  We study Liouville fillable contact manifolds $(\Sigma,\xi)$ with non-zero
Rabinowitz Floer homology and assign spectral numbers to paths of
contactomorphisms. As a consequence we prove that
$\widetilde{\mathrm{Cont}_0}(\Sigma,\xi)$ is orderable in the sense of
Eliashberg and Polterovich. This provides a new class of orderable contact
manifolds. If the contact manifold is in addition periodic or a prequantization
space $M \times S^1$ for $M$ a Liouville manifold, then we construct a contact
capacity. This can be used to prove a general non-squeezing result, which
amongst other examples in particular recovers the beautiful non-squeezing
results from [EKP06].
