Nuclear collisions can compress nuclear matter to densities achieved within
neutron stars and within core-collapse supernovae. These dense states of matter
exist momentarily before expanding. We analyzed the flow of matter to extract
pressures in excess of 10^34 pascals, the highest recorded under
laboratory-controlled conditions. Using these analyses, we rule out strongly
repulsive nuclear equations of state from relativistic mean field theory and
weakly repulsive equations of state with phase transitions at densities less
than three times that of stable nuclei, but not equations of state softened at
higher densities because of a transformation to quark matter.Comment: 26 pages, 6 figures; final versio