# The physics of Santa

As the festive season approaches, we look at some of the physical challenges faced by Santa as he distributes presents across the globe.

Image credit: Michael Lorenzo

## Nick of time

Just one night is not much time to deliver presents to around two billion children all over the world.

That time can be extended to up to 48 hours by taking advantage of the Earth’s time zones – starting by delivering presents in the (saint) nick of time at the International Date Line and travelling west.

With a total global population of seven billion, then assuming an average family size of four people, he’d have to deliver to around 10 000 homes every second in order to get the job done within those 48 hours.

By way of comparison, the US Postal Service delivers around 170 billion items of mail every year – equivalent to a little over 5000 per second over the course of 12 months, and that’s with a workforce of more than 600 000 employees and ownership of the largest vehicle fleet in the world.

Santa’s delivery outfit consists only of himself and a handful of reindeer. As has been pointed out before – notably by Spy Magazine – to deliver all his presents in time he’d have to travel at such a high speed that Rudolph and co would burn up due to friction, just like small meteors entering the atmosphere. Maybe that explains the red nose.

But could he get the job done using either of the two great theories of 20th-century physics: relativity and quantum mechanics?

## Relativity

In his special theory of relativity, Albert Einstein showed that time runs at different rates for observers who are moving relative to one another (and passes more slowly for excited children waiting for presents).

This wouldn’t be much good though, as the sleigh-pulling reindeer would still be going so fast they’d combust – if they could even stay in orbit.

But gravitational fields also bend time – clocks run slower the closer they are to a source of mass. Could the Earth’s gravity help?

Probably not. If orbiting on the edge of space, then even doubling the amount of available present-delivery time would require the planet to be 1000 times more massive than the Sun – and if the Earth were this heavy at its current size it would collapse as a black hole.

But if there are no natural configurations of spacetime that might help, Santa could in theory still create a custom one.

In 1994, a physicist then based at Cardiff University, Miguel Alcubierre, discovered that there is a solution of general relativity roughly analogous to Star Trek’s warp drive. By artificially contracting the section of spacetime in front of the sleigh and expanding that behind, Santa and his reindeer can travel at an arbitrarily large speed relative to the Earth while still remaining stationary within their own ‘bubble’ of space.

The trouble is this would require an enormous amount of energy to accomplish – several billion times that in the entire observable universe.

## Quantum mechanics

Quantum mechanics also allows for things to be transported great distances in little time, and could avoid the need for Santa to take to the skies at all.

Because their position isn’t a definite point but a wave spread out over space, particles can sometimes “tunnel” through barriers that, according to classical mechanics, they shouldn’t be able to pass.

Again, assuming Santa actually knows how to accomplish this (he does, after all, know when you are sleeping; he knows when you’re awake; he knows if you’ve been bad or good…), it would take a huge amount of energy to realize.

This is not to say that he doesn’t have such tremendous amounts of energy at his disposal, but it may not be the most efficient solution to his present-delivery problem.

## Von Neumann probes

Maybe the problem of present-delivery could adapt a suggestion originally made when considering space exploration.

Physicist John von Neumann proposed that a spacecraft could be sent to another star system and programmed to make replicas of itself using raw materials found there. These in turn would travel to further solar systems, exponentially increasing the volume of space that can be covered.

A similar strategy could be used to send a delivery-sleigh to each continent, replicating itself to send one to each country, to each state, territory or county, and so on.

But, other than the odd bit of space junk, there are few natural resources available to convert, and to do so would be time-consuming anyway. Santa would have to be able to readily transmute elements from one form to another and then assemble them into the correct toys and gifts – perhaps by using nanotechnology.

Whichever means are used to deliver presents to billions of homes during the festive season, it’s clear that Father Christmas is way more technologically advanced than us.

Or he could just put gifts in the post.