  We present a new analysis of the properties of the young massive star
clusters, which demonstrates that these objects are plausible progenitors of
old globular clusters (GCs). The method is based on the tight relationship for
old GCs between their V-band luminosities and (central) velocity dispersions,
sigma_0. We improve the significance of the relationship and find that its
functional form, L_V/Lsun \propto sigma_0^(1.57 +- 0.10) (km/s), is fully
consistent with previous determinations for smaller Galactic and M31 GC
samples. The tightness of the relationship for a GC sample drawn from
environments as diverse as those found in the Local Group implies that its
origin must be sought in intrinsic properties of the GC formation process
itself. We evolve the luminosities of the young massive star clusters (YMCs) in
the local Universe to an age of 12 Gyr and find that most YMCs will evolve to
loci close to, or to slightly fainter luminosities than the improved GC
relationship. In the absence of significant external disturbances, this implies
that these objects may potentially survive to become old GC-type objects over a
Hubble time. The main advantage of our new method is its simplicity; the only
observables required here are the system's velocity dispersion and luminosity.
The most important factor affecting the robustness of our conclusions is the
adopted form of the initial mass function. We use N-body simulations to confirm
that dynamical evolution of the clusters does not significantly alter our
conclusions. [ABRIDGED]
