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The second law of thermodynamics demands that if we want to make a clock more precise – thereby reducing the disorder, or entropy, in the system – we must add energy to it. Any increase in energy, however, necessarily increases the amount of waste heat the clock dissipates to its surroundings. Hence, the more precise the clock, the more the entropy of the universe increases – and the tighter the ultimate limits on the clock’s precision become.
This constraint might sound unavoidable – but is it? According to physicists at TU Wien in Austria, Chalmers University of Technology, Sweden, and the University of Malta, it is in fact possible to turn this seemingly inevitable consequence on its head for certain carefully designed quantum systems. The result: an exponential increase in clock accuracy without a corresponding increase in energy.
Solving a timekeeping conundrum
Accurate timekeeping is of great practical importance in areas ranging from navigation to communication and computation. Recent technological advancements have brought clocks to astonishing levels of precision. However, theorist Florian Meier of TU Wien notes that these gains have come at a cost.
“It turns out that the more precisely one wants to keep time, the more energy the clock requires to run to suppress thermal noise and other fluctuations that negatively affect the clock,” says Meier, who co-led the new study with his TU Wien colleague Marcus Huber and a Chalmers experimentalist, Simone Gasparinetti. “In many classical examples, the clock’s precision is linearly related to the energy the clock dissipates, meaning a clock twice as accurate would produce twice the (entropy) dissipation.”
Clock’s precision can grow exponentially faster than the entropy
The key to circumventing this constraint, Meier continues, lies in one of the knottiest aspects of quantum theory: the role of observation. For a clock to tell the time, he explains, its ticks must be continually observed. It is this observation process that causes the increase in entropy. Logically, therefore, making fewer observations ought to reduce the degree of increase – and that’s exactly what the team showed.
“In our new work, we found that with quantum systems, if designed in the right way, this dissipation can be circumvented, ultimately allowing exponentially higher clock precision with the same dissipation,” Meier says. “We developed a model that, instead of using a classical clock hand to show the time, makes use of a quantum particle coherently travelling around a ring structure without being observed. Only once it completes a full revolution around the ring is the particle measured, creating an observable ‘tick’ of the clock.”
The clock’s precision can thus be improved by letting the particle travel through a longer ring, Meier adds. “This would not create more entropy because the particle is still only measured once every cycle,” he tells Physics World. “The mathematics here is of course much more involved, but what emerges is that, in the quantum case, the clock’s precision can grow exponentially faster than the entropy. In the classical analogue, in contrast, this relationship is linear.”
“Within reach of our technology”
Although such a clock has not yet been realized in the laboratory, Gasparinetti says it could be made by arranging many superconducting quantum bits in a line.
“My group is an experimental group that studies superconducting circuits, and we have been working towards implementing autonomous quantum clocks in our platform,” he says. “We have expertise in all the building blocks that are needed to build the type of clock proposed in in this work: generating quasithermal fields in microwave waveguides and coupling them to superconducting qubits; detecting single microwave photons (the clock ‘ticks’); and building arrays of superconducting resonators that could be used to form the ‘ring’ that gives the proposed clock its exponential boost.”
While Gasparinetti acknowledges that demonstrating this advantage experimentally will be a challenge, he isn’t daunted. “We believe it is within reach of our technology,” he says.
Solving a future problem
At present, dissipation is not the main limiting factor for when it comes to the performance of state-of-the-art clocks. As clock technology continues to advance, however, Meier says we are approaching a point where dissipation could become more significant. “A useful analogy here is in classical computing,” he explains. “For many years, heat dissipation was considered negligible, but in today’s data centres that process vast amounts of information, dissipation has become a major practical concern.
“In a similar way, we anticipate that for certain applications of high-precision clocks, dissipation will eventually impose limits,” he adds. “Our clock highlights some fundamental physical principles that can help minimize such dissipation when that time comes.”
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NASA’s New Horizons spacecraft has been used to demonstrate simple interstellar navigation by measuring the parallax of just two stars. An international team was able to determine the location and heading of the spacecraft using observations made from space and the Earth.
