I was thinking today about configurations where one measures that a certain observable is not in a certain state.
I was getting confused about what this means for decoherence. If I observe a detector and I measure when a particle does not interact with it, then, I don’t understand how this can be entirely equivalent to allowing the particle to interact with further macroscopic objects (f.i. detectors, my brain) in such a way that the wave functions collapse. I’m detecting when it doesn’t interact so, I’m not interacting with it..
If the Schrödinger equation yields solutions that show the probability as the square of the amplitude, then the ‘negative’ Schrödinger equation’s solution is an operator $\sqrt(1-x^2)$ applied to the normal solution.
Under what conditions is that still a solution of Schrödinger equation? And is it possible to define hermitian operators that give the probability of “not observing” a property?
I don’t see how physically decoherence of non-observance can happen in the same way as regular observing, and at the same time it feels like it has to, although this may just be another aspect of QP that defies intuition.