Renninger Negative-result Experiment - Renninger's Negative-result Experiment

Renninger's Negative-result Experiment

In the Renninger formulation, the cloud chamber is replaced by a pair of hemispherical particle detectors, completely surrounding a radioactive atom at the center that is about to decay by emitting an alpha ray. For the purposes of the thought experiment, the detectors are assumed to be 100% efficient, so that the emitted alpha ray is always detected.

By consideration of the normal process of quantum measurement, it is clear that if one detector registers the decay, then the other will not: a single particle cannot be detected by both detectors. The core observation is that the non-observation of a particle on one of the shells is just as good a measurement as detecting it on the other.

The strength of the paradox can be heightened by considering the two hemispheres to be of different diameters; with the outer shell a good distance farther away. In this case, after the non-observation of the alpha ray on the inner shell, one is led to conclude that the (originally spherical) wave function has "collapsed" to a hemisphere shape, and (because the outer shell is distant) is still in the process of propagating to the outer shell, where it is guaranteed to eventually be detected.

In the standard quantum-mechanical formulation, the statement is that the wave-function has partially collapsed, and has taken on a hemispherical shape. The full collapse of the wave function, down to a single point, does not occur until it interacts with the outer hemisphere. The conundrum of this thought experiment lies in the idea that the wave function interacted with the inner shell, causing a partial collapse of the wave function, without actually triggering any of the detectors on the inner shell. This illustrates that wave function collapse can occur even in the absence of particle detection.