  We calculate the equation of state of neutron matter with realistic two- and
three-nucleon interactions using quantum Monte Carlo techniques, and illustrate
that the short-range three-neutron interaction determines the correlation
between neutron matter energy at nuclear saturation density and higher
densities relevant to neutron stars. Our model also makes an experimentally
testable prediction for the correlation between the nuclear symmetry energy and
its density dependence -- determined solely by the strength of the short-range
terms in the three neutron force. The same force provides a significant
constraint on the maximum mass and radius of neutron stars.
