In
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, the Mott problem is a
paradox that illustrates some of the difficulties of understanding the nature of
wave function collapse and
measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
in quantum mechanics. The problem was first formulated in 1929 by Sir
Nevill Francis Mott
Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. ...
and
Werner Heisenberg
Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...
, illustrating the paradox of the collapse of a spherically symmetric
wave function into the linear tracks seen in a
cloud chamber.
online
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In practice, virtually all high energy physics experiments, such as those conducted at particle collider
A collider is a type of particle accelerator which brings two opposing particle beams together such that the particles collide. Colliders may either be ring accelerators or linear accelerators.
Colliders are used as a research tool in particle ...
s, 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.
A related variant formulation was given in 1953 by Mauritius Renninger, and is now known as Renninger's negative-result gedanken experiment. In this formulation, it is noted that the absence of a particle detection can also constitute a quantum measurement; namely, that a measurement can be performed even if no particle whatsoever is detected.
Mott's analysis
In the original 1929 formulation by Mott and Heisenberg, the spherical wave function of an alpha ray
Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
emitted from the decay of a radioactive atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i ...
was considered. It was noted that the result of such a decay is always observed as linear tracks seen in Wilson's cloud chamber. Intuitively, one might think that such a wave function should randomly ionize atoms throughout the cloud chamber, but this is not the case. Mott demonstrated that by considering the interaction in configuration space, where all of the atoms of the cloud chamber play a role, it is overwhelmingly probable that all of the condensed droplets in the cloud chamber will lie close to the same straight line. What is uncertain is which straight line the wave packet will reduce to; the probability distribution of straight tracks is spherically symmetric.
Modern applications
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
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
or other astrophysical phenomena is considered.
See also
* Spontaneous symmetry breaking
References
* Nevill Mott
Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. ...
, "The Wave Mechanics of α-Ray Tracks", Proceedings of the Royal Society (1929) A126, pp. 79-84, {{doi, 10.1098/rspa.1929.0205. (reprinted as Sec.I-6 of ''Quantum Theory and Measurement'', J.A. Wheeler. and W.H. Zurek, (1983) Princeton).
Quantum measurement