page_title: Fizeau experiment
section_title: Hoek experiment
hierarchical_section_title: Fizeau experiment / Hoek experiment
caption_attribution_description: English: An indirect confirmation of Fresnel's dragging coefficient was provided by Martin Hoek (1868). In the particular version of the experiment shown here, Hoek used a prism P to disperse light from a slit into a spectrum which passed through a collimator C before entering the apparatus. With the apparatus oriented parallel to the hypothetical aether wind, Hoek expected the light in one circuit to be retarded 7/600&#160;mm with respect to the other. Where this retardation represented an integral number of wavelengths, he expected to see constructive interference; where this retardation represented a half-integral number of wavelengths, he expected to see destructive interference. In the absence of dragging, his expectation was for the observed spectrum to be continuous with the apparatus oriented transversely to the aether wind, and to be banded with the apparatus oriented parallel to the aether wind. His actual experimental results were completely negative.
context_page_description: The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Fizeau used a special interferometer arrangement to measure the effect of movement of a medium upon the speed of light.
  According to the theories prevailing at the time, light traveling through a moving medium would be dragged along by the medium, so that the measured speed of the light would be a simple sum of its speed through the medium plus the speed of the medium. Fizeau indeed detected a dragging effect, but the magnitude of the effect that he observed was far lower than expected. His results seemingly supported the partial aether-drag hypothesis of Fresnel, a situation that was disconcerting to most physicists. Over half a century passed before a satisfactory explanation of Fizeau's unexpected measurement was developed with the advent of Albert Einstein's theory of special relativity. Einstein later pointed out the importance of the experiment for special relativity, in which it corresponds to the relativistic velocity-addition formula when restricted to small velocities.
context_section_description: An indirect confirmation of Fresnel's dragging coefficient was provided by Martin Hoek (1868).
  His apparatus was similar to Fizeau's, though in his version only one arm contained an area filled with resting water, while the other arm was in the air. As seen by an observer resting in the aether, Earth and hence the water is in motion. So the following travel times of two light rays traveling in opposite directions were calculated by Hoek (neglecting the transverse direction, see image):
  The travel times are not the same, which should be indicated by an interference shift. However, if Fresnel's dragging coefficient is applied to the water in the aether frame, the travel time difference (to first order in v/c) vanishes. Using different setups Hoek actually obtained a null result, confirming Fresnel's dragging coefficient. (For a similar experiment refuting the possibility of shielding the aether wind, see Hammar experiment).
  In the particular version of the experiment shown here, Hoek used a prism P to disperse light from a slit into a spectrum which passed through a collimator C before entering the apparatus. With the apparatus oriented parallel to the hypothetical aether wind, Hoek expected the light in one circuit to be retarded 7/600 mm with respect to the other. Where this retardation represented an integral number of wavelengths, he expected to see constructive interference; where this retardation represented a half-integral number of wavelengths, he expected to see destructive interference. In the absence of dragging, his expectation was for the observed spectrum to be continuous with the apparatus oriented transversely to the aether wind, and to be banded with the apparatus oriented parallel to the aether wind. His actual experimental results were completely negative.
caption: Figure 6. Hoek expected the observed spectrum to be continuous with the apparatus oriented transversely to the aether wind, and to be banded with the apparatus oriented parallel to the wind. In the actual experiment, he observed no banding regardless of the instrument's orientation.
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