  It is pointed out that an agreement of the one particle energy spectrum of
the cosmic background radiation (CMBR) with Plank distribution of 2.725 [K]
does not give a strong constraint on the coherence length of CMBR if the mean
free path of CMBR is very long. The coherence length in this situation is
estimated as a few times of $k_BT$. Due to this finite coherence length, the
attenuation length of ultra-high energy cosmic rays (UHECR) is reduced in the
$\Delta $ resonance region,i.e., around $10^{20}$ [eV]. The small attenuation
length makes the suppression of the flux of cosmic rays in this energy region
less prominent than the naive estimation
