A Difficulty with the Magical Behavior of Elementary Particles
In a previous article the wave function within an infinite square well was discussed. A particle (e.g. an electron), trapped in the well, can have only discrete energies. The energies must be such that the wave function standing wave within the well has nodes at the well walls. At energies above the ground state, the wave function will also have one or more nodes between the walls. To Born (and doubtless, others), the nodes between the well walls posed the interesting question of how the particle got from one wall to the other and back again. For if, as Born suggested, the square of the wave function is the probability of the particle being found at such points, then how does the particle get across a node?
Modern thinking is that the particle never is at the node. Rather it disappears at some point on the incident side of a node, and reappears simultaneously on the other side of the node. Evidently there is experimental reason to believe that this strange behavior actually occurs.
A theoretical difficulty with this idea is that simultaneity is relative. For example, let us suppose that, viewed from inertial frame K, the particle disappears at N-x and reappears at N+x (where N is the x value of a node). We find that, viewed from frame K’, the particle disappears at one instant and reappears at a different instant. If nothing else, this implies that there is a period of time (brief, no doubt) when the particle either does not exist, or that it exists at more than one point simultaneously. If we assume that the total energy of the Universe is constant in time, then this assumption would appear to be violated.
It isn’t clear to the author what the solution to this conundrum might be.