The Michelson and Morley experiment
REFERENCE: None
Recall the addition of velocities in Newtonian physics:
(S) to (S')
(S') to (S)
Vx' = Vx - v
Vx = Vx' + v
y'
y
V = V
Vy = Vy'
z'
z
V = V
Vz = Vz'
[Eq. 1]
Consider the following scenario:
A stationary sound source is projecting a sound toward an observer at
Vsound, the speed of sound in air (about 373 m/s),
Vsound
vobs
and the observer is traveling toward the sound
source at vobs.
Let (S') be the IRF attached to
the observer.
Then from the perspective of the
[Fig. 1]
source (in (S)), v = - vobs so that from Eq. 1, Vx'
= Vx - v tailors into
[Eq. 2]
V'sound = Vsound + vobs.
It has been shown that a wave's speed v is related to its wavelength 
and frequency f by
[Eq. 3]
v = f
so that Eq. 2 becomes, with the proper subscripts,
'soundf'sound = soundfsound + vobs.
[Eq. 4]
It has also been shown that the wavelength is a property of the medium
through which the wave travels, and is thus the same for all observers.
Thus 'sound = sound   so that Eq. 4 becomes
f'sound = fsound + vobs/.
[Eq. 5]
From Eq. 3 vsound = soundfsound = fsound so that  can be substituted out of
Eq. 5:
f'sound = fsound(1 + vobs/vsound).
[Eq. 6]
Eq. 6 is the familiar Doppler effect and predicts that the frequency of
the sound heard by the moving observer will increase with the speed of
the observer. It also predicts that the frequency will decrease if vobs
is reversed.
Two important properties of waves are revealed in the analysis of the
Doppler effect.
(1)
There is a medium through which the wave must travel.
In the
case of sound, the medium is air, and the wave energy travels via
pressure-oscillations of the air molecules.
(2)
There is a favored IRF where the wave has its "natural" speed.
In this case, it is in (S), the IRF in which the source is stationary.
Around
1860,
James
Maxwell
derived
the
equations
describing
electromagnetic phenomena (called Maxwell's equations), which predicted
that light was a wave and that it had a particular speed c = 3108 m/s
associated with it.
At the time of Maxwell, physicists knew that all
waves required a medium through which to propagate, and they thus
postulated a medium for light waves and called it the luminiferous
ether.
Just as sound has a favored reference frame (the air's rest
frame), so does light (the ether's rest frame). Quite a bit of effort
was put into the discovery of the ether rest frame (through which the
earth must be traveling).
It was not until 1886 that an experiment of sufficient precision was
designed by Michelson and Morley to detect the ether frame, using the
Doppler effect as applied to light. Here is how it worked:
From the Doppler effect we know that when we
vobs = 0
approach a source, the frequency increases.
Consider a light source and a stationary
observer (Fig. 2). The observer then measures
[Fig. 2]
a frequency f' = f(1 + 0/c) = f.
This means
that the frequency measured by the observer is
the same as the frequency of the light source
(say starlight from a distant star).
If, on
vobs
the other hand, we approach the light source
(Fig. 3), we will measure a frequency given by
f' = f(1 + vobs/c). Note that in this case, f'
[Fig. 3]
> f by the small correction vobs/c.
The main
reason
no
experiment
had
detected
this
frequency change to the time of Michelson and Morley was precisely
because the ratio vobs/c was so small. After all, c = 186,000 miles per
second.
The properties of wave addition and interference
illustrated in Fig. 4 were used in the design
and
interpretation
of
the
Michelson-Morley
experiment. The heavy black wave is the sum of
the other two.
Constructive interference
A heavy marble platform floating in a vat of
mercury held the apparatus, absorbing street
Interference
vibrations and allowing the experimenters to
rotate the apparatus through any desired angle.
A light source sent a beam of light to a beamsplitter (Fig. 5), which then sent two in-phase
Destructive interference
beams down perpendicular arms of length L, to be
[Fig. 4]
reflected at mirrors A and B, collected at the
detector, and observed for interference.
The
platform was rotated so that one arm was parallel to the direction of
motion of the earth through the ether.
It was expected that the
frequency would be higher in arm A than
mirror A
in arm B (perpendicular to the motion VE
VE
through the ether). Interference fringes
could be tallied as the apparatus was
beam splitter
rotated slowly through 90, and frequency
L
source
differences could be calculated. Then f'
= f(1 + vobs/c) could be solved for vobs,
mirror B
L
and we would thus know what our relative
speed through the ether frame was.
The results were null.
fringes were detected.
No interference
detector
[Fig. 5]