  We discuss the canonical structure of a spacetime version of the radial
gauge, i.e. Gau{\ss}ian normal spacetime coordinates. While it was found for
the spatial version of the radial gauge that a "local" algebra of observables
can be constructed, it turns out that this is not possible for the spacetime
version. The technical reason for this observation is that the new gauge
condition needed to upgrade the spatial to a spacetime radial gauge does not
Poisson-commute with the previous gauge conditions. It follows that the
involved Dirac bracket is inherently non-local in the sense that no complete
set of observables can be found which is constructed locally and at the same
time has local Dirac brackets. A locally constructed observable here is defined
as a finite polynomial of the canonical variables at a given physical point
specified by the Gau{\ss}ian normal spacetime coordinates.
