In quantum mechanics, the consistent histories or simply "consistent quantum theory"[1] interpretation generalizes the complementarity aspect of the conventional Copenhagen interpretation.
[1] First proposed by Robert Griffiths in 1984,[3][4] 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.
are strictly ordered and called the temporal support of the history.
These propositions can correspond to any set of questions that include all possibilities.
One of the aims of the approach is to show that classical questions such as, "where are my keys?"
In this case one might use a large number of propositions each one specifying the location of the keys in some small region of space.
acting on the system's Hilbert space (we use "hats" to denote operators).
It is then useful to represent homogeneous histories by the time-ordered product of their single-time projection operators.
This is the history projection operator (HPO) formalism developed by Christopher Isham and naturally encodes the logical structure of the history propositions.
represents the initial density matrix, and the operators are expressed in the Heisenberg picture.
is simply which obeys the axioms of probability if the histories
The interpretation based on consistent histories is used in combination with the insights about quantum decoherence.
Quantum decoherence implies that irreversible macroscopic phenomena (hence, all classical measurements) render histories automatically consistent, which allows one to recover classical reasoning and "common sense" when applied to the outcomes of these measurements.
It has, of course, the advantage of being more precise, of including classical physics, and of providing an explicit logical framework for indisputable proofs.
But, when the Copenhagen interpretation is completed by the modern results about correspondence and decoherence, it essentially amounts to the same physics.
The logical equivalence between an empirical datum, which is a macroscopic phenomenon, and the result of a measurement, which is a quantum property, becomes clearer in the new approach, whereas it remained mostly tacit and questionable in the Copenhagen formulation.
One is abstract and directed toward logic, whereas the other is empirical and expresses the randomness of measurements.
We need to understand their relation and why they coincide with the empirical notion entering into the Copenhagen rules.
The main difference lies in the meaning of the reduction rule for 'wave packet collapse'.
In the new approach, the rule is valid but no specific effect on the measured object can be held responsible for it.
Decoherence in the measuring device is enough.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[7] this still does not make a complete theory as no predictions are possible about which set of consistent histories will actually occur.
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;[8] 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,[9] 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.