This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of the multiverse idea presented in this paper, that is shared by the fields in the standard model coupled to gravity, is different from other notions of a multiverse. Via analyticity we are able to establish definite relations among the universes. In this paper we illustrate these properties for the extended Rindler space, while black hole spacetime and the cosmological geometry of mini-superspace (see Appendix B) will appear in later papers. In classical general relativity, extended Rindler space is equivalent to flat Minkowski space; it consists of the union of the four wedges in (u,v) light-cone coordinates as in Fig.(1). In quantum mechanics, the wavefunction is an analytic function of (u,v) that is sensitive to branch points at the horizons u=0 or v=0, with branch cuts attached to them. The wavefunction is uniquely defined by analyticity on an infinite number of sheets in the cut analytic (u,v) spacetime. This structure is naturally interpreted as an infinite stack of identical Minkowski geometries, or universes, connected to each other by analyticity across branch cuts, such that each sheet represents a different Minkowski universe when (u,v) are analytically continued to the real axis on any sheet. We show in this paper that, in the absence of interactions, information doesnt flow from one Rindler sheet to another. By contrast, for an eternal black hole spacetime, which may be viewed as a modification of Rindler that includes gravitational interactions, analyticity shows how information is lost due to a flow to other universes, enabled by an additional branch point and cut due to the black hole singularity.
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