frequency for this electromagnetic wave is then obtained by the relation

f = v/λ = c/λ = (2.998 x 10^{8}) / (3.970 x 10^{-15})
= 7.552 x 10^{22} Hz,

which could conceivably be related to the spin of the electron.
The electron may gain rotational inertia through a synchronized encounter
with an oncoming electromagnetic wave of this type, transitioning to a new
quantum spin energy level and carrying the inertia with a larger radial center
of mass. It is proposed that the
photon is generated near the end of an electron turn, the Doppler effect aiding
in assuring that the electromagnetic wave can only add energy to another
electron when that electron is traveling toward the source of the photon, that
being another mass, or a molecule within the same mass.
The increased electron mass, through its also increased linear momentum
and centrifugal pull, will produce an increased centripetal pull by the Coulomb
attraction on the nucleus of the atom, before the electron finishes its turn,
and releases the energy again. It is
also noted that with the de Broglie wavelength of the electron in orbit around
the nucleus of an atom being somewhere on the order of 10^{-10} to 10^{-12}
m, the synchronization necessary would not be thrown off by the particle wave
action of the electron.

The
effect of the increased electron momentum can also be presented through the
relationship mv = F_{c} dt, with F_{c} representing the Coulomb
force, and the turn time remaining constant.

*Rotational Energy
*

In
order to be sure there is sufficient energy in the electron to release a photon
with an energy of 5.0 x 10^{-11 } J,
we can estimate the rotational kinetic energy.
Starting with a spin angular momentum of ћ/2, and 2 x 10^{-15}
meter [3] once again as the diameter of the electron, an estimated angular
velocity, ω, can be found through the following equation if we consider the
electron as a spinning sphere:

ћ/2
= ½ m v r = ½ m r^{2}
ω = ½ (9.1095 x 10^{-31} kg) (1.0 x 10^{-15}m)^{2}
ω

Using
the resulting 1.16 x 10^{26} r/s as the angular velocity, the rotational
energy can be found:

E_{k}
= ½ I ω^{2}

= ½ [ ½ (9.1095 x 10^{-31} kg) (1.0 x 10^{-15}m)^{2}
] (1.16 x 10^{26} rad/sec)^{2} = 3.06 x 10^{-9} J

Using
1.4 x 10^{-15} meter as the radius of the electron, if this is more
accurate, gives an alternative spin energy of 1.56 x 10^{-9} J.

While
the actual radius of the electron is not precisely known, it remains evident
that the energy is substantial enough for the graviton energy to exist in the
electron.

The
angular velocity of the electron, as a uniformly spinning sphere of mass, has no
real physical basis however, since by almost any realistic radius of the
electron this would produce mass velocities that are greater than the speed of
light, v = rω > c.

A
new theory that has the potential of getting around this problem is one that
hypothesizes that the electron is made up of several spinning vortices within
the electron, where each vortex is a “vector field rotating coherently at
ω = mc^{2}/ћ” [4]. Assuming
for purposes of discussion that this is indeed the case, it can be shown that an
approximation of the total rotational energy of the electron using its mass and
experimental spin angular momentum is valid, because the total spin energy
within the boundary of the electron is analogous to the sum of spin energies
over a cross section. In
mathematical terms this can be summarized by Green’s Theorem:

_{C}∫
P dx + Q dy = ∫_{R}∫ (∂Q/∂x - ∂P/∂y)
dx dy

In
terms of the magnetic dipole moment of the electron, this becomes

_{C}∫
E dl = ∫_{R}∫ (∂E_{y}/∂x - ∂E_{x}/∂y)
dx dy,

or

_{C}∫
E dl =
- d/dt _{S}∫ B∙n dA,

which
is Faraday’s Law, written in terms of one of Maxwell’s equations.

It
is readily accepted that the energy responsible for the gravitational force is
likely to exist in a band of frequencies of a certain width, and that there may
be multiple quantum energy levels related to the angular momentum of the
electron. A frequency of 7.55 x 10^{22}
Hz would serve as the average, and the peak.
The bandwidth may be quite narrow however, based on the supposition that
our wavelength, which is approximately twice the diameter of the electron, is
ideal for transferring energy and mass under the circumstances.

