ep - t h / 99 12 20 3 v 1 2 1 D ec 1 99 9 The Rest - Frame Instant Form of Dynamics and Dirac ’ s Observables

Since our understanding of both general relativity and the standard model of elementary particles either with or without supersymmetry is based on singular La-grangians, whose associated Hamiltonian formalism requires Dirac-Bergmann theory of constraints[1], it is very difficult to identify which are the physical degrees of freedom to be used in the description and interpretation of the fundamental interactions. This is the problem of the physical observables in gauge theories and general relativity. While behind the gauge freedom of gauge theories proper there are Lie groups acting on some internal space so that the measurable quantities must be gauge invariant, the gauge freedom of theories invariant under diffeomorphism groups of the underlying spacetime (general relativity, string theory and reparametrization invariant systems of relativistic particles) concerns the arbitrariness for the observer in the choice of the definition of " what is space and/or time " (and relative times in the case of particles), i.e. of the definitory properties either of spacetime itself or of the measuring apparatuses. This is the classical mathematical background on which our understanding of the quantum field theory of electromagnetic, weak and strong interactions in the modern BRS formulation is based. The same is true for our attempts to build quantum gravity notwithstanding our actual incapacity to reconcile the influence of gravitational physics on the existence and formulation of spacetime concepts with the basic ideas of quantum theory, which requires a given absolute background spacetime.