Abstract

It is shown that the time operatorQ 0 appearing in the realization of the RCCR's [Qμ,Pv]=−jhgμv, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over Σ m =σ×v m , where σ is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Qμ appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that the metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements