Question and answers about consistent histories

Books and papers which provide an introduction to consistent histories quantum theory

Consistent Quantum Theory, by Robert B. Griffiths

Transparencies for lectures on consistent histories (2005)


Brief Introduction to Consistent (Decoherent) Histories

Modern quantum mechanics is based upon two distinct ideas. One is that wave functions develop in time according to the equation invented in 1926 by Erwin Schrödinger. The other is that wave functions can be used to calculate probabilities, an idea first proposed, also in 1926, by Max Born. Combining these two ideas in a consistent way has turned out to be difficult. The approach found in many textbooks, in which a wave function is used to calculate the probability that a measurement carried out on some quantum system will yield a particular outcome, is not very satisfactory, for two reasons. First, one often wants to apply quantum theory to situations which do not involve a measuring apparatus; for example, in the center of the sun. Second, all real measuring instruments are themselves made up of quantum particles, and should therefore be described in quantum terms. But trying to do so gives rise to difficulties and inconsistencies in an approach to quantum theory that is based in essential way upon the concept of a measurement.

The consistent histories approach combines wave functions and probabilities in a fully consistent way which does not rely upon the use of measurements. It was first proposed by Robert Griffiths in 1984, and further developed by Roland Omnès in 1988, and by Murray Gell-Mann and James Hartle, who used the term ``decoherent histories'', in 1990. A history is a sequence of quantum events (i.e., wave functions) at successive times. Probabilities can be assigned to histories provided certain consistency conditions are satisfied. Histories can be used to describe how a particle interacts with a measuring apparatus, and how the outcome of a measurement (e.g., the position of a pointer) is related to some property of the particle before the measurement took place. However, they can also be employed for a single particle, or any number of particles, in the absence of any measurement. For example, by using consistent histories it is possible to assign a probability for the time at which an unstable particle, such as a radioactive atom, will decay, even if it is out in interstellar space far from any measuring device.

Consistent histories can be used to analyze various quantum paradoxes, such as the interference produced by a particle passing through a double slit, or the correlated pair of particles considered by Einstein, Podolksy, and Rosen. This allows the paradox to be understood in quantum terms, without any need to invoke peculiar long-range influences or other ghostly effects. The consistent histories approach has also been employed to analyze problems in quantum computation and quantum cryptography.


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Last modified May 2007.