Galileo's Pendulum : From the Rhythm of Time to the Making of Matter

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Summary: Simple Harmonic Oscillators Through the Centuries
Review: Like so many stories about Galileo, his flash-of-inspiration about pendulums is an unverifiable legend, but it is a great one. Bored by mass in the cathedral of Pisa, he started watching the chandelier hanging from a long chain, and timing it with the best clock he had available, his own pulse. Maybe he wasn't the first one to notice this, or to wonder about it, but the pendulum blown by drafts took as long to swing back and forth whether it was making a big arc or a small one. The observation was not exactly true, and his means of measuring it were not exact, and maybe the whole thing didn't happen anyway. Nonetheless, Galileo did discover a secret about pendulums that has profoundly affected physics and the whole world ever since. In _Galileo's Pendulum; From the Rhythm of Time to the Making of Matter_ (Harvard University Press), Roger G. Newton has started from this very first observation of a "simple harmonic oscillator" and briskly traced the concept up through quantum theory. The book contains some daunting math, which the author invites those so inclined to skip, but has scientific history and a summary of physics that is exhilarating and clear.

A simple harmonic oscillator (SHO) is only deceptively simple. It can be completely understood mathematically, but gives enough complexity in its variants to be eternally interesting. The most obvious SHO, the pendulum, has its most famous use in clocks, and there are four chapters here on the history of clock-making. It was Galileo himself who, having noticed the regularity of the pendulum swing, realized that a pendulum would be the perfect timer to regulate a clock. He himself designed an escapement for such a pendulum, but only after his death did the design get put into action. Pendulum clocks had their problems, as readers of _Longitude_ know. The coiled balance spring of clocks that could be used aboard ship has, via its elastic properties, the same oscillation potential as a pendulum. Eventually clocks were regulated by tuning forks; the tines of the fork, too, show SHO. Even better results came from electrically vibrating a quartz crystal at millions of times a second, another SHO. Crystals do slowly age, and their periodicity eventually varies, but electrons do not. Atomic clocks, which are more accurate even than the rotations and revolutions of the Earth which clocks are supposed to measure, are based on the frequency of electromagnetic waves emitted when cesium electrons are excited.

Having brought clocks into the quantum realm, the author goes back to trace the physics of oscillation. It was Isaac Newton with his laws of motion who explained why a pendulum acted the way it did, and enabled its motion to be mathematically evaluated. The movement and forces on a pendulum can be graphed, and show up as sinusoidal waves, which are observed all over the place in nature. Fourier discovered that time functions, even if they weren't sinusoidal, could be expressed as sums of different sinusoidal waves. Metaphorically, acoustical and electromagnetic phenomena could be reduced into summed pendulums. Michael Faraday originated the idea of the electromagnetic field, and James Maxwell put the field on a mathematical basis, with, of course, a sinusoidal foundation. Einstein rode an imaginary wave of light to come to his conclusions that reformulated the concepts of space and time. During the last part of the twentieth century, quantum electrodynamics showed that every constituent of matter can be regarded as quantum of different fields, and at the heart of quanta are, surprise, harmonic oscillators. _Galileo's Pendulum_ takes only thirty pages to go from Faraday to quantum electrodynamics, and there are other books to give deeper analysis of the history of physics. However, for the non-physicist, the author has provided a small history with the unique viewpoint of keeping pendulums in sight throughout. Readers will find this an excellent brief review of a surprisingly universal natural phenomenon.