Quantum lightcone fluctuations

The existence of fixed lightcone structures is one of the characteristics of classical gravitational theory. However, if gravity is to be quantized, it is natural to expect that the quantum metric fluctuations would smear out the lightcone, and therefore the concept of a fixed lightcone structure has to be abandoned.; In this thesis, we briefly review a basic formalism describing quantum lightcone fluctuations, in which the source of the underlying metric fluctuations is taken to be gravitons in quantum states. We first discuss how to calculate the mean deviation from the classical propagation time, Δt, of a light pulse traveling between a source and a detector caused by lightcone fluctuations. We then show that the formalism is gauge invariant in that Δ _t is a gauge invariant quantity. With the framework fully established, we examine the quantum lightcone fluctuations both in four-dimensional flat spacetimes with nontrivial topology, and in higher dimensional theories with extra dimensions compactified on a small scale. Here lightcone fluctuations are produced by gravitons in the vacuum states associated with the nontrivial topology or with the compactification of extra dimensions.; In the four-dimensional case, we find that changes in the topology of flat spacetime produce lightcone fluctuations. These fluctuations are in general larger in the directions in which topology changes occur and are typically of the order of the Planck scale, but they grow as the path length r increases, or the compactification scale L decreases.; In the higher dimensional cases, we discuss two scenarios of compactification, the usual periodic compactification of extra dimensions into a torus and the brane-world scenario. All cases up through eleven dimensions are examined and conjectures for arbitrary dimensions are proposed. Our studies show that significant lightcone fluctuations arise in the uncompactified dimensions as a result of the compactification of extra dimensions. These lightcone fluctuation effects are potentially observable because they may lead to broadening of spectral lines from distant astrophysical sources, or introduce additional quantum-gravity noise in gravity-wave interferometers. We use data from gamma ray burst sources to constrain the five-dimensional Kaluza-Klein model with periodic compactification. We find a very strong lower bound of L $\gtrsim$ 105cm on the size of extra dimension or a bound on its rate of change, ≤ 10−67 yr−1. The latter is much stronger than any existing bound derived from the limits on the. time variation of fundamental constants. No significant constraint on the compactification scale can be given for other higher dimensional cases, however. In the brane-world scenario, we find that the five-dimensional case predicts too large a position uncertainty Δt, so this model can be ruled out. However, for six or higher dimensions, quantum- gravity-induced position noise of order of ∼10−21cm is predicted, which might be testable in the next LIGO/VIRGO generation of gravity-wave interferometer.; Our results seem to suggest that quantum gravity effects might be large enough in some special contexts to be observable in the near future or even at the present, despite forecasts to the contrary. The phenomenon discussed in this thesis can not only constrain models with extra dimensions, but could conceivably lead to positive confirmation of the existence of such dimensions.