Wave Function Collapse?

Consider an electron in a box. Imagine partitioning the box into N identical cubes and assume that the amplitude Ψ for finding the electron in the box is the superposition Ψ = ψ₁ + ψ₂ + ψ₃ + . . . , that is, the sum over all N imagined identical cubes in the box. Now use a photon to observe where the electron is by recording the scattered photon and so on. Suppose your incident probe photon passes right through the box and does not interact with the electron, which you determine because the photon took a straight-line path to your detector. What happens to the electron wave function Ψ?

Answer

The original wave function Ψ = ψ₁ + ψ₂ + ψ₃ + . . . will change. The probe photon did not scatter off the electron in particular imaginary boxes, so we know immediately that the wave function should not include their amplitudes. One could say that there has been a partial collapse of the wave function even though there has been no interaction! We believe that this gedanken experiment was discussed first by physicist Robert H. Dicke in the reference below.