Rhoades

Levi Rhoades

Astrophysics 89s

Dr. Bray

10 February, 2016

The Michelson-Morley Experiment: A View of the Experiment, Findings, and

Influences on Special Relativity

Acknowledging that light, or water, requires a medium in which to travel

across appears intuitive to understanding the motion of light. However because

light can travel through a vacuum and with such little resistance, theoretical

physicists of the late 19th century hypothesized that light must travel through a still

undetectable substance they called the “luminiferous aether”. It remained clear

that the aether possessed a unique combination of properties, although the

possibility of the aether’s state of motion was highly disputed. In 1818 Augustin-

Jean Fresnel was the first to propose that the aether was partially dragged by the

Earth and thus shares only limited motion of the Earth’s surface. In contrast Sir

George Stokes, in 1844, proposed that the Earth’s orbit completely dragged the

aether and thus the movement patterns of the aether could be defined by the

state of motion existing on the Earth’s surface. Fresnel’s theory of partial aether

movement was the most widely accepted during the 19th century and it

demonstrated the idea of an “aether wind”, suggesting that the aether and Earth

are in relative motion and neither can remain at rest with respect to the other, but

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it is possible for the aether’s motion to match the Earth’s at one moment in time.

Frensel attributed changes in the behavior of the aether to variations in the time of

day or current season.

Prior to the Michelson-Morley Experiment in 1887, the Michelson

experiment of 1881 attempted to confirm or dispute the presence of an aether

wind by analyzing the return of the speed of light during various conditions of time

and season. However, the expected discrepancies in return of speed were

estimated to be a change of 0.01% and technologies capable of measuring the

speed of light to that degree were simply not practical for the time period. The

most advanced measurement system for light speed was provided by Fizeau

Foucault which could measure the speed of light to an estimated 5% accuracy.

This limitation was transcended by the unique design of the Michelson

interferometer which did not directly gauge speed but rather calculated velocity

indirectly through patterns of constructive and deconstructive interference

produced by mirror and reflected back onto a microscopic lens. The Michelson

interferometer consisted of narrow vertical stand with two long arms protruding at

right angles to each other. In the center of the apparatus was a sodium flame,

which produced monochromatic light through a half-silver mirror which was used

to split the light into two beams travelling along the arms of the machine. Located

at the end of each arm was a mirror which reflected the beams back into the

center where they recombined with each other to produce a measureable amount

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of interference whose transverse displacement would depend upon the relative

amount of time it took for each beam to travel the equidistant length of the arms.

See sequence of images below:

In theory Michelson believed that the dragging motion of the earth would

cause a shift in the constructive and destructive interferences resulting in a fringe

shift of 0.04 fringes. A shift in fringe is defined as the separation between areas of

equal intensity. The highest fringe shift that Michelson’s experiment produced was

that of 0.018 fringes and because this was still subject to experimental errors it

was accepted that the value of shift could still remain zero. The experimental error

consisted of weather anomalies, passing carriages, and drops in pressure which

all were believed to have an impact on aether wind.

The Michelson-Morley experiment occurred 6 years later after Michelson

had recovered from a mental breakdown in 1885. The newly devised experiment

featured the same Michelson interferometer with several precision improvements

in the form of limiting available vibrational and thermal sources of interferences.

Deep in the stone basement of what would become Case Western Reserve

University the interferometer was placed upon a block of sandstone floating in a

pool of mercury, allowing detection of up to 0.01 fringe. The mercury provided the

interferometer with virtually undetectable resistance. The improved experiment

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also featured only white light because its dark central fringe made it easily

identifiable. However monochromatic sodium flame was used in every test except

those of official results because it had the most easily recognizable pattern of

interference and was used as the base constant. The then arms turned at a

constant rate, assuming that one arm would be heading into the aether wind while

another would be traveling perpendicular thus slowing the speed of light

demonstrating fringe values greater than 0.04 fringe.

See apparatus below:

The experiment did not confirm the presence of an aether wind, and

subsequently concluded that the movement of aether must be zero, or too small

to detect accurately with the currently available technology. Morley concluded that

the results indicated a velocity that was less than 1/6 the velocity of the Earth’s

motion and thus could not accurately be applied to the speed of an aether wind.

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However, two physicists Fitzgerald and Lorentz provided a theory to defend the

lack of evidence for an aether wind. They proposed that the body in motion

relative to the aether wind produces a contraction of said body just great enough

to compensate for the differences in time discovered in the experiment. This

theory is similar to why the earth is shaped slightly elliptically because as it

follows the pattern of orbit around the sun. Lorentz argued that every body which

is moving at velocity u with respect to the ether contracts along the axis of motion

by the factor. This is significant because in 1905 Albert Einstein formulated his

theory of special relativity, and called for no aether motion. The detection of 1/6

velocity by the Michelson-Morley experiment at least in some regarded, casted

doubt onto the validity of Einstein’s theory, but the Fitzgerald-Lorentz theory was

not a widely accepted defense of limited net motion and it was more widely

acknowledged that the light beams in the experiment simply traveled at the same

speed regardless of their initial velocity or position within the aether.

Perhaps the Michelson-Morley’s most conclusive results come in its

description of the movement of light with regards to Einstein’s Theory of Special

Relativity. By following Newtonian physics, if light were to travel through a

stationary medium called the aether and via the stationary interferometer it would

transition to its respective mirror and back at exactly the same time. However

when the interferometer is moving at velocity, v, with respect to the stationary

aether the equations for light transit time change to become:

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This would lead the observer to expect a difference in transit times of at least 0.4

fringes. The Michelson-Morley experiment, and even modern spectrometers are

unable to detect a fringe greater than 0.01. While some fringe detection is non-

conducive to Special Relativity, the results of these experiments are so close to a

zero value that they can be used to ultimately support Einstein’s theory and

contend Newtonian physics.

The Michelson-Morley experiment was designed to determine if light

traveled at a constant velocity in all directions, discover the speed of the Earth in

orbit, and confirm the existence of the aether. The failure of this experiment to

produce conclusive results instead proved it impossible to measure (at the time)

the speed of the earth relative to an aether of questionable existence. However

the experiment did generate interest in discovering the speed of light and added

to support to Einstein’s theory of relativity to come.

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Works Cited

Dongen, Jeroen Van. On the Role of Michelson-Morley Experiment: Einstein in

Chicago. N.p.: n.p., 2009. Print.

Hamerla, R. R. "Chapter 4: Kindered Spirits, the Ether Drift." An American

Scientist on the Research Frontier: Edward Morley, Community, and

Radical Ideas in Nineteenth-century Science. Dordrecht: Springer, 2006. N.

pag. Print.

Livingston, Dorothy Michelson. "Michelson-Morley: The Great Failure." The

Scientist, n.d. Web.

Marrett, Doug. "The Michelson Morley Experiment (1887)." The Michelson Morley

Experiment (1887). N.p., 2010. Web. 22 Feb. 2016.

Maxwell, J. Clerk. "314-316." Societies and Academies. N.p.: Nature Group,

1880. N. pag. Print.

Statchel, J. "Experiments and Einsteinian Synthesis." Astronomical Notes. N.p.:

n.p., n.d. N. 37-45. Print.