Wheeler's it from bit proposal in loop quantum gravity

摘要

As an attempt to realize Wheeler's "it-from-bit proposal" that physics should be reduced to simple yes-no questions, we consider a model of loop quantum gravity, where the only allowed values of the quantum numbers j(p) at the punctures p of the spin network on the spacelike two surfaces of spacetime are 0 and 1/2. When j(p) = 0, the puncture is in the vacuum, and it does not contribute to the area of the two surface, whereas when j(p) = 1/2, the puncture is in an excited state, and the allowed values of the associated quantum number m(p) are -1/2 and +1/2. As a consequence, the spin network used as a model of spacetime is analogous to a system of particles with spin 1/2, and every puncture carries exactly one bit of information. When applied to spacetimes with horizon, our model enables us to find an explicit expression for the partition function of spacetime. Using this partition function we may, among other things, obtain the Bekenstein-Hawking entropy law for black holes. When applied to cosmological models with horizon, the partition function predicts a cosmic phase transition in the early universe, where the cosmological constant went through a dramatic decrease and the matter of the universe was created out of the vacuum.