[amsat-bb] A Quantum Mechanical Analysis of the Santa Claus problem

[Daniel Schultz]

Every year about this time, various analyses go out over the net purporting to
show that Santa Claus cannot possibly exist, because of the extremely high
speeds and accelerations required for him to make his rounds, absence of
chimneys or other means of ingress, etc.

The analysis about the death of Santa Claus, based on classical physics, is
seriously flawed owing to its neglect of quantum phenomena that become
significant in his particular case. An application of Quantum Mechanics to the
Santa Claus problem shows that the situation is not nearly so hopeless as a
classical analysis would have you believe:

Consider the following:

* Santa is never directly observed, but indirect evidence of him abounds.

* If direct observation is attempted (say, by staying up all night with the
lights on), not only is Santa not observed, but the indirect evidence of his
presence does not appear either--only if no attempt is made to observe Santa
do the stockings get filled.

* Evidence of Santa appears in multiple locations simultaneously throughout
the world. (The multiplicity of time zones does not substantially alter this
argument, and will therefore be ignored.)

* Evidence of Santa appears even in rooms that are separated from the rest of
the universe by  barriers (small or non-existent chimneys) that Santa cannot
classically pass through.

It is obvious, then, that Santa can best be described by a quantum-mechanical
wavefunction SC, which is nonzero at midnight on Christmas eve throughout the
world. Like other quantum-mechanical wavefunctions, it is not confined to one
spatial location, and can "tunnel" through classical barriers (house walls and
roof), producing a potentially nonzero expectation value in (classically
forbidden) living rooms and apartments. Children expect Santa to arrive;
therefore, in living spaces with the child operator (closely related to the
annihilation operator), the expectation value is small but finite, and a small
but finite fraction of Santa's presents are deposited. However, if an attempt
is made to observe Santa, the observation finds the Santa wavefunction in
either a "not-Santa" (OC|SC> = |SC->) or "Santa" (OC|SC> = |SC+>) eigenstate.
Because of the very small expectation value of the Santa function
(approximately the reciprocal of the number of houses Santa visits, adjusted
by local "naughty" and "nice" operators), the eigenstate is extremely likely
to be "not-Santa" (|SC->)--no presents appear. One cannot really blame these
intrepid experimentalists, however: if one of them did succeed in finding
Santa in the "Santa" (|SC+>) state, he or she would not only have
unprecedented direct evidence of Santa Claus, but would find Santa's entire
load of presents deposited in his or her living room. 

(The foregoing analysis attributed to R. Carey Woodward, Jr., Ph.D.)

Another, less mathematical, analysis (gotta love Google) is that:

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.

(Author unknown)

Merry Christmas. Get to bed tonight and maybe Santa will bring Amsat a launch
vehicle in 2009.

Dan Schultz N8FGV