Ives–Stilwell experiment

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The Ives–Stilwell experiment exploits the Transverse Doppler effect (TDE) described by Albert Einstein in his 1905 paper.

Einstein subsequently suggested an experiment based on the measurement of the relative frequencies of light perceived as arriving from a light source in motion with respect to the observer. Herbert E. Ives and G. R. Stilwell undertook the task of executing the experiment and they came up with a very clever way of separating the much smaller TDE from the much bigger longitudinal Doppler effect. The experiment was executed in 1938 and it was reprised multiple times [1],[2].

Ives wanted to do a positive test of time dilation, as followed from the "theory of Lorentz and Larmor" and as was first suggested "by Einstein and Ritz". This was the first direct, quantitative test of the time dilation factor.

The Ives–Stilwell experiment forms one of the fundamental tests of special relativity theory. Other such tests were the Michelson–Morley and Kennedy–Thorndike experiments as well as the Kauffman experiments.

[edit] Analysis

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If we assume that the speed of light is fixed with respect to the observer (“Classical Theory”), then the forward and rearward Doppler-shifted frequencies seen on a moving object will be f'/f = c/(c±v), where v is recession velocity. Under special relativity, the two frequencies will also include an additional “Lorentz factor” redshift component.

When we invert these relationships so that they relate to wavelengths rather than frequencies, “Classical Theory” predicts redshifted and blueshifted wavelength values of 1+v/c and 1-v/c, so if all three wavelengths (redshifted, blueshifted and original) are marked on a linear scale, according to Classical Theory the three marks should be perfectly evenly spaced.

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But if the light is shifted by special relativity's predictions, the additional Lorentz offset means that the two outer marks will be offset in the same direction with respect to the central mark.

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Ives and Stilwell found that there was a significant offset of the centre of gravity of the three marks, and therefore the Doppler relationship was not that of "Classical Theory".

This approach had two main advantages:

didn't require us to commit to an exact value for the velocity involved (which might have been theory-dependent), and
it didn't require an understanding or interpretation of angular aberration effects, as might have been required for the analysis of a "true" transverse test.