King's College London

A newly discovered set of mathematical equations describes how to turn any sequence of random events into a clock, scientists at King’s College London reveal.

The researchers suggest that these formulae could help to understand how cells in our bodies measure time and to detect the effects of quantum mechanics in the wider world.

Studying these timekeeping processes could have far-reaching implications, helping us to understand proteins with rhythmic movements which malfunction in motor neurone disease or chemical receptors that cells use to detect harmful toxins.

Einstein famously said that “Time is whatever a clock measures” and while a wristwatch keeps time because it ticks at regular intervals, events which don’t follow a pre-determined pattern can also be used to measure time.

For example, some processes consist of inherently random ‘jumps’ at irregular times. If each jump only depends on the previous jump, the process is called Markovian. Examples can be seen throughout nature, from fluctuating stock prices to the beating of a heart.

By analysing these jumps, the scientists can estimate how much time has passed and place the strictest mathematical bound to date on how accurate that ‘clock’ is.

If the clock behaves differently than the equations suggest, then it isn’t a classical Markovian process and there might be underlying quantum effects in the system. By the same token, clocks that use quantum physics are not restricted by the bound, which explains why quantum technologies such as atomic clocks can do better than any classical clock like those commonly used by the public.

Dr Mark Mitchison, Proleptic Senior Lecturer in the Department of Physics at King’s and lead author explains, “Our goal was to find out the minimum ingredients you need to build a clock. For example, could you still measure time precisely even when stranded on a desert island? We found equations that tell you how to create a ‘clock’ by counting random events around you, like waves lapping on the shore or your heartbeats.

“This turns out to be the best possible clock you can build by counting Markovian events in a system governed by classical physics. So, if you find a system that doesn’t follow the expected pattern, you can be sure something else is going on like underlying quantum behaviour.”

The team also hope that these mathematical procedures can be used to study how biological systems operate efficiently in the presence of random fluctuations. For example, the motor protein kinesin transports other proteins within the cell, walking across small ‘microtubules’ which cross-cross the cell using two ‘feet’ to take directed steps along the tube. These tiny ‘molecular machines’ convert random thermal energy into a repeated, regular motion, much like the ticking of a clock. They are also crucial for biological function: malfunctioning kinesin has been implicated in motor neurone disease.

Dr Mitchison said, “Thinking about molecular machines as ‘clocks’ gives us insight into how some natural processes spontaneously generate order from chaos. We see this occurring at many different scales in our universe, from biological organisms and ecosystems down to the microscopic world. By establishing a fundamental limit on how well clocks can operate in the realm of classical physics, we also gain a better understanding of what makes quantum clocks different.

“Time lies at the heart of many unsolved mysteries in quantum physics. Why does time seem to flow in only one direction? Why do we only remember the past and not the future? Is time quantised in discrete chunks, in the same way as energy? By thinking about what clocks can do, we ultimately hope to answer some of these questions about the nature of time itself.”