124
12 The Measurement of the Critical Velocity
omnipresent. Such a description is mathematically consistent, however when examined more closely, collides with our conception of the world and can be falsified
experimentally.
As quoted above, the criticism of the opinion of an absolute, a proiri given, reference system independent simultaneity as promoted by Newton’s theory of gravitation
was undertaken by H. Poincaré [73, 74] in 1898. A quantitative definition for simultaneity is found for the first time in Einstein’s [14, 15] paper from 1905. Here, the
relativity of simultaneity is a consequence of the principle of the universal constancy of the critical velocity (there the speed of light c L ) including the definition of
simultaneity with the help of this principle,
3 cf. also our discussion in Chap. 16. We
however have taken an alternative way and receive the same result as a consequence
of the Lorentz contraction and time dilatation of measuring-rods and clocks, respectively, that move with respect to the preferred frame o and under the condition of
our elementary principle of relativity which enables a synchronisation of clocks in
the moving reference systems
. This synchronisation makes easier a comparison
of velocities in the different reference systems. Nevertheless, nobody can force us to
apply even thus method for synchronisation of clocks in the ‘moving’ frames
.
Due to the fact that the consequences arising from the synchronisation of clocks
according to our elementary principle of relativity in connection with the time dilatation of moving clocks and the Lorentz contraction of moving lengths are so fundamental for our lines of thought, we once again want to stray a little.
If we just ignore our elementary principle of relativity we could following Poincaré
choose a different rule by which we could start our clocks in
. This could be for
example the following:
We once again consider the point of time t = 0, defined in our preferred frame o
by the positions of the ‘static’ clocks. In
, we distribute sufficiently many ‘moving’
clocks. We start all of these clocks at the position t
= 0 when they meet the static
clocks of o , which also have the hand setting t = 0, as illustrated in Fig. 12.8.
Then, by definition, two events that take place simultaneously in o also take place
simultaneously in the moving reference system
. Our need for simultaneity would
thus be fulfilled. The
clocks still underlie the principle of time dilatation, so that
admittedly at t = 0 in o all clocks including the ones in
would show t
= 0.
However, for an arbitrary point of time t, t
= γ t is valid. If we insert x − vt in
place of x according to (130) into Eq. (113a), then we get the coordinates x
=
(x − v t)/γ. We thus receive as a total, including the inversion,
3 The correction of, Newton’s theory of gravitation could not be achieved just by taking this fact
into consideration. The consistent incorporation of universal gravitation in physics throws up new
fundamental questions which were answered by, A. Einstein’s General Theory of Relativity from
1915. The measurable effects of this theory are under ‘earthly conditions’ relatively minute. The
depiction of special relativistic phenomena allows us to drop the premise of gravitation. This we
have done throughout this book.
12 The Measurement of the Critical Velocity
omnipresent. Such a description is mathematically consistent, however when examined more closely, collides with our conception of the world and can be falsified
experimentally.
As quoted above, the criticism of the opinion of an absolute, a proiri given, reference system independent simultaneity as promoted by Newton’s theory of gravitation
was undertaken by H. Poincaré [73, 74] in 1898. A quantitative definition for simultaneity is found for the first time in Einstein’s [14, 15] paper from 1905. Here, the
relativity of simultaneity is a consequence of the principle of the universal constancy of the critical velocity (there the speed of light c L ) including the definition of
simultaneity with the help of this principle,
3 cf. also our discussion in Chap. 16. We
however have taken an alternative way and receive the same result as a consequence
of the Lorentz contraction and time dilatation of measuring-rods and clocks, respectively, that move with respect to the preferred frame o and under the condition of
our elementary principle of relativity which enables a synchronisation of clocks in
the moving reference systems
. This synchronisation makes easier a comparison
of velocities in the different reference systems. Nevertheless, nobody can force us to
apply even thus method for synchronisation of clocks in the ‘moving’ frames
.
Due to the fact that the consequences arising from the synchronisation of clocks
according to our elementary principle of relativity in connection with the time dilatation of moving clocks and the Lorentz contraction of moving lengths are so fundamental for our lines of thought, we once again want to stray a little.
If we just ignore our elementary principle of relativity we could following Poincaré
choose a different rule by which we could start our clocks in
. This could be for
example the following:
We once again consider the point of time t = 0, defined in our preferred frame o
by the positions of the ‘static’ clocks. In
, we distribute sufficiently many ‘moving’
clocks. We start all of these clocks at the position t
= 0 when they meet the static
clocks of o , which also have the hand setting t = 0, as illustrated in Fig. 12.8.
Then, by definition, two events that take place simultaneously in o also take place
simultaneously in the moving reference system
. Our need for simultaneity would
thus be fulfilled. The
clocks still underlie the principle of time dilatation, so that
admittedly at t = 0 in o all clocks including the ones in
would show t
= 0.
However, for an arbitrary point of time t, t
= γ t is valid. If we insert x − vt in
place of x according to (130) into Eq. (113a), then we get the coordinates x
=
(x − v t)/γ. We thus receive as a total, including the inversion,
3 The correction of, Newton’s theory of gravitation could not be achieved just by taking this fact
into consideration. The consistent incorporation of universal gravitation in physics throws up new
fundamental questions which were answered by, A. Einstein’s General Theory of Relativity from
1915. The measurable effects of this theory are under ‘earthly conditions’ relatively minute. The
depiction of special relativistic phenomena allows us to drop the premise of gravitation. This we
have done throughout this book.