The 1953 and 1960 Renninger negative-result thought experiments illustrate conceptual paradoxes in the Copenhagen formulation of quantum mechanics. In the 1953 paradox we can infer the presence of a detector in one arm of a Mach-Zehnder interferometer without any particle interacting with the detector. In the 1960 paradox we can infer the collapse of a wavefunction without any change in the state of a detector. I resolve both of these paradoxes by using a time-symmetric formulation of quantum mechanics. I also describe a real experiment that can distinguish between the Copenhagen and time-symmetric formulations.
