Space and time in special relativity

In this review of the kinematic part of Einstein’s Theory of Special Relativity, the physical meaning of the Lorentz Transformations is elucidated from basic physical facts that, although implicit in the formulation of the theory, are usually overlooked in literature and textbooks. The consequence of the invariance of $c$ that distinguishes this theory from its classical version is the relativity of simultaneity at a distance that causes time intervals to be frame dependent, space and time being otherwise completely equivalent in different inertial frames. Lorentz Transformations are derived from a graphical representation of the axes of a pair of inertial frames that preserves their equivalence, implied by the Principle of Relativity. Transformations of space and time intervals are analyzed from a perspective wider than the usual. The problems related to the derivation of the time dilation formula using light-clocks and the twin paradox are treated in detail.

Keywords:
Special relativity; Lorentz transformations; length contraction; time dilation; twin paradox