Michelson-Gale-Pearson experiment

{{Physics}}
The {{wpl|Michelson–Gale–Pearson_experiment|Michelson-Gale-Pearson experiment}} is a variant of the [[Michelson-Morley experiment]], that was used to detect [[speed of light]] changes due to [[Earth]]'s rotation in the [[aether]] wind. 

This experiment has been widely misquoted by [[Flat_Earth|flat-earthers]] as a proof of Earth being stationary. 

==The experiment==
[[File:Sagnac_interferometer.svg|thumb|right|The Sagnac interferometer.]]
The experiment used a large ring interferometer, also known as a Sagnac interferometer, with a sides of 2010 ft and 1113 ft (giving a perimeter of about 1.9 kilometers). The apparatus utilized a 12" water pipe, which was pumped down to roughly 0.018 PSI (reduced by a 50-horsepower pump).

The interferometer worked by splitting a beam of light with a half-silvered mirror. The light then traveled through three mirrors, with one beam going clockwise and the other counter-clockwise. When both beams returned to the half-silvered mirror, they recombined and produced an interference pattern, similar to the Michelson-Morley experiment.

The hypothesis was that light would experience a different speed when traveling in the direction of Earth's rotation compared to the opposite direction (due to the {{wpl|Sagnac_effect|Sagnac effect}}). Specifically, the beam traveling counter-clockwise would be delayed relative to the beam traveling clockwise. This shift was observed:

{{cquote|Observations showed that the beam going in the counter-clockwise direction was retarded with respect to the other by 0·230 of a fringe.|||Michelson, Gale (1925)}}

With the resulting {{wpl|Fringe_shift|fringe shift}} of 0.230,<ref>Michelson, A. A.; Gale, Henry G (April 18, 1925). [https://www.nature.com/articles/115566a0 "The Effect of the Earth's Rotation on the Velocity of Light"]. Via nature.com</ref> and [https://www.wolframalpha.com/input?i=41%C2%B0+46%27+to+degrees 41° 46' = 41.767°] latitude, they measured Earth's angular velocity to be

<math> \begin{align} \Delta &= \frac{4A\omega\sin(\varphi)}{\lambda c} \\ \omega &= \frac{\Delta \cdot \lambda c}{4A\sin(\varphi)} \\ A &= 2010 \times 1113\ \text{ft}^2 = 2,236,530\ \text{ft}^2 = 207044\ \text{m}^2 \\ \omega &= \frac{0.230 \cdot (5.7\times10^{-7}) \cdot (3\times10^8)}{4(207044)\sin(41.767^\circ)} \\ \omega &= \frac{0.230 \cdot 171}{4(207044) \cdot 0.665} \\ \omega &\approx \frac{39.330}{550996} \\ \omega &\approx 7.140 \times 10^{-5}\ \text{rad/s} \\ \omega &= 7.140 \times 10^{-5} \cdot \frac{180}{\pi} \cdot 3600\ \frac{\text{deg}}{\text{hr}} \\ \omega &\approx 15.0\ \frac{\text{deg}}{\text{hr}} \end{align}</math>

==The bitching and whining from flat-earthers==

In his [https://www.youtube.com/watch?v=J7RwAcL4Iq0&t=4115s video], [[Eric Dubay]] claims again that the Sagnac and Michelson-Gale-Pearson experiments "''attempted to measure the change in speed of light due to Earth's assumed motion through space''".

However, this experiment had nothing to do with Earth's motion through space. The goal was to detect if the Earth's rotation (specifically, its rotation through the hypothetical aether) caused any change in the speed of light; It was an attempt to observe the Sagnac effect caused by Earth's rotation. The result showed no significant deviation in the speed of light due to Earth's rotation in relation to the aether, thus again debunking the idea of aether.

In 2018, unconvinced of the results, a flat earther named Bob Knodel splurged 20,000 USD on a ring-laser gyroscope (RLG), that also relies on Sagnac effect, [[Flat_Earth#Bob_Knodel.27s_RLG_experiment_.282018.29|and conducted an independent experiment]]. To the surprise of no one, the RLG had no trouble detecting Earth's rotation.

==References==
{{reflist}}

[[Category:Flat Earth]]

Categories: Flat Earth