14 The Linear Approximation of Special Relativity
139
The definition of simultaneity is a matter of convenience. All physical effects
of Special Relativity as Lorentz contraction (7) and time dilatation (8) start with
non-linear terms in v/c . It is a matter of convenience to change the definition of
simultaneity in the linarised Lorentz transformation (154) from (156) to absolute
simultaneity (153) with the result of Galilei transformation (152).
2
2 The linear, in v/c approximation (155) of Lorentz transformation corresponds to the linear, in
v/c approximation of the transformation formula for the so-called four-vector k i normal to an
electromagnetic wave. Notice that also the transformation formula for the Minkowski tensor of
the electromagnetic field has a non-trivial linear, in v/c approximation. Therefore, the linearised
transformation (155) works very well, if we consider wave phenomena as, e.g. aberration, cf. the
footnote on Chap. 19.
139
The definition of simultaneity is a matter of convenience. All physical effects
of Special Relativity as Lorentz contraction (7) and time dilatation (8) start with
non-linear terms in v/c . It is a matter of convenience to change the definition of
simultaneity in the linarised Lorentz transformation (154) from (156) to absolute
simultaneity (153) with the result of Galilei transformation (152).
2
2 The linear, in v/c approximation (155) of Lorentz transformation corresponds to the linear, in
v/c approximation of the transformation formula for the so-called four-vector k i normal to an
electromagnetic wave. Notice that also the transformation formula for the Minkowski tensor of
the electromagnetic field has a non-trivial linear, in v/c approximation. Therefore, the linearised
transformation (155) works very well, if we consider wave phenomena as, e.g. aberration, cf. the
footnote on Chap. 19.