Hall Voltage Fluctuations as a Diagnostic of Internal Magnetic Field Fluctuations in High Temperature Superconductors and the Half-Filled Landau Level

Fluctuations of the Hall voltage reveal information about long wavelength magnetic field fluctuations. If gauge theories of strongly correlated electrons are correct, such fluctuations are particularly large in the half-filled Landau level and in high $T_c$ superconductors. We present estimates for the magnitude, system size, and frequency dependence of these fluctuations. The frequency dependence contains information about instantons in the gauge field.