Quantum Gravitational Fluctuations of Time Delay Observable in Minkowski Vacuum

Abstract

In this thesis, I will discuss a clock synchronization thought experiment which models a diffeomorphism invariant time delay observable. For calculational purposes, the thought experiment takes place in an approximately Minkowski spacetime. The time delay observable is expanded to linear order in the gravitational field and its mean and variance are computed in the Fock vacuum of linearized quantum gravity. For the later calculation, we resorted to the use of computer algebra software due to the large amount of integrals that need to be evaluated. Divergences are regularized using a smearing procedure, which relies on the detector sensitivity profile. The results show that the quantum mean is given by s e^(-theta) where s and theta are experimental input: s is the determining length scale and theta the hyperbolic rapidity between the worldlines of the lab and the probe. The leading order term of the quantum variance is proportional to (s lp\mu)^2 where mu determines the detector resolution. All circumstances alike, the quantum variance increases for increasing detector sensitivity. Additionally, the quantum variance is heavily influence by theta. The variance appears to become unbounded for small relative velocities. In particular, it changes by eight orders of magnitude between typical laboratory velocities and highly relativistic speeds. The observable was constructed to probe the causal structure of quantum spacetimes as well as serve as a benchmark to compare different approaches to quantum gravity.