Developed by an international team of researchers, the technique could one day be used by other spacecraft exploring the outermost regions of the solar system or even provide navigation for the first truly interstellar missions.
New Horizons visited the Pluto system in 2015 and has now passed through the Kuiper Belt in the outermost solar system.
Now, NOIRLab‘s Tod Lauer and colleagues have created a navigation technique for the spacecraft by choosing two of the nearest stars for parallax measurements. These are Proxima Centauri, which is just 4.2 light–years away, and Wolf 359 at 7.9 light–years. On 23 April 2020, New Horizons imaged star-fields containing the two stars, while on Earth astronomers did the same.
At that time, New Horizons was 47.1 AU (seven billion kilometres) from Earth, as measured by NASA’s Deep Space Network. The intention was to replicate that distance determination using parallax.
Difficult measurement
The 47.1 AU separation between Earth and New Horizons meant that each vantage point observed Proxima and Wolf 359 in a slightly different position relative to the background stars. This displacement is the parallax angle, which the observations showed to be 32.4 arcseconds for Proxima and 15.7 arcseconds for Wolf 359 at the time of measurement.
By applying simple trigonometry using the parallax angle and the known distance to the stars, it should be relatively straightforward to triangulate New Horizons’ position. In practice, however, the team struggled to make it work. It was the height of the COVID-19 pandemic, and finding observatories that were still open and could perform the observations on the required night was not easy.
Edward Gomez, of the UK’s Cardiff University and the international Las Cumbres Observatory, recalls the efforts made to get the observations. “Tod Lauer contacted me saying that these two observations were going to be made, and was there any possibility that I could take them with the Las Cumbres telescope network?” he tells Physics World.
In the end, Gomez was able to image Proxima with Las Cumbres’ telescope at Siding Spring in Australia. Meanwhile, Wolf 359 was observed by the University of Louisville’s Manner Telescope at Mount Lemmon Observatory in Arizona. At the same time, New Horizons’ Long Range Reconnaissance Imager (LORRI) took pictures of both stars, and all three observations were analysed using a 3D model of the stellar neighbourhood based on data from the European Space Agency’s star-measuring Gaia mission.
The project was more a proof-of-concept than an accurate determination of New Horizons’ position and heading, with the team describing the measurements as “educational”.
“The reason why we call it an educational measurement is because we don’t have a high degree of, first, precision, and secondly, reproducibility, because we’ve got a small number of measurements, and they weren’t amazingly precise,” says Gomez. “But they still demonstrate the parallax effect really nicely.”
New Horizons position was calculated to within 0.27 AU, which is not especially useful for navigating towards a trans-Neptunian object. The measurements were also able to ascertain New Horizon’s heading to an accuracy of 0.4°, relative to the precise value derived from Deep Space Network signals.
Just two stars
But the fact that only two stars were needed is significant, explains Gomez. “The good thing about this method is just having two close stars as our reference stars. The handed-down wisdom normally is that you need loads and loads [of stars], but actually you just need two and that’s enough to triangulate your position.”
There are more accurate ways to navigate, such as pulsar measurements, but these require more complex and larger instrumentation on a spacecraft – not just an optical telescope and a camera. While pulsar navigation has been demonstrated on the International Space Station in low-Earth orbit, this is the first time that any method of interstellar navigation has been demonstrated for a much more distant spacecraft.
Today, more than five years after the parallax observations, New Horizons is still speeding out of the solar system. It has cleared the Kuiper Belt and today is 61 AU from Earth.
When asked if the parallax measurements will be made again under better circumstances Gomez replied. “I hope so. Now that we’ve written a paper in The Astronomical Journal that’s getting some interest, hopefully we can reproduce it, but nothing has been planned so far.”
In a way, the parallax measurements have brought Gomez full-circle. “When I was doing [high school] mathematics more years ago than I care to remember, I was a massive Star Trek fan and I did a three-dimensional interstellar navigation system as my mathematics project!”
Now here he is, as part of a team using the stars to guide our own would-be interstellar emissary.
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