(1)My interest in this subject came about in the following way. I received a PhD in physical chemistry at MIT in 1956, with a thesis on the intermolecular potential of krypton, under James A. Beattie (unpublished, owing to his worsening health and my getting involved in other research). One thing drilled into me was a basic characteristic of interacting systems, namely, if one has a mixture of A and B atoms, the A-A force constant will almost certainly be different from the B-B force constant. When I read about the hypothetical "experiment" recounted by P.W. Bridgman (please refer to the text below), I was reminded again of this characteristic. Among protons and electrons interacting in ordinary matter, it would seem highly improbable that the proton-proton force constant would be identical to the electron-electron force constant. Therefore, I thought, Bridgman's hypothesis was not so far-fetched after all. The account given below is an attempt to render the hypothesis a little more quantitative. I am quite aware that this kind of material explanation for gravity is likely to be considered "crank science" by serious gravity workers. However, I strongly feel that the question posed above, namely that there logically should be a difference between the proton-proton interaction and the electron-electron interaction. If this is not so, I think it is up to those studying relativistic gravitation to show why. -- Emory Menefee ( em@operanut.com )
ARGUMENT FOR A MATERIAL ORIGIN OF GRAVITY
8Emory Menefee
Since the early 1900s, the outlook for a material origin of gravity has become very faint indeed. Einstein introduced a "flat" four dimensional space that is warped by mass objects, the warping giving rise to a restoring gravitational force (1). Space curvature due to the presence of mass objects has been amply verified by experiment, so the duality that mass generates a curvature of space and that space curvature conversely "produces" mass (that is, makes it apparent via a gravitational force) would seem secure. Nevertheless, the classical view that gravity is an "innate" characteristic of a mass object is not necessarily ruled out. The magnitude of space curvature, or its very presence, depends on the magnitude of the gravitational effect, which can originate as a material effect.
P.W. Bridgman long ago speculated about a material origin of gravity: "Lorentz has pointed out that gravitational action between bodies can be accounted for if we assume a slight difference in the electric force between equal positive and negative charges, so that there is a resultant force between two electrically neutral bodies. It is possible by a proper adjustment of the constant determining the difference between the action of the two sorts of charge to reproduce the gravitational constant, and it was shown by Lorentz that the change in the law of force between elementary charges necessary to do this is so slight that it is forever beyond reach of any possible experiment on electrical forces, and that it could be detected only by the ordinary gravitational experiments." (2)
The Lorentz article (3) revealed that he did not claim this idea as original, but referred to earlier work by Mossotti: "I shall start from an idea that has been suggested long ago by Mossotti and has been afterwards accepted by Wilhelm Weber and Zollner. According to these physicists, every particle of ponderable matter consists of two oppositely electrified particles. Thus, between two particles of matter, there will be four electric forces, two attractions between the charges of different, and two repulsions between those of equal signs. Mossotti supposes the attractions to be somewhat greater than the repulsions, the difference between the two being precisely what we call gravitation." Lorentz gave no reference, either to Mossotti or others (4).
The suggestion of a neutral charge model of gravitation stems from one's "physical intuition," which suggests that because protons and electrons are so different in size and structure it would be surprising if the force constants between them were exactly equal. However, the assumption of equality of force constants is a cornerstone of electromagnetic theory, which asserts that the force between any two charged particles at some distance apart in a vacuum is given by
(1)
where ,0 is the permittivity of free space, Q is the charge, and d the distance between the particles. The crucial assumption here is that permittivity is assumed to be the same whether the particles are protons or electrons.
When Lorentz examined this problem, the notion of an "ether" was current. He assumed that a positively charged particle would interact with the ether through a different force constant than that of a negatively charged particle. He furthermore considered the particles to be in motion. Disregarding the ether, we can begin with a general model that is conceptually simpler, namely the existence of three slightly differing permittivities: proton-proton, electron-electron, and electron-proton. In this case, two separated neutral particles, each containing a proton and an electron, will interact with a force
(2)
Here, K1 represents 1/4B, for, say, the electron-electron pair, K2 for the proton-proton pair, and K12 for the two opposite-signed pairs. It is apparent that if 2K12 > K1 + K2 then the two neutral particles will show a net attraction. Although many averages to produce this inequality are possible, one of the simplest is K 12 = [(K1m + K2 m ) / 2]1/ m, with m>1. But notice that there is no fundamental rule other than our experience that dictates the relative values of K1 , K2 , and K12 . Thus, the inquality 2K12 < K1 + K2 would open the possibility of the existence of a repulsive gravitational force.
The connection between the force given in Eq. 2 and the gravitational force is straightforward. Between two distant bodies containing n1 and n2 neutral pairs of oppositely-charged particles, the number of interactions will be proportional to n1n2 . The mass of a body containing n1 pairs will be m1 = µ n1 , where µ is the mass of each neutral pair (essentially the mass of a proton). Equating the gravitational force to the neutral interaction given by Eq. 2, we find for K
(3)
The approximate value of k is 7.2 x 10-27 newton-meter2 / coulomb2 .
Several predictions are possible from the neutral charge model. For example, one would expect antimatter to produce the same gravitation as normal matter. Perhaps more interestingly, however, the model suggests that not all matter has exactly the same attraction. Instead of only neutral pairs of protons and electrons, matter is considered to be made up of 12 fundamental particles: six leptons (electrons, muons and tau particles), and six quarks. Each kind of lepton can have a neutrino form (charge 0), and a charged form (charge -1). Principally, ordinary matter contains electrons (charge -1), up-quarks (charge +2/3), and down-quarks (charge -1/3). A proton contains two up-quarks and one down, to give a net charge of +1. A neutron has two down-quarks and an up-quark for a net charge of 0. Hence, it seems apparent that K between two neutral proton-electron pairs should be slightly different from that between two neutrons. This could be of considerable importance in defining the gravitational field of, say, a neutron star, or in dealing with a system collapsed to quark dimensions. A "truly" neutral particle (e.g., a neutrino) should show no gravitational attraction. However, aside from photons and possibly neutrinos, there seem to be no neutral particles that are not made up of combinations of quarks and leptons.
Another prediction would bear on the currently discredited "fifth force," were it to gain sufficient experimental validation. Although matter is largely empty space, one might expect slight shielding effects to be observed within the neutral charge model, the effect probably being a lessening of the gravitational interaction in more dense material. The "fifth force" is supposed to arise from such a difference. For example, a feather would, for the same mass, show a slightly larger gravitational attraction than a more dense metal ball, since its zero-charge elements would be less shielded from earth's gravity.
Since the neutral charge model involves electrostatic interactions, the question may arise as to whether it would predict cancellation of gravitational attraction between objects electrostatically isolated by, for example, a Faraday cage. Isolation of this kind screens against the electrostatic field of a relatively few isolated or separated charges. Interactions leading to the neutral gravitational attraction should not be affected.
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1. Frankel, T., Gravitational Curvature, W.H. Freeman, San Francisco, 1979.
2. Bridgman, P.W., The Nature of Physical Theory, Dover Publications, New York [from Princeton Univ. Press, 1936], p. 93.
3. Lorentz, H.A., Proc. Kon. Akad. Amst. 2 559-574 (1900).