# If Einstein is Right, Santa is Even Fatter Than We Thought

By Ryan F. Mandelbaum on at

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 Father Christmas'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 maths.

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 four 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.

### “He’d look like a hyper massive flattened pancake Santa to a child on the ground.”

Einstein’s special relativity came about to help describe how things moving at different velocities relate to one another. Special relativity causes strange behaviours to arise in objects travelling 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 behaviours, 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 four 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 travelling.

“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, maths 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 visualise 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 colour. 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 colour. Travelling 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-coloured pancake streaking through the sky. Don’t blink, or you’ll miss it.