  Consider the configuration space Q for some physical system, and a continuous
group of transformations G whose action on the configurations is declared to be
physically irrelevant. Implement G indirectly by adjoining 1 auxiliary g per
independent generator of G to Q, by writing the system's action in an arbitrary
G-frame (G-AF), and then passing to the quotient Q/G thanks to the constraints
encoded by g-variation. I show that this G-AF principle supercedes (and indeed
leads to a derivation of) the Barbour--Bertotti (BB) best matching principle.
My other consideration is that absolute external time is meaningless for the
universe as a whole. For various choices of Q and G, these lead to BB's
proposed absolute structure free replacement of Newtoninan mechanics, to Gauge
Theory and to the 3-space approach (TSA) formulation of GR. For the latter with
matter fields, I discuss the SR postulates, Principle of Equivalence (POE) and
simplicity postulates. I explain how a full enough set of fundamental matter
fields to describe nature can be accommodated in the TSA, and compare the TSA
with the `split spacetime formulation' of Kuchar. I explain the emergence of
broken and unbroken Gauge Theories as a consequence of the POE. I also consider
as further examples of the G-AF principle the further quotienting out of
conformal transformations (CT) or volume preserving CT. Depending on which
choices are made, this leads to York's initial value formulation (IVF) of GR,
new alternative foundations for it, or alternative theories of gravity built
out of similar conformal mathematics which nevertheless admit no GR-like
spacetime interpretation.
