# Low-altitude skiing can slow down ageing - relativistically

**A doctor could tell you that skiing and running will most likely slow down ageing. But how come mathematicians and physicists give their scientific support to this point of view?**

Most biologists and medical professionals would agree that skiing and running can delay ageing. This is essentially because of the direct positive impact on the body due to good exercise and physical fitness. However there is a much more subtle effect in this direction from a mathematician’s and physicist’s point of view.

As most of you already know, time and relativity have a unique connection between them. There was a time in history when hardly anyone from the general public understood Einstein’s special theory of relativity formulated in 1905. Initially only some mathematicians and physicists could decipher his equations and understand the concept of time dilation in a moving body. Time dilation means that a clock moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference.

Within few years, more scientists and more people from the general audience started to understand and appreciate the significance of his result. Time dilation, twin paradox experiment, clock cartoons and so on became talk of the day!

In 1915, Einstein came up with the general theory of relativity which puzzled academics and laymen even more. Only a handful of mathematicians and physicists at the time could digest his concept of explaining gravity by unifying space and time into a mathematical fabric using tensor calculus. In later years, people started to notice and measure the effect of gravitational fields on the passage of time. In today’s world, these are well established and time tested theories which even gain occasional mentions in popular sci-fi comics and sci-fi movies.

## The dangers of climbing the stairs

Last year an article in Titan focused on this general relativity part. This is to do with the acceleration of passage of time (i.e. time running faster) due to change in gravitational field when you go up a mountain or climb stairs! Technically this is due to the change in curvature of space-time when you move farther away from the centre of Earth. It is commendable that Norway is one of very few countries where they try to include aspects of general theory of relativity in the curricula for training school and college students.

The simple summary of the above result is: if someone spends decades of their life consistently on some very high mountain peaks (like Himalayas), one would age faster by some hundreds of microseconds; exact count depending on the specific height and respective times spent (about 100 microseconds per decade at 3000 metres above). An accuracy of order microseconds over a decade-long span is something that is achievable using modern-day Cesium atomic clocks. Hence this is a realistically measurable range in today’s times if you plant one clock each on the summit and the base of the mountain.

## The perks of being a skier

However, there is an interesting counter effect from the special relativistic side, if you are a Norwegian. A blind assumption that all Norwegians ski a lot plus run a lot is not too far from reality!

For a top-end skiing professional, assuming typical speeds of about 100 km/hr and duration of one race of about 2 minutes, one gains about half a picosecond. Assuming an active skiing career spanning a decade (about 1000 races), the person would age lesser by about half a nanosecond.

For a recreational skier/runner, decades of running and ski-training would result in gaining a few nanoseconds over an average Norwegian’s lifespan (assuming an average recreational skiing/running speed of 12 km/hr, gaining a nanosecond would require about 5000 hours of training, which is easily achievable in an average lifetime of a nordic person).

### Small amounts of time

One nanosecond is 1 part in 1,000,000,000 second i.e. one-billionth of a second.

Picosecond is a further smaller quantity i.e. one-trillionth of a second.

The accuracy and precision levels of atomic clocks are improving dramatically every year.

A nanosecond-precision time measurement over decades might sound like an impossible feat at the level of conventional engineering we are familiar with. However, the level of sophistication that exists today at the cutting edge of engineering and instrumentation is quite remarkable.

The latest example is the LIGO experiment which won the Nobel prize for physics this year. The experimental set up is a technological marvel capable of detecting ripples in space-time that cause changes of the order of one-ten thousandth the size of an atomic nucleus. Moreover the observation which fetched the Nobel was a collision event that happened 1.3 billion years ago between two black holes with masses each of about 30 times that of our sun. This measurement in itself shows the standards of accuracy and precision levels in modern scientific instrumentation. This applies to the latest atomic clocks too.

You may also want to read this: Jupiter and the theory of relativity gets the blame for celestial bodies changing course

## Measuring time has become easier

More pertinent to this discussion is the advent of optical lattice clocks, that have an accuracy of about one second in 13.8 billion years (i.e. age of universe), or equivalently, about a nanosecond per decade.

Clearly, measuring a nanosecond-scale time shift resulting from many years or decades of high-speed skiing or long-distance running is not hopelessly beyond the reach of present-day technology.

## Astronaut twins are no longer the same age

Moreover this core concept was tested using twin astronaut brothers last year. One of the twins, Scott Kelly, a NASA astronaut, spent 340 days aboard the International Space Station while his twin brother Mark Kelly was enjoying his life on ground (i.e. planet Earth).

The International Space Station is about 400 km up from the Earth's surface and hence the astronaut will age faster by about 1.1 milliseconds during this period due to space-time curvature effect (as discussed in the case of mountains).

However the astronaut was racing at about 28,000 km/hr around the Earth during this period (a faster version of skiing). This leads to a counter effect which estimates that the astronaut on the shuttle aged slower by about 9.6 milliseconds due to this high velocity.

The net effect is that the astronaut aged slower (or gained a bit of time!) by about 8.5 milliseconds during this period which is a good reason to celebrate!

It turns out that, in low-earth orbits, the special relativistic slowdown dominates over the gravitational speedup - the two effects become roughly equal when the spacecraft’s orbital radius is 1.5 times the Earth's radius. Any astronaut orbiting at a larger radius would in fact age faster than their colleagues on Earth. A similar calculation has been done for frequent air travellers.

Realistically, of course, there are much more serious effects to consider, like increased radiation exposure, zero gravity challenges, bio-rhythm changes and dietary problems on board space shuttles and hence it is not just clocks which matter for health & overall well being of a human!!!

But with regular skiing and running (at low altitudes only!), you certainly are slowing down ageing (both fitness-wise and relativistically speaking!) without all these ill effects from space! As they say, every little counts!

*Aswin Sekhar is an astrophysicist based at CEED, UiO and Amol Patwardhan is a high energy physicist based at the University of Wisconsin, Madison, USA. Sekhar acknowledges the Crater Clock project (235058/F20) based at CEED (through the Centres of Excellence scheme project number 223272 (CEED) funded by the Research Council of Norway) and USIT UNINETT Sigma2 computational resource allocation through Notur.*