Transverse contractions of moving bodies

One of the most important theoretical consequences of the principle of relativity, i.e. the absence of transverse Lorentz-Fitzgerald contractions in moving bodies, has never been subjected to direct experimental tests. The existing indirect evidence of this absence is discussed, and a simple experiment for testing it directly and with high accuracy is proposed. Some implications of a possible nonnull result of this experiment are also pointed out. (author)