Violation of Unitarity in Gravitational Subregions

TL;DR

This paper argues that in quantum gravity, certain regions lack a unitary Hilbert space due to CPT symmetry breaking, leading to negative probability states, which may resolve the firewall paradox and impact cosmological theories.

Contribution

It introduces the idea that some gravitational subregions do not admit a unitary Hilbert space, challenging conventional quantum gravity assumptions.

Findings

Negative norm states are tolerable, similar to quantum mechanics.

Broken CPT symmetry leads to non-unitary regions in quantum gravity.

Proposes a resolution to the firewall paradox via black hole complementarity.

Abstract

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, "states" with negative probability can be identified on either side of trapped surfaces. I argue that these negative norm states are tolerable, by analogy to quantum mechanics. This viewpoint suggests a resolution of the firewall paradox, similar to black hole complementarity. Implications for cosmology are briefly discussed.