In order to establish the geometry of space, it is necessary to give meaning to the distance between two points or, more concretely, to the length of a rigid object. If the object is at rest, there is no difficulty; there is no need to worry about the simultaneity of the events used in the measurement. But when the object whose length is to be measured is moving with respect to the observer who will perform the measurement, care must be taken to guarantee that the events selected at each extremity of the object, in order to calculate the distance between them, occur simultaneously for the observer in question. In classical Physics, time is absolute and, therefore, so is simultaneity. But in Special Relativity, time and simultaneity are concepts that are relative to a given observer. Events that are simultaneous for a first observer are, in general, not simultaneous for a second observer that is moving with respect to the first. This is the origin of length contraction, that is, the fact that an object that is moving will appear contracted in its direction of motion.
Here is the link to the text “Concepts of Special Relativity” in PDF format. Length contraction is analyzed in Chapter 6. As mentioned above, the approach known as k-calculus is adopted, so that length contraction is first derived in terms of Bondi's k factor. The more familiar expression, in terms of the so-called Lorentz factor, is then deduced by using results obtained in Chapter 4 to express the k factor in terms of the relative velocity.
A numerical example of length contraction can be found in Appendix A.4.
In order to understand clearly the concepts and the nomenclature used, it is recommended to begin by reading the first three chapters of the text.
An animation software written in the Java language is available. Length contraction is illustrated by the fifth animation proposed.
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