Revisiting quantum field theory in Rindler spacetime with superselection rules

Abstract

Quantum field theory (QFT) in Rindler spacetime is a gateway to understanding unitarity and information loss paradoxes in curved spacetime. Rindler coordinates map Minkowski spacetime onto regions with horizons, effectively dividing accelerated observers into causally disconnected sectors. Employing standard quantum field theory techniques and Bogoliubov transformations between Minkowski and Rindler coordinates yields entanglement between states across these causally separated regions of spacetime. This results in a breakdown of unitarity, implying that information regarding the entangled partner may be irretrievably lost beyond the Rindler horizon. As a consequence, one has a situation of pure states evolving into mixed states. In this paper, we introduce a novel framework for comprehending this phenomenon using a recently proposed formulation of direct-sum quantum field theory (DQFT), which is grounded in superselection rules formulated by the parity and time reversal ($\mathcal{P}\mathcal{T}$) symmetry of Minkowski spacetime. In the context of DQFT applied to Rindler spacetime, we demonstrate that each Rindler observer can, in principle, access pure states within the horizon, thereby restoring unitarity. However, our analysis also reveals the emergence of a thermal spectrum of Unruh radiation. This prompts a reevaluation of entanglement in Rindler spacetime, where we propose a novel perspective on how Rindler observers may reconstruct complementary information beyond the horizon. Furthermore, we revisit the implications of the Reeh-Schlieder theorem within the framework of DQFT. Lastly, we underscore how our findings contribute to ongoing efforts aimed at elucidating the role of unitarity in quantum field theory within the context of de Sitter and black hole spacetimes.

21 pages, 4 figures. Matches with the version published in Universe, minor typos corrected

References in corpus (11)

• Disappearing cosmological constant in f(R) gravity
• The Unruh effect and its applications
• The Page curve of Hawking radiation from semiclassical geometry
• Soft Hair on Black Holes
• Notes on Some Entanglement Properties of Quantum Field Theory
• Interior of a Schwarzschild black hole revisited
• Entanglement of the Vacuum between Left, Right, Future, and Past: The Origin of Entanglement-Induced Quantum Radiation
• Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
• Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect
• Reversing the Arrow of Time
• Finding origins of CMB anomalies in the inflationary quantum fluctuations

Cited by in corpus (5)

• Hawking radiation with pure states
• Towards a unitary formulation of quantum field theory in curved space-time: the case of Schwarzschild black hole
• Towards a unitary formulation of quantum field theory in curved spacetime: the case of de Sitter spacetime
• Memory Effects and Entanglement Dynamics of Finite time Acceleration
• CMB parity asymmetry from unitary quantum gravitational physics