Here, we will take a completely different approach in formulating the Special
Theory of Relativity. We will specifically abandon the process of accepting a priori
the validity of any abstract physical principle of the likes of EINSTEIN’S principle. In
opposition to traditional representations of Special Relativity, we at first suppose a
preferred reference system for our observations, and we ask what happens if
measuring-rods and clocks are moving with respect to this system.
Nevertheless, if we want to arrive at the covariant relativistic formalism, we
cannot however continue without a certain principle of relativity. We need a rule or
a regulation to be able to synchronise clocks in a moving frame after this has been
done in a supposed preferred ‘static’ system. It is a most simple and not in the least
controversial principle that we use for this, the so-called reciprocity principle, an
elementary principle of relativity, as we will see it that anticipated should sound
like:
If you observe that I have the velocity v, then I observe that you have velocity – v.
We demand no more and no less of relativity. The original paper deriving
EINSTEIN’S Special Theory of Relativity along these lines is published in GÜNTHER
[31]. The axiomatic system we use is without any restraint equivalent to the
axiomatic system used by EINSTEIN. In Chap. 16, we will show a comparable
representation of the different axiomatic approaches to the Special Theory of
Relativity. Here too, we will state that our method is in fact just a continuation
of the old ideas of H. A. LORENTZ.
However, we want to continue. We want to understand how it can happen that
measuring-rods change their length and clocks change their pace? Which familiar
and for us comprehensible processes can cause such phenomena? In order to answer
this question, we are looking for a physical model, a ‘miniatur’ of the Special
Theory of Relativity’ which should be present in reality.
To this end, we will concentrate on using the laws of NEWTONian mechanics on
the lattice structure of matter. We will ask ourselves the following question: How
can we measure spatial distances and time differences in a lattice if we exclusively
use geometrical objects that physically exist in this lattice? Such physical objects
that come into question are dislocations. These dislocations can be found in great
measure inside of a crystal. Firstly, we search for those physically stabile forms of a
dislocation that will be able to provide us with a measure of length. We then
secondly continue our search for a stabile oscillating dislocation that will provide us
with an oscillation period for a clock. This can be achieved using the so-called
sine-GORDON equation, for which we can give a most simple physical explanation.
We will discover, building on this procedure, one relativistic effect after another,
and at the end, we will arrive at the principle of the universal constancy of critical
signal velocity, which is itself defined in a lattice.
With other words, the ideal space lattice represents our model for the vacuum,
whereas certain local deviations from the ideal structure existing in this lattice
(configurations of dislocations in the crystal) possess those inertial masses with
respect to the lattice whose motions within certain boundaries of validity lead to the
vi
Preface
Theory of Relativity. We will specifically abandon the process of accepting a priori
the validity of any abstract physical principle of the likes of EINSTEIN’S principle. In
opposition to traditional representations of Special Relativity, we at first suppose a
preferred reference system for our observations, and we ask what happens if
measuring-rods and clocks are moving with respect to this system.
Nevertheless, if we want to arrive at the covariant relativistic formalism, we
cannot however continue without a certain principle of relativity. We need a rule or
a regulation to be able to synchronise clocks in a moving frame after this has been
done in a supposed preferred ‘static’ system. It is a most simple and not in the least
controversial principle that we use for this, the so-called reciprocity principle, an
elementary principle of relativity, as we will see it that anticipated should sound
like:
If you observe that I have the velocity v, then I observe that you have velocity – v.
We demand no more and no less of relativity. The original paper deriving
EINSTEIN’S Special Theory of Relativity along these lines is published in GÜNTHER
[31]. The axiomatic system we use is without any restraint equivalent to the
axiomatic system used by EINSTEIN. In Chap. 16, we will show a comparable
representation of the different axiomatic approaches to the Special Theory of
Relativity. Here too, we will state that our method is in fact just a continuation
of the old ideas of H. A. LORENTZ.
However, we want to continue. We want to understand how it can happen that
measuring-rods change their length and clocks change their pace? Which familiar
and for us comprehensible processes can cause such phenomena? In order to answer
this question, we are looking for a physical model, a ‘miniatur’ of the Special
Theory of Relativity’ which should be present in reality.
To this end, we will concentrate on using the laws of NEWTONian mechanics on
the lattice structure of matter. We will ask ourselves the following question: How
can we measure spatial distances and time differences in a lattice if we exclusively
use geometrical objects that physically exist in this lattice? Such physical objects
that come into question are dislocations. These dislocations can be found in great
measure inside of a crystal. Firstly, we search for those physically stabile forms of a
dislocation that will be able to provide us with a measure of length. We then
secondly continue our search for a stabile oscillating dislocation that will provide us
with an oscillation period for a clock. This can be achieved using the so-called
sine-GORDON equation, for which we can give a most simple physical explanation.
We will discover, building on this procedure, one relativistic effect after another,
and at the end, we will arrive at the principle of the universal constancy of critical
signal velocity, which is itself defined in a lattice.
With other words, the ideal space lattice represents our model for the vacuum,
whereas certain local deviations from the ideal structure existing in this lattice
(configurations of dislocations in the crystal) possess those inertial masses with
respect to the lattice whose motions within certain boundaries of validity lead to the
vi
Preface