Let's say there is a particle confined in a box, and therefore there's a wave function which we can use to determine the probability of the particle's state. Next, a measurement is performed which quickly scans a large portion of the box but does not detect the particle. While this measurement has not definitely determined the position of the particle, it has changed the wave function without interfering with the particle.
But how is it that the wave function before the measurement and the wave function after the measurement can both a) completely describe the system in the box for their respective moments, and b) differ from each other due to a measurement that never interacted with the particle?
It seems that the measurement is changing the state of the particle without even interacting with the particle, and that doesn't seem right.