Unitarity and causality in generalized quantum mechanics for nonchronal spacetimes

Journal Article · Wed Jun 15 04:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.49.6543· OSTI ID:7050788

Hartle, J B ^[1]

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1. Department of Physics, University of California, Santa Barbara, California 93106-9530 (United States)

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime possesses nonchronal regions which cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives on two spacelike surfaces lying in regions of spacetime where foliating families [ital can] be defined may be nonunitary if a nonchronal region lies between them. This paper describes a sum-over-histories generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such nonunitarity. The usual notion of state on a spacelike surface is lost in this generalization. Anomalies such as nonconservation of energy or Everett phones'' that are exhibited by some generalizations of quantum mechanics are not found in this one. However, the generalization is acausal in the sense that the existence of nonchronal regions of spacetime in the future can affect the probabilities of alternatives today and signaling outside the light cone is possible. The detectability of nonunitary evolution and violations of causality in measurement situations are briefly considered.

• OSTI ID: 7050788
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
661310* -- Relativity & Gravitation-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CAUSALITY
ELEMENTS
LIGHT CONE
MATTER
MECHANICS
METALS
PROBABILITY
QUANTUM MECHANICS
SPACE-TIME
TRANSITION ELEMENTS
UNITARITY