Section 7–7 What is gravity?

(Mechanisms of gravity / Strength of gravity / Test of gravity)

In this section, the three main points discussed are mechanisms of gravitational force, the relative strength of gravitational force, and a test of gravitational force.

1. Mechanisms of gravitation:

“Many mechanisms for gravitation have been suggested. It is interesting to consider one of these, which many people have thought of from time to time (Feynman et al., 1963, section 7.7 What is gravity?).”

Feynman explains that many mechanisms of gravitation have been suggested, but no one has given any satisfactory machinery. On the other hand, Newton made no hypotheses about gravitation and he was satisfied with mathematical laws for which no machinery is available. Thus, Feynman cites the law of conservation of energy as a theorem concerning quantities that can be calculated with no mention of the machinery. From a perspective of pragmatism, physicists may continue with this approach such that there are more discoveries or inventions. However, some physicists are deducing how Higgs mechanism may result in gravity. Importantly, we can now detect gravitational waves that are propagating in the speed of light.

Feynman briefly describes Le Sage’s kinetic theory of gravity in terms of tiny invisible particles that impact material objects from all directions. In this theory, any two bodies partially shield each other from the impinging corpuscles, resulting in a net pressure exerted by the impact of corpuscles on the bodies. Feynman reasons that the Earth would stop as a result of the continuous bombardments from these particles. Historically, Newton said that the only possible mechanical cause of gravity was conceptualized by Nicolas Fatio de Duillier in 1690 (Cohen & Whitman, 1999). At present, there are new perspectives on Le Sage’s theory of gravity (Edwards, 2002), and more important, the tiny invisible particles can now be known as gravitons.

2. Strengths of gravitation:

“…The relative strengths of electrical and gravitational interactions between two electrons (Feynman et al., 1963, section 7.7 What is gravity?).”

Feynman expresses the relative strengths of electrical and gravitational interactions between two electrons as 1 divided by 4.17×10⁴². This is similar to the ratio of the volume of the flea to the volume of the Earth. Interestingly, Dirac suggests that the gravitational constant is time dependent and it may be related to the age of the universe. However, Feynman raises an issue if one considers the age of the universe in years: years are not “natural” units of time. That is, years were arbitrarily defined by men depending on the rotational period of a planet. In Feynman’s lectures on gravitation for postgraduate students, he further criticizes Dirac and mentions that “he might just as well describe the situation by saying that the electric charge is time-dependent... (Feynman et al., 1995, p. 8).”

Feynman adds that there is no explanation of gravitation in terms of other forces at the present time. According to Wilczek, a possible mechanism of gravity may be a residual effect of fundamental forces. In his own words, “Gravity might be derived from the other fundamental forces. Because it is a small (feeble) effect, maybe gravity is a byproduct, a small residual after the near-cancellation of effects of opposite electric or color charges, or something more exotic (Wilczek, 2008, p. 149).” Nevertheless, one needs to justify why this force is universal. Moreover, Wilczek suggests that the question “Why is gravity so feeble?” may be rephrased as “Why are protons so light?” In essence, the gravitational force is relatively weak because the object is very light.

3. Tests of gravitation:

“The absence of such an effect has been checked with great accuracy by an experiment done first by Eötvös in 1909 and more recently by Dicke (Feynman et al., 1963, section 7.7 What is gravity?).”

Eötvös first investigated the proportionality (or equivalence) of gravitational mass and inertial mass in 1889 instead of 1909 (Bod et al., 1991). Feynman explains that the gravitational force is exactly proportional to the mass with great precision because there should be an observable effect if the inertia (inertial mass) and weight (gravitational mass) are numerically different. In other words, in his first Messenger lecture, Feynman (1965) states that “[o]ne other test of the law of gravity is very interesting, and that is the question whether the pull is exactly proportional to the mass (p. 29).” Importantly, the uncertainty of this experiment pertaining to the two kinds of mass is within 1 part in 1,000,000,000, or less based on all of the substances tried.

Eötvös’s apparatus consists of two objects which have different materials and are connected by a rod that is suspended horizontally by a thin fiber or torsion balance. Due to Earth’s rotation, the two strings that support the weights of the two objects are not exactly vertical. Based on the Earth’s reference frame, the sum of the string’s tension and the weight of the object are equal to the inertial (centrifugal) force. Note that the weight of the object is dependent on the gravitational mass of the object, whereas the centrifugal force is related to the inertial mass of the object. Essentially, if the gravitational mass and inertial mass are not exactly the same, the rod will rotate.

Feynman explains that the experiment was first done by Eötvös and more recently by Dicke. To give a better picture, Roll, Krotkov, and Dicke (1964) clarify that Eötvös experiment has a precision of 3 ´ 10^-9 and thus, it only supports a weaker form of Einstein’s principle of equivalence (in short, weak equivalence principle). More significantly, Einstein’s general theory of relativity is based on the assumption of “strong equivalence principle.” Furthermore, Roll, Krotkov, and Dicke (1964) argue that the accuracy of the experiment is reduced by effects such as gravitational field gradients, varying magnetic fields, variable electrostatic forces, temperature variation effects, and ground vibration disturbances. By improving their experimental design, they reported that this experiment achieves an accuracy of 1 ´ 10^-11.

Questions for discussion:

1. Should there be a mechanism of gravity?

2. Why is the gravitational force relatively weak?

3. Why should the test of gravity be more precise?

The moral of the lesson: the gravitational force is relatively weak and there should be more precise tests of gravity.

References:

1. Bod, L., Fischbach, E., Marx, G., & Náray-Ziegler, M. (1991). One hundred years of the Eötvös experiment. Acta Physica Hungarica, 69(3-4), 335-355.

2. Edwards, M. R. (ed.) (2002). Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation. Montreal: Apeiron.

3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

4. Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1995). Feynman Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley.

5. Newton, I. (1999). The Principia: Mathematical Principles of Natural Philosophy (Translated by, I. B. Cohen & A. Whitman). Berkeley: University of California Press.

6. Roll, P. G., Krotkov, R., & Dicke, R. H. (1964). The equivalence of inertial and passive gravitational mass. Annals of Physics, 26(3), 442-517.

7. Wilczek, F. (2008). The lightness of being: Mass, ether, and the unification of forces. New York: Basic Books.