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For those physicists and philosophers puzzled by nature's fourth dimension, Patrick Gill has a wry response. "Time," he says, "is what you measure in seconds."

For Gill, that is a statement of professional pride. He is what you might call Britain's top timekeeper. Within the windowless - and largely clockless - cream-brick confines of the UK's National Physical Laboratory (NPL), near London, Gill and his colleagues are busy developing the next, staggeringly accurate generation of atomic clocks. These tiny timepieces are the devices that ensure radio, television and mobile-phone transmissions stay in sync, prevent the internet from turning into a mess of missing data packets, make GPS accurate enough to navigate by, and safeguard electricity grids from blackout. They are, in short, the heartbeat of modern life.

These are momentous times for Gill and others like him in timekeeping laboratories around the world. A new generation of atomic tickers, known as optical clocks, have just wrested the record for accuracy from the ensembles of oscillating caesium atoms that held it for half a century. Soon, the new technology will be so refined that if such a clock had ticked away every second since the big bang 13.7 billion years ago, it would not yet have missed a beat. That is an awesome accomplishment - but it's also a problem. At this astonishing precision, we might have to rethink not only how we measure time, but also our concept of time.

For most of us, the closest we get to thinking about the nuts and bolts of time is watching the seconds tick away on a wristwatch or wall clock. Thinking a bit deeper, we might light on the idea that those seconds we are counting ultimately just subdivide a natural unit of time: the time it takes our planet to turn once about its axis, a day. That is indeed the historical logic of timekeeping. But Earth's rotation is an imperfect metronome. As time has become an ever more important governing factor in our lives, we have sought faster, more stable beats against which to measure its passage.

A leap forward came in 1955 when, building on the work of Isidor Rabi of Columbia University in New York, and prototype clocks at what is now the US National Institute of Standards and Technology (NIST) in Boulder, Colorado, NPL physicist Louis Essen made the first reliable atomic clock. This took its beat from the precise frequency of microwave radiation emitted and absorbed when electrons oscillate back and forth between two closely spaced energy levels in caesium atoms. The result was a timepiece accurate to 1 part in 1010, or 1 second in 300 years.

From that point, the days were numbered for the traditional astronomical second. In 1967, the base unit of time was officially redefined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom".

Over the following decades, the accuracy of atomic clocks improved still further. The next big advance came in 1989, when Stanford University physicist Steven Chu - now US energy secretary - and colleagues developed the "atomic fountain". This technique involves a ball of a million or more caesium atoms, trapped and cooled to a few millionths of a degree above absolute zero in criss-crossed laser beams, being launched upwards through a cavity in which microwave radiation excites the atoms to oscillate. The atoms' pulse is taken at the top of the trajectory, where the effects of temperature and motion that disturb their energy levels are at a minimum.

By tossing caesium clouds upwards over the course of a day and averaging the resulting frequency, the most accurate caesium-fountain clocks, the NIST-F1 clock in Boulder and similar devices at the Reference Systems for Time and Space (SYRTE) lab of the Paris Observatory in France, can now keep time with an accuracy of 1 second in around 80 million years - just a few parts in 1016.

With caesium, that is about the best that can be achieved. But caesium is by no means the fastest atomic oscillator. It was chosen as a matter of convenience: it was easy to excite using microwaves, and its oscillation produced a signal of the right frequency to be fed into the counters used in existing microelectronic circuits. Other atoms have transitions 100,000 times quicker, and so might make more precise clocks. The catch is that they cannot be probed by microwaves, but only by laser light oscillating at much higher optical frequencies, close to those of visible light.

At the time the first atomic time standards were established, laser technology was in its infancy, so nobody gave the possibility of optical clocks a second's thought. Then came the problem that the high oscillation rates involved - around a million billion times a second - were very difficult to count accurately. That stumbling block was cleared only in 1999, with the invention by Theodor Hänsch at the Max Planck Institute for Quantum Optics in Garching, Germany, and John Hall at NIST of a nifty device called a frequency comb, which "geared down" optical frequencies, spreading them out to produce frequencies back in the microwave range. That allowed optical clock rates to be calibrated against each other or against a known standard, such as caesium.

Succeeding caesium

In 2001, this technique brought Scott Diddams and colleagues at NIST the sought-after breakthrough. They trapped a single mercury ion in an electromagnetic field, an environment in which it is subjected to a minimum of outside interference. Using a frequency comb to compare the frequency of the solitary ion's optical oscillations with those of an ensemble of calcium atoms, the team produced a clock accurate to better than 1 part in 1014, about 1 second in 4.5 million years (Science, vol 293, p 825). In 2004, Gill and his NPL team upped the ante with a strontium clock accurate to 1 second in 9 million years - only one-third as precise than the best caesium clocks at that time (Science, vol 306, p 1355). The German standards lab, the Federal Physical-Technical Institute (PTB) in Braunschweig, also got in on the act, reaching comparable accuracy with an ytterbium ion.

The baton soon passed back across the Atlantic, with the NIST team achieving a precision on a par with its own NIST-F1 caesium clock in 2006. Finally, in March 2008, NIST compared a single-ion mercury transition with a transition in trapped aluminium atoms, obtaining accuracies of just 5 parts in 1017 - about 1 second in 650 million years (Science, vol 319, p 1808). Caesium's 53-year reign as king of the clocks was over.

In the meantime, caesium has been under attack via another, parallel route. Teams from several institutes have been investigating the timekeeping properties of clouds of identical atoms held in an evenly spaced pattern by a lattice of interfering laser beams. The stronger signals produced by the many atoms of these "optical lattice clocks" could ultimately be a better bet than single-ion clocks for achieving stable, highly accurate frequency standards. "They're a very hot topic right now," says John Bernard of the Institute for National Measurement Standards in Montreal, Canada. The record is currently held by strontium, an atom pioneered in lattice clocks by researchers at Tokyo University, Japan, in 2005 (Nature, vol 435, p 321). In March 2008, NIST researchers reported a strontium lattice clock with an accuracy of 1 part in 1016 - beyond caesium and chasing the accuracy of the single-ion clocks (Science, vol 319, p 1805).

