  We introduce observables associated with the space-time position of a quantum
point defined by the intersection of two light pulses. The time observable is
canonically conjugated to the energy. Conformal symmetry of massless quantum
fields is used first to build the definition of these observables and then to
describe their relativistic properties under frame transformations. The
transformations to accelerated frames of the space-time observables depart from
the laws of classical relativity. The Einstein laws for the shifts of clock
rates and frequencies are recovered in the quantum description, and their
formulation provides a conformal metric factor behaving as a quantum
observable.
