  The transverse proximity effect is the expected decrease in the strength of
the Lya 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 HeII Lya
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.
