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

Kevin Fruechte
Fairmont, Minnesota, USA
April 2007


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.


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 20th 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-m2/kg2.

The calculation is done as follows:

[(6.626 x 10-34 J-s) (2.998 x 108 m/s) / λ] x [(4πr3/3) / (4πr2 )] x 2 x (2 kg-2) = 6.672 x 10-11 N-m2/kg2

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 108) / (3.970 x 10­-15) = 7.552 x 1022 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 = Fc dt, with Fc 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 r2 ω = ½ (9.1095 x 10-31 kg) (1.0 x 10-15m)2 ω

Using the resulting 1.16 x 1026 r/s as the angular velocity, the rotational energy can be found:

Ek = ½ I ω2

   = ½ [ ½ (9.1095 x 10-31 kg) (1.0 x 10-15m)2 ] (1.16 x 1026 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 = mc2/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∫ (∂Ey/∂x - ∂Ex/∂y) dx dy,


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 1022 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 1022 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 1022 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 Readings > 100 MeV

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 1022 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 Compton scattered photons of wavelength 3.970 x 10-15 meter, that stay within the measurement range, are shown below.

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

     λ2 –λ1 = (h/mec) (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 108 m/s) / (7.295 x 10-15 m) = 4.11 x 1022 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 1022 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 1022 Hz photon, which is another possible scenario for having reached the EGRET instrument.

First, a 1 degree scatter:

The change in wavelength is:

     λ2 –λ1 = (h/mec) (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 108 m/s) / (4.340 x 10-15 m) = 6.91 x 1022 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 1022 Hz) = 286 MeV

Then, a 2 degree scatter:

The change in wavelength is:

     λ2 –λ1 = (h/mec) (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 108 m/s) / (5.818 x 10-15 m) = 5.15 x 1022 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 1022 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 / (cm2 – 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 1022 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 1022 Hz) = 312.4 MeV

One third the mass of the proton is:

mp / 3 = (938.28 MeV/c2) / 3 = 312.8 MeV/c2

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 106 eV) / (4.136 x 10-15 eV-sec] x [(4πr3/3) / (4πr2 )] x 2 x (2 kg-2) = 6.6807 x 10-11 N-m2/kg2

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 1022 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 Compton scatter gravitons than absorb them.  Additionally, the activity of the Coulomb force while an electron is in an atomic quantum orbit must play a part in the gravitational process.

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.


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 108 m/sec
Mass of electron, me = 9.1095 x 10-31 kg
Mass of proton, mp = 1.673 x 10-27 kg = 938.28 MeV/c2
Gravitational constant, G = 6.672 x 10-11 N-m2/kg2


[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:

[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:

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

[6]  Worthy, Guy, “The Milky Way Galaxy All-sky maps and images”, Washington State University, Department of Physics and Astronomy, 1999:

[7]  Keel, William C., “Markarian 421 across the Electromagnetic Spectrum”, University of Alabama, Department of Physics and Astronomy:

[8]  Thompson, D. et al., “Astronomy Picture of the Day”, NASA (GSFC), Feb. 10, 1997:

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

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

[11]  “GLAST Burst Monitor”, NASA Marshall Space Flight Center, Oct. 19, 2006:

[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:


 This document is not for sale, reproduction, or publication without written permission from the author.