  We demonstrate that in sufficiently long diffusive
superconducting-normal-superconducting ($SNS$) junctions dc Josephson current
is exponentially suppressed by electron-electron interactions down to zero
temperature. This suppression is caused by the effect of {\it Cooper pair
dephasing} which occurs in the normal metal and defines a new fundamental
length scale $L_\varphi$ in the problem. Provided the temperature length
exceeds $L_\varphi$ this dephasing length can be conveniently extracted from
equilibrium measurements of the Josephson current.
