An outline for a modal interpretation in terms of possible worlds is presented. The so-called Schmidt histories are taken to correspond to the physically possible worlds. The decoherence function defined in the histories formulation of quantum theory is taken to prescribe a non-classical probability measure over the set of the possible worlds. This is shown to yield dynamics in the form of transition probabilities for occurrent events in each world. The role of the consistency condition is discussed.
An outline for a modal interpretation in terms of possible worlds is presented. The so-called Schmidt histories are taken to correspond to the physically possible worlds. The decoherence function defined in the histories formulation of quantum theory is taken to prescribe a non-classical probability measure over the set of the possible worlds. This is shown to yield dynamics in the form of transition probabilities for occurrent events in each world. The role of the consistency condition is discussed.
Modal Actualism offers a realist, non-Everettian interpretation of quantum mechanics that preserves unitary dynamics while explaining definite outcomes without invoking collapse or branching. The central distinction is between modal structure—the full set of decoherent histories physically supported by the universal wavefunction—and actuality, the single decoherent history that is realised. Decoherence partitions modal structure into quasiclassical trajectories, but only one such trajectory constitutes the actual worldline. Probability is interpreted as modal measure: a structural feature of the wavefunction that quantifies the weight of possible histories without implying their actuality. This framework dissolves foundational paradoxes by blocking the inference from modal multiplicity to ontological multiplicity, thereby avoiding Everettian inflation while retaining the explanatory power of decoherence. Modal Actualism reconciles quantum correlations with relativistic locality and reframes cosmological fine-tuning as a feature of modal structure rather than evidence for multiverse ensembles
This paper discusses the relation between the decoherent histories approach to quantum mechanics that is based on coarse-grained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in the Copenhagen interpretation. We show how the a classical world used in such formulations is not to something to be postulated but rather explained by suitable sets of alternative histories of quasiclassical variables. We discuss the general definition of measurement, the collapse of the wave function, and irreversibility from the perspective of decoherent histories quantum theory..
The world of quantum theory is not deterministic; however, the quantum theory of an isolated system describes its state as evolving deterministically.How can these two points be reconciled? The modal interpretation (of which a number of variants have been developed) answers this as follows. An observable may have a value even if the system is not in the corresponding eigenstate of that observable. The state of the system only constrains the possible values the observable can have, and (at least under certain conditions) the probabilities that it has those values. Hence, the eigenvalue–eigenstate link is violated. There is no collapse; the state of an isolated system always evolves in accordance with the Schroedinger equation. Hence the values of observables can change indeterministically, though this stochastic process is constrained by the deterministically evolving quantum state. Terminology varies but in this book the quantum state is then called the dynamical state, and a summary of the values of the observables pertaining to the system is called the value state. Since not all observables are mutually compatible, they will not all have simultaneous sharp values, but for each there is a minimum Borel set of values as its current range. The specific modal interpretation developed here is the Copenhagen Variant of the Modal Interpretation, which places holistic constraints on values of observables pertaining to parts of composite systems.
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
The consistent histories formulation of the quantum theory of a closed system with a pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set. We explain the problems which arise, set out some possible algorithms, and explain their properties with the aid of simple models. Though the discussion is framed in the language of the consistent histories approach, it is intended to highlight the difficulty in making any interpretation of quantum theory based on decoherence into a mathematically precise theory.
We study a formulation of quantum mechanics in which the central notion is that of a quantum-mechanical history---a sequence of events at a succession of times. The primary aim is to identify sets of ``decoherent'' (or ``consistent'') histories for the system. These are quantum-mechanical histories suffering negligible interference with each other, and, therefore, to which probabilities may be assigned. These histories may be found for a given system using the so-called decoherence functional. When the decoherence functional is exactly diagonal, probabilities may be assigned to the histories, and all probability sum rules are satisfied exactly. We propose a condition for approximate decoherence, and argue that it implies that most probability sum rules will be satisfied to approximately the same degree. We also derive an inequality bounding the size of the off-diagonal terms of the decoherence functional. We calculate the decoherence functional for some simple one-dimensional systems, with a variety of initial states. For these systems, we explore the extent to which decoherence is produced using two different types of coarse graining. The first type of coarse graining involves imprecise specification of the particle's position. The second involves coupling the particle to a thermal bath of harmonic oscillators and ignoring the details of the bath (the Caldeira-Leggett model). We argue that both types of coarse graining are necessary in general. We explicitly exhibit the degree of decoherence as a function of the temperature of the bath, and of the width to within which the particle's position is specified. We study the diagonal elements of the decoherence functional, representing the probabilities for the possible histories of the system. To the extent that the histories decohere, we show that the probability distributions are peaked about the classical histories of the system, with the distribution of their initial positions and momenta given by a smeared version of the Wigner function. We discuss this result in connection with earlier uses of the Wigner function in this context. We find that there is a certain amount of tension between the demands of decoherence and peaking about classical paths.