Gauge Invariance, Nonlocality and Observables in Gravitational Wave Physics
Open a gravitation textbook and you'll be told the fractional distortion of space responsible for the interference pattern in a laser interferometer, due to the passage of a gravitational wave (GW) signal, is directly proportional to its "transverse-traceless" (TT) part. What precisely does this TT projection mean? Field theorists may think that this TT GW must of course be the divergence-free piece of the spatial metric perturbations, since it is not only gauge-invariant, but also the only one (about a Minkowski background) that obeys a wave equation. I will discuss why the TT GW cannot be a standalone observable because of its nonlocal character -- a direct computation of its Green's function will reveal it receives contributions from outside the observer's past light cone -- before clarifying how all the gauge-invariant variables are needed to produce a causal tidal force on GW detectors. If time permits, I will also discuss why these results transparently demonstrate that the quantum field operators associated with the massless spin-1 photon and the spin-2 graviton violate microcausality; namely, they do not commute outside the light cone.
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