junglebeast said:In this case, the question has a physical meaning and so the question can be answered via direct measurements without resorting to wave packet theory. ie, take a closed system containing a barrier and a free particle. Fire the free particle at the barrier with no holes, then put a detect on both sides of the barrier. If a particle is detected on both sides of the barrier, then this proves that a particle can split itself into non-entangled reflected and transmitted particles via quantum tunneling, which effectively answers the original question without resorting to wave theory
This has been done already. The double-slit experiment is not much different from the passage of a particle through a barrier. The details vary, but you are still dealing with the same wave interference effect. I think it is well established that particles do not "split" in the double slit setup, so there is no reason to believe that they would "split" in the barrier setup.