An experiment has been performed to measure the quadratic Doppler shift, , predicted by the special theory of relativity. A moving beam of radiating hydrogen atoms with velocities ranging up to 2.8 × 108 cm/sec has been viewed from the incoming and outgoing directions simultaneously. Averaging wavelength measurements of a particular spectral line for the two observations gives a measurement of the quadratic shift. The number in the theoretically predicted exponent can be compared to the experimental results. The latter gives the value of this exponent to be 0.498 ± 0.025. The predominant factor leading to the experimental uncertainty is the width of the spectral lines involved in the measurement.
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