  A spacetime interval connecting two neighbouring points can be measured in
different unit systems. For instance, it can be measured in atomic unit defined
in terms of fundamental constants existing in quantum theories. It is also
possible to use a gravitational unit which is defined by using of properties of
macroscopic objects. These two unit systems are usually regarded as
indistinguishable up to a constant conversion factor. Here we consider the
possibility that these two units are related by an epoch-dependent conversion
factor. This is a dynamical changes of units. Regarding a conformal
transformation as a local unit transformation, we use a gravitational model in
which the gravitational and the matter sectors are given in different conformal
frames (or unit systems). It is relevant to the cosmological constant problem,
namely the huge discrepancy between the estimated and the observational values
of the cosmological constant in particle physics and cosmology, respectively.
We argue that the problem arises when one ignores evolution of the conversion
factor relating the two units during expansion of the Universe. Connection of
the model with violation of equivalence principle and possible variation of
fundamental constants are also discussed.
