 The constraints in electromagnetism may be viewed as stemming from the U(1) gauge invariance of Maxwell’s theory, while the constraints of general relativity stem from the diffeomorphism invariance of the theory.  Diffeomorphism invariance  means, informally, that one can take a solution of Einstein’s equations and drag it (meaning the metric and the matter fields) around on the spacetime manifold and obtain a mathematically distinct but physically equivalent solution. The three ‘supermomentum’ constraints in the canonical theory reflect the freedom to drag the metric and matter fields around in various directions on a given three-dimensional spacelike hypersurface, while the ‘super-Hamiltonian’ constraint reflects the freedom to drag the fields in the “time” direction, and so to the “next” hypersurface. (Each constraint applies at each point of the given spacelike hypersurface, so that there are actually 4 × ∞3 constraints: four for each point.) In the classical (unquantized) canonical formulation of general relativity, the constraints do not pose any particular conceptual problems (though one does face a problem in defining suitable observables that commute with the constraints, and this certainly has a conceptual flavour). One effectively chooses a background space and time (via a choice of the lapse and shift functions) “on the fly”, and one can be confident that the spacetime that results is independent of the particular choice. Effectively, different choices of these functions give rise to different choices of background against which to evolve the foreground. However, the constraints pose a serious problem (as much conceptual as technical) when one moves to quantum theory.