As
it is logically necessary that the electron be able to accept this high
frequency energy from an oncoming photon within some inclusive conical angle
that is greater than zero, it is proposed that rectification of the photon is
provided by that part of the magnetic field of the electron which is due to its
high spin angular momentum and negative charge.

*Light bending vector analysis
*

A
vector analysis done by adding the Electric (E) component and the Magnetic (B)
component of an electromagnetic wave of 7.55 x 10^{22} Hz frequency to
the same components of a visible light wave as it crosses that light wave at
various rotational angles shows that the resultant cross product E x B is always
directed outward at some angle relative to the source of the 7.55 x 10^{22}
Hz waves. To achieve conservation of
momentum, the light wave must bend slightly toward the source of the higher
frequency waves, and will be measurable if the flux density of those waves is
high enough.

*EGRET
*

When
the Energetic Gamma Ray Experiment Telescope [5], - EGRET, was configured to
measure photons of energy > 100 MeV, the range included the energy of the
proposed gravity photons, which center frequency in units of MeV is:

(4.136 x 10^{-15} eV-sec) (7.55 x 10^{22} Hz) = 312 MeV.

One
of the directions EGRET was aimed was toward the center of our own Milky Way
Galaxy. Though it has not been
determined how wide the band of frequencies for gravity photons would be, the
telescope would likely have measured some photons within the band, and some with
lower frequencies due to Compton scatter over the large distances that the
proposed photons would have had to travel while traversing portions of the Milky
Way from some of its far reaches.

Two
examples of ^{-15} meter, that stay
within the measurement range, are shown below.

A
θ = 3 degree scatter brings a change in wavelength of:

λ_{2} –λ_{1} = (h/m_{e}c) (1-cos
θ) = 3.325 x 10^{-15} m

The
corresponding wavelength of the scattered gravity photon is:

(3.970 x 10^{-15} m) + (3.325 x 10^{-15} m) = 7.295 x 10^{-15}
m

The
frequency, determined in the usual way, is:

f = c/λ = (2.998 x 10^{8} m/s) / (7.295 x 10^{-15}
m) = 4.11 x 10^{22} Hz

The
energy, in units used with the EGRET instrument, is found as:

E = hf = (4.136 x 10^{-15} eV –sec) (4.11 x 10^{22} Hz)
= 170 MeV

This
is within the range of E > 100 MeV that was used for the mapping of gamma
rays from the Milky Way.

Let
us now try a scattering of 1 degree, and then 2 degrees, of the original 7.55 x
10^{22} Hz photon, which is another possible scenario for having reached
the EGRET instrument.

First,
a 1 degree scatter:

The
change in wavelength is:

λ_{2} –λ_{1} = (h/m_{e}c) (1-cos
θ) = 3.695 x 10^{-16} m

The
corresponding wavelength of the scattered photon is:

(3.970 x 10^{-15} m) + (3.695 x 10^{-16} m) = 4.340 x 10^{-15}
m

The
frequency becomes:

f = c/λ = (2.998 x 10^{8} m/s) / (4.340 x 10^{-15}
m) = 6.91 x 10^{22} Hz

The
energy, in units used with the EGRET instrument, is found as:

E = hf = (4.136 x 10^{-15} eV –sec) (6.908 x 10^{22}
Hz) = 286 MeV

Then,
a 2 degree scatter:

The
change in wavelength is:

λ_{2} –λ_{1} = (h/m_{e}c) (1-cos
θ) = 1.478 x 10^{-15} m

The
corresponding wavelength of the twice scattered photon is:

(4.340 x 10^{-15} m) + (1.478 x 10^{-15} m) = 5.818 x 10^{-15}
m

The
frequency of the photon that has been scattered at 1 degree and then 2 degrees
is then:

f = c/λ = (2.998 x 10^{8} m/s) / (5.818 x 10^{-15}
m) = 5.15 x 10^{22} Hz

The
energy, in units used with the EGRET instrument, is found as:

