How does Bohmian mechanics explain quantum bomb testing?

[greypilgrim]

Hi.

In an Elitzur–Vaidman bomb tester, will the guiding wave be different in a situation with a live bomb compared to one with only a dud? And if yes, how does the bomb interact with the guiding wave? Because usually it is described as a pointlike device that only explodes when hit by the photon and doesn't have a potential that could enter the Schrödinger equation for the guiding wave $\psi$.

 

[Demystifier]

To answer your question, it is not sufficient to study the guiding wave of the photon. One must study the guiding wave of everything involved, including that of particles constituting the bomb. In the case of a properly working bomb, the full guiding wave is a superposition of exploding and non-exploding bomb, so in this sense it differs from a dud bomb case. This superposition is a consequence of interaction between the photon wave with the bomb wave. However, depending on initial particle positions, the particles guided by such a superposition enter either the exploding or the non-exploding branch of the full wave. If they enter the non-exploding wave, then the exploding branch will have no influence on the behavior of particles, which effectively looks as if that branch doesn't exist.