The Quantum Santa Hypothesis

I teach a first year seminar called "Einstein in Wonderland: Physics, Philosophy, and Other Nonsense" in which we consider the classical notion of sense from Descartes and Newton, classical nonsense from Lewis Carroll, and then look at relativity theory and quantum mechanics to decide whether they violate the classical notion of sense, whether modern science forces us to not only rework our understanding of the world, but also our understanding of understanding. This year's bunch went beyond philosophy and actually framed their own scientific theory -- the quantum Santa hypothesis.

In quantum mechanics, when a system is unobserved it behaves according to Schrodinger's equation. This means that it finds itself in what we call a superposed state, that is, a combination of all possible values for its observable properties. In the case of position, for example, it means that a things "spreads out" over all of the places it might be found. But we never see a system in its superposed state, when we make an observation, the system collapses into one of its property states, into one single value of the observable quantity, for example, into one place.

The class realized that this might be the answer to the Santa paradox -- how can Santa visit every house in one night when doing so would require him to move faster than the speed of light, which, of course, is prohibited by the theory of relativity? The proposed answer hinges on the fact that Santa always comes in the middle of the night when no one is watching. Because no one observes Santa, he would be in a superposed state, that is in every house simultaneously.

Further, the presents he brings are not truly independent of him, but rather part of a larger system that is superposed. The potential of the system is set by the children's behavior throughout the year making the bicycle/coal coefficient lean in one direction or the other and as soon as the first little one wakes up and looks under the tree, a present measurement is made and the Santa wave function collapses into a single present state in which the value of all presents are instantly determined throughout the whole world at that moment, just like electron spin in the Einstein-Podolsky-Rosen-type cases.

Is the quantum Santa theory testable? I suppose one way would be to make constant observations throughout the night which would mean that Santa would be forced to remain in single positions throughout the entire eventing and thereby would be unable to deliver gifts to his full contingent of children. Perhaps there are some experiments that science shouldn't carry out.