Today’s most advanced clocks keep time with an incredibly precise rhythm. But a new experiment suggests that clocks’ precision comes at a price: entropy.
Entropy, or disorder, is created each time a clock ticks. Now, scientists have measured the entropy generated by a clock that can be run at varying levels of accuracy. The more accurate the clock’s ticks, the more entropy it emitted, physicists report in a paper accepted to Physical Review X.
“If you want a better clock, you have to pay for it,” says physicist Natalia Ares of the University of Oxford.
Time and entropy are closely intertwined concepts. Entropy is known as the “arrow of time,” because entropy tends to grow as time passes — the universe seems to consistently move from lower entropy to higher entropy (SN: 7/10/15). This march toward increasing entropy explains why some processes can proceed forward in time but not in reverse: It’s easy to mix cream into coffee but exceedingly difficult to separate it again. Machines also increase disorder as they operate, for example by giving off heat that boosts the entropy of their surroundings. That means even a standard, battery-powered clock produces entropy as it ticks.
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Physicists had previously calculated that, for tiny quantum clocks, there’s a direct relationship between the maximum possible accuracy of their ticks and the amount of entropy emitted. But larger clocks are too complex for such calculations. So it wasn’t clear if such a rule held for other types of clocks, too.
To test how much entropy was released in the ticking of a simplified clock, Ares and colleagues made a clock from a thin membrane, tens of nanometers thick and 1.5 millimeters long, suspended across two posts. An electrical signal sent into the clock jostled the membrane, causing it to flex up and down. This bending motion repeated at regular intervals, like the steady ticks of a clock, and an antenna registered that motion. The more powerful the electrical signal was, the more accurately the clock ticked. And as the clock’s accuracy increased, the entropy — a result of heat produced in the antenna’s circuit — increased in lockstep.
That result suggests that the theoretical relationship for quantum clocks also applies to other types of clocks. “It’s nice to have that,” says physicist Juan Parrondo of the Complutense University of Madrid, who was not involved with the study. “What I’m not so sure of is how universal is this type of relationship that they find.” The researchers studied only one variety of clock. It’s not yet clear whether the relationship between accuracy and entropy applies to clocks more generally, Parrondo says.
But some scientists suspect the relationship may be universal, revealing a fundamental aspect of how clocks function. The new study “would push us even more in this direction,” says quantum physicist Ralph Silva of ETH Zurich, who was not involved with the research. “It’s a data point in favor that it’s probably the case for all clocks. But that’s not been proven.”
In order for a clock to operate reliably, it must undergo a process that has a preferred direction in time. If the clock didn’t create entropy, it would be just as likely to run forward as backward. And the more entropy the clock creates, the less likely it is that the clockwork will suffer from fluctuations — temporary backward steps that would degrade its accuracy.
So if the accuracy of all clocks does come at a cost of increased entropy, that trade-off may reflect a close link between the passage of time and its measurement.