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The Michelson-Morley experiment

This experiment, first performed in 1887 by Michelson and Morley, was designed to establish the existence of the ether. The ether was a massless fluid that was supposed to pervade all space and it was by a disturbance of the ether that is was thought electromagnetic radiation travelled. Scientists believed in the existence of the ether because they thought that all waves required a medium through which to travel.

They reasoned that a beam of light moving parallel to the Earth's direction of motion through the ether would take a different time to return to the detector than one that moved at right angles to the Earth's motion.

A simplified diagram of their apparatus is shown in Figure 1. The measurements were made using an optical interferometer where the interference fringes made by the two beams were observed. It was capable of detecting differences in the speed of less than one tenth of the speed of the Earth in its orbit round the Sun.

The Earth was considered to be moving from right to left and the 'ether wind' was therefore flowing past it from left to right.
A beam of light was emitted by the source S and split by the glass plate P. One beam then travelled along the direction of motion of the Earth, reflected from mirror M2 and returned to the observer. The other beam was bent through 90o so that it travelled at right angle to the motion of the earth and was reflected by the mirror M1 before returning to the observe. They actually used multiple reflections so that the path length was about eleven metres.

If the velocity of the ether is v relative to the Earth then this must affect the velocity of light relative to the Earth.

In the down wind direction the velocity of light will be c + v, in the upwind direction c v.
The time (t2) taken for the light to travel to the beam splitter and back is:

t2 = d/[c+v] + d/[c v] = 2d/c[1 d2/c2]-1

See the following diagram.


However if the light beam was shone at right angles it would mean that the Earth would be travelling at right angles to the direction of the ether wind. The time taken for it to return to the observer would then be:

t1 = 2d/v[c2 + v2] = 2d/c[1 d2/c2]-1/2 .

Now these two times (t1 and t2) are different and so the light beams should return to the observer with a difference in phase and so the interference pattern should show a shift.

The apparatus was rotated to check the fringe shift for varying directions of the light beam.

However no matter in which direction the apparatus was pointed no such shift in the interference fringes was observed although the apparatus could detect movements as small as 0.01 of a fringe.

The two times measured by the experiement were therefore equal and so the speed of light seemed to be constant no matter in which direction the light beam was travelling relative to the Earth's motion.

This result proved that the ether did not exist.

This null result was to form a verification of the constancy of the speed of light, one of Einstein's postulates in his Special Theory of Relativity proposed in 1905.

 

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© Keith Gibbs 2020