Star-forming galaxies at high redshifts are the ideal targets to probe the hypothetical variation of the fine-structure constant alpha over cosmological time scales. We propose a modification of the alkali doublets method which allows us to search for variation in alpha combining far infrared and submillimeter spectroscopic observations. This variation manifests as velocity offsets between the observed positions of the fine-structure and gross-structure transitions when compared to laboratory wavelengths. Here we describe our method whose sensitivity limit to the fractional changes in alpha is about 5×10^-7. We also demonstrate that current spectral observations of hydrogen and [C II] 158 micron lines provide an upper limit on |Δα/α| < 6×10^-5 at redshifts z = 3.1 and z = 4.7.

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