Mott problem

The problem later associated with Mott concerns a spherical wave function associated with an alpha ray emitted from the decay of a radioactive atomic nucleus. Intuitively, one might think that such a wave function should randomly ionize atoms throughout the cloud chamber, but this is not the case. The result of such a decay is always observed as linear tracks seen in Wilson's cloud chamber. The origin of the tracks given the original spherical wave predicted by theory is the problem requiring physical explanation. In practice, virtually all high-energy physics experiments, such as those conducted at particle colliders, involve wave functions which are inherently spherical. Yet, when the results of a particle collision are detected, they are invariably in the form of linear tracks (see, for example, the illustrations accompanying the article on bubble chambers). It is somewhat strange to think that a spherically symmetric wave function should be observed as a straight track, and yet, this occurs on a daily basis in all particle collider experiments. ==History==

The problem of alpha particle track was discussed at the Fifth Solvay conference in 1927. Max Born described the problem as one that Albert Einstein pointed to, asking "how can the corpuscular character of the phenomenon be reconciled here with the representation by waves?". Born answers with Heisenberg's "reduction of the probability packet", now called wavefunction collapse, introduced in May 1927. Born says each droplet in the cloud chamber track corresponds to a reduction of the wave in the immediate vicinity of the droplet. At the suggestion of Wolfgang Pauli he also discusses a solution that includes the alpha emitter and two atoms all in the same state and without wave function collapse, but does not pursue the idea beyond a brief discussion. Werner Heisenberg analyzed the problem qualitatively but in detail. He considers two cases: wavefunction collapse at each interaction or wavefunction collapse only at the final apparatus, concluding they are equivalent. In 1929 Charles Galton Darwin analyzed the problem without using wavefunction collapse. He says the correct approach requires viewing the wavefunction as consisting of the system under study (the alpha particle) and the environment it interacts with (atoms of the cloud chamber). Starting with a simple spherical wave, each collision involves a wavefunction with more coordinates and increasing complexity. His model coincides with the strategy of modern quantum decoherence theory. The Renninger negative-result experiment from the 1960s is a refinement of the Mott problem to further sharpen one of the paradoxes associated with wave-function collapse. ==Mott's analysis==

Nevill Mott picks up where Darwin left off, citing Darwin's paper explicitly. What is uncertain is which straight line the wave packet will reduce to; the probability distribution of straight tracks is spherically symmetric. ==Modern applications==

Erich Joos and H. Dieter Zeh adopt Mott's model in the first concrete model of quantum decoherence theory. Mott's analysis, while it predates modern decoherence theory, fits squarely within its approach. Bryce DeWitt points to the dramatic mass difference between the alpha particle and the electrons in Mott's analysis as characteristic of decoherence of the state of the more massive system, the alpha particle. In modern times, the Mott problem is occasionally considered theoretically in the context of astrophysics and cosmology, where the evolution of the wave function from the Big Bang or other astrophysical phenomena is considered. ==See also==