Weigh yourself with time (Image: Roberto A Sanchez/getty)

Imagine ditching the bathroom scales and instead weighing yourself with a watch. That’s now possible, in principle at least, following the creation of the first clock with a tick that depends on the mass of a single atom. The physicists behind it say it’s the most fundamental clock ever invented, and that it could help to re-define the mass of the kilogram.

Existing atomic clocks, the most accurate clocks that exist, measure how often a caesium atom’s electrons jump between two different energy levels – roughly 9 billion of these transitions equal 1 second.

But that’s not the only way to count time using an atom. Quantum mechanics says that all matter exists as both a wave and a particle. As a wave has a frequency, this means each particle also has a frequency, known as its Compton frequency, which depends on its mass.


In principle, it should be possible to build a “Compton clock” with a tick defined by the Compton frequency of a particular atom. The problem is that the Compton frequency of an atom is 100 billion times faster than the frequency of visible light waves. “This frequency is so high that it is very far beyond any way of counting,” says Holger Müller at the University of California, Berkeley.

Twin paradox

To solve this problem, his team turned to a strange quirk of Einstein’s theory of relativity, known as the twin paradox. It says that a twin who flies off in a fast-moving spacecraft and returns will have aged less than the one who stayed on Earth, as time passes slower for moving objects.

Müller replicated this at the atomic scale by sending the matter wave of a caesium atom through a device called an atom interferometer. This split the wave into two, with one half remaining stationary and the other continuing to move, before recombining the two halves. The moving wave becomes slightly out of phase – a result of the twin paradox.

Instead of measuring the Compton frequency directly, the researchers used a laser to measure this difference in frequency, which amounts to around 100,000 hertz. Because this also depends on the mass of the atom, it can act as the tick of a clock. This clock is more fundamental than any before because it depends on the behaviour of a single particle.

The clock loses about 1 second every eight years, comparable to the earliest atomic clocks. “As a clock it’s not very good,” says Müller. By contrast, the best atomic clock today would only have lost 4 seconds had it started ticking at the big bang.

But the Compton clock has a quality that atomic clocks lack: as its frequency depends on the mass of an atom, it could be used as a gold standard weighing device.

Kilogram, redefined

The scientific standard for mass is currently defined by a kilogram of metal stored at the International Bureau of Weights and Measures in Paris, but metrologists are keen to change this because its mass is drifting due to microscopic contaminants.

Two competing methods are vying to replace the lump of metal. The first is to count out the exact number of silicon atoms in a ball that weighs a near-perfect kilogram, known as an Avogadro sphere. The second is to use a device known as a watt balance, which relates mass to a current and voltage using the fundamental Planck constant.

The Compton clock offers a third alternative. The mass of the clock’s caesium atom can be calculated from its Compton frequency, the Planck constant and the speed of light, with an accuracy of four parts in a billion.

As the relative masses of all atoms are known, this technique could be used to come up with very precise measurements for the masses of other atoms. It’s then possible to calculate how many atoms should be in a kilogram of a given element. This chain of calculations reduces the accuracy to 30 parts per billion, but that is still comparable to the accuracy of the watt balance method, says Müller.

“Their technique is extremely powerful,” says Ian Robinson of the UK National Physical Laboratory. He points out that it offers a method to accurately measure the mass of a single atom. That is not possible with the watt balance, which can only measure macroscopic objects.

Using the Compton clock for macroscopic masses may be more difficult however, as cheap, accurate methods for scaling up from atomic masses are not readily available, says Richard Steiner of the US National Institute of Standards and Technology in Gaithersburg, Maryland.

Journal reference: Science, DOI: 10.1126/science.1230767