A failed experiment which reveals the reality of space time

 Many physicists devoted their life to prove something. Some of them have succeeded and wrote their name in the pages of history. Many of them have failed also. But, in the experiment, if someone fails to prove something, he won’t be a failure. The failed experiment could lead to a new theory. The same thing had happened in the case of the Michelson-Morley experiment. They try to prove the existence of ether medium. Although they failed, it led to describe the nature of light. Due to this experiment, the genius scientist Einstein was able to give the new theories of relativity. With the help of this experiment, he described how time is different for different frames of reference.

Waves and nature of light

Waves generally refer to the vibration in any medium. In nature, different types of waves can be observed. The waves are the vibration in the medium. Due to this nature of waves scientists believed that every wave needs a medium to propagate. James Clark Maxwell had already proved that light is an electromagnetic wave. The interference phenomena also show that light is a wave. With the help of those pieces of evidence, scientists believed that the universe is covered by an ether medium through which light propagates. The ether medium was believed to be at rest. The question arises here whether the relative motion between earth and ether can be detected? If so we can choose a fixed frame of reference in a stationary ether. Then we can express all motion relative to this frame of reference.

The relative velocity of wave

The velocity of any body is relative to the motion of the frame of reference from where the body is observed. It means that let us consider a body has some velocity. If the velocity of that body is observed from another body at a different phase of motion (at rest or moving with some velocity), then the velocity will be different at each phase. To understand this let us consider a pond where water is at rest. Let a boy is on the boat which is moving with constant velocity v on the pond. Then, suddenly another boy dropped a stone into the pond. A water wave will start to appear on the pond. Assume that the wave is spread with velocity u.

Illustration of wave produced in the pond

The relative velocity of the water wave with respect to the boy on the boat will be different when he is going nearer to the wave and when he is going away from the water wave.

The relative velocity of wave on the surface of pond with respect to a boat

on the same pond

Clearly, from the above example, we can see that the velocity of the wave is relative to the motion of the boat. The boy on the boat will observe the wave velocity is higher when he travels towards it than away from it.

In this illustration, that water is the medium where the wave is produced. In a similar manner, scientists assumed that light propagates in a rest medium, which they named ether. They believed that the whole universe is covered with ether and light propagates in that medium just like water wave propagates on the pond in the previous example.  Although the water itself is at rest, the wave in the water travels with some velocity. This arises the question that Whether the velocity of light is relative to earth just like the wave on the pond is relative to a person on the boat? To answer this question Michelson and Morley performed an experiment which is known as the Michelson Morley Experiment.

The Michelson and Morley Experiment

In 1887, two scientists Michelson and Morley set up an experiment to measure the velocity of light with respect to the motion of the earth. The principle of this experiment was to find the shift in the fringes due to the path difference between two coherent sources of light which are moving in the perpendicular direction to each other. To understand this let consider an example. If a person on the surface of the earth turns on two sources of light perpendicular to each other. Because the earth is in motion the relative velocity of light will be different in those different directions. With the help of vector addition law of parallelogram, we can easily calculate the relative velocity of light in that different direction.

Relative velocity of light at different direction to the direction velocity of earth 
if velocity of light is relative

The above diagram shows that the relative velocity of light is lower along the direction of the motion of the earth than in the perpendicular direction. This difference in velocity results in the path difference between the two lights. This path different will create an interference pattern.

Michelson-Morley Experimental Set-up

To performed this experiment, they used Michelson interferometer. The experimental setup of Michelson Morley experimental is as below

The Michelson-Morley Experimental Set-up

In this diagram, the dotted lines represent the shift in the whole apparatus because of the velocity of the earth. PA’P represents the light moving along the direction to velocity of earth and PB’P’ represents the light moving perpendicular direction to the velocity of the earth. By considering the velocity of light relative to the earth they calculated the path difference will be dv²/c² (where, PA = PB = d) and they rotated the whole apparatus by 90˚ and they calculated the path difference theoretically. They found that after rotating the whole set up the new path difference will be 2dv²/c². This change in path difference will result in the shift in the fringe in interference pattern. They expected a shift of about 0.4. They believed that they could detect a shift as small as 0.01 of a fringe. Despite their best effort, they didn’t find any shift in the fringe. So this experiment is known as a failed experiment.

Conclusion 

What did Michelson and Morley actually prove?

After completing this experiment Michelson and Morley reach to a conclusion that the relative velocity of earth with respect to ether can’t be determine. The earth dragged along with the ether in its immediate neighborhood. But the proper explanation of Michelson Morley Experiment is given by Einstein in this theory of relativity.

What was the main objective of the Michelson-Morley experiment?

Lorentz and Fitzgerald observed that the length PA is contract due to the motion of earth. Let L_o be the length of a body when it is at rest. The length of a body moving with velocity v will be L_o  .In this experiment the length PB remains same but length PA will get shortened to d  . If the old value of PA were replaced by d   the path difference will be same and there will be no interference pattern.

In special theory of relativity Einstein explain how light behave in different frame of reference. He concluded that the velocity of light is constant in all frames of reference and independent of the motion of the frame of reference. This opens the door for theories of relativity.

Does the Aether exist?

With those pieces of evidence from Michelson Morley Experiment and Einstein’s special theory of relativity, scientists believed that the concept of ether medium is unnecessary. The light had believed to propagate in space without any medium. The concept of ether was abandon.