Implications of the Lorentz signature of spacetime: from clock synchronization to relativistic entanglement

by Luca Lusanna (FI)

Thursday 10 Apr 2014, 15:00 → 16:00 Europe/Rome

248 (BUilding C, First Floor)

The Lorentz signature of the spacetimes of special and general relativity is a source of problems absent in non-relativistic theories. The absence of timelike excitations in relative times in spectroscopy and the need of a sound formulation of the Cauchy problem in field theory require a metrological convention about the instantaneous 3-spaces, namely a clock synchronization convention. This can be done in a Wigner covariant way with a 3+1 splitting of spacetime, the use of radar 4-coordinates centered on a timelike observer and the separation of the non-local (non-measurable) relativistic center of mass of the 3-universe, both in special relativistic inertial frames and in (either special or general) relativistic non-inertial ones of globally hyperbolic spacetimes. Only relative variables are measurable: there is a basic spatial non-separability already at the classical level. In relativistic quantum mechanics it is an obstruction to the identification of subsystems and leads to a theory of relativistic entanglement strongly different from the non-relativistic one, in which Alice and Bob cannot be decoupled observers. In field theory the separation of the relativistic center of mass may help in avoiding Haag theorem, but leads to extra problems for the definition of particles besides the known ones in non-inertial frames and in curved spacetimes. In general relativity and cosmology the trace of the extrinsic curvature (the York time) of the non-Euclidean 3-spaces is a gauge variable to be fixed with a metrological convention: the dark side (or at least part of it) of the universe may be a relativistic inertial effect.