Editing Relativistic Doppler effect (section)

== Experimental verification ==
{{Main|Ives–Stilwell experiment|l1=Ives–Stilwell-, Mössbauer rotor-, and Spectroscopy tests of time dilation}}

Since the transverse Doppler effect is one of the main novel predictions of the special theory of relativity, the detection and precise quantification of this effect has been an important goal of experiments attempting to validate special relativity.

=== 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>

=== Direct measurement of transverse Doppler effect ===
The advent of [[particle accelerator]] technology has made possible the production of particle beams of considerably higher energy than was available to Ives and Stilwell. This has enabled the design of tests of the transverse Doppler effect directly along the lines of how Einstein originally envisioned them, i.e. by directly viewing a particle beam at a 90° angle. For example, Hasselkamp et al. (1979) observed the ''H''α line emitted by hydrogen atoms moving at speeds ranging from 2.53×10<sup>8</sup>&nbsp;cm/s to 9.28×10<sup>8</sup>&nbsp;cm/s, finding the coefficient of the second order term in the relativistic approximation to be 0.52±0.03, in excellent agreement with the theoretical value of 1/2.<ref group=p>{{cite journal |last1=Hasselkamp |first1=D. |last2=Mondry |first2=E. |last3=Sharmann |first3=A. |title=Direct observation of the transversal Doppler-shift |journal=Zeitschrift für Physik A |date=1979 |volume=289 |issue=2 |pages=151–155|doi=10.1007/BF01435932 |bibcode=1979ZPhyA.289..151H |s2cid=120963034 }}</ref>

Other direct tests of the TDE on rotating platforms were made possible by the discovery of the [[Mössbauer effect]], which enables the production of exceedingly narrow resonance lines for nuclear gamma ray emission and absorption.<ref>{{cite book |author1=Saburo Nasu |editor1-last=Yoshida |editor1-first=Yutaka |editor2-last=Langouche |editor2-first=Guido |title=Mössbauer Spectroscopy: Tutorial Book |url=https://archive.org/details/mssbauerspectros00nasu |url-access=limited |publisher=Springer |isbn=978-3642322198 |pages=[https://archive.org/details/mssbauerspectros00nasu/page/n7 1]–22 |year=2013 |chapter=General Introduction to Mössbauer Spectroscopy}}</ref> Mössbauer effect experiments have proven themselves easily capable of detecting TDE using emitter-absorber relative velocities on the order of 2×10<sup>4</sup>&nbsp;cm/s. These experiments include ones performed by Hay ''et al.'' (1960),<ref group=p>{{cite journal|author1=Hay, H. J. |author2=Schiffer, J. P. |author3=Cranshaw, T. E. |author4=Egelstaff, P. A. |date=1960|title=Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in <sup>57</sup>Fe|journal=Physical Review Letters|volume=4|issue=4|pages=165–166|doi=10.1103/PhysRevLett.4.165|bibcode=1960PhRvL...4..165H}}</ref> Champeney ''et al.'' (1965),<ref group=p>{{cite journal|author1=Champeney, D. C. |author2=Isaak, G. R. |author3=Khan, A. M. |date=1965|title=A time dilatation experiment based on the Mössbauer effect|journal=Proceedings of the Physical Society|volume=85|issue=3|pages=583–593|doi=10.1088/0370-1328/85/3/317|bibcode = 1965PPS....85..583C }}</ref> and Kündig (1963).<ref group=p name=Kundig/>

=== Time dilation measurements ===
The transverse Doppler effect and the kinematic time dilation of special relativity are closely related. All validations of TDE represent validations of kinematic time dilation, and most validations of kinematic time dilation have also represented validations of TDE. An online resource, "What is the experimental basis of Special Relativity?" has documented, with brief commentary, many of the tests that, over the years, have been used to validate various aspects of special relativity.<ref name="Roberts">{{cite web |last1=Roberts |first1=Tom |last2=Schleif |first2=Siegmar |title=What is the experimental basis of Special Relativity? |url=http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html |website=The Original Usenet Physics FAQ |publisher=Department of Mathematics, University of California, Riverside |access-date=16 October 2018}}</ref> Kaivola et al. (1985)<ref group=p>{{cite journal |last1=Kaivola |first1=Matti |last2=Riis |first2=Erling |last3=Lee |first3=Siu Au |title=Measurement of the Relativistic Doppler Shift in Neon |journal=Phys. Rev. Lett. |date=1985 |volume=54 |issue=4 |pages=255–258 |doi=10.1103/PhysRevLett.54.255|pmid=10031461 |bibcode=1985PhRvL..54..255K |url=https://aaltodoc.aalto.fi:443/bitstream/123456789/15656/1/A1_kaivola_matti_1985.pdf }}</ref> and McGowan et al. (1993)<ref group=p>{{cite journal |last1=McGowan |first1=Roger W. |last2=Giltner |first2=David M. |last3=Sternberg |first3=Scott J. |last4=Lee |first4=Siu Au |title=New measurement of the relativistic Doppler shift in neon |journal=Phys. Rev. Lett. |date=1993 |volume=70 |issue=3 |pages=251–254 |doi=10.1103/PhysRevLett.70.251|pmid=10054065 |bibcode=1993PhRvL..70..251M }}</ref> are examples of experiments classified in this resource as time dilation experiments. These two also represent tests of TDE. These experiments compared the frequency of two lasers, one locked to the frequency of a  neon atom transition in a fast beam, the other locked to the same transition in thermal neon. The 1993 version of the experiment verified time dilation, and hence TDE, to an accuracy of 2.3×10<sup>−6</sup>.