Subject: Classic PackyHumor: The Physics of Santa Claus
Original-Date: Tue, Dec 7 1999
This is the combination of two missives sent on Mon, 7 Dec 1998 and
Fri, 25 Dec 1998 by Atul Jagga and Gene Gregor, respectively. I've
tacked them together because the second is a rebuttal to the first.
II.
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 purposes of our calculations), we are now talking about 0.78 miles per household; a total trip of 75.5 million miles, not counting bathroom stops or breaks. This means Santa's sleigh is moving at 650 miles per second -- 3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle, the Ulysses space probe, moves at a poky 27.4 miles per second, and a conventional reindeer can run (at best) 15 miles per hour.
III.
The payload of the sleigh adds another interesting element.
Assuming that each child gets nothing more than a medium sized
Lego set (two pounds), the sleigh is carrying over 500 thousand
tons, not counting Santa himself. On land, a conventional
reindeer can pull no more than 300 pounds. Even granting that the
"flying" reindeer could pull ten times the normal amount, the job
can't be done with 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, or roughly seven times
the weight of the Queen Elizabeth (the ship, not the monarch).
IV.
600,000 tons traveling at 650 miles per second crates enormous
air resistance -- 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 into 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 thousandths of a second, 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 a dead stop to 650 m.p.s. in .001 seconds,
would be subjected to centrifugal forces of 17,500 g's. A 250
pound Santa (which seems ludicrously slim) would be pinned to the
back of the sleigh by 4,315,015 pounds of force, instantly
crushing his bones and organs and reducing him to a quivering blob
of pink goo.
V.
Therefore, if Santa did exist, he's dead now.
As it happens, the terminal velocity of a reindeer in dry December air over the Northern Hemisphere (for example) is known with tremendous precision. The mass of Santa and his sleigh (since the number of children and their gifts is also known precisely, ahead of time, and the reindeer must weigh in minutes before the flight) is also known with tremendous precision. His direction of flight is, as you say, essentially east to west.
All of that, when taken together, means that the momentum vector of Mr Claus and his cargo is known with incredible precision. An elementary application of Heisenberg's uncertainty principle yields the result that Santa's location, at any given moment on Christmas Eve, is highly imprecise. In other words, he is "smeared out" over the surface of the earth, analogous to the manner in which an electron is "smeared out" within a certain distance from the nucleus in an atom. Thus he can, quite literally, be everywhere at any given moment.
In addition, the relativistic velocities which his reindeer can attain for brief moments make it possible for him, in certain cases, to arrive at some locations shortly before he left the North Pole. Santa, in other words, assumes for brief periods the characteristics of tachyons. I will admit that tachyons remain hypothetical, but then so do black holes, and who really doubts their existence anymore?