The physics of space and time I: The description of rulers and clocks in uniform translational motion by Galilean or Lorentz transformations
arXiv:physics/0612039
Abstract
A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean or Lorentz transformations is then studied using new, simple, and practical clock synchronisation procedures. It is found that measured length intervals are Lorentz invariant, whereas moving clocks show a universal time dilatation effect. The `relativistic length contraction' and `relativity of simultaneity' effects of conventional special relativity theory are shown to be the consequence of calculational error. Two derivations of the Lorentz transformation from simple postulates, without reference to electrodynamics or any other dynamical theory, are reviewed in an appendix.
43 pages, 12 figures, 2 tables. v2 Primary and reciprocal experiments discussed and improved Lorentz transformation derivation. 3 figures removed, references updated. v3 typos and LT derivation corrected. v4 typos removed, small text improvements, references updated