A low-density polyethylene was shear modified by repeated extrusions. These operations resulted in no detectable changes in the polymer molecular weight distribution. The apparent melt viscosity and elasticity decreased after extrusion, as is commonly observed in shear modification. These rheological effects were fully reversible by annealing the melt. Transverse proton relaxation measurements showed the existence of four identifiable different regions in the polymer melt. The range of relaxation times encompassed two orders of magnitude. These reflect the existence of regions with different degrees of conformational order. Shear modification results in the breakup of a minor proportion of the most constrained regions, which have the shortest relaxation times. The apparent "entanglements" that are inferred from rheological measurements probably reflect the coexistence of segments of more than one macromolecule in chain-folded domains, as indicated by molecular dynamics calculations. These results are evidence that the equilibrium state of LDPE is not a chain-entangled, highest entropic condition, but rather a lowest free energy state in which chain folding is favored. They are consistent with other longstanding observations, such as the failure of experiments to produce amorphous polyethylene and the apparent lack of mixing of HDPE and LDPE on a molecular level.