The Universe as an Eigenstate: Spacetime Paths and Decoherence

Francesc S. Roig

Using the Gell-Mann and Hartle formalism of generalized quantum mechanics of closed systems, we study the classical limit of coarse-grained spacetime histories and their decoherence. The system under consideration is one-dimensional and consists of a particle coupled to a von Neumann apparatus that performs a measurement of the position of the particle during the finite time interval during which the histories of this system take place. We consider two cases: a free particle and a harmonic oscillator. The real line is divided into intervals of the same length, and coarse-grained histories are defined by the time average of the position of the particle on a given Feynman path to be within one of these intervals. The position of the pointer in each Feynman path correlates with this time average. The class operators for this system have been evaluated, and the decoherence functional shows that these coarse-grained histories do not decohere, not even when initially either the particle or the pointer is in an eigenstate of position. Decoherence is obtained only when the classical limit is taken. Qualitative arguments for decoherence in the classical limit are presented for the case of a general particle potential.

Masa‐aki Sakagami, Takashi Okamura, Hiroto Kubotani

Claus Kiefer

Li Peng

Modern physics faces a constellation of foundational puzzles: the Big Bang singularity, time's arrow, dark matter and dark energy, the cosmological constant problem, fine-tuning, quantum measurement, and quantum gravity unification. This Perspective proposes a unified resolution grounded in complexity-driven selection from diverse quantum paths. Prior to the Big Bang, reality comprises a pre-temporal quantum substrate (lacking classical time coordinate but governed by unitary quantum evolution), evolving reversibly across multiple trajectories—including opposing time arrows. The Big Bang marks an emergence threshold (λ) where decoherence locks spacetime parameters, yielding our classical universe as a "survivor" of local emergence rather than a closed totality. Dark matter and dark energy represent unevolved quantum paths—residuals exerting gravitational influence without full manifestation. This framework reframes cosmology as the study of layered emergence, dissolving "why" questions into "when/how" selection dynamics, with testable predictions in CMB perturbations, quantum decoherence experiments, and gravitational wave observations. By shifting from reductionism to emergentism, it suggests a universal pattern: threshold-gated emergence from diverse substrates, applicable from the cosmos to consciousness.

Carl Friedrich von Weizsäcker, Thomas Görnitz, Holger Lyre

James B. Hartle

Sum-over-histories generalizations of nonrelativistic quantum mechanics are explored in which probabilities are predicted, not just for alternatives defined on spacelike surfaces, but for alternatives defined by the behavior of spacetime histories with respect to spacetime regions. Closed, nonrelativistic systems are discussed whose histories are paths in a given configuration space. The action and the initial quantum state are assumed fixed and given. A formulation of quantum mechanics is used which assigns probabilities to members of sets of alternative coarse-grained histories of the system, that is, to the individual classes of a partition of its paths into exhaustive and exclusive classes. Probabilities are assigned to those sets which decohere, that is, whose probabilities are consistent with the sum rules of probability theory. Coarse graining by the behavior of paths with respect to regions of spacetime is described. For example, given a single region, the set of all paths may be partitioned into those which never pass through the region and those which pass through the region at least once. A sum-over-histories decoherence functional is defined for sets of alternative histories coarse-grained by spacetime regions. Techniques for the definition and effective computation of the relevant sums over histories by operator-product formulas are described and illustrated by examples. Methods based on Euclidean stochastic processes are also discussed and illustrated. Models of decoherence and measurement for spacetime coarse grainings are described. Issues of causality are investigated. Such spacetime generalizations of nonrelativistic quantum mechanics may be useful models for a generalized quantum mechanics of spacetime geometry.