But, on the more fundamental side, the above proximity may hint at
a deep connection between cosmology and local dynamics in systems
that are very small on cosmological scales. Either cosmology
somehow enters and affects local laws of physics, such as the law
of inertia or the law of gravity, or a common agent affects both
cosmology and local physics so as to leave on them the same
imprint. This would mean that MOND-and perhaps more cherished
notions, such as inertia-is a derived concept, or an effective
theory as we would say nowadays. An observed relation between
seemingly unrelated constants appearing in a theory (in our case,
*a*_{0}, the speed of light, and the radius of the horizon) may
indicate that it is only an approximation of a theory at a deeper
stratum, in which some of the constants do not really have any
special role. A parable will help clarify the point:
In experiments and observations confined to the vicinity of the
earth surface, there appears a constant: the free-fall
acceleration, *g*. If, for some reason, we were restricted to such
an ant world (for example because the earth is ever clothed in a
thick layer of clouds) unaware of planetary motions, universal
gravity, etc., we would have looked on *g* as a true constant of
nature. We would also notice a mysterious relation between this
acceleration and two other important constants: the escape speed
*c*_{e} (objects thrown with a higher velocity never
return) and the radius of the earth
*R*_{}.
This relation: *g* = *c*_{e}^{2} /
2*R*_{}, is
practically the same as that between
*a*_{0}, the speed of light, and the Hubble radius, in
MOND. But, we
do see beyond the earth's surface, and we do know about universal
gravity, which tells us that the "constants" *g* and
*c*_{e}
actually derive from the mass and radius of the earth (hence the
relation between the three). They are useful parameters when
describing near-earth-surface phenomena, but quite useless in most
other circumstances. In a similar vein, *a*_{0} might turn
out to be
a derived constant, perhaps variable on cosmic time scales,
perhaps even of no significance beyond the non-relativistic
regime, where MOND has been applied so far. Its connection with
the speed of light and the radius of the universe will, hopefully,
follow naturally in the underlying theory that still eludes us.

Many instances of such effective theories are known. Even General Relativity is now thought to be an effective, low-energy approximation of a "higher" theory (e.g. a string-inspired theory); an idea that has been anticipated by Sakharov's "induced gravity" idea.