Let\'s take a closer look at the Michelson-Morley experiment and what would happ
ID: 2303736 • Letter: L
Question
Let's take a closer look at the Michelson-Morley experiment and what would happen if there was an aether - a medium filling "empty" space that light moved through. Classically, we would interpret the speed of light c to be the speed of light relative to the aether. Consider the following Michelson interferometer setup: Screen Beam splitter Recombined beam Incident beam Arm 2 Arm 1 Mirror 2 Mirror I Let Arm 1 have a length 21 and let Arm 2 have a length l2 and let the whole setup be moving with speed v in the +t-direction with respect to the hypothetical "stationary aether." Recall that if light is rnoving at a speed vl other than c that we can say the index of refraction is effectively n = c/v1. (a) What is the optical path length difference between Arm 1 and Arm 2 when Arm 1 is pointing in the -^-direction and Arm 2 is pointing in the +a-direction as shown in the earlier diagram? (b) How does this change if we rotate the apparatus 90° counterclockwise (so Arm 1 is in the +-direction and Arm 2 is in the +ý-direction)?Explanation / Answer
The famous experiment designed to detect small changes in the speed of light
with motion of an observer through the ether was performed in 1887 by
American physicist Albert A. Michelson (1852–1931) and the American
chemist Edward W. Morley (1838–1923).4 We should state at the outset that
the outcome of the experiment was negative, thus contradicting the ether hypothesis. The highly accurate experimental tool perfected by these pioneers
to measure small changes in light speed was the Michelson interferometer,
shown in Figure 1.4. One of the arms of the interferometer was aligned along
the direction of the motion of the Earth through the ether. The Earth moving
through the ether would be equivalent to the ether flowing past the Earth in
the opposite direction with speed v, as shown in Figure 1.4. This ether wind
blowing in the opposite direction should cause the speed of light measured in
the Earth’s frame of reference to be c v as it approaches the mirror M2 in
Figure 1.4 and c v after reflection. The speed v is the speed of the Earth
through space, and hence the speed of the ether wind, and c is the speed of
light in the ether frame. The two beams of light reflected from M1 and M2
would recombine, and an interference pattern consisting of alternating dark
and bright bands, or fringes, would be formed.
During the experiment, the interference pattern was observed while the interferometer was rotated through an angle of 90°. This rotation would change
the speed of the ether wind along the direction of the arms of the interferometer. The effect of this rotation should have been to cause the fringe pattern to
shift slightly but measurably. Measurements failed to show any change in the interference pattern! The Michelson–Morley experiment was repeated by
other researchers under various conditions and at different times of the year
when the ether wind was expected to have changed direction and magnitude,
but the results were always the same: No fringe shift of the magnitude required was
ever observed.5
The negative results of the Michelson–Morley experiment not only meant
that the speed of light does not depend on the direction of light propagation
but also contradicted the ether hypothesis. The negative results also meant
that it was impossible to measure the absolute velocity of the Earth with
respect to the ether frame. As we shall see in the next section, Einstein’s
postulates compactly explain these and a host of other perplexing questions,
relegating the idea of the ether to the ash heap of history. Light is now
understood to be a phenomenon that requires no medium for its propagation.
As a result, the idea of an ether in which these waves could travel became
unnecessary.
Diagram of the Michelson interferometer. According to the ether wind concept, the speed of light should
be c v as the beam approaches mirror M2 and c v
after reflection.
Details of the Michelson–Morley Experiment
To understand the outcome of the Michelson–Morley experiment, let us assume that the interferometer shown in Figure 1.4 has two arms of equal
length L. First consider the beam traveling parallel to the direction of the
ether wind, which is taken to be horizontal in Figure 1.4. According to Newtonian mechanics, as the beam moves to the right, its speed is reduced by the
wind and its speed with respect to the Earth is c v. On its return journey, as
the light beam moves to the left downwind, its speed with respect to the Earth
is c v. Thus, the time of travel to the right is L/(c v), and the time of
travel to the left is L/(c v). The total time of travel for the round-trip along the horizontal path is
t1= L/c+v + L/c-v = 2Lc/c2-v2 =2L/c (1-v2/c2)-1
The precision instrument designed by Michelson and Morley had the capability of detecting a shift in the fringe pattern as small as 0.01 fringe. However,
they detected no shift in the fringe pattern. Since then, the experiment has been
repeated many times by various scientists under various conditions, and no
fringe shift has ever been detected. Thus, it was concluded that one cannot
detect the motion of the Earth with respect to the ether.
Many efforts were made to explain the null results of the Michelson–
Morley experiment and to save the ether concept and the Galilean addition law
for the velocity of light. Because all these proposals have been shown to be
wrong, we consider them no further here and turn instead to an auspicious
proposal made by George F. Fitzgerald and Hendrik A. Lorentz. In the 1890s,
Fitzgerald and Lorentz tried to explain the null results by making the following
ad hoc assumption. They proposed that the length of an object moving at
speed v would contract along the direction of travel by a factor of .
The net result of this contraction would be a change in length of one of the
arms of the interferometer such that no path difference would occur as the interferometer was rotated.
Never in the history of physics were such valiant efforts devoted to trying
to explain the absence of an expected result as those directed at the
Michelson–Morley experiment. The difficulties raised by this null result
were tremendous, not only implying that light waves were a new kind of wave
propagating without a medium but that the Galilean transformations
were flawed for inertial frames moving at high relative speeds. The stage
was set for Albert Einstein, who solved these problems in 1905 with his special
theory of relativity
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