Sep. 25, 2000 While recovering from an illness in 1665, Dutch astronomer and physicist Christiaan Huygens noticed something very odd. Two of the large pendulum clocks in his room were beating in unison, and would return to this synchronized pattern regardless of how they were started, stopped or otherwise disturbed.
An inventor who had patented the pendulum clock only eight years earlier, Huygens was understandably intrigued. He set out to investigate this phenomena, and the records of his experiments were preserved in a letter to his father. Written in Latin, the letter provides what is believed to be the first recorded example of the synchronized oscillator, a physical phenomena that has become increasingly important to physicists and engineers in modern times.
More than 300 years after Huygens' letter, physicists at the Georgia Institute of Technology have recreated his original experiment. Beyond the historical curiosity, the researchers hope this straightforward mechanical system of gears, springs, weights and levers may help them gain insights into more modern and complex synchronized oscillators.
"Having a system available that lends itself to an intuitive and physical understanding could be quite useful," said Dr. Kurt Wiesenfeld, a Georgia Tech professor of physics. "We might be able to learn how this system is like laser systems or superconducting electronic systems. If there are general mechanisms affecting coupled oscillators, then perhaps we can learn about these mechanisms by using the clocks as mechanical analogs for electronic systems."
In particular, Wiesenfeld says the clocks may offer a new way to look at a type of electronic device known as a Josephson Junction.
"It's a very old-fashioned idea, not the way people who study coupled oscillators have been thinking about nonlinear dynamics over the past decade or so," he added. "Classical physics still has things to teach us."
The system under study consists of two spring-powered pendulum clocks attached to a wooden platform with metal weights added. The platform is set on wheels, free to move along a level metal track. Though the clocks are much smaller than those built by Huygens, the relationship between the masses of the pendulum bobs and that of the overall platform is similar. The clocks' period time between ticks is also approximately the same.
The modern clock system includes a feature not available to Huygens: laser monitoring that records the pendulum swings for computer analysis.
So far, the clocks have shown an ability to synchronize only in anti phase -- that is, with their pendulums swinging in opposite directions. This is true even when the pendulums are started in-phase -- swinging in the same direction. The 1665 letter recounts that Huygens also observed only anti phase synchronization, helping confirm that the Georgia Tech researchers have successfully duplicated his experimental conditions.
But the Georgia Tech clocks also display behavior Huygens did not describe: what the researchers call "amplitude death." Instead of synchronizing, one or both pendulums ultimately stop moving altogether. This becomes more likely as weight is removed from the platform carrying the clocks.
Working 20 years before Sir Isaac Newton formulated the now-familiar laws of mechanics, Huygens was hampered in his ability to explain what he saw. Because the clocks are attached to a platform able to move, Huygens suggested that the swinging of the pendulums somehow caused the platform to move "imperceptibly." He also ruled out other theories, including the possibility that air currents caused the synchronization.
Unlike Huygens, Wiesenfield and collaborators Dr. Michael Schatz and undergraduate student Matthew Bennett do have theories to explain what they see.
"In modern terms, the general motion of pendulums can be roughly described as a combination of in-phase and anti-phase synchronized motions, which are 'normal modes,'" explained Schatz, a Georgia Tech assistant professor of physics. "A key feature of our understanding of Huygens' clocks is that the in-phase motion doesn't couple to the platform in the same way as the anti-phase motion. In-phase motion can drive the very small platform movement, which drains energy out of the system through friction between the platform and the surface on which it rests."
But when the clocks are synchronized in anti phase, the swinging pendulums balance each other, generating no movement in the platform. This conserves their energy, thus, providing a mechanism for favoring anti phase motion by the system, he suggested.
"The heavier the platform, the smaller the coupling between the two clocks," Schatz said. "If it's really heavy, the platform doesn't move at all and there is no coupling and no synchronization. But on the other hand, if the platform is too light and there is too much motion, it will damp out the clocks' energy and create 'amplitude death.'"
Despite the differences introduced by improved clock-making, the fact that both systems display stable anti phase synchronization shows the robustness of that feature, Wiesenfeld pointed out.
Recreating the system required considerable research that spanned not only 335 years, but also two languages. Dr. Heidi Rockwood, chairperson of Georgia Tech's Department of Modern Languages, worked with Wiesenfeld to decipher the original Latin -- which turned out to be not as scientifically clear as the researchers had hoped.
"Only with Kurt's help did some of the passages make sense," said Rockwood. "Since he understood the physics, he could ask questions like, 'could this mean such-and-such?' And then things often fell into place." From Rockwood, Wiesenfeld learned that the Huygens letter actually described two different experiments.
But questions remain. "There's a lot of detective work in this," said Wiesenfeld. "You can get some pieces of it, but you're not sure what to fill in. The more you think about it, the more you can imagine other possibilities."
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