http://www.ck12.org Chapter 22. The Special Theory of Relativity
another instance, we should be able to measure ourselves moving at different speeds relative to the sound. Similarly,
if we move through the ether while light is traveling toward us in one instance and away from us in another instance,
we should be able to measure the speed of the Earth relative to the light.
The results, of course, would need to be indirectly determined since the experiment relied upon using an interferom-
eter. The interferometer, as you recall, is based upon the constructive and destructive interference of light waves. A
very small difference in the time of travel between two light waves separating and recombining would be detected
in the interferometer as a shift in the position of bright and dark fringes. One light wave traveled in the direction of
the Earth’s motion through the ether while the other light wave traveled perpendicular to the Earth’s motion through
the ether. Michelson thought that there should be a time difference in the light traversing the two paths. Here is his
reasoning in his own words, used as an explanation to his daughter:Two beams of light race against each other,
like two swimmers, one struggling upstream and back, while the other, covering the same distance, just crosses and
returns. The second swimmer will always win if there is any current in the river.
With the help of E.W Morley, Michelson’s interferometer,Figure22.4, was calibrated so that it could detect a shift
of one part in a hundred in the position of a fringe. The shift they anticipated due to the Earth’s velocity through the
ether was some forty times that! Clearly, the effect was measureable. Curiously, though, there was no discernible
shift in the interference fringes.
FIGURE 22.4
Diagram of the Michelson Interferometer.The null result of the experiment, from the point of view of measuring the relative velocity between the Earth and
the velocity of light through the ether, can be understood as follows:
The velocity of Earth in orbit about the sun is, on average, about 30kms. Using that velocity, Michelson calculated
the expected shift in an interference fringe. Thus, the experiment should show a shift in fringe corresponding to that
speed. When the Earth moves in the same direction as the light in the ether, the shift in fringe should verify the
velocity of light with respect to the ether asvrel to earth=c− 30 kms. When the Earth is moving toward the light, a
shift in fringe should verify the velocity of light asvrel to earth=c+ 30 kms. The predicted fringe shift would confirm
the velocity of the Earth in orbit about the sun and establish the absolute reference frame of the ether.
However, regardless of which way the light moved through the ether (and, therefore, through the interferometer), it
never indicated a change in velocity relative to the Earth. There was no way to detect the Earth’s motion through the
ether. That result was absolutely shocking.
What would the result of the Michelson-Morley experiment imply if the results of this experiment applied to
everyday objects, such as the ball that the girl on the skateboard had thrown in the example above? (Imagine the ball
playing the role of a beam of light, like a flashlight being turned on.) It would mean that a stationary observer would
measure the speed of the ball as 6. 0 ms,regardless of the direction the ball was thrown or the motion of the girl!
This meant that the Galilean relativity failed to provide the correct results when applied to light (and therefore any