Precision measurements of weak neutral current amplitudes at Q(2) >> M
Z 2 are a sensitive probe of contact interactions arising from new hig
h energy physics. Such measurements significantly enhance the analysis
of precision data on the Z(0) resonance, permitting tests of the runn
ing of the electroweak coupling constants. The behavior of the couplin
g constants as a function of Q(2) can reveal the presence of many poss
ible new physics scenarios, such as new gauge bosons, superparticles a
nd substructure; some of these effects are difficult to observe on the
Z(0) pole. In order to probe energy scales up to 1 TeV, future low Q(
2) measurements must be precise enough to measure electroweak radiativ
e corrections. Two experimental programs which aim to reach this sensi
tivity are deep inelastic neutrino nucleon scattering and atomic parit
y violation experiments. Another important technique is polarized elec
tron scattering off unpolarized targets. We review the current status
and future prospects of such measurements. We present an experimental
design to measure the left-right parity violating asymmetry in polariz
ed Moller scattering (e(-)e(-) --> e(-)e(-)), which could constitute t
he most precise measurement of the weak mixing angle sin(2) theta(W)(M
(Z)) at Q(2) << M(Z)(2).