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The Michelson-Morley Experiment
Maxwell proposed that light is an electro-magnetic wave.  
A wave results from a disturbance of a medium; in other words, if a wave exists, there must be something "waving"!  
What is the medium for the propagation of light (which we know can travel through a vacuum)?
 
It was suggested that all of space contained an invisible medium called the "aether".  
Since all of space was thought to contain this aether, many people thought that it might give us a frame of reference which could be considered to be at absolute rest.  
   
Michelson and Morley constructed an interferometer with which they hoped to detect the motion of the earth through the aether.  
A simplified diagram of their apparatus is shown below (also, a possibly helpful analogy of the experiment can be seen here  
   
 
   
The half-silvered mirror splits the light from the source into two coherent* beams. After reflection at the two mirrors these two coherent beams of light form an interference pattern which can be studied using the microscope.  
   
Now suppose that the earth (and therefore the interferometer) is moving through a "stationary" aether with velocity v as shown.  
Galilean relativity tells us that the velocity of the light moving parallel to v, relative to the apparatus, will be (c - v) when the light is going towards mirror 2 and (c + v) when the light is going the opposite way.  
Clearly, the light which moves in a direction perpendicular to v will have a velocity (relative to the apparatus) of a different magnitude.  
Thus, if the whole apparatus is rotated through 90, so that beam 1 is now parallel to v and beam 2 is perpendicular to v, we would expect a change in the interference pattern.  
   
Michelson and Morley measured the positions of the interference fringes very carefully and then rotated the apparatus through 90 and looked at the pattern again.  
   
No change in the pattern was observed.  
   
Conclusions:  
1. The aether does not exist; there is no frame of reference which can be considered to be absolutely at rest.  
2. The speed of light is the same for all observers.  
   
* coherent beams: beams having a constant phase relation (so that any interference pattern produced does not change with time)  
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