Is the Elitzur-Vaidman bomb problem based on incorrect assumptions?

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Are the following assumptions about this thought experiment correct?...

If an interference pattern is detected the bomb is defective because there was never any possibility of a photon being observed and collapsing the wave function.

In the case that no interference pattern is detected and the photon arrives at the detector at the end of the interferometer a photonless beam of light must have traveled through a functional photon detector/bomb trigger. This means the bomb is not defective because the photon that wasn't actually on the path to set off the bomb somehow knew that it would be detected there and the wave function collapsed even thought the photon was on the other path.
 
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No, these assumptions are not correct. The thought experiment does not involve a photon detector or bomb trigger, and the wave function can collapse without any photons being observed. Additionally, the fact that an interference pattern is detected does not necessarily mean that the bomb is defective.
 
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