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The Lyman-alpha absorption systems observed in the spectra of QSOs are likelyto possess bulk peculiar velocities. The free electrons in these systemsscatter the microwave background and distort its spectrum through the kinematicSunyaev-Zel'dovich effect. I calculate the temperature fluctuations of themicrowave sky due to variations in the number of Lyman-alpha systems alongdifferent lines-of-sight throughout the universe. The known population ofabsorbers out to z=5 introduces anisotropies on angular scales <1' with an rmsamplitude of order (DeltaT/T)= 10^{-6}*(Omega_Lya/0.05)*(v/400km/s), whereOmega_Lya is the cosmological density parameter of ionized gas in Lyman-alphaabsorption systems, and v is the rms line-of-sight peculiar velocity of thesesystems at z=3. Detection of this signal will provide valuable informationabout the cosmic velocity field and the gas content of Lyman-alpha absorptionsystems at high redshifts.Comment: 10 pages, latex, no figure

Microwave Background Anisotropies Due to the Kinematic Sunyaev-Zeldovich Effect of the Lyα Forest