A Cultural History of Gravity and the Equivalence Principle

Our word gravity and its more precise derivative gravitation come from the Latin word gravitas, from gravis (heavy), which in turn comes from a still more ancient root word thought to have existed because of numerous cognates in related languages. For example, compare the Old English word grafan (grave), the Old Slavic pogreti (to bury), the Sanskrit guru (weighty, venerable), and Greek barus (heavy, grievous) among others. These words have common meanings of heaviness, importance, seriousness, dignity, grimness; the modern, physical sense of a field of attraction did not appear until Newton's time. Indeed, for Galileo, Newton, and scientists up to the beginning of the twentieth century, gravity was no more than an empty name for the phenomenon, a fact that they were well aware of.

The modern term inertia can be traced to its Latin roots in + ars, hence iners, meaning unskilled or artless. Kepler first applied the word in a physical sense, but did not use the modern meaning: he used it only for bodies at rest. Galileo discovered the law of inertia, but did not name it. Newton gave the word inertia its modern sense in the Principia: "A body, from the inert state of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita may, by a most significant name, be called vis inertia, or force of inactivity... ."

In modern physics, inertia is the property of an object which resists changes in the object's motion. For example, it is difficult to push a car even on level ground and in the absence of friction; it is equally difficult to stop it once it is moving. This is conceptually independent of the weight of the car, with which it is often confused.

Gravitational mass is the property of an object which connects to a gravity field, much as the charge on an object couples to an electric field. We might distinguish two kinds of gravitational mass, active and passive. The active gravitational mass is the source of the object's gravitational field, while the passive gravitational mass responds to it. Objects with a lot of gravitational mass respond strongly to gravity and are consequently very heavy. The force due to gravity on a heavy object is called its weight, which depends on the local gravity field and its gravitational mass. How fast the object falls, or accelerates, under the force of gravity depends on the ratio of its weight to its inertia, which resists any change in motion.

The remarkable experimental fact that all objects fall with the same acceleration was known to the ancients. In the fifth century, a Byzantine philosopher, Iohannes Philiponus, recorded and possibly performed a Galileo-style experiment, as part of his commentary on Aristotle's Physics. The fact of the uniqueness of free fall is even more remarkable in the light of modern physics, because it requires that two fundamentally different quantities, inertia and passive gravitational mass, always be exactly proportional to one another. This is usually interpreted as implying that the two quantities are equivalent measures for a single physical property, the quantity of mass of an object; hence, the term Equivalence Principle. There is no similar principle for any of the other fundamental forces.

A direct consequence of assuming the Equivalence Principle is true, is that all bodies fall with the same acceleration under the influence of gravity. The great explanatory power of Equivalence causes it to be promoted to a Principle and taught as Truth. In fact, like all physics, it is only as valid as the experimental measurements (in this case, and at the present time, no better than a few parts in a trillion).

Einstein extended the Equivalence Principle and made it a postulate for his theory of General Relativity. The Strong or Einstein Equivalence Principle states that all of the laws of physics (not just the laws of gravity) are the same in all small regions of space, regardless of their relative motion or acceleration. Since the weaker universality of free fall is a logical consequence of this, the entire theory of General Relativity rests on the single experimental fact that all objects fall with the same acceleration.

Galileo's experiment from the Leaning Tower of Pisa is arguably the best known of all physics stories. Unfortunately no one quite knows whether it really happened. Evidence that someone did it in Galileo's time is in Two New Sciences, in which Galileo has Sagredo say, "But I, Simplicio, who have made the test can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits."

Galileo's pupil and amanuensis Viviani reported that Galileo had done the experiment "in front of all the faculty and students assembled" but there is no other record. Current historical thinking is either that Galileo never did the experiment, intending his descriptions in Two New Sciences and elsewhere as a thought experiment, or if he did do it, intended it as a classroom demonstration rather than an experiment. Galileo had discovered and clearly understood the law of falling bodies from previous experiments, and therefore didn't need to do the Leaning Tower experiment.

Galileo's major contributions to physics were the law of inertia and the law of falling bodies.

Newton and Equivalence

After Galileo, dropping objects to see how they fall became a popular experiment. Perhaps a lot of funding became available. "It has been, now for a long time, observed by others," Newton wrote in 1686, "that all sorts of heavy bodies (allowance being made for the inequality of retardation which they suffer from a small power of resistance in the air) descend to earth from equal heights in equal times."

