  Entov and Polterovich defined heaviness for closed subsets of a symplectic
manifold by using the Hamiltonian Floer theory on contractible trajectories.
Heavy subsets are known to be non-displaceable. In the present paper, we define
a relative symplectic capacity $C(M,X,R;e)$ for a symplectic manifold
$(M,\omega)$ and its subset $X$ which measures the existence of
non-contractible trajectories of Hamiltonian isotopies on the product with
annulus. We prove that $C(M,X,R;e)$ is finite if $(M,\omega)$ is monotone and
$X$ is a heavy subset. We also prove that $C(M,X,R;e)$ is infinite if $X$ is a
displaceable compact subset.
