There’s a controversial little interpretation of Einstein’s theory of special relativity that could affect what happens to masses moving at a really high speeds: they appear to get heavier.

The effect isn’t huge until something nudges right up to the speed of light, when its mass seems to shoot up to infinity. This happens because you can’t break the speed limit set by light speed. As an object approaches that limit, it requires more and more energy to accelerate it, until eventually, it seems like you’re trying to push an infinitely massive thing, which would require infinite energy.

But that got me thinking. Santa probably has to travel at speeds *close* to the speed of light if he’s hoping to hit every house and still be home to spend some time with Mrs. Claus on Christmas Eve. Does that mean that Santa’s annual present-delivering jaunt would cause him to pack on extra pounds?

Before we try to answer that question, some important caveats. One, Santa’s mass would only change with respect to a kid on the ground, and Santa would still measure himself at his jolly 400 or so pounds. Two, a lot of physicists think this so-called relativistic mass is meaningless. I’ll talk about that after we do some fun math.

First off, how fast would Santa have to go to hit every house on Christmas eve? Let’s do a quick back-of-the-envelope calculation:

There are around 2.2 billion Christians on earth, and maybe around 4 people per household, on average, making 550 million total households. Sure, lots of homes are really close together and others are spread out over long distances, but there’s a huge amount of vacant space where no one lives on Earth, so let’s average it all out to around a mile in between each household (this is most certainly too high, but work with me here). Jolly Saint Nick probably has to travel that long, coiled-up zig zag in 24 hours, so that will be around 23 million miles per hour.

Einstein’s special relativity came about to help describe how things moving at different velocities relate to one another. Special relativity causes strange behaviors to arise in objects traveling at high speeds, those approaching the speed of light.

One of the theory’s most important concepts is the Lorentz factor, which explains some of those behaviors, and is represented by gamma, or γ:

If you plug Santa’s velocity (v) and the speed of light (c) into gamma, and then multiply that by his usual 400-or-so pound mass, you arrive at his relativistic mass, 400.2 pounds, as observed by a child on the ground, thanks to Santa’s high speed. But 0.2 extra pounds is boring.

Let’s say Santa overslept, and now he only has 6 hours to deliver all those presents. Now, that gamma goes up, and poor ol’ Saint Nick weighs closer to 404 pounds. But if he only had an hour, then we’re talking 699 pounds. The closer he pushes to the speed of light, the heavier you’d measure him; at 600 million miles per hour, he’d measure a hefty 895 or so pounds. But despite this enormous weight, Santa** **would appear to be way thinner, since the Lorentz factor would squish Santa lengthwise along the direction he’s traveling.

“He’d look like a hyper massive flattened pancake Santa to a child on the ground,” said Stefan Countryman, a friend and LIGO physicist who I forced to help me with the calculation.

The relativistic mass is pretty meaningless. Since the mass of a stationary object is a constant value, math says that physicists can ignore it in their calculations, and then plug it in later after handling the changing properties more relevant at high speeds, such the gamma value itself, momentum, or energy. But, Countryman explained, the mass changing still gives students a way to visualize what happens to things moving at the speeds where special relativity applies.

Another physics-savvy friend of mine, Andrea Egan, pointed out that relativity would cause another strange effect—to a child on the ground, Rudolph’s nose would change color. That’s because the light waves will either stretch or squish together, based on the speed. This would change the wavelength of the light, also known as the color. Traveling towards you at 22 million miles per hour, Rudolph’s nose would look orange, but should he travel even faster, the wavelength would shorten until, at a certain point approaching the speed of light, his nose would look blue.

So, if you want to test Einstein’s theory of relativity for yourself, be on the lookout Christmas Eve for an enormous, Santa-colored pancake streaking through the sky. Don’t blink, or you’ll miss it.

## DISCUSSION

There are approximately two billion children (persons under 18) in the world. However, since Santa does not visit children of Muslim, Hindu, Jewish or Buddhist religions, this reduces the workload for Christmas night to 15% of the total, or 378 million (according to the Population Reference Bureau). At an average (census) rate of 3.5 children per house hold, that comes to 108 million homes, presuming that there is at least one good child in each.

Santa has about 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west (which seems logical). This works out to 967.7 visits per second. This is to say that for each Christian household with a good child, Santa has around 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left for him, get back up the chimney, jump into the sleigh and get on to the next house.

Assuming that each of these 108 million stops is evenly distributed around the earth (which, of course, we know to be false, but will accept for the purpose of the calculations), we are now talking about 0.78 miles (1.3 km) per household; a total trip of 75.5 million miles (125.83 million km), not counting bathroom stops or breaks. This means Santa’s sleigh is moving at 650 miles per second (1083 km/s), 3000 times the speed of sound. For purposes of comparison, the fastest manmade vehicle, the Ulysses space probe, moves at poky 27.4 miles per second (45.7 km/s), and a conventional reindeer can run (at best) 15 miles per hour (25 km/h) - that is four thousands of a mile (4/1000) per second (6.9 m/s).

The payload of the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium size Lego set (two pounds, or 0.906 kg, that is), the sleigh is carrying over 500 thousand tons US (508,000 t metric), not counting Santa himself. On land, a conventional reindeer can pull no more than 300 pounds (136 kg). Even granting that the “flying” reindeer could pull ten times the normal amount, the job can’t be done with only eight or even nine of them - Santa would need 360,000 of them. This increases the payload, not counting the weight of the sleigh, another 54,000 tons (54,864 t metric), or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch).

600,000 tons (606,600 t metric) travelling at 650 miles per second (1083 km/s) creates enormous air resistance, and this would heat up the reindeer in the same fashion as a spacecraft re-entering the earth’s atmosphere. The lead pair of reindeer would absorb 14.3 quintillion Joules of energy per second each. In short, they would burst in flames almost instantaneously, exposing the reindeer behind them and creating deafening sonic booms in their wake. The entire reindeer team would be vaporized within 4.26 thousands of a second (0.00426 s), or right about the time Santa reached the fifth house on his trip.

Not that it matters, however, since Santa, as a result of accelerating from dead stop to 650 miles per second (1083 km/s) in 0.001 seconds, would be subjected top acceleration forces of 17,500 g’s. A 250 pound (113 kg) Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by 4,315,015 pounds of force (195,470 kg force, or 1.9547 MN), instantly crushing his bones and organs and reducing him to a quivering blob of pink goo.

Therefore, if Santa did exist, he’s dead now!