12 The Measurement of the Critical Velocity
131
symmetry, which becomes obviously by synchronising clocks according to the elementary principle of relativity is a little bit hidden here. Nevertheless, it survives due
to the fact that any inertial frame is equally qualified to take the part of the preferred
frame, i.e. in the procedure of absolute simultaneity the reference systems o and
could be replaced by each other. Then the length of a rod resting in
would
be extended as measured from the reference system o . Both situations are indistinguishable, which most easily could be seen with the help of Einstein’s formulation
of SRT. It would be not very useful to formulate the fundamental laws of physics
with the help of an absolute simultaneity.
We were in the physically enviable position of being able to construct measuringrods and clocks as solutions of a physical equation, the sine-Gordon equation, which
made their behaviour calculable. This is obviously a far more simple situation than
that of the physicists at the turn of the century, who faced the question of electrodynamics in moving reference systems. The author counts himself to the mass of those
who draw any conclusions out of the vicious circle of the never-ending debate on
the speed of light, however, not the conclusion that clocks change their pace and that
lengths shorten. Notice that there is no difference in derivation of Special Relativity
for our physical spacetime with c L or for its miniature version in the crystalline solid
with c o . We will return to the axiomatic systems of the Special Theory of Relativity
in Chap. 16.
We will now make it clear for ourselves that all of the consequences of Special
Relativity apply to our crystal without restriction and what this means for every single
case. Of special interest are the circumstances of our mechanically based Special
Relativity, with which we can reach the boundaries of its validity more easily and
that we can get a physical overview of these conditions. In the framework of SRT,
the crazy phenomenon of tachyons arises. We will be able to make simple statements
in our lattice model of relativity in the Chaps. 28–30.
131
symmetry, which becomes obviously by synchronising clocks according to the elementary principle of relativity is a little bit hidden here. Nevertheless, it survives due
to the fact that any inertial frame is equally qualified to take the part of the preferred
frame, i.e. in the procedure of absolute simultaneity the reference systems o and
could be replaced by each other. Then the length of a rod resting in
would
be extended as measured from the reference system o . Both situations are indistinguishable, which most easily could be seen with the help of Einstein’s formulation
of SRT. It would be not very useful to formulate the fundamental laws of physics
with the help of an absolute simultaneity.
We were in the physically enviable position of being able to construct measuringrods and clocks as solutions of a physical equation, the sine-Gordon equation, which
made their behaviour calculable. This is obviously a far more simple situation than
that of the physicists at the turn of the century, who faced the question of electrodynamics in moving reference systems. The author counts himself to the mass of those
who draw any conclusions out of the vicious circle of the never-ending debate on
the speed of light, however, not the conclusion that clocks change their pace and that
lengths shorten. Notice that there is no difference in derivation of Special Relativity
for our physical spacetime with c L or for its miniature version in the crystalline solid
with c o . We will return to the axiomatic systems of the Special Theory of Relativity
in Chap. 16.
We will now make it clear for ourselves that all of the consequences of Special
Relativity apply to our crystal without restriction and what this means for every single
case. Of special interest are the circumstances of our mechanically based Special
Relativity, with which we can reach the boundaries of its validity more easily and
that we can get a physical overview of these conditions. In the framework of SRT,
the crazy phenomenon of tachyons arises. We will be able to make simple statements
in our lattice model of relativity in the Chaps. 28–30.