Quantum mechanics of a charged scalar boson with respect to an observer’s past light cone

Abstract

An observer whose instantaneous ‘‘here-now’’ has Minkowski coordinates zλ(λ=0,1,2,3) can only be aware of events within or on the past light cone with vertex at zλ. In conventional quantum mechanics his current quantum state would refer to some spacelike surface containing zλ, for example, x0=z0. This is, however, a region of space-time about which the observer can know nothing except the single event zλ, his current here-now. The aim of the present paper is to give a version of quantum mechanics in which the intrinsically unknowable ‘‘quantum state at the present time’’ is replaced by the ‘‘quantum state on the past light cone.’’ The theory is an extension and adaptation of Dirac’s point mechanics [Rev. Mod. Phys. 21, 392 (1949)].