It has been argued that, underlying M-theoretic dualities, there should exist
a symmetry relating the semiclassical and the strong-quantum regimes of a given
action integral. On the other hand, a field-theoretic exchange between long and
short distances (similar in nature to the T-duality of strings) has been shown
to provide a starting point for quantum gravity, in that this exchange enforces
the existence of a fundamental length scale on spacetime. In this letter we
prove that the above semiclassical vs. strong-quantum symmetry is equivalent to
the exchange of long and short distances. Hence the former symmetry, as much as
the latter, also enforces the existence of a length scale. We apply these facts
in order to classify all possible duality groups of a given action integral on
spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page
