The Mott problem is an iconic challenge to quantum mechanics theory: how can the prediction of spherically symmetric wave function result in linear tracks seen in a cloud chamber. The problem was first formulated in 1927 by Albert Einstein and Max Born and solved in 1929 by Nevill Francis Mott. Mott's solution notably only uses the wave equation, not wavefunction collapse, and it is considered the earliest example of what is now called decoherence theory.
Spherical waves, particle tracks
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. 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. 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.