Chapter 14
The Linear Approximation of Special
Relativity
As we have seen in the preceding chapters, the physical contents of Special Relativity
shortly can be summarised in this way: We assume Lorentz contraction
1
L
= L o
1 −
v 2
c
2
L
(7)
time dilatation
t
= t
1 −
v 2
c
2
L
(8)
as well as a well defied synchronisation of clocks in a frame o . At the end, this
must be completed by the synchronisation of clocks in the ’moving frames’
. In
principle, this synchronisation is arbitrary and can be described by a synchron function φ(x) = t
(x, 0) . If we introduce absolute simultaneity, we assume a synchron
function φ according to, cf. Fig.12.8,
φ(x) = t
(x, 0) = 0
(153)
with the result of Reichenbach transformation,
x
=
x − vt
γ
,
t
= γ t .
(143)
1 Here, the velocity c stands for the speed of light c L in the case of Special Relativity of our spacetime
and for c o of sine-Gordon equation in the case of our mechanical model.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_14
137