21 Violation of Relativity—The Rediscovered Crystal
233
theory of so-called Uralternatives. In his essay, ‘Matter, Energy, Information’, C. F.
v. Weizsäcker [98] writes ‘All forms consist of combinations of the last simple
alternatives. …Matter is form. Today we understand matter as elementary particles.
These are constructed from Uralternatives. Uralternatives are the last elements of
real forms. …According to the simplest model of a massive particle, its restmass is
the number of Uralternatives needed to construct a particle at rest’.…
It is a fact that a dislocation in a crystal is indeed nothing other than a succession of
decisions concerning the occupation of a possible lattice position with atoms. These
are the last elements of possible forms, i.e. C. F. v. Weizsäcker’s Uralternatives. In
line with this, we can calculate, in Chap. 23, an expression using Eq. (299) for the
inertial mass m a of a dislocation along the length a of a lattice parameter. Kröner’s
[50] hypothesis on the inertial mass of a dislocation finds in C. F. v. Weizsäcker’s
analysis its philosophical confirmation. Our general equation of motion (79) for
dislocations can thus be seen from a more general standpoint and is thus better
founded.
Let us consider a kink on a dislocation line, the change of a dislocation line from
one potential minimum to the neighbouring, our solution q
I of the sine-Gordon equation, cf. (111) . Such a kink is nothing other than a sequence of decisions concerning
the occupation of possible lattice positions, the last element of possible forms for the
dislocation line. Hence, the inertial mass m o of a kink relative to the crystal lattice is
a direct consequence of C. F. v. Weizsäcker’s theory of Uralternatives. In Chap. 23,
see Eqs. (296) and (300), we will calculate this inertial mass m o and prove that the
kink does in fact possess all properties of a relativistic particle with respect to the
crystal lattice.
In Chap. 8, we used Newton’s axiomatics to explain the motion of dislocations
relative to the crystal lattice and thus actually discovered the sine-Gordon equation. Dislocations, the ‘linear mispositioning of the ideal lattice’, possess Newtonian
inertia with respect to the lattice. If we therefore consider agglomerates of such mispositioning, or parts of these that represent the objects, the ‘particles’ of the internal
observers, then these also possess inertia with respect to the lattice. If one takes
the elastic deformations, which originate from such dislocation structures, into consideration, then one can calculate that these structures actually generate forces that
energetically influence one another, with the aim of reaching a minimum energy state.
These forces are called configurational forces in the field of continuum mechanics
and can be calculated according to a general law found by J. D. Eshelby [19].
One can also construct, in the boundaries of our model assumptions for internal
observers, equations of motion for the particles of the internal observers. We do not
however intend here on going into the details and problems of such equations of
motion. However, no matter how such equations of motion may look like in detail,
they will be, in the boundaries of our model assumptions, differential equations of
such a type that the motion of a single kink, for example under the influence of
a stress field of other surrounding dislocation structures, would satisfy a certain
path-time law, just as we could exactly calculate the trajectory of a stone thrown up
into the air. We can calculate the position of any particle at any point of time if we
know sufficiently exact the initial conditions. Here, we inevitably get caught up in the
233
theory of so-called Uralternatives. In his essay, ‘Matter, Energy, Information’, C. F.
v. Weizsäcker [98] writes ‘All forms consist of combinations of the last simple
alternatives. …Matter is form. Today we understand matter as elementary particles.
These are constructed from Uralternatives. Uralternatives are the last elements of
real forms. …According to the simplest model of a massive particle, its restmass is
the number of Uralternatives needed to construct a particle at rest’.…
It is a fact that a dislocation in a crystal is indeed nothing other than a succession of
decisions concerning the occupation of a possible lattice position with atoms. These
are the last elements of possible forms, i.e. C. F. v. Weizsäcker’s Uralternatives. In
line with this, we can calculate, in Chap. 23, an expression using Eq. (299) for the
inertial mass m a of a dislocation along the length a of a