The history of quantum theory

Lewis Pyenson

S. Schreckenberg

The basic ingredients of the ‘‘consistent histories’’ approach to quantum theory are a space 𝒰𝒫 of ‘‘history propositions’’ and a space 𝒟 of ‘‘decoherence functionals.’’ In this article we consider such history quantum theories in the case where 𝒰𝒫 is given by the set of projectors 𝒫(𝒱) on some Hilbert space 𝒱. We define the notion of a ‘‘physical symmetry of a history quantum theory’’ (PSHQT) and specify such objects exhaustively with the aid of an analog of Wigner’s theorem. In order to prove this theorem we investigate the structure of 𝒟, define the notion of an ‘‘elementary decoherence functional,’’ and show that each decoherence functional can be expanded as a certain combination of these functionals. We call two history quantum theories that are related by a PSHQT ‘‘physically equivalent’’ and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously.

Hendrik B. G. Casimir

Don Nelson Page

Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur when the number of observers is not uniquely predicted by the theory. In single-history theories, each history is weighted simply by its quantum-mechanical probability, but in many-worlds theories in which random observations are considered, there should also be the weighting by the numbers or amounts of observations occurring in each history.

Freeman Hui

We present Quantum-Informational History Optimization Theory (QIHOT) as a formal proposal for selecting a single realized quantum history from a space of dynamically admissible histories subject to boundary constraints. In the present paper, we restrict attention to finite-dimensional and toy-model settings, where the framework can be stated explicitly. QIHOT separates two levels: a dynamical prior over admissible histories generated by standard quantum evolution, and an informational selection rule that reweights those histories by an entropy-based cost functional. Within this structure, we show that standard Born statistics are recovered in symmetric-cost measurement scenarios when the prior is the usual Hilbert-space quantum prior. We further formulate conditions under which operational no-signaling is preserved, provided the selection functional factorizes locally for spacelike-separated regions. A fully worked two-outcome model illustrates how the framework interpolates between coherent evolution and measurement-like branch selection. We contrast QIHOT with the Many-Worlds Interpretation, the Transactional Interpretation, the Consistent Histories formalism, the Schwinger–Keldysh formalism, and Lagrangian-based retrocausal models, highlighting structural similarities and key differences. We emphasize that the present paper develops QIHOT as a scoped formal proposal with partial consistency results rather than as a complete replacement for quantum theory. Possible extensions to consciousness and cosmology are deferred to brief outlook-level discussion.

Jagdish Mehra, Helmut Rechenberg