The Black Hole Firewall Transformation and Realism in Quantum Mechanics

A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal requires that one starts off with the entire Penrose diagram for the eternal black hole as the background metric, after which one has to invoke the antipodal identification in order to see how the two asymptotic domains of this metric both refer to the same outside world. In this paper, we focus on the need to include time reversal in applying this identification. This forces us to postulate the existence of an ‘anti-vacuum’ state in our world, which is the state where energy density reaches a maximal value. We find that this squares well with the deterministic interpretation of quantum mechanics, according to which quantum Hilbert space is to be regarded as the ‘vector representation’ of a real world. One has to understand how to deal with gravity in such considerations. The non-perturbative component of the gravitational force seems to involve cut-and-paste procedures as dynamical features of space and time, of which the re-arrangement of space-time into two connected domains in the Penrose diagram is a primary example. Thus, we attempt to obtain new insights in the nature of particle interactions at the Planck scale, as well as quantum mechanics itself.

Antipodal Identification in the Schwarzschild Spacetime

"Through a Möbius transformation, we study aspects like topology, ligth cones, horizons, curvature singularity, lines of constant Schwarzschild coordinates r and t, null geodesics, and transformed metric, of the spacetime (SKS/2)^' that results from: i) the antipode identification in the Schwarzschild-Kruskal-Szekeres (SKS) spacetime, and ii) the suppression of the consequent conical singularity. In particular, one obtains a non simply-connected topology: (SKS/2)^' = R^2* ×S^2 and, as expected, bending light cones."

TOWARDS A CPT INVARIANT QUANTUM FIELD THEORY ON ELLIPTIC DE SITTER SPACE

Consequences of Schrödinger's antipodal identification on quantum field theory in de Sitter space are investigated. The elliptic ℤ2 identification provides observers with complete information. We show that a suitable confinement on dimension of the elliptic de Sitter space guarantees the existence of globally defined spinors and orientable dS/ℤ2 manifold. In Beltrami coordinates, we give exact solutions of scalar and spinor fields. The CPT invariance of quantum field theory on the elliptic de Sitter space is presented explicitly.

QUANTUM FIELD THEORY AND THE ANTIPODAL IDENTIFICATION OF SPACE TIME

We investigate the “elliptic interpretation” of space-time (identification of antipodal points or events) in anti-deSitter and in Rindler manifolds and its consequences for QFT. We compare and give a complete description of antipodal identification in space-times with and without event horizons. Antipodal identification relates the field theories on deSitter and on anti-deSitter spaces. In the “elliptic” Rindler manifold, imaginary time is periodic with period β/2 but the Green functions (for both identifications with and without “Conical singularity”) have period β. (Here β=2π/α, α is the acceleration.) Additional new properties for the Green functions are obtained and the new terms added to the stress tensor computed.