Editing Michelson–Morley experiment (section)

== Subsequent experiments ==
[[File:Illingworth simulation.png|thumb|250px|Simulation of the Kennedy/Illingworth refinement of the Michelson–Morley experiment. (a) Michelson–Morley interference pattern in monochromatic [[mercury-vapor lamp|mercury light]], with a dark [[interference fringe|fringe]] precisely centered on the screen. (b) The fringes have been shifted to the left by 1/100 of the fringe spacing. It is extremely difficult to see any difference between this figure and the one above. (c) A small step in one mirror causes two views of the same fringes to be spaced 1/20 of the fringe spacing to the left and to the right of the step. (d) A [[telescope]] has been set to view only the central dark band around the mirror step. Note the symmetrical brightening about the center line. (e) The two sets of fringes have been shifted to the left by 1/100 of the fringe spacing. An abrupt discontinuity in luminosity is visible across the step.]]
Although Michelson and Morley went on to different experiments after their first publication in 1887, both remained active in the field. Other versions of the experiment were carried out with increasing sophistication.<ref group=A name=Swenson1 /><ref group=A name=Swenson2 /> Morley was not convinced of his own results, and went on to conduct additional experiments with [[Dayton Miller]] from 1902 to 1904. Again, the result was negative within the margins of error.<ref name=morley1 /><ref name=morley2/>

Miller worked on increasingly larger interferometers, culminating in one with a {{Convert|32|m|adj = on|sp = us}} (effective) arm length that he tried at various sites, including on top of a mountain at the [[Mount Wilson Observatory]]. To avoid the possibility of the aether wind being blocked by solid walls, his mountaintop observations used a special shed with thin walls, mainly of canvas. From noisy, irregular data, he consistently extracted a small positive signal that varied with each rotation of the device, with the [[sidereal time|sidereal day]], and on a yearly basis. His measurements in the 1920s amounted to approximately {{Convert|10|km/s|abbr = on}} instead of the nearly {{Convert|30|km/s|4 = 1|abbr = on}} expected from the Earth's orbital motion alone. He remained convinced this was due to [[aether drag hypothesis#Partial aether dragging|partial entrainment or aether dragging]], though he did not attempt a detailed explanation. He ignored critiques demonstrating the inconsistency of his results and the refutation by the [[Hammar experiment]].<ref group=A name=Thirring /><ref group=note name=Thirring>Thirring (1926) as well as Lorentz pointed out that Miller's results failed even the most basic criteria required to believe in their celestial origin, namely that the azimuth of supposed drift should exhibit daily variations consistent with the source rotating about the celestial pole. Instead, while Miller's observations showed daily variations, their oscillations in one set of experiments might center, say, around a northwest–southeast line.</ref> Miller's findings were considered important at the time, and were discussed by Michelson, [[Hendrik Lorentz|Lorentz]] and others at a meeting reported in 1928.<ref group=A name=michel1928 /> There was general agreement that more experimentation was needed to check Miller's results. Miller later built a non-magnetic device to eliminate [[magnetostriction]], while Michelson built one of non-expanding [[Invar]] to eliminate any remaining thermal effects. Other experimenters from around the world increased accuracy, eliminated possible side effects, or both. So far, no one has been able to replicate Miller's results, and modern experimental accuracies have ruled them out.<ref group=A name=shankland /> Roberts (2006) has pointed out that the primitive data reduction techniques used by Miller and other early experimenters, including Michelson and Morley, were capable of ''creating'' apparent periodic signals even when none existed in the actual data. After reanalyzing Miller's original data using modern techniques of quantitative error analysis, Roberts found Miller's apparent signals to be statistically insignificant.<ref name=Roberts2006 group=A>{{cite arXiv |last=Roberts |first=T.J. |title=An Explanation of Dayton Miller's Anomalous "Ether Drift" Result |eprint=physics/0608238 |year=2006 }}</ref>

Using a special optical arrangement involving a 1/20 wave step in one mirror, Roy J. Kennedy (1926) and K.K. Illingworth (1927) (Fig.&nbsp;8) converted the task of detecting fringe shifts from the relatively insensitive one of estimating their lateral displacements to the considerably more sensitive task of adjusting the light intensity on both sides of a sharp boundary for equal luminance.<ref name=Kennedy/><ref name=Illingworth/> If they observed unequal illumination on either side of the step, such as in Fig.&nbsp;8e, they would add or remove calibrated weights from the interferometer until both sides of the step were once again evenly illuminated, as in Fig.&nbsp;8d. The number of weights added or removed provided a measure of the fringe shift. Different observers could detect changes as little as 1/1500 to 1/300 of a fringe. Kennedy also carried out an experiment at Mount Wilson, finding only about 1/10 the drift measured by Miller and no seasonal effects.<ref group=A name=michel1928 />