But why go to so much trouble to build ever more precise clocks? Does it make a difference if a clock drifts by 1 second in a billion years or in 10 billion? Yes, says Gill. For one thing, a clock accurate to a second over the age of the cosmos would allow tests of whether physical laws and constants have varied over the universe's history. "If they have, that would be pretty Earth-shattering," says Gill.

And it is not just fundamental physics that could benefit. Upgrading GPS to optical-clock accuracy could track moving objects in real time to an accuracy of substantially better than a metre, rather than the tens of metres now possible. That is precise enough to moot technologies such as automated motorway driving, or landing aircraft without human intervention.

Gill cautions that such innovations might still be a while off. First, to achieve the necessary accuracy, optical clocks must be built not only into the ground-based GPS master clocks, but also into the slave clocks on each of the system's 32 satellites - no mean undertaking. Also, any system whose workings put human lives on the line has to be shown to be fail-safe. That will require a better understanding of how atmospheric conditions and multiple reflections on Earth's surface - off buildings in urban environments and rocks in mountainous terrain - affect the accuracy of GPS readings.

How soon optical clocks become widespread elsewhere - in underpinning high-bandwidth data networks, for example - depends on how swiftly we can arrange a new time standard to supplant caesium. There is, for now, no agreement as to what that replacement should be; each national lab has its own expertise and preferred choice of atom or ion. In 2006, the International Committee of Weights and Measures, which is charged with ensuring worldwide consistency in measurement units, approved optical transitions in mercury, strontium and ytterbium as secondary representations of the second until the primary caesium standard can be replaced.

Uwe Sterr of Germany's PTB thinks a definitive switch is inevitable - eventually. "It will still take several years, maybe 10," he says. David Wineland of NIST agrees. "If we could confidently say that a mercury clock is 100 times more accurate than caesium, many other labs would need to verify the claim, and many clocks built to satisfy the needs of the local users."

The complications don't end there. If these local clocks are going to be used to maintain a new international time standard, they will have to be kept in sync somehow. With the accuracies now being achieved, this too starts to be a problem. Existing optical fibres are too noisy to transmit the signals reliably, leaving only satellite links. Even then, synchronising clocks at, say, NIST and a lab in Europe to an accuracy of 1 second in many trillions will be no easy task. It would require averaging the signal's pulse over an unfeasibly long time. "Extrapolated optimistically, it would take the entire scientific lifetime of the clock-maker," says Diddams.

There is an even more profound problem facing the world's timekeepers. It has to do with the nature of time itself - in particular as described by Albert Einstein's general theory of relativity. This theory shakes together matter, space and time to generate our best idea yet of how gravity works. One of its predictions is that a clock will tick faster by 1 second in 1018 for every centimetre it is raised in Earth's gravitational field. GPS already takes into account such effects, which (assuming you spend most of your life upright) cause your scalp to age a few nanoseconds a year more than the soles of your feet.

Mind-boggling as such effects are, they are apparently not detrimental to our well-being. For optical clocks, they could be. To tell the time consistently, all clocks need to be at a known height relative to Earth's "geoid", an imaginary surface that links points at which the gravitational field has the same strength. But the height of this geoid varies over time at any given place by up to 20 centimetres, because of effects such as tectonic movements, glacial melting and changes in ocean levels, and varying atmospheric pressure. Changes of that magnitude could wreak havoc with any attempt to establish a global time standard at an accuracy of 1 part in 1018 or better.

Dan Kleppner of the Massachusetts Institute of Technology has spent a career pioneering techniques to manipulate the ultracold atoms that power optical clocks. He thinks the fact that we can no longer neglect gravity's effect on them could have profound consequences. "It will make us think a little harder about what we really mean by time," he says. No longer can we think lazily of time as a constantly flowing, uniform background entity. Optical clocks confront us with difficult realities of general relativity. In your home, time is not the same upstairs as downstairs. Soon, if you were to have one of the future ultra-precise atomic-synchronised clocks in your home, the time it told would be different according to how far up the wall it was fixed.

That is a world away from the how most of us - even the time-masters themselves - still deal with time. Anxious that I don't miss my train after I visit him at NPL, Gill offers to run me back to the station. As I get into his car, I glance at the dashboard clock. It's 15 minutes fast.

An inconstant constant

If the fine-structure constant were different, the world would fall apart: its value sets the strength of the electromagnetic interaction that is the glue of atoms. Its physical origin is unclear, but its numerical value - about 1/137 - is all-pervasive. Or is it?

A variable fine-structure constant might indicate an influence of gravity on the strength of the electromagnetic force - a variation predicted by many attempts to unify the fundamental forces of nature in a "theory of everything", but which so far has not been found.

If the value of the fine-structure constant has in fact been shifting since the universe began, an optical clock that would not have missed a beat over that period should be able to pin that movement down. Oscillations of different atoms - even different oscillations of the same atoms - depend on the fine structure constant in different ways. If the constant shifts, so will the atoms' oscillation frequencies. Comparing oscillators at known frequencies over the course of a year, and seeing whether or not they drift out of sync, will provide a definitive test.

"A clock accuracy of a part in 1018 would give the theorists something to design around," says astrophysicist John Webb of the University of New South Wales in Sydney, Australia. He has been looking for evidence of variations in the fine-structure constant over time in light from distant quasars that has taken billions of years to get to us. Optical clocks provide an opportunity to do the same kind of tests more easily in the lab.