Quantum Mechanics, Spacetime Locality, and Gravity (original) (raw)

2013, Foundations of Physics

Quantum mechanics introduces the concept of probability to physics at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are intimately related with each other, developing a complete picture for quantum measurement and cosmological histories in the quantum mechanical universe. On one hand, quantum mechanics eliminates the arbitrariness of defining probabilities in the multiverse, as discussed previously in arXiv:1104.2324. On the other hand, the multiverse allows for understanding why we observe an ordered world obeying consistent laws of physics, by providing an infinite-dimensional Hilbert space. This results in the irreversibility of quantum measurement, despite the fact that the evolution of the multiverse state is unitary. In order to describe the cosmological dynamics correctly, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality in the description, which plays a crucial role in understanding quantum measurement, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from fixing/eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime-these phenomena arise because changes of the reference frame are represented in the Hilbert space defined on restricted spacetime regions. This can be viewed as an extension of the Lorentz/Poincaré transformation in the quantum gravitational context, as the Lorentz transformation is viewed as an extension of the Galilean transformation. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics-it evolves deterministically and unitarily, asymptoting to the "heat death" consisting of supersymmetric Minkowski and singularity states. The beginning of the multiverse, however, is still an open issue.