Relative locality: A deepening of the relativity principle

We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which $\hbar$ and $G_N$ may be neglected, while their ratio, the Planck mass $M_p =\sqrt{\hbar / G_N}$, is important. We propose that $M_p$ governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concept of locality. The description of events in spacetime now depends on the energy used to probe it. But there remains an invariant description of physics in phase space. There is furthermore a reasonable expectation that the geometry of momentum space can be measured experimentally using astrophysical observations.Comment: 8 pages, Latex; this essay was awarded Second Prize in the 2011 Essay Competition of the Gravity Research Foundatio

The relation between Hardy's non-locality and violation of Bell inequality

We give a analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for violation of Bell inequality, the upper bound of Hardy's non-locality allowed by information causality just correspond to Tsirelson bound of Bell inequality, and the upper bound of Hardy's non-locality allowed by the principle of no-signaling just correspond to the algebraic maximum of Bell operator. Then we study the Cabello's argument of Hardy's non-locality (a generalization of Hardy's argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy's non-locality under the constraint of information causality with the aid of above derived relation between Hardy's non-locality and Bell operator, this bound is the main result of a recent work of Ahanj \emph{et al.} [Phys. Rev. A {\bf81}, 032103(2010)].Comment: 4 pages, no figure, minor chang