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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Regaining quantum incoherence for matter fields

Pedro F. González-Dı́az

Published Jan 15, 1992• 15 citations
Publisher

Abstract

The possible quantum state of wormholes or little baby universes should be described by a nonfactorizable density matrix given by the path integral over the class of asymptotically flat four-geometries and asymptotically vanishing matter-field configurations which suitably match the prescribed data on three-surfaces which do not divide the manifold on the inner boundary. An instanton is here obtained which can represent such a nonsimply connected wormhole manifold, and is used to evaluate the asymptotic effective interaction of the resulting correlated baby universes with ordinary quantum fields at low energies in the Fock representation. It is argued that the demand of locality on the interacting quantum field commutators is no longer valid for correlated baby universes, and it is therefore concluded that quantum coherence in the matter-field sector is lost as a consequence of the interaction with nonsimply connected wormholes. A proposal is advanced that wormholes may provide us with a complementary quantum state sector that would induce the collapse of the state vector in the quantum measurement of any observable for ordinary microscopic matter systems.

DOI
10.1103/physrevd.45.499

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The possible quantum state of wormholes or little baby universes should be described by a nonfactorizable density matrix given by the path integral over the class of asymptotically flat four-geometries and asymptotically vanishing matter-field configurations which suitably match the prescribed data on three-surfaces which do not divide the manifold on the inner boundary. An instanton is here obtained which can represent such a nonsimply connected wormhole manifold, and is used to evaluate the asymptotic effective interaction of the resulting correlated baby universes with ordinary quantum fields at low energies in the Fock representation. It is argued that the demand of locality on the interacting quantum field commutators is no longer valid for correlated baby universes, and it is therefore concluded that quantum coherence in the matter-field sector is lost as a consequence of the interaction with nonsimply connected wormholes. A proposal is advanced that wormholes may provide us with a complementary quantum state sector that would induce the collapse of the state vector in the quantum measurement of any observable for ordinary microscopic matter systems.
In the 1980's, work by Coleman and by Giddings and Strominger linked the\nphysics of spacetime wormholes to `baby universes' and an ensemble of theories.\nWe revisit such ideas, using features associated with a negative cosmological\nconstant and asymptotically AdS boundaries to strengthen the results, introduce\na change in perspective, and connect with recent replica wormhole discussions\nof the Page curve. A key new feature is an emphasis on the role of null states.\nWe explore this structure in detail in simple topological models of the bulk\nthat allow us to compute the full spectrum of associated boundary theories. The\ndimension of the asymptotically AdS Hilbert space turns out to become a random\nvariable ZZZ, whose value can be less than the naive number kkk of independent\nstates in the theory. For k>Zk>Zk>Z, consistency arises from an exact degeneracy in\nthe inner product defined by the gravitational path integral, so that many a\npriori independent states differ only by a null state. We argue that a similar\nproperty must hold in any consistent gravitational path integral. We also\ncomment on other aspects of extrapolations to more complicated models, and on\npossible implications for the black hole information problem in the individual\nmembers of the above ensemble.
We discuss some arguments in favour of the proposal that the quantum correlations contained in the pure state-vector evolving according to Schoedinger equation can be eliminated by the action of multiply connected wormholes during measurement. We devise a procedure to obtain a proper master equation which governes the changes of the reduced density matrix of matter fields interacting with doubly connected wormholes. It is shown that this master equation predicts an appropriate damping of the off-diagonal correlations contained in the state vector.
