Chapter 11
A Clock Paradox
The Einsteinian theory of relativity is based on the fact that the speed of light is
a natural constant and thus has the same value in any arbitrary inertial system,
c L = 299 792 458 m/s. According to Einstein’s Special Relativity one and the same
Maxwellian equations are applicable for all inertial systems. We measure this velocity for every signal sent out from a light source. It makes no difference if we remain
relatively at rest to the light source or if we move with the velocity v towards or away
from the wavefront of the light signal. For the unprepared reader, these somewhat
unbelievable facts are just as unbelievingly explained by Einstein’s Special Relativity: The moving clock goes behind and the moving measuring-rod is contracted. In
detail, this means: We construct a number of identical clocks. A few of these are
distributed and synchronised in order to obtain a perfect timing along the x-axis. We
now take one of the remaining clocks and move it with a constant velocity v along
the line of the distributed clocks. If we compare the hand setting t
of the moving
clock to the hand setting t of the stationary clock at the moment it passes by, we
see that t
= t
1 − v 2 /c
2
L where we assumed t = t
= 0 at x = x
= 0. This is
what Einstein’s theory of relativity states. The hand of the moving clock goes behind.
The only physical parameter in this equation is the speed of light c L , which is an
absolute natural constant. It, thus, makes no difference what type of clock we use in
the experiment to prove this equation, as long as our methods of measurement are
exact enough. In such an experiment, we should, if we move an old golden pocket
watch with the velocity v or an atomic caesium clock, always exactly determine the
factor
1 − v 2 /c
2
L . The rules for the construction of a clock do not appear in the
equation for time dilatation.
1
1 Clocks that are driven on by gravity, i.e. pendulum clocks, egg timers, water clocks, etc., have
to be excluded in such experiments. We expressed that we intended to ignore gravity because
© 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_11
107
A Clock Paradox
The Einsteinian theory of relativity is based on the fact that the speed of light is
a natural constant and thus has the same value in any arbitrary inertial system,
c L = 299 792 458 m/s. According to Einstein’s Special Relativity one and the same
Maxwellian equations are applicable for all inertial systems. We measure this velocity for every signal sent out from a light source. It makes no difference if we remain
relatively at rest to the light source or if we move with the velocity v towards or away
from the wavefront of the light signal. For the unprepared reader, these somewhat
unbelievable facts are just as unbelievingly explained by Einstein’s Special Relativity: The moving clock goes behind and the moving measuring-rod is contracted. In
detail, this means: We construct a number of identical clocks. A few of these are
distributed and synchronised in order to obtain a perfect timing along the x-axis. We
now take one of the remaining clocks and move it with a constant velocity v along
the line of the distributed clocks. If we compare the hand setting t
of the moving
clock to the hand setting t of the stationary clock at the moment it passes by, we
see that t
= t
1 − v 2 /c
2
L where we assumed t = t
= 0 at x = x
= 0. This is
what Einstein’s theory of relativity states. The hand of the moving clock goes behind.
The only physical parameter in this equation is the speed of light c L , which is an
absolute natural constant. It, thus, makes no difference what type of clock we use in
the experiment to prove this equation, as long as our methods of measurement are
exact enough. In such an experiment, we should, if we move an old golden pocket
watch with the velocity v or an atomic caesium clock, always exactly determine the
factor
1 − v 2 /c
2
L . The rules for the construction of a clock do not appear in the
equation for time dilatation.
1
1 Clocks that are driven on by gravity, i.e. pendulum clocks, egg timers, water clocks, etc., have
to be excluded in such experiments. We expressed that we intended to ignore gravity because
© 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_11
107