In 1930, [[Georg Joos]] conducted an experiment using an automated interferometer with {{Convert|21|m|ft|-long|sp = us|adj = mid}} arms forged from pressed quartz having a very low coefficient of thermal expansion, that took continuous photographic strip recordings of the fringes through dozens of revolutions of the apparatus. Displacements of 1/1000 of a fringe could be measured on the photographic plates. No periodic fringe displacements were found, placing an upper limit to the aether wind of {{Convert|1.5|km/s|abbr = on}}.<ref name=joos />

In the table below, the expected values are related to the relative speed between Earth and Sun of {{Convert|30|km/s|4 = 1|abbr = on}}. With respect to the speed of the [[Solar System]] around the galactic center of about {{Convert|220|km/s|abbr = on}}, or the speed of the Solar System relative to the [[cosmic microwave background radiation#CMBR dipole anisotropy|CMB rest frame]] of about {{Convert|370|km/s|abbr = on}}, the null results of those experiments are even more obvious.

{| class="wikitable"
|-
!Name
!Location
!Year
!Arm length (meters)
!Fringe shift expected
!Fringe shift measured
!Ratio
!Upper Limit on V<sub>aether</sub>
!Experimental Resolution
!Null result
|-
|Michelson<ref name=michel1 />||[[Potsdam]]||1881||1.2||0.04||≤ 0.02||2||~ 20&nbsp;km/s||0.02||<math>\approx</math> yes
|-
|Michelson and Morley<ref name=michel2 />||[[Cleveland]]||1887||11.0||0.4||< 0.02<br />or ≤ 0.01|| 40||~ 4–8&nbsp;km/s||0.01||<math>\approx</math> yes
|-
|Morley and Miller<ref name=morley1 /><ref name=morley2 />||[[Cleveland]]||1902–1904||32.2||1.13||≤ 0.015||80||~ 3.5&nbsp;km/s||0.015||yes
|-
|Miller<ref name=mill />||[[Mount Wilson (California)|Mt. Wilson]]||1921||32.0||1.12||≤ 0.08||15||~ 8–10&nbsp;km/s||unclear||unclear
|-
|Miller<ref name=mill/>||[[Cleveland]]||1923–1924||32.0||1.12||≤ 0.03||40||~ 5&nbsp;km/s||0.03||yes
|-
|Miller <small>(sunlight)</small><ref name=mill/>||[[Cleveland]]||1924||32.0||1.12||≤ 0.014||80||~ 3&nbsp;km/s||0.014||yes
|-
|[[Rudolf Tomaschek|Tomaschek]] <small>(star light)</small><ref name=Tomaschek />||[[Heidelberg]]||1924||8.6||0.3||≤ 0.02||15||~ 7&nbsp;km/s||0.02||yes
|-
|Miller<ref name=mill/><ref group=A name=Miller1933 />||[[Mount Wilson (California)|Mt. Wilson]]||1925–1926||32.0||1.12||≤ 0.088||13||~ 8–10&nbsp;km/s||unclear||unclear
|-
|Kennedy<ref name=Kennedy />||[[Pasadena, California|Pasadena]]/[[Mount Wilson (California)|Mt. Wilson]]||1926||2.0||0.07||≤ 0.002||35||~ 5&nbsp;km/s||0.002||yes
|-
|Illingworth<ref name=Illingworth />||[[Pasadena, California|Pasadena]]||1927||2.0||0.07||≤ 0.0004||175||~ 2&nbsp;km/s||0.0004||yes
|-
|Piccard & Stahel<ref name=piccard1 />||with a [[Balloon]]||1926||2.8||0.13||≤ 0.006||20||~ 7&nbsp;km/s||0.006||yes
|-
|Piccard & Stahel<ref name=piccard2 />||[[Brussels]]||1927||2.8||0.13||≤ 0.0002||185||~ 2.5&nbsp;km/s||0.0007||yes
|-
|Piccard & Stahel<ref name=piccard3 />||[[Rigi]]||1927||2.8||0.13||≤ 0.0003||185||~ 2.5&nbsp;km/s||0.0007||yes
|-
|Michelson ''et al.''<ref name=michel5 />||[[Pasadena, California|Pasadena (Mt. Wilson optical shop)]]||1929||25.9||0.9||≤ 0.01||90||~ 3&nbsp;km/s||0.01||yes
|-
|[[Georg Joos|Joos]]<ref name=joos />||[[Jena]]||1930||21.0||0.75||≤ 0.002||375||~ 1.5&nbsp;km/s||0.002||yes
|}