Scientists in Boulder, Colorado say they have proved what every schoolchild learns in the classroom about Einstein’s theory of relativity — that time flies at altitude but paradoxically slows down when people speed up.

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Decades ago, experiments proved the basic premise of Albert Einstein’s theory, sending an atomic clock into space on a rocket and comparing it to one kept behind on Earth, where gravity acts to slow down the passage of time.

But now experiments at the National Institute of Standards and Technology (NIST) have enabled physicists to demonstrate the theory in the smallest facets of daily life.

In the study, published on Friday in Science, they showed how they measured the effect on a scale of about 30cm to demonstrate how people age faster when standing a couple of steps higher on the staircase.

They used a pair of highly sophisticated experimental atomic clocks, dubbed “quantum logic clocks”, which use laser lights to measure an electrically charged aluminium ion as it vibrates more than a million billion times a second.

One clock keeps time within one second in about 3.7 billion years, the study said, and the other is close behind.

The aluminum clocks can detect small relativity-based effects because of their extreme precision, the study said.

“You can think about it as how long a tuning fork would vibrate before it loses the energy stored in the resonating structure,” said lead author James Chin-Wen Chou.

Although the results are infinitessimally small, they showed that climbing up steps will age you faster — adding up to about 90 billionths of a second over a 79-year lifespan.

In one of the experiments, scientists raised one of the clocks by elevating the laser table to 30cm above the second clock. “Sure enough, the higher clock ran at a slightly faster rate than the lower clock, exactly as predicted,” the study said.

The NIST team also studied another feature of relativity — that time passes more slowly when you move faster — but measured the effect at speeds such as a car travelling at about 32km/h, rather than on jet aircraft.