We present a first-principles implementation of spatial scale invariance as a
local gauge symmetry in geometry dynamics using the method of best matching .
In addition to the 3-metric, the proposed scale invariant theory also contains
a 3-vector potential Akβ as a dynamical variable. Although some of the
mathematics is similar to Weyl's ingenious but physically questionable theory,
the equations of motion of this new theory are second order in
time-derivatives. Thereby we avoid the problems associated with fourth order
time derivatives that plague Weyl's original theory. It is tempting to try to
interpret the vector potential Akβ as the electromagnetic field. We exhibit
four independent reasons for not giving into this temptation. A more likely
possibility is that it can play the role of "dark matter". Indeed, as noted in
scale invariance seems to play a role in the MOND phenomenology. Spatial
boundary conditions are derived from the free-endpoint variation method and a
preliminary analysis of the constraints and their propagation in the
Hamiltonian formulation is presented.Comment: 11 page