E = hf = (4.136 x 10^{-15} eV–sec) (5.15 x 10^{22} Hz)
= 213 MeV

*Radio Wavelengths
*

Looking
at other telescopic electromagnetic wave mappings that are available on the
internet, one carbon monoxide emission image provided through telescopes on
earth can apparently give us good correlation to mass.
Looking at the fifth and ninth images on a Washington State University web
site, we can see fairly well coinciding image patterns between EGRET’s >
100 MeV (ninth image) and the CO emission (fifth image) labeled “Radio
wavelengths. Carbon monoxide emission from very cool, dense regions.” [6] at
the base of the map.

Since
we know that the gravitational force is relatively stable over temperature, I
would expect that a > 100 MeV gamma ray map of the Milky Way would correlate
fairly well with a map of much lower frequencies that are said to represent
areas that are “dense”, and “very cool”, in the same view.

*Broad Band Spectrum
*

Furthermore
to finding possible evidence of gravity photons in the gamma ray spectrum, a
search of the internet for graphs yielded a useful one called “Markarian 421
across the Electromagnetic Spectrum” [7].
The diagram provided there shows units of energy per area, per time on
the vertical axis, or erg / (cm^{2} – sec), plotted against
electromagnetic wave frequency on the horizontal axis.
Along with visible light, X-ray, and radio frequency energies indicated,
the broad-band spectrum of Markarian 421 shows a cluster of flux density
readings seemingly centered on the proposed 7.55 x 10^{22} Hz frequency.
These readings were obtained by EGRET on board the Compton Gamma Ray
Observatory, - CGRO, according to the text.

*Earth, Moon, Planets
*

The
moon being a relatively cold object in space, near enough to project lots of
gravity photons in the gamma ray range at and around 312 MeV, and far enough
away possibly to present a “diffuse” [5] level so that the gamma rays could
produce indications through EGRET, an internet search into the matter quickly
found that the telescope was indeed aimed at the moon when it was on board CGRO.
The NASA image “generated from eight exposures made during
1991-1994”, and called “Astronomy Picture of the Day” [8] from February
10, 1997, is shown as being very bright after scientists converted the flux
density to “false color” so that we can get a good mental picture of what
was found.

The
flux density of gravity photons from the moon that reached EGRET would have been
approximately 1 / 250,000 of that which reached it from the earth, which I am
assuming was a discernable level for the instrument, providing the “bright
gamma-ray moonglow”.

The
earth, on the other hand, shows only a perimeter glow and some lighter spots in
the range of 100 MeV < E < 1GeV in a false color image commissioned by the
“GLAST team at NASA”. The
atmosphere of the earth, if generating its own gamma rays due to electrons
accelerating within their orbits as part of air molecules, would have been
releasing a much more diffuse level of photons at and around 312 MeV from its
perimeter, as viewed by EGRET, than that which came from the area that included
the solid mass of the earth.

As
for other planets, the producer of the earth images, D. Petry, gives us the
following:

"Other
planets -- most famously, Jupiter -- have a gamma-ray glow, but they are too far
away from us to image in any detail." [9]

*A Calculated Value of G
*

One
thing that can be noticed about the energy of the proposed gravity photon is
that it is very close to being one third the mass equivalent energy of the
proton, which is also the energy of each of three quarks said to make up a
proton. The gravity photon energy,
to one more decimal place than that used for the astronomical comparisons, is:

(4.136
x 10^{-15} eV-sec) (7.552 x 10^{22} Hz) = 312.4 MeV

One
third the mass of the proton is:

m_{p}
/ 3 = (938.28 MeV/c^{2}) / 3 = 312.8 MeV/c^{2}

It
is interesting that the quark energy can be arrived at through the use of a
measured value of the universal gravitational constant and the principles of the
Planck blackbody radiation law, which is how the center frequency of gravity
photons was calculated in this paper. The
coincidence is within 0.5 MeV.

