The Inverse Square Law and
The Source of Gravitational Energy
David W. Talmage, M.D.
When Newton considered the connection between the fall of the apple and the fact that the moon stays in its orbit, he noticed that the moon fell toward the earth in one minute the same distance that the apple fell in one second. (sixteen feet). It seemed strange that there were 60 seconds in a minute and the moon was 60 times farther from the center of the earth than the apple. From this bizarre coincidence Newton derived the inverse square law. The force of gravity is inversely proportional to the square of the distance. Newton delayed publishing this finding for twenty years while he worked out the mathematical proof that the sum of the forces from the different parts of the earth was the same as if the entire mass of the earth were at its center.
Less than a century after Newton, Charles Coulomb demonstrated the law that bears his name. This was that the force between two stationary electric charges is inversely proportional to the square of the distance. This remarkable similarity between the forces of gravity and electric charge has stimulated the efforts of physicists over two centuries to unify the two forces. Before Newton, Kepler had proposed that the planets were kept in their orbits by some kind of magnetic force. Einstein spent the last thirty years of his life in an unsuccessful effort to find a common equation that would describe the two forces. And quantum physicists in the last 75 years have tried with equal lack of success to quantize gravity. Thus, the construction of a bridge between gravity and electromagnetism (EM) has failed from both directions.
The usual interpretation of the inverse square laws is that they represent the natural effect of an expanding sphere the area of which is proportional to the square of the radius. This would imply that the forces of gravity and electromagnetism are radiated like a beam of light, the intensity of which is inversely proportional to the square of the distance.
But what about electric and gravitational potential? With both gravity and EM, the force is equal to the gradient of the potential, which implies that the potential is inversely proportional to the distance, not the square of the distance. There is good reason to think that the force is created by the potential, not the other way around. There can be potential without force if the potential is flat, i.e. without a gradient. But there is no force without a gradient in the potential. In the case of gravity there is strinking evidence that the potential is primary. Changes in both clock rate and speed of light are inversely proportional to the changes in potential and unrelated to the gravitational acceleration. Thus, the important question is “Why is the potential inversely proportional to the distance?”
There are three reasons for concluding that the potential is not a radiation. The first is that potential is not inversely proportional to the square of the distance. The second is that the gravitational potential cannot be absorbed by any substance and the electric potential can only be neutralized by the opposite charge. The third reason is that there is no evidence that something has been lost from the source. Thus, it is safe to conclude that potential is not radiated energy. So what is it?
To add to the confusion both electric charge and gravity can radiate energy when the sources are moving rapidly relative to other sources. In the case of electric charges, EM waves are radiated that possess energy and momentum, can transmit information or heat a cup of coffee. The energy in radiated EM waves is inversely proportional to the square of the distance. According to the General Relativity Theory (GRT), large double masses such as binary stars radiate gravitational waves that contain energy and momentum. Evidence that such waves exist was obtained from observations of the Hulse-Taylor binary system. One of the stars is a pulsar and the rate of revolution can be determined from Doppler effects. Over a period of many years sufficient energy has radiated from the system to cause the stars to spiral inward toward each other. The amount of energy lost corresponded to that predicted by GRT. A great deal of time and money has been spent attempting to detect these gravitational waves. So far none has been detected. According to GRT the amplitude of gravitational waves is inversely proportional to the distance from its source, but the energy in the waves is inversely proportional to the square of the distance. Current efforts to detect the gravitational waves are based on the possibility of detecting the amplitude of the waves, not their energy, because the square of the distance is a prohibitively large number. This seems strange, because the stationary gravitational potential, which corresponds to the amplitude, can only be detected by the changes it produces in clock rate. Perhaps this is the reason that gravitational waves have not been detected after 30 years of effort.
Regardless of the explanation of the failure to detect gravitational waves, a clear distinction should be made between the stationary fields that surround electric charges and gravitational masses, and the radiated energy that can be produced by relative motion. According to quantum electrodynamics (QED), the stationary electric charge is the result of a cloud of virtual photons that surround the charges. The density of these virtual photons is inversely proportional to the distance. Virtual photons cannot be detected directly and the evidence of their presence is that their existence permits the calculation of the magnetic moment of an electron that corresponds to observation to ten decimal places. The usual explanation of the action of the virtual photons is that their exchange between charges results in either attraction or repulsion depending on the charges. In the case of gravity there is only attraction. At the end of this article I will propose an alternate explanation of how the exchange of photons can produce an attractive or repulsive force.
Thus, the inverse square laws of stationary gravity and EM are not the result of a radiated field. The inverse square laws are a result of the fact that the force is equal to the gradient of a potential field, the density of which is inversely proportional to the distance. The potential field is not a radiated field but is tethered to the mass from which it is derived. It may be considered as a part of that mass that is distributed over space according to the Uncertainty Principle. In general, radiation contains energy and obeys the inverse square law. But both gravitational and electric potential are not radiation and they contain no usable energy. They produce a force, not by contributing their own energy but by their ability to extract energy from the matter particles they affect.
Matter is made of two different stable particles, electrons and protons, and one other particle, the neutron, that is stable only when attached to an atomic nucleus. All three particles contain very large amounts of energy according to the equation E = mc2. Under a given set of conditions of motion and interaction with other particles, the amount of energy in each particle is precisely determined. The result is that every electron is exactly the same as every other electron under the same conditions. The same is true for every proton and every neutron. A proton contains approximately 1838 time as much energy as an electron, and the neutron contains slightly more energy than a proton.
Under different conditions the amount of energy required to form one of the three particles changes. There are two situations where this change has been large enough to be observed as a change in mass. The first is with nuclear energy where there is clear evidence that the energy is derived from a reduction in mass. The second is with accelerated charged particles where the increase in mass is observed by a change in the mass/charge ratio, which affects the path that the particle takes in a magnetic field. A change in mass from a change in gravitational or electric potential has not been observed. But there is an exact correlation that suggests that there is an undetectable change in rest mass with a change in gravitational potential. This is the observation that the fractional change in clock rate of matter is exactly equal to the fractional amount of mass/energy that is released from a gravitational fall..
In conclusion, the forces of gravity and electric charge are inversely proportional to the square of the distance because they are equal to the gradient of the potential, which is inversely proportional to the distance. The potential does not follow the inverse square law because it is not a radiation but is a tethered part of the source mass which is distributed according to the Uncertainty Principle, The energy obtained from a gravitational fall or electric discharge is not obtained from the potential field but from the enormous rest mass of the matter particles.