Newton saw that this equality of descent marked off gravity from all other forces. Consider the force of magnetism. If magnetism were substituted for gravity, soft iron objects would fall quickly, stone and aluminum ones slowly or not at all; some materials, such as bismuth or graphite, would very slowly rise. Magnets would rise or fall depending on their orientation. Gravity, on the other hand, treats all materials and circumstances alike. Very surprisingly, its force is proportional to the same property, mass, that characterizes a body's inertia. As Newton said, the "weight" of a body (its response to gravity) is proportional to the "quantity of matter" in it. Modern physicists instead often distinguish two kinds of mass, gravitational and inertial, which are said to be "equivalent."

Newton's profound insight was that this Equivalence was essential to understanding the laws of motion, and he devised two tests of it. First, he made two identical pendulums, each 11 feet long ending in a wooden box. One was a reference; he started the pendulums together and timed how quickly their cycles drifted apart. In the other he put successively "gold, silver, lead, glass, common salt, wood, water and wheat". If Equivalence holds, the times of swing should be independent of the material, and they were -- to better than a part in 1000. Good enough for government work, and good enough for Newton. Second, Newton realized that if Equivalence is wrong, the motions of Jupiter's moons and of the Earth-Moon system in the gravity of the Sun would be greatly altered. After further refinement by Pierre-Simon Laplace in 1787, this argument yielded a test of Equivalence to a few parts in 107.

Rediscovered in 1968 by Kenneth Nordtvedt, this second test of Newton's is more important even than to Newton because it can check Einstein's idea that gravity pulls on gravity. Through measurement of the Earth-Moon distance by laser signals (to an accuracy of a couple of centimeters!) it has reached a precision of 5 parts in l012.

In the 18th and early 19th centuries, space, time and mass were Newton's three absolutes. Nineteenth-century physics added a fourth, energy. The increasing understanding of James Clerk Maxwell's electromagnetic theory after about 1850 led to deep questions about all of these ideas. In 1881, J.J. Thomson deduced that an electric charge moving through its own 'field' acquires, in addition to any ordinary mass it may have, an electromagnetic mass -- just as a moving ship gains extra mass from the water it drags along with it. In fact, by connecting electromagnetic energy with mass, Thomson anticipated Einstein's E=mc2. When he discovered the electron 16 years later, he conjectured that its mass was entirely electromagnetic. Though he was wrong, he raised issues about mass that remain unresolved. Later in the 19th century Ernst Mach speculated, vaguely, about the origins of mass and inertia in distant bodies.

Maxwell made the velocity of light, c, central to electromagnetism. Where Maxwell's and Newton's ideas came into conflict, Einstein modified Newton to fit Maxwell. His special theory of relativity (1905) replaced Newton's three absolutes by a single one, the velocity of light, and established two paired quantities, space-time and mass-energy, related through c. In Einstein's special theory mass and energy are interconvertible through the relationship E=mc2.

Einstein's next project was a new theory of gravity. He began by linking E=mc2 with Equivalence. Light has energy; therefore it has mass; it must gravitate and be bent by the Sun, and redden as it rises through a gravitational field. The argument is nice, testable experimentally, but puzzling. For light, unlike the electron, has no "rest mass"; its mass is entirely the result of its motion. To extend the Equivalence of mass and weight to so elusive a thing seemed odd. Soon Einstein reinterpreted the same phenomena by considering the effect of gravity not on mass but on time. He hypothesized an equivalence not between two kinds of mass but between observers with different accelerated reference frames. The two observers must find the same laws of physics. Arguing that the laws of physics in a laboratory under uniform gravity is identical to those in a laboratory undergoing an acceleration, Einstein developed the idea of gravitation as spacetime curvature. He found that the gravitational field, like the electric field, should also have mass. Gravity, too, will be a source of gravity; distorted space contributes to its own further distortion. Finally, in 1915, Einstein reached his new theory of gravitation -- his general theory of relativity.

General relativity is a magnificent theory, deep, potent, and aesthetically appealing, but Einstein was not satisfied. Gravity remained separate from electricity, and the connection of mass to geometry was incomplete. For thirty years, Einstein tried to formulate a theory that would solve these problems and unify physics. He failed.

 Investigator Approximate Sensitivity Method Philiponus, 500 (?) "small" Drop Tower Galileo, 1590 (?) 10-2 Drop Tower Newton, 1686 10-3 Pendulum Bessel, 1832 10-5 Pendulum Potter, 1923 10-6 Pendulum Eotvos, 1922 10-8 Torsion Balance Dicke et al., 1964 10-11 Torsion Balance Braginskii & Panov, 1972 10-12 Torsion Balance Shapiro et. al., 1976 10-12 Lunar Laser Ranging Keiser &Faller, 1981 10-10 Fluid Support Niebauer et al., 1987 10-10 Drop Tower Adelberger 1990 10-12 Torsion Balance MiniSTEP ~2003 10-18 Earth Orbit
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