# Length contraction in Michelson-Morley experiment

The length contraction in longitudinal arm is required to explain the null result, i.e. no destructive interference. Can't we just explain the null result without involving the length contraction because both arms are equal length and hence light only has to travel the same distance for both arms. Or, perhaps I can put the question differently, does the special theory of relativity require the length contraction to explain the null result? I don't think it does because the observer and apparatus are in the same inertial frame of reference.

I understand that Lorentz came up with the length contraction hypothesis to save the aether theory. In the experiment the following times were calculated where '$$c$$' is speed of light, '$$v$$' is orbiting speed of earth around the sun with respect to absolute frame of reference of aether, and 'd' is length of both arms.

$$t_{total1 }$$for longitudinal arm along the direction of motion$$= 2dc/(c^2 - v^2)$$

$$t_{total2}$$for transverse arm $$= 2d/sqrt(c^2 - v^2)$$

From the equations, it could be seen that $$t_{total1 }$$would be greater than $$t_{total_2}$$.

Earth is almost an inertial frame of reference therefore if "$$v$$" is removed, we are left with$$t_{total1}=t_{total2}$$. In my view, the aether was the only reason "$$v$$" was introduced in the equation. It was assumed that the distance along the direction of longitudinal mirror would take longer time because during half part of its trip the light move against the aether or aether wind, but during the second half of its round trip aether wind moves with the light.

In short, using our current understanding, Lorentz and others had unknowingly changed the scenario into one which assumed as if the experiment was being looked at by some stationary space observer who was looking at the apparatus moving at speed of '$$v$$' relative to him. For such an observer, length contraction in the direction of motion is definitely required. The stationary space observer would also notice time dilation for the frame of reference of apparatus.

Do I make any sense?

• Where did you read or hear that "length contraction in the longitudinal arm is required to explain the null result"? Of course, that's what those who believed in ether thought over a century ago, but I don't know why anyone would think that now. Jan 16 at 12:33