The
action that naturally arises next then pertains to finding the value of the
gravitational constant when exactly one third the mass equivalent energy of the
proton is used. The calculation
becomes:

G
= [(6.626 x 10^{-34} J-s) (312.76 x 10^{6} eV) / (4.136 x 10^{-15}
eV-sec] x [(4πr^{3}/3) / (4πr^{2} )] x 2 x (2 kg^{-2})
= 6.6807 x 10^{-11 }N-m^{2}/kg^{2}

The
wavelength of a graviton based on one third the mass of a proton is then 3.965 x
10^{-15} m, the frequency 7.562 x 10^{22} Hz, and the photon
energy in standardized units 5.011 x 10^{-11 } J.
Of particular note is that the
gravitational constant calculated this way is within the range determined by
recent free fall experimentation [10].

It
should be possible within the field of quantum electrodynamics also, to show
that a gravity photon is related to one third the mass of the proton.
For now it will suffice to say that since protons are required to keep
electrons in orbit through the photon mediated Coulomb force, and the same
Coulomb force being the final mediator of the gravitational force as proposed,
the mass energy of the proton appears to be integral to gravitational field
action.

*More on Synchronization*

In
order to reinforce why an electron would be able both to absorb a 312.76 MeV
photon in one circumstance, and Compton scatter another photon of the same
energy in another circumstance, it is noted that for an electron to absorb a
graviton it must be traveling at the speed electrons travel when in atomic
orbitals. Additionally, the graviton
must be traveling in an oncoming direction within some inclusive conical angle
that allows the electron to accept the energy and gain mass.
Gravitons approaching electrons in a sideways direction may be deflected
or may simply step through or around an electron in an atomic orbital, while
those traveling in the same direction will obviously be unable to synchronize
for absorption. Electrons not in
atomic orbitals, and traveling at other speeds, are more likely to

As
an example of what can happen when electrons gather in large concentration,
gamma ray bursts are detected in space coming from the Earth in the milliseconds
before a lightning strike. By the
theory here presented, when gravitons coming out of the Earth scatter through a
concentrated field of displaced electrons they lower in frequency past a point
where they, though still gamma rays, cease to be gravitons.
For the Gamma-Ray Large Area Space Telescope – GLAST, a satellite
scheduled to go up in 2007, the GLAST Burst Monitor on board will be able to
measure gamma rays coming from the Earth once they scatter in energy to below 25
MeV [11].

*Free Nucleons, Alpha, and Beta Particles
*

One
logical conclusion to the theory here presented is that free neutrons,
electrons, and nuclei do not participate in the gravitational interaction.
As an example, a neutron, when not bound to a proton by the strong
nuclear force, and without at least one electron in orbit around it, is not
pulled by the gravitational force, and does not exert a gravitational pull, even
though it has mass.

In
1998, a NASA spacecraft called Lunar Prospector was sent to orbit the moon,
carrying Los Alamos National Laboratory’s Neutron Spectrometer, which measured
neutron flux leakage coming off the surface of the moon [R. C. Elphic et al.,
2001]. Apparently, the neutron flux
was measured at LP orbital distances of both 30 km and 100 km.
Figure 2, in the paper cited, is built from data taken at 100 km, and I
assume that this is the case for figure 1 also.
It is interesting that below the 0.029 eV energy in figure 1 that
corresponds to the “escape velocity” of 2.36 km/s, the curves still look
fairly piecewise smooth, which would indicate that the cosmic ray energies that
released the neutrons are discrete. The
cutoff point under 0.01 eV may represent binding energy or instrument
limitation, however I make no assertions on this, not having been part of the
team which analyzed the data.

The
point I would like to make here is that a free neutron coming off the surface of
the moon, if not pulled by the gravity of the moon, would be able to reach a
spacecraft 100 km high regardless of what velocity it was traveling when it left
the surface, as long as distance / velocity does not exceed the “910 s
characteristic decay time” [12], and there are no other interfering forces.

