The wave function as a mathematical description of a free particle's possible motion: The 2-slit problem with attempted detection

Abstract

Starting with a down to earth interpretation of quantum mechanics for a free particle, the disappearance and reappearance of interference in the 2 slit problem with a detector behind one are treated in detail. A partial interpretation of quantum theory is employed which is simple, emphasizing description, yet adequate for addressing the present problem. Given that the eigenvalue equation is essential to predict a free particle's probability of collision, it is argued that there is equal need for a realistic theory to describe its possible motion. Feynman's point-to-point space-time wave packet is put forth and used as the appropriate description of the field-free motion between collisions. For a particle in a conventional 2-slit experiment with attempted detection behind one, the disappearance of interference is explained - both when the detection succeeds and when it doesn't. Also a definite prediction is made, when the inter-slit distance is reduced, of where the first signs of interference should appear on the detection screen.