Superposition in Measuring Apparatus: A Thought Experiment

The measurement problem in quantum mechanics arises from the apparent collapse of a superposition state to a definite outcome when a measurement is made. Although treating the measuring apparatus as a classical system has been a successful approach in explaining quantum phenomena, it raises fundamental questions about the nature of measurement and the validity of wave function collapse. In this paper, we discuss a thought experiment that explores superposition in the measuring apparatus when it is treated as a quantum system. The experiment uses the Hong-Ou-Mandel effect in a two-photon interference setup, and its outcome is indicated by the coincidence count. Specifically, a zero count implies the existence of superposition, while a non-zero count indicates a wave function collapse. The discussions provide insight into the measurement problem, particularly regarding wave function collapse and nested measurement, and highlight the importance of indistinguishability to it. It provides a framework that probes the exact conditions necessary for a wave function collapse to happen.