Consistent histories

In quantum mechanics, the consistent histories (also referred to as decoherent histories) approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. 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, particularly the Copenhagen interpretation, 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. history approach, although it was initially independent of the Copenhagen approach, is in some sense a more elaborate version of it. 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. In quantum mechanics, the consistent histories (also referred to as decoherent histories) approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. 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, particularly the Copenhagen interpretation, 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. A homogeneous history H i {displaystyle H_{i}} (here i {displaystyle i} labels different histories) is a sequence of Propositions P i , j {displaystyle P_{i,j}} specified at different moments of time t i , j {displaystyle t_{i,j}} (here j {displaystyle j} labels the times). We write this as: H i = ( P i , 1 , P i , 2 , … , P i , n i ) {displaystyle H_{i}=(P_{i,1},P_{i,2},ldots ,P_{i,n_{i}})} and read it as 'the proposition P i , 1 {displaystyle P_{i,1}} is true at time t i , 1 {displaystyle t_{i,1}} and then the proposition P i , 2 {displaystyle P_{i,2}} is true at time t i , 2 {displaystyle t_{i,2}} and then … {displaystyle ldots } '. The times t i , 1 < t i , 2 < … < t i , n i {displaystyle t_{i,1}<t_{i,2}<ldots <t_{i,n_{i}}} are strictly ordered and called the temporal support of the history. Inhomogeneous histories are multiple-time propositions which cannot be represented by a homogeneous history. An example is the logical OR of two homogeneous histories: H i ∨ H j {displaystyle H_{i}lor H_{j}} .