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The Laws of Attraction

By Steve Humphrey

 

Love is mysterious. What draws one person to another? Why does A love B, while C has no use for either one? Why does A love B, but B doesn’t know A is alive? There is another attractive force that is no less mysterious: gravity. Unlike love, gravity is universal. It can’t be shielded and it affects everything in exactly the same way. If you take a magnet and hold it some distance from two iron balls of different masses, the smaller one will accelerate more quickly than the larger one. But everything falls at the same rate in a gravitational field. A field source creates a force field that has a particular strength at a distance from the source, and the strength of this force falls off as a function of distance. In the case of gravity, it falls off as the square of the distance, so that something twice as far from the source will experience one-fourth of the force. For example, anyone who has tried to conduct a long-distance relationship can attest to this. But, the acceleration due to a force is also a function of the mass of the test bodies. Something twice as heavy should fall faster than something lighter if they are dropped from the same height. Galileo is alleged to have tested this by dropping cannonballs of different masses from the Leaning Tower of Pisa. This story is almost certainly apocryphal. Though he was born and raised in Pisa in the 16th century, and though the Tower was completed in the 14th, and began leaning well before it was finished, the difference between falling times would be so small as to be indiscernible. He did most of his work on gravity using balls rolling down slightly inclined planes. It has since been shown to very high orders of precision that everything falls at the same rate in a gravitational field, regardless of mass or composition.

Einstein used this fact in developing his General Theory of Relativity, which is his theory of gravity. He used the example of an elevator, both in a gravitational field and being accelerated outside a gravitational field. Someone inside this elevator would not be able to tell the difference between them. Articles of clothing dropped in the accelerating elevator would appear to fall at the same rate, just as they would in a gravitational field. Einstein took this to imply that the two situations are exactly equivalent and produced a remarkable prediction based upon his “Principle of Equivalence.” Consider a flashlight beam shining through a hole in the accelerating elevator. The path of that beam would appear to bend as a result of the acceleration. But, if the Equivalence Principle is correct, then the same thing should happen in a gravitational field. In 1919 during a solar eclipse, astronomers led by Arthur Eddington observed that starlight grazing the edge of the sun was actually bent by exactly the amount predicted by Einstein. This discovery was trumpeted around the world and made Einstein the famous public figure he is today.

So next time you and your lover see the effects of gravity, you can ruminate on the mysterious nature of falling, both in love and toward the Earth.

Steve Humphrey has a Ph.D. in the history and philosophy of science, with a specialty in the philosophy of physics. He teaches courses in these subjects at the University of California, Santa Barbara and has taught them at the University of Louisville.