Meanwhile, Fitzgerald (1893) and Lorentz (1895) independently put forward explanation to account for the negative results of the Michelson-Morley experiment. The experimenters had in fact tried to make two rays of light travel simultaneously to and fro over two courses of equal length. Without losing anything of the essence of the experiment, we may imagine that the lengths of the two courses had been measured or compared by ordinary measuring rods-footrules, if we like. How was it known, Fitzgerald and Lorentz asked, that these rods, or the course laid out by them, retained their exact length while they were moving forward through a sea of ether? They argued that if the measuring rod, when it moves, undergoes a contraction in length, it would not be possible for us to comprehend the effect of ether on the velocity of light. Thus, if the apparatus used by Michelson and Morley contracted in the same way, the up-and-down stream course would always be shorter than the cross-stream course. This reduction of length would do something to compensate for the other disadvantages of the up-and-down stream course. A contraction of exactly the right amount would compensate for them completely, so that this and the cross-stream course would require precisely equal times. In this way, Fitzgerald and Lorentz suggested, it might be possible to account for the nil result of the experiment.

The idea was not wholly fanciful or hypothetical, for Lorentz showed very shortly afterwards in his mathematical transformations that if a body moves with a velocity comparable to the velocity of light, it would experience a considerable contraction in length in the direction of the motion.^{[1]}

Lorentz, in his mathematical transformation, also showed that when a system moves, a contraction occurs in the time-dimension too. This not only explained, fully and completely, why the Michelson-Morley experiment had failed, but it further showed that every material measuring rod would necessarily contract just sufficiently to conceal the earth's motion through the ether, so that all similar experiments, were doomed to failure in advance. But other types of measuring rods are known to science; beams of light, electric forces, and so on, can be made to span the distances from point to point, and so provide the means for measuring distances. It was thought that where material measuring rods had failed, optical and electrical measuring rods might succeed. The trial was made, repeatedly and in many forms-the names of the late Lord Rayleigh, of Brace and of Trouton are eminent in this connection. And every time it failed. If the earth had a speed x through the ether, every apparatus that the wit of man could devise confused the measurement of x by adding a spurious speed exactly equal to-x, and so reiterating the apparent zero answer of the original Michelson-Morley experiment.^{[2]}

Thus, the upshot of many years arduous experimenting was that the scientists failed to detect the earth's motion through the ether.

Conclusively, "Every rigid body appears to have maximum dimensions when at rest relative to the observer. Its dimensions appear to be contracted in the direction of relative motion by the factor {{7c902d58c30f51ee3a2ebfb6320b44796b041676}} when it moves with velocity v relative to the observer."

This fact can be stated by the following equation. If.h = length of measuring rod at rest,

l

_{2}= length of measuring rod in motion,

v = velocity of moving rod,

c = velocity of light (which is nearly 186000 miles per second), and

t = time taken by body travelling with velocity,

then,

{{489bc7d38d2994dfa51bd22a0876e6b2025b8364}}

**Problem.**

A rod has length 1 metre. When the rod is in a satellite moving with velocity 0.8 c relative to laboratory, what is the length of the rod as determined by an observer (a) in the satellite and (b) in the laboratory?

**Solution**

- The observer in the satellite is at rest relative to the rod, therefore the length of the rod as measured by an observer in the satellite is 1 meter,
- The length of the rod in the laboratory is given by

{{90c604f5a928ba3eb4d7d7454fdb4e8d1e82fefa}}

_{0}= 1 metre, v = 0.8c, therefore

{{2ca5386b02554d6b4f4cbb4eb0c15b5014838348}}It is obvious that when v is negligible in comparison to c, 12 will be nearly equal to h; but when v is comparable to c, 12 will be much less than h.{{85aca4ea3e64907c8b4b9a06bb598bd69984c36c}}