*Verification
*

With
the postulation that isolated neutrons are not pulled by gravity, an experiment
along this line may be the best way to test the theory.
A new technology that shows promise toward the advancement of nuclear and
molecular physics experimentation is the production of ultra-cold neutrons.
It is said that these UCN’s can be launched at low speed.
If a vertical velocity of 5 m/s can reliably be produced in a 2 meter
high vacuum chamber with a neutron sensor at the top, any neutrons sensed would
indicate a lack of gravitational pull, or at least a reduction in what would be
expected based on the neutron having a mass of 1.675 x 10^{-27} kg.
If gravity is not due to the exchange of kinetic energy between electrons
of different molecules, and if the physical principles that cause the
gravitational force act on all objects with mass, in direct proportion to the
mass, then the neutrons at this velocity would reach a height of only 1.27 meter
before falling back down. Auxiliary
challenges in running such a test, however, may be the production of a vacuum
that will allow some neutrons to reach the top without being deflected by gas
molecules, and keeping magnetic fields low enough to prevent deflection due to
their spin and resulting dipole moment.

*Constants used in calculations:
*

Planck’s
constant, h = 6.626 x 10^{-34} J-sec = 4.136 x 10^{-15} eV–sec

Speed of light, c = 2.998 x 10^{8} m/sec

Mass of electron, m_{e} = 9.1095 x 10^{-31} kg

Mass of proton, m_{p} = 1.673 x 10^{-27} kg = 938.28 MeV/c^{2}

Gravitational constant, G = 6.672 x 10^{-11 }N-m^{2}/kg^{2}

*References:
*

[1]
Tipler, Paul A., __Physics__,
Worth Publishers, Inc., 1976, p. 962.

[2]
Robinson, Andrew, EINSTEIN, A HUNDRED YEARS OF RELATIVITY, Harry N.
Abrams, Inc, Publishers, 2005, p. 89.

[3]
Rutherford, Ernest, “The Structure
of the Atom”, Philosophical Magazine, Series 6, Volume 27, March 1914, p. 488
– 498; available online at:

http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Rutherford-1914.html

[4]
Kadin, A. M., “Circular Polarization and Quantum Spin: A Unified
Real-Space Picture of Photons and Electrons”, ArXiv Quantum Physics preprint,
2005, p.2:

http://arxiv.org/ftp/quant-ph/papers/0508/0508064.pdf

[5]
“The Diffuse High-Energy
Background”, NASA Goddard Space Flight Center, 1997-2006:

http://imagine.gsfc.nasa.gov/docs/science/know_l1/diffuse_background.html

[6]
Worthy, Guy, “The Milky Way Galaxy All-sky maps and images”,

http://astro.wsu.edu/worthey/astro/html/lec-milky-way.html

[7]
Keel, William C., “Markarian 421
across the Electromagnetic Spectrum”, University of

http://www.astr.ua.edu/keel/agn/mkn421.html

[8]
Thompson, D. et al., “Astronomy
Picture of the Day”, NASA (GSFC),

http://antwrp.gsfc.nasa.gov/apod/ap970210.html

[9]
Petry, D., “New Image of Earth, Seen Through
Gamma-Ray Eyes”, NASA Goddard, 03.24.05:

http://www.nasa.gov/vision/earth/lookingatearth/gamma_earth.html

[10]
Schwarz, Robertson, Niebauer, Faller, “A Free-Fall Determination of the
Newtonian Constant of Gravity”, *Science*, 282, 2230-2234; 1998:

http://www.ngs.noaa.gov/PUBS_LIB/BigG/bigg.html

[11]
“GLAST Burst Monitor”, NASA Marshall
Space

http://gammaray.msfc.nasa.gov/gbm/

[12]
Elphic, R. C. et al., "THE
LUNAR NEUTRON LEAKAGE FLUX AND ITS MEASUREMENT BY LUNAR PROSPECTOR NEUTRON
SPECTROMETERS”, Los Alamos National Laboratory, Group NIS-1, MS D466;
Observatoire Midi-Pyrenees, Toulouse, France; Lunar Research Institute, Tucson,
Arizona:

http://lunar.lanl.gov/pubs/2001/1489.pdf