Quantum Probes, curvature, and the small scale structure of spacetime

Most of our observations that characterize space and time are expressed in terms of non-local, bi-tensorial objects such as geodesic or null intervals between events and two-point (Green's) functions.

In this talk, I will highlight the importance of characterizing behavior of classical and quantum probes in terms of two fundamental bi-tensors, Synge's World function and the van Vleck determinant. I will first discuss two specific recent results: (i) Non-perturbative tidal corrections to Unruh-deWitt detector response, and (ii) generalised uncertainty principle on curved space(time)s. I will then describe a formalism to construct an effective quantum metric - qmetric - in terms of these bi-tensors, which can describe spacetime with a zero point length. Some non-trivialities of the qmetric, its classical limit, and its role in quantum gravity will then be discussed.