This paper proposes the "Quantum Klein Bottle Universe Model," which defines the ultimate reality of the universe as a four-dimensional, static, compact manifold with a Klein bottle topology that is self-intersection-free and has no distinction between inside and outside. Time is a coordinate axis on this manifold, equal to the other three spatial dimensions; it does not flow nor is it closed. The model inherits and upgrades the classical Block Universe theory and Everett's Many-Worlds Interpretation, weaving all possible quantum histories as static fiber bundles on the manifold. Decoherence is interpreted as the progressive topological separation of worldline fibers, yet the residual wormhole network, guaranteed by topological conservation laws, maintains the manifold's integrity. The core law of the model is the "Principle of No-Collapse": wave function collapse lacks physical reality at the ontological level and is merely a cognitive illusion of low-dimensional observers. Quantum entanglement is explained as a direct geometric connection within the manifold, a thorough generalization of the ER=EPR conjecture. The origin of probability is reduced to a measure counting of ontological fiber bundles by the low-dimensional observer's cross-section. This framework deconstructs the contradiction between determinism and free will and proposes a verification scheme centered on the "Collapse Reductio ad Absurdum" method.
A bstract In holography, gauging symmetries of the boundary theory leads to important modifications in the bulk. In this work, we study constraints to gauge symmetry sectors in the chord Hilbert space of the double-scaled SYK (DSSYK) with matter, and we connect them to different proposals of its bulk dual. These sectors include chord parity symmetry, corresponding to End-Of-The-World (ETW) branes and Euclidean wormholes in sine dilaton gravity; and relative time-translations in a doubled DSSYK model (resulting from a single DSSYK with an infinitely heavy matter chord) used in de Sitter holography. We define and evaluate partition functions and thermal correlation functions of the ETW brane and Euclidean wormhole systems in the boundary theory. We deduce the holographic dictionary by matching geodesic lengths in the bulk with the spread complexity of the parity-gauged DSSYK. The Euclidean wormholes of fixed size are perturbatively stable, and their baby universe Hilbert space is non-trivial only when matter is added. We conclude studying the constraints in the path integral of the doubled DSSYK. We derive the gauge invariant operator algebra of one of the DSSYKs dressed to the other one and discuss its holographic interpretation.
In holography, gauging symmetries of the boundary theory leads to important modifications in the bulk. In this work, we study constraints to gauge symmetry sectors in the chord Hilbert space of the double-scaled SYK (DSSYK) with matter, and we connect them to different proposals of its bulk dual. These sectors include chord parity symmetry, corresponding to End-Of-The-World (ETW) branes and Euclidean wormholes in sine dilaton gravity; and relative time-translations in a doubled DSSYK model (resulting from a single DSSYK with an infinitely heavy matter chord) used in de Sitter holography. We define and evaluate partition functions and thermal correlation functions of the ETW brane and Euclidean wormhole systems in the boundary theory. We deduce the holographic dictionary by matching geodesic lengths in the bulk with the spread complexity of the parity-gauged DSSYK. The Euclidean wormholes of fixed size are perturbatively stable, and their baby universe Hilbert space is non-trivial only when matter is added. We conclude studying the constraints in the path integral of the doubled DSSYK. We derive the gauge invariant operator algebra of one of the DSSYKs dressed to the other one and discuss its holographic interpretation.
Universal hallmarks of quantum chaos---such as the ramp and plateau in the spectral form factor---and the ramp's gravitational duals involving wormholes are widely interpreted as consequences of spectral or ensemble averaging. In this paper, following an earlier proposal of~\cite{Liu25c}, we develop an alternative approach: these phenomena arise as macroscopic smooth structures hidden within erratic microscopic data, which can be isolated through a smooth filter projection. Using the semiclassical Gutzwiller trace formula as a paradigmatic example, we illustrate how many features characteristic of random matrix models---including the ramp, the plateau, the spectral curve, and single-eigenvalue instantons---can be derived in the semiclassical limit without invoking ensemble or explicit spectral averages. We postulate the existence of a minimal Gutzwiller-like structure in the large-NNN limit of holographic systems and explore its consequences. Beyond deriving the ramp and the plateau, this Gutzwiller-like structure predicts universal rapid macroscopic oscillations in the density of states and the possible existence of hyper-instantons, both of which involve double exponentials in 1/N21/N^21/N2. On the gravity side, we demonstrate how spacetime wormholes enable the construction of emergent hyper-non-perturbative objects---such as baby-universe and wormhole condensates---which yield double exponential effects in GNG_NGN​. This mirrors the postulated boundary Gutzwiller-like structure and provides a dual gravitational derivation of the universal rapid macroscopic oscillations in the density of states and the spectral plateau.