Definition
Consistent histories is an interpretation of quantum mechanics, developed by Robert Griffiths, Roland Omnès, Murray Gell-Mann, and James Hartle, in which probabilities are assigned not to single instantaneous events but to whole histories — sequences of properties at successive times. A history is admissible only if it belongs to a family that satisfies a consistency condition, which guarantees that probabilities add as in classical reasoning.
It is one of the main alternatives to the Copenhagen and many-worlds interpretations.
Why it matters
How it works
In standard quantum mechanics, the state evolves unitarily until a measurement, at which point it collapses to one of the measurement outcomes with probabilities given by the Born rule. The Copenhagen framework treats this collapse as a primitive — observer-dependent and external to the dynamics.
Consistent histories drops the collapse step. Instead, a history is a list of properties P₁ at time t₁, P₂ at time t₂, and so on, encoded as projection operators. The probability of a history is given by a trace formula involving the projections and the initial state. For this probability to make sense, the histories in a family must be consistent: the interference between distinct histories, measured by the off-diagonal terms in the decoherence functional, must vanish.
Environments naturally enforce this consistency by decoherence — entangling the system with many uncontrolled degrees of freedom and washing out the off-diagonal terms. So the practical question is not "what does the observer see?" but "which sets of histories decohere?" Those are the histories that can be assigned probabilities and reasoned about classically.
Two consistent families can describe the same situation while contradicting each other if combined naively. This is the single-framework rule: you can use one family or the other, but not both at once. It is the consistent-histories analogue of the older injunction not to ask about a particle's path in a two-slit experiment.