  High-resolution neutron scattering experiments on optimally doped
La$_{2-x}$Sr$_x$CuO$_4$ have been performed which reveal that the magnetic
excitations are dispersive. The dispersion is found to be the same as in the
YBa$_2$Cu$_3$O$_{6+x}$ family, and is quantitatively related to that observed
with charge sensitive probes. The excitations are also found to broaden rapidly
with increasing energy, forming a continuum at higher energy, and bear a
remarkable resemblance to multi-particle excitations observed in
low-dimensional antiferromagnets and some magnetic metals. The magnetic
correlations are two dimensional, and so rule out the simplest scenarios where
the copper oxide planes are subdivided into weakly interacting one-dimensional
magnets.
