In quantum mechanics, the consistent histories or simply "consistent quantum theory" interpretation generalizes the complementarity aspect of the conventional Copenhagen interpretation. The approach is sometimes called decoherent histories and in other work decoherent histories are more specialized. this interpretation of quantum mechanics is based on a consistency criterion that then allows probabilities to be assigned to various alternative histories of a system such that the probabilities for each history obey the rules of classical probability while being consistent with the Schrödinger equation. In contrast to some interpretations of quantum mechanics, the framework does not include wavefunction collapse as a relevant description of any physical process, and emphasizes that measurement theory is not a fundamental ingredient of quantum mechanics. Consistent histories allows predictions related to the state of the universe needed for quantum cosmology.

Key assumptions

The interpretation rests on three assumptions:

  1. states in Hilbert space describe physical objects,
  2. quantum predictions are not deterministic, and
  3. physical systems have no single unique description.

The third assumption generalizes complementarity and this assumption separates consistent histories from other quantum theory interpretations.

In order to obtain a complete theory, the formal rules above must be supplemented with a particular Hilbert space and rules that govern dynamics, for example a Hamiltonian.

In the opinion of others this still does not make a complete theory as no predictions are possible about which set of consistent histories will actually occur. In other words, the rules of consistent histories, the Hilbert space, and the Hamiltonian must be supplemented by a set selection rule. However, Robert B. Griffiths holds the opinion that asking the question of which set of histories will "actually occur" is a misinterpretation of the theory; histories are a tool for description of reality, not separate alternate realities.

Proponents of this consistent histories interpretation—such as Murray Gell-Mann, James Hartle, Roland Omnès and Robert B. Griffiths—argue that their interpretation clarifies the fundamental disadvantages of the old Copenhagen interpretation, and can be used as a complete interpretational framework for quantum mechanics.

In Quantum Philosophy, Roland Omnès provides a less mathematical way of understanding this same formalism.

The consistent histories approach can be interpreted as a way of understanding which sets of classical questions can be consistently asked of a single quantum system, and which sets of questions are fundamentally inconsistent, and thus meaningless when asked together. It thus becomes possible to demonstrate formally why it is that the questions which Einstein, Podolsky and Rosen assumed could be asked together, of a single quantum system, simply cannot be asked together. On the other hand, it also becomes possible to demonstrate that classical, logical reasoning often does apply, even to quantum experiments – but we can now be mathematically exact about the limits of classical logic.

See also

  • HPO formalism

References

  • The Consistent Histories Approach to Quantum Mechanics – Stanford Encyclopedia of Philosophy