Santa’s flight is relatively easy

Albert Einstein writes out an equation for the density of the Milky Way on the blackboard at the Carnegie Institute, Mt Wilson Observatory headquarters in Pasadena, California, on January 14, 1931. APShow more

Millions of festive deliveries made in a single night? According to Albert Einstein, Santa may use more than reindeers to get around, writes Robert Matthews

For parents of small children, the festive season can be stressful. As if finding presents capable of keeping them quiet for a few minutes wasn’t enough, there is also the challenge of explaining how they are going to arrive.

It is not easy convincing a six-year-old that just one old guy in a red outfit really can get so much to so many youngsters so quickly.

Is it really possible to make the hundreds of millions of deliveries needed in barely a day? And do it unseen?

Left unanswered, such questions can lead to doubts in tiny minds about the very existence of Santa Claus.

Fortunately, help is at hand. It turns out that Santa is exploiting some of the most bizarre phenomena known to science.

Ironically, the sheer speed required of Santa is a big clue to how he does it.

Calculations made public this month by physicist Dr Katy Sheen of the University of Exeter, UK, show that Santa is benefiting from effects that kick in when travelling at close to the speed of light, or about 300,000 kilometres per second.

There’s no doubt Santa must be zooming around at something close to such speeds. Even if he exploits time-zone effects, he has barely 30 hours to cover the estimated 350 million kilometres involved in achieving his global delivery target.

So how does Santa travel so fast?

On the face of it, he’s up against the ultimate speed limit set by Albert Einstein’s theory of relativity.

This shows that achieving speeds close to that of light rapidly requires ever more energy – and becomes literally infinite at the speed of light itself.

There is, however, a loophole provided by Einstein’s more sophisticated theory of space and time, known as General Relativity.

This allows truly radical ways of travelling at – or even beyond – the speed of light.

Imagine an ant wanting to travel across a tablecloth to reach a sugar lump. The obvious method is for the ant simply to walk there.

But there’s another option, at least in principle: bring the sugar lump closer by crumpling up the tablecloth.

In 1994, theoretical physicist Miguel Alcubierre at Cardiff University suggested something similar could allow travel faster than the speed of light.

His idea exploited the fact that according to Einstein, it’s possible to warp the very fabric of space and time. Strange types of quantum matter can affect space and time in such a way as to wrinkle space-time and bring distant points closer together – thus making travelling to them much faster.

The technical hitch is that scientists don’t know how to create such bizarre forms of matter, but it can exist in theory. And judging by Santa’s success in meeting his annual deadlines, a good place to start looking for it is somewhere near the North Pole.

Travel at near light-speed resolves other notoriously tricky questions asked by children about Santa – such as why he’s never seen making his deliveries.

According to Einstein, objects moving at near-light speeds appear shrunken as they zoom across our field of view, and pitch-black as they recede.

This shrinking effect, known as relativistic length contraction, also explains why even the portly Santa can flash through small spaces such as chimney-stacks with so little difficulty.

Einstein’s theory can even explain Santa’s cheery demeanour and apparent agelessness. The reason lies in the fact that according to relativity, travelling close to the speed of light affects not only physical sizes but also the flow of time.

Put simply, time flows more slowly the faster one travels.

This bizarre effect is no mere theoretical possibility. Laboratory studies of particles called muons show that when stationary in a lab they have a lifetime of around a millionth of a second.

Zipping through the atmosphere from deep space at speeds close to that of light, however, they survive more than 10 times longer, because their internal “clock” appears to us to be running more slowly.

That same effect becomes substantial at speeds close to the speed of light. According to calculations published by physicists at Purdue University in Indiana, and Fermilab National in Chicago, both US, in 2013, if Santa travels at 99.999999 per cent of the speed of light, he can meet his deadline in what to him seems like less than 10 minutes, leaving himself the rest of the 30 hours to take things easy.

There’s one last question about the Man in Red that science can help resolve: what is he up to for the rest of the year? The most likely answer is that he’s planning for next Christmas – as it involves solving a notorious mathematical problem: finding the fastest route between destinations.

This so-called Travelling Salesman Problem (TSP) seems simple enough. For example, to find the fastest route between three cities – A, B and C – you can just check out the six different possibilities: ABC, ACB, BCA and so on.

The scale of the challenge becomes clear as the number of destinations increases.

Double the number of destinations from three to half a dozen, and the number of possible routes zooms from six to 720.

For a dozen cities, you’re looking at finding the single fastest route among almost half a billion.

And Santa is trying to do that for hundreds of millions of households.

Special techniques are needed even to estimate how many permutations that involves, and the answer is vastly greater even than the number of atoms in the visible universe.

Indeed, it’s a number so vast it’s hard even to write down – very roughly 1 followed by over 10 billion zeros, which would cover a strip of paper reaching halfway around the world.

So how does Santa tackle so humungous a calculation?

A lot of people would like to know, as the TSP is a challenge faced daily by everyone from airlines and shipping companies to, well, travelling salesmen. Computer scientists have found some pretty fast algorithms, but nothing capable of what Santa does every year.

There’s only one thing for it. Go along to Santa’s grotto with the children and ask him.

Robert Matthews is visiting ­professor of science at Aston University, Birmingham, England.