The transverse proximity effect is the expected decrease in the strength of the Ly \alpha forest absorption in a QSO spectrum when another QSO lying close to the line of sight enhances the photoionization rate above that due to the average cosmic ionizing background .
We select three QSOs from the Early Data Release of the Sloan Digital Sky Survey that have nearby foreground QSOs , with proper line of sight tangential separations of 0.50 , 0.82 , and 1.10 h ^ { -1 } { Mpc } .
We estimate that the ionizing flux from the foreground QSO should increase the photoionization rate by a factor ( 94 , 13 , 13 ) in these three cases , which would be clearly detectable in the first QSO and marginally so in the other two .
We do not detect the transverse proximity effect .
Three possible explanations are provided : an increase of the gas density in the vicinity of QSOs , time variability , and anisotropy of the QSO emission .
We find that the increase of gas density near QSOs can be important if they are located in the most massive halos present at high redshift , but is not enough to fully explain the absence of the transverse proximity effect .
Anisotropy requires an unrealistically small opening angle of the QSO emission .
Variability demands that the luminosity of the QSO with the largest predicted effect was much lower 10 ^ { 6 } years ago , whereas the transverse proximity effect observed in the He ii Ly \alpha absorption in QSO 0302-003 by Jakobsen et al .
( 2003 ) implies a lifetime longer than 10 ^ { 7 } years .
A combination of all three effects may better explain the lack of Lya absorption reduction .
A larger sample of QSO pairs may be used to diagnose the environment , anisotropy and lifetime distribution of QSOs .