Making use of the principle of relativity prove that the lateral dimensions of an object do not change with a change in the reference frame.

Answer

Hint. Compare the dimensions of the rod and of the hole which at rest are precisely the same.

Explanation

Suppose that in the course of motion with respect to some frame of refrence the lateral dimensions of a body change, for instance, become smaller. Let there be a close fit of the rod and the hole in

the board in some reference frame (Fig. 6.1a). Now fix the reference frame to Xhe board and let the rod uove in it (Fig. 6.1b). Then, according to our assumption about the decrease in the lateral dimen- sions, thc rod wlll pass freely through the hole. If we fix the reference frame to the rod, the dimensions of the hole will, according to our assumption, decrease, and the rod will be unable to pass through it (Pig. 6.1c). The resulting .contradiction proves the assumption about the decrease in the lateral dimensions to he wrong. The result follows from the Lorentz transformations.