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*Subject*: [amsat-bb] A Quantum Mechanical Analysis of the Santa Claus problem*From*: "Daniel Schultz" <n8fgv@xxxxxxx>*Date*: Thu, 25 Dec 2008 02:17:56 -0500*Z-USANET-MsgId*: XID141mLyHR51472X36

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 _______________________________________________ Sent via AMSAT-BB@amsat.org. Opinions expressed are those of the author. Not an AMSAT-NA member? Join now to support the amateur satellite program! Subscription settings: http://amsat.org/mailman/listinfo/amsat-bb

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