Can the universe be described by a wave function?

Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkhoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the “mostly empty” universe we observe around us cannot be described by an exact wave function [Formula: see text]. Rather, the weakly coupled particles we see are approximate quasiparticles arising as excitations of a “fuzz”. The “fuzz” does have an exact wave function [Formula: see text], but this exact wave function does not directly describe local particles. The argument proceeds by relating the cosmological setting to the black hole information paradox, and then using the small corrections theorem to show the impossibility of an exact wave function describing the visible universe.

FRESNEL OPERATOR, SQUEEZED STATE AND WIGNER FUNCTION FOR CALDIROLA–KANAI HAMILTONIAN

Based on the technique of integration within an ordered product (IWOP) of operators, we introduce the Fresnel operator for converting a kind of time-dependent Hamiltonian into the standard harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A, B, C, D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of coupled partial differential equations set up in the above-mentioned converting process. In this way, the Caldirola–Kanai Hamiltonian has been easily converted into the standard harmonic oscillator Hamiltonian. And then the exact wave function solution of the Schrödinger equation governed by the Caldirola–Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations.