13 The Lorentz Transformation
135
x
= x − v t , t
= t
Galilei transformation
(152)
with the inversion
x = x
+ v t
, t = t
.
(152a)
If one replaces the variables x and t in the Newtonian inertia term m d
2 x(t)/dt
2 , considered here in one space dimension, with the variables x
and t
according to (152a),
then m d
2 x
(t
)/dt
2 follows. The differential equation of Newtonian mechanics has
the same form in all inertial systems. Measuring-rods keep their length; clocks run
synchronically, whether moved or not, if only the critical velocity c o for signal propagation is infinitely large.
Questions linked to ’infinitely large velocities’ will be considered during our
discussion on tachyons and causality in the Chaps. 20 and 28–30.
135
x
= x − v t , t
= t
Galilei transformation
(152)
with the inversion
x = x
+ v t
, t = t
.
(152a)
If one replaces the variables x and t in the Newtonian inertia term m d
2 x(t)/dt
2 , considered here in one space dimension, with the variables x
and t
according to (152a),
then m d
2 x
(t
)/dt
2 follows. The differential equation of Newtonian mechanics has
the same form in all inertial systems. Measuring-rods keep their length; clocks run
synchronically, whether moved or not, if only the critical velocity c o for signal propagation is infinitely large.
Questions linked to ’infinitely large velocities’ will be considered during our
discussion on tachyons and causality in the Chaps. 20 and 28–30.