Any random sequence of events, such as the lapping of ocean waves on the shore, can become a clock – and physicists have now devised a mathematical procedure for making such an odd timepiece and for measuring its precision.
“How can you turn anything into a clock? We decided to tackle that problem by thinking about processes that, in a way, look the least like clocks,” says at Trinity College Dublin in Ireland.
A wristwatch can be used to keep time because its ticks are both regular and predictable rather than being random. But Mitchison and his colleagues imagined a situation in which someone has been castaway on a desert island without a watch, and is trying to time the cooking of their food by relying on natural processes that repeat, but not in a strictly regular way.
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The castaway could, for instance, make a clock using the semi-regular lapping of ocean waves on the shore, their own heartbeat or the motion of the sun across the sky – which may seem regular and predictable, but that actually vary slightly in a random way if you try to measure them precisely. These processes are called Markovian, and they are composed of “jumps”, or events whose timing does not follow any pre-determined pattern, like a wave hitting the shore.
The team mathematically analysed Markovian processes in their most general form, so that the results would apply as broadly as possible, and calculated just how precisely you could extract time from a set of recorded notes about the jumps.
For instance, in the castaway example, the unfortunate individual would have to record their observations of the many randomly occurring events around them. “It would essentially be a kind of counting, but more precisely,” says Mitchison. “You would note: okay, a wave just came up, then my heart just beat, and then my heart beat again, then another wave.”
His team’s equations, which capture statistical properties of how random jumps are distributed in time, would make it possible to estimate how much time passed between the events and how accurate that time estimate is.
“If you have a set of irreversible Markovian processes, you can turn them into a clock, and this study tells you how to do so,” says at the Austrian Academy of Sciences, who wasn’t involved in the work.
at the University Grenoble Alpes in France, who wasn’t involved in the research, says that for classical (non-quantum) clocks it is important to know the frequency of their ticks and the precision of each tick – and that the new equations put the tightest bound yet on how perfectly such a classical clock can perform with respect to either metric. In other words, beyond providing a way to turn random processes into a clock, the new research also allows us to assess how close a particular classical clock comes to its theoretically best possible performance.
This mathematical work may have implications for how biological systems, which are rich with randomness, keep time, says Mitchison. He says that theoretical bounds on how well molecular machines in cells can keep time have been derived before, but biological systems rarely reached them in experiments. His team’s bound, on the other hand, is tighter and therefore likelier to be detected in the lab.
Because the new results do not account for any quantum processes, Woods says they could also be a tool for diagnosing the “quantumness” of clocks. The accuracy of quantum clocks is far higher than that of classical ones – which is why the world’s best clocks rely on quantum effects for their extreme precision. As such, any clock that is measured using the new equations and that is found to surpass the bound on its theoretical performance limit is probably operating in the quantum realm. All of the researchers that żěè¶ĚĘÓƵ spoke with said that understanding exactly how those quantum phenomena take over to improve the precision of a clock is a compelling subject.
“For me, this work really closes a whole chapter of questions that I had about classical clocks, and the next step is going quantum,” says Huber.
arXiv
