All this quantum theory as all well and good, as it pertains to Touhou characters, but what of Gensokyo itself? How do we explain the border, which is unseen to human eyes yet cannot be penetrated by us? Does the border extend into the atmosphere, and if so, how far? And what of geology - if there is a major earthquake in Japan, is it also felt in Gensokyo? And can one tunnel under the border?
I await the responses of the scientific community.
The effect of the border could be approximated to a zero probability solution to the Chen-Orin equation which, barring specific exceptions, prevents the existence of all forces and matter in its presence. Considering the typically symmetrical wave-like solutions of the equation which can be presented as a circle in a polar frame of reference, it only makes sense that the border maps out to a sphere, which is also the lowest-energy configuration available, making other shapes increasingly unlikely.
An additional theory presents itself from the observation that no such border exists within Gensokyo itself, which suggests that the discussed border, also called the Great Barrier, is the first zero probability solution to the Chen-Orin equation when applied to the Gensokyo-Earth system. This, of course, suggests that a similar border exists beyond the bounds of
the Earth itself, with more and more such borders existing beyond these until there no longer exists a possibility for a zero probability solution.
We should consider the Yakumo-Han effect, shown by the ability of certain individuals to cross this border in both directions. Alternatively, the effect is observed in certain geographical locations. It is proposed that the Yakumo-Han effect is, in fact, a form of
tunnelling, which allows for matter to, essentially, ignore the border's zero solution.
Due to the high energy required for a wave-particle to tunnel through the border, it is only obvious that this is an exceedingly rare effect. It still remains in question as to why the Yakumo-Han Tunnelling is observed at all in the specific exceptions mentioned above.