The Entropic Price of Building the Perfect Clock: Q&A with Natalia Ares

It would take 15 billion years for the world’s most accurate atomic clock to lose a single second, suggesting physicists are pretty good at measuring time. What exactly they are measuring with these mindbogglingly accurate devices, however, is less clear. Time ultimately remains one of the greatest mysteries in physics. We don’t even know why time’s arrow points forward rather than backward.

Quantum physicist Natalia Ares at the University of Oxford, UK, and her colleagues suspect the key to understanding time may be to study the fundamental physics of timekeeping which, unlike the technological aspect, is largely unknown. With a grant of over $1.8-million from FQXi, they are making discoveries that may one day help us make sense of the enigmatic fourth dimension.

Why did you want to be a physicist?

I didn’t know that somebody could be a physicist back when I was at school in Buenos Aires. Nobody in my family did science, and I was the first to go to university. I was always very good at maths, and I really liked it. I even tried accountancy at high school, but it was not what I was looking for. Eventually, I discovered a science course which was run by actual scientists. I soon realised that’s what I wanted to do—something that was maths-related, but also connected to experiments and probing physical laws in action. That science course made very clear for me the importance of outreach and the need for role models.

You work at the boundary between quantum mechanics, the theory that governs nature on the smallest scales, and thermodynamics, the science of heat and work. What interests you about this interface?

Quantum mechanics puts everything you thought you knew upside down. And the laws of thermodynamics are so robust and limiting, they even give us the arrow of time. (Read FQXi’s in-depth report on the nature of time to learn more about how time’s arrow is associated with thermodynamics and increasing entropy, or disorder, of a system.) So working out how quantum mechanics affects the laws of thermodynamics is fascinating. It has the potential to discover completely new effects and that’s very exciting.

Is it fair to say that we don’t have a very good understanding of how clocks actually work on a fundamental level?

There’s been an amazing advance on the precision with which we can measure time, and we have incorporated that knowledge in technologies such as GPS. We mostly know what the technological limitations are, but what are the fundamental, theoretical ones? What are the minimum requirements for measuring the passage of time and what does it mean to measure time? We didn’t set out to build a good clock, we wanted to understand what you have to do in order to build a clock and what the fundamental limitations are on how accurate that clock can be.

Your research suggests clocks are a type of thermodynamic machine, meaning they increase in entropy as they record the passage of time. Where did this idea come from?

There was a lot of work done in terms of understanding the theory before our experiment, suggesting there was an analogy between clocks and thermodynamic machines such as heat engines. So we worked closely with theorists, including Marcus Huber, at the Institute of Quantum Optics and Quantum Information, in Vienna, Austria, and Gerard Milburn, at the University of Queensland, Australia. And they have done a lot of thinking on the theory of this analogy in the quantum regime. So for us, it was basically putting that thinking to the test in the laboratory.

What did you do in your experiment?

We built a clock in which we could precisely control the amount of thermodynamic resources that we put in, and measure it with high precision. We started with a thin membrane, 50 nanometers thick. If heated, it would start to oscillate at its natural frequency. So that’s like a pendulum clock, with each oscillation corresponding to one tick. At the same time, we could control the thermodynamic resources, which was electrical noise, in order to heat the membrane.

We could then correlate this with precise measurements of how accurate our ticks were. What we found was that if you increase noise, the membrane will oscillate more, making it easier to detect the ticks of the clock and the oscillation becoming more regular. That means the clock is more accurate. You can then calculate the entropy dissipated by the electronic circuit as a result.

We found that the more entropy the clock produced, the more accurate it became. It was a linear relationship between entropy production and accuracy. Our collaborators had already theoretically found that to be the case in the quantum regime. But this experiment is classical (not quantum), so this points to a universal behaviour of entropy production and clock accuracy.

Does that mean that you’d need an infinite amount of energy to create a perfectly accurate clock?

Yes, but only in theory. In reality, there is a limitation where you see a saturation in accuracy as you deliver more power to the system. That’s because the thermodynamic resources you are delivering are not used to increase the accuracy anymore. So even if you deliver power, the accuracy doesn’t improve beyond a certain point. A pendulum, for example, becomes more regular as you drive it harder, but at some point, it might break or twist, and that also requires energy.

Does your research suggest that the arrow of time, causing time to move forward rather than backwards, is somehow fundamentally built into the act of timekeeping through ever-increasing entropy, rather than having anything to do with our human, conscious experience?

I think that’s true. We know little about the arrow of time and anything that sheds a bit of light on it is very interesting. We need to study more to understand exactly how it arises but there is definitely this connection that we are exploring.

Time is a huge problem in physics, with the treatment of it in quantum mechanics clashing with that in general relativity. The latter also assumes time can be measured perfectly, when your research suggests it can’t. Will a better understanding of clocks help reveal how the two theories fit together?

Definitely. In quantum mechanics, time is a big issue. There is largely no arrow of time—events can happen backwards or forwards. So you have to bring quantum mechanics together with thermodynamics and ask where exactly in the quantum formalism do we find the arrow of time? There is also the whole measurement problem (in which a quantum system is in a superposition of different states until you actually measure it), which may be related. There is work suggesting measurements might be used as a thermodynamic resource, but it is still debated. It’s really exciting stuff.

Ultimately, the link between the arrow of time, measurement and timekeeping is still a territory we have to map. And that’s why it is so important to work on the fundamental questions of clocks and timekeeping because that will allow us to understand how thermodynamics is applied in the quantum world, and how the arrow of time arises.

What’s next?

We are pushing our experiments down to the quantum regime. We want to study some of these quantum limits because nobody has investigated them before.

What applications could come out of this?

The understanding of thermodynamic limits of these processes are quite important for understanding machines in the quantum realm. Could we get efficiencies that surpass what we see in the classical, macroscopic world? A topic we are studying is the thermodynamics of learning, how systems learn and what the thermodynamics of that process is. How do you build machines that learn efficiently?

Also by understanding these thermodynamic processes, could we uncover more about how biomotors work (another type of thermodynamic machine)—as well as essentially biological processes that govern life. Life is ultimately about entropy production, after all.