An observer can know only data on his past light-cone; is there a best estimate for the probability distribution of given dynamical variables in a future experiment? This paper describes the first step to answering this by developing a Hamiltonian approach in which data is specified on the past light-cone instead of at a given time (this is got by what turns out to be a canonical transformation from the conventional formulation). A spinor form of this is written in terms of the Dirac matrices.