  This is the first measurement and detection of coherence in the intergalactic
medium (IGM) at substantially high redshift (z~3.8) and on large physical
scales (~2.5 h^-1 Mpc). We perform the measurement by presenting new
observations from Keck LRIS of the high redshift quasar pair PC 1643+4631A, B
and their Ly-alpha absorber coincidences. This experiment extends multiple
sightline quasar absorber studies to higher redshift, higher opacity, larger
transverse separation, and into a regime where coherence across the IGM becomes
weak and difficult to detect. We fit 222 discrete Ly-alpha absorbers to
sightline A and 211 to sightline B. Relative to a Monte Carlo pairing test
(using symmetric, nearest neighbor matching) the data exhibit a 4sigma excess
of pairs at low velocity splitting (<150 km/s), thus detecting coherence on
transverse scales of ~2.5 h^-1 Mpc. We use spectra extracted from an SPH
simulation to analyze symmetric pair matching, transmission distributions as a
function of redshift and compute zero-lag cross-correlations to compare with
the quasar pair data. The simulations agree with the data with the same
strength (~4sigma) at similarly low velocity splitting above random chance
pairings. In cross-correlation tests, the simulations agree when the mean flux
(as a function of redshift) is assumed to follow the prescription given by
Kirkman et al. (2005). While the detection of flux correlation (measured
through coincident absorbers and cross-correlation amplitude) is only
marginally significant, the agreement between data and simulations is
encouraging for future work in which even better quality data will provide the
best insight into the overarching structure of the IGM and its understanding as
shown by SPH simulations.
