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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.

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  • $\begingroup$ This question may be simpler phrased in terms of a double-slit experiment. If we have a detector only at one slit, we would know whether a particle went through this slit. After detecting the particle on the screen, we would know that it must have gone through the other slit. Would there be lines on the screen? $\endgroup$ – safesphere Nov 2 '17 at 16:04
  • $\begingroup$ A quantum state (wave function) is the information available to you about the physical system. When you look in some region and don't find the particle, the information available to you has changed. Does that help to begin explaining it? $\endgroup$ – DanielSank Nov 2 '17 at 16:35
  • $\begingroup$ @DanielSank That's mighty $\psi$-epistemic, though, isn't it? Not that there's anything wrong with that, but it feels like there should be a $\psi$-ontic way to explain this as well. $\endgroup$ – Emilio Pisanty Nov 2 '17 at 16:45
  • $\begingroup$ To DanielSank. If the wave function is just the information available to me about the system, does that mean that the later wave function is a more accurate representation of the system than the earlier wave function? Or are both functions just equally accurate about different systems, the earlier function for a system without a measurement interference and the later function for a system with a measurement interference? $\endgroup$ – Michael C. Nov 2 '17 at 16:50
  • $\begingroup$ @EmilioPisanty I'm not sure the distinction is really important, but please do hit me up in the chat room to explain why I'm wrong ;-) $\endgroup$ – DanielSank Nov 2 '17 at 19:47

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