Abstract
Pure states in quantum field theory can be represented by many-fingered block-time wave functions, which treat time on an equal footing with space and make the notions of “time evolution” and “state at a given time” fundamentally irrelevant. Instead of information destruction resulting from an attempt to use a “state at a given time” to describe semi-classical black-hole evaporation, the full many-fingered block-time wave function of the universe conserves information by describing the correlations of outgoing Hawking particles in the future with ingoing Hawking particles in the past.
Highlights
The semi-classical description of black-hole evaporation [1] predicts that the final state after the complete evaporation cannot be represented by a pure state [2]
We start with the observation that all these previous approaches share one common assumption: that the quantum state should be a function of time, or more generally, a functional of the spacelike hypersurface
One of the main messages of the theory of relativity is that time should be treated on an equal footing with space
Summary
The semi-classical description of black-hole evaporation [1] predicts that the final state after the complete evaporation cannot be represented by a pure state [2]. Many approaches to restore a pure-state description at late times have been attempted, but none of them seems to be completely satisfying (for reviews see, e.g., [4]) To overcome this problem, we start with the observation that all these previous approaches (with a notable exception in [5]) share one common assumption: that the quantum state (either pure or mixed) should be a function of time, or more generally, a functional of the spacelike hypersurface. We start with the observation that all these previous approaches (with a notable exception in [5]) share one common assumption: that the quantum state (either pure or mixed) should be a function of time, or more generally, a functional of the spacelike hypersurface Such an assumption is deeply rooted in our intuitive understanding of the concept of time, according to which universe evolves with time.
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