  We study long range interactions between two Rydberg atoms and predict the
existence of ultralong range Rydberg dimers with equilibrium distances of many
thousand Bohr radii. We calculate the dispersion coefficients $C_{5}$, $C_{6}$
and $C_{8}$ for two rubidium atoms in the same excited level $np$, and find
that they scale like $n^{8}$, $n^{11}$ and $n^{15}$, respectively. We show that
for certain molecular symmetries, these coefficients lead to long range
potential wells that can support molecular bound levels. Such macrodimers would
be very sensitive to their environment, and could probe weak interactions. We
suggest experiments to detect these macrodimers.
