Researchers in the United States have for the first time shown that time passes faster the higher up you are.

In a curious aspect of Albert Einsten's theory of relativity, they show that someone living or working long hours in a top floor apartment or office will age more quickly than someone on the ground floor.

To understand this research, you first need to grasp an idea thrown up by Einstein more than 100 years ago.

In his theory of general relativity, Einstein predicted that a clock at a higher elevation would run faster than a clock on the planet's surface because it experiences a weaker gravitational force.

The theory has been proven before, using jumbo jets flown at high altitudes, but this is the first time scientists have shown the theory holds if you elevate one of the clocks by just 33 centimetres.

James Chin-Wen Chou, a research associate at the US National Institute of Standards and Technology and a co-author of the study published in the journal Science, says his team wanted to demonstrate that.

"We also want to show people that now clocks are at this precision level, that we can see such small time dilation and gravitational shift," he said.

"In terms of measurements with atomic clocks, this is turning a new scale."

The clocks he is talking about are the world's best experimental atomic clocks. They keep time based on the ticking of a single aluminium ion as it vibrates between two energy states.

They are so accurate they lose or gain less than one second every 3.7 billion years.

The findings prove that time moves more quickly the higher up a staircase you travel. So people living in top floor apartments will age more quickly, but Dr Chou says it is not a difference that is worth worrying about.

"Just one foot height difference would get you older by 100 billionths of a second or 90 billionths of a second over 79 years of life, so that is quite negligible, so people shouldn't worry about high elevation they are living," he said.

The researchers also tested Einstein's theory of special relativity, in which he predicted that a stationary clock would tick faster than a moving clock.

This gave rise to what is known as the twin paradox, which suggests a twin taking a round-trip journey in a spaceship at some high speed would return to Earth to find his twin sibling left behind had aged faster.

By making the ion in one clock move faster than the other, the scientists were able to simulate a velocity for the clock of several metres per second.

Time on the moving clock moved more slowly than on the stationary one, just like that travelling twin.