Editing Relativistic Doppler effect (section)

=== Ives and Stilwell-type measurements ===
[[File:Ives-Stilwell rationale.svg|thumb|300px|Figure 9. Why it is difficult to measure the transverse Doppler effect accurately using a transverse beam.]]
Einstein (1907) had initially suggested that the TDE might be measured by observing a beam of "[[canal rays]]" at right angles to the beam.<ref group=p name=Einstein1907/> Attempts to measure TDE following this scheme proved to be impractical, since the maximum speed of a particle beam available at the time was only a few thousandths of the speed of light.

Fig.&nbsp;9 shows the results of attempting to measure the 4861 Angstrom line emitted by a beam of canal rays (a mixture of H1+, H2+, and H3+ ions) as they recombine with electrons stripped from the dilute hydrogen gas used to fill the Canal ray tube. Here, the predicted result of the TDE is a 4861.06 Angstrom line. On the left, longitudinal Doppler shift results in broadening the emission line to such an extent that the TDE cannot be observed. The middle figures illustrate that even if one narrows one's view to the exact center of the beam, very small deviations of the beam from an exact right angle introduce shifts comparable to the predicted effect.

Rather than attempt direct measurement of the TDE, [[Ives–Stilwell experiment|Ives and Stilwell (1938)]] used a concave mirror that allowed them to simultaneously observe a nearly longitudinal direct beam (blue) and its reflected image (red). Spectroscopically, three lines would be observed: An undisplaced emission line, and blueshifted and redshifted lines. The average of the redshifted and blueshifted lines would be compared with the wavelength of the undisplaced emission line. The difference that Ives and Stilwell measured corresponded, within experimental limits, to the effect predicted by special relativity.<ref group="p" name=Ives1938>{{cite journal |last=Ives |first=H. E. |author2=Stilwell, G. R.  |year=1938 |title=An experimental study of the rate of a moving atomic clock |journal=Journal of the Optical Society of America |volume=28 |issue=7 |pages=215 |bibcode=1938JOSA...28..215I |doi=10.1364/JOSA.28.000215 }}</ref>

Various of the subsequent repetitions of the Ives and Stilwell experiment have adopted other strategies for measuring the mean of blueshifted and redshifted particle beam emissions. In some recent repetitions of the experiment, modern accelerator technology has been used to arrange for the observation of two counter-rotating particle beams. In other repetitions, the energies of gamma rays emitted by a rapidly moving particle beam have been measured at opposite angles relative to the direction of the particle beam. Since these experiments do not actually measure the wavelength of the particle beam at right angles to the beam, some authors have preferred to refer to the effect they are measuring as the "quadratic Doppler shift" rather than TDE.<ref group=p>{{cite journal |last1=Olin |first1=A. |last2=Alexander |first2=T. K. |last3=Häusser |first3=O. |last4=McDonald |first4=A. B. |last5=Ewan |first5=G. T. |title=Measurement of the Relativistic Doppler Effect Using 8.6-MeV Capture γ Rays |journal=Phys. Rev. D |date=1973 |volume=8 |issue=6 |pages=1633–1639 |doi=10.1103/PhysRevD.8.1633|bibcode=1973PhRvD...8.1633O }}</ref><ref group=p>{{cite journal |last1=Mandelberg |first1=Hirsch I. |last2=Witten |first2=Louis |title=Experimental Verification of the Relativistic Doppler Effect |journal=Journal of the Optical Society of America |date=1962 |volume=52 |issue=5 |pages=529–535 |doi=10.1364/JOSA.52.000529 |bibcode=1962JOSA...52..529M}}</ref>