Quantum mechanics can
be applied
to spacetime provided that
the formulation
of quantum theory
is suitably generalized. A generalization is necessary because, in one way or another, the usual formulations rely on a fixed spacetime geometry to define states on spacelike surfaces
and the time in which they evolve unitarily one surface to another. But in a quantum theory of gravity, spacetime geometry is generally fluctuating and without definite value. The usual formulations are emergent from a more general perspective when geometry is approximately classical and can supply the requisite fixed notions of space and time. A framework for investigating generalizations of usual quantum mechanics can be abstracted from the modern quantum mechanics of closed systems which enables quantum mechanics to be applied to cosmology. The resulting framework — generalized quantum theory — defines a broad class of generalizations of usual quantum mechanics. A generalized quantum theory of a physical system (most generally the universe) is built on three elements which can be very crudely characterized
as follows:
• The possible fine-grained descriptions of the system.
• The coarse-grained descriptions constructed from the fine-grained ones.
• A measure of the quantum interference between different coarse-grained descriptions incorporating the principle of superposition
Abstrak lain tentang Generalizing Quantum Mechanics for Quantum Spacetime