TIME DILATION & SANTA CLAUSE
December 20, 2023
Ever wonder how Santa Claus manages to deliver his toys to all the expectant little kids around the world in just one night? Maybe it's elven magic. Or it could be the dogged determination of Rudolph and the other reindeer to ensure all the gifts are delivered. Some might even propose that Santa travels with superhuman quickness, even approximating the speed of light, in order to achieve successful package fulfillment. But would the ability to travel that fast actually help jolly old St. Nick? Hold that thought for just a moment.
You may already know this, but I believe Christmas isn't about the gifts or or the toys or about all the glitter & dazzling lights. As nice as those things can be, there's a deeper reason to celebrate the season. But if you would just humor me for the sake of S.T.E.A.M., let's continue to explore this concept of near-speed of light travel as it pertains to Santa's busiest night of the year.
As you begin to travel closer to the speed of light, some incredibly interesting things begin to happen. Your mass begins to increase. And time begins to slow down for you, but time continues at its normal rate for others who are stationary or who may be traveling at routine, non-speed of light velocities. Far out, isn't it? (For more information on this, check out space.com or emc2-explained.info) So in theory, Santa and his team could somehow be traveling at tens of thousands of miles per second and getting a number of things done, while we remain in normal time. And wouldn't you know it, there's a formula to measure these differences in time, also known as time dilation :
T - Time observed
(Time as experienced by stationery person or another traveler)
To - Time observed at rest
(Time as experienced by near-speed of light traveler)
v - Velocity of object
(Velocity of near-speed of light traveler)
c - The speed of light: 3.0 x 108 m/s2
(In the key directly below the formula, I've included the official description for each term, and in parenthesis I've also included my own interpretations of what they represent. Perhaps my interpretations are wrong, especially considering that apparently some mathematicians also use this equation to come up with the relative time dilation of two moving objects. But it helps me better grasp the corresponding value assignments, at least for this illustration. And don't be put off by the speed of light value, 3.0 x 108. It's known as scientific notation, a shorthand way of writing long numbers. In this case, it saves us from having to write 300,000,000 every single time for the value of "c" !)
So let's theoretically say that Santa with his reindeer & sleigh could move at 80% of the speed of light. (In the equation below, as a space saving measure, I've denoted this as .80c.) And let's assume he works for 8 hours (the 9pm-5am night shift) starting on Christmas Eve for his toy delivery. So go ahead and plug in these values into the formula below and perform the calculations:
And as you can see, we've run into a problem. If Santa & his team indeed move at 80% of the speed of light for 8 hours, that works fine for them. However, since the rest of us aren't moving at that high speed, time would pass differently for us, and the time dilation equation shows that more than 133 hours would have elapsed for us by the time Santa was done with his gift distribution!! And it wouldn't be good for Santa's resume to have people already looking towards the New Year without having received their gifts!
Such is the intriguing nature of relativity and speed of light travel. Of course, the speed of light constant is supposed to occur within a vacuum, and many experts also say there's no way any person could travel at the exact same speed of light. And since I'm in no way a specialist in relativity or this type of travel, perhaps my calculations & setup are off. But either way, it looks like resolving the mystery of Santa Clause's gift delivery system will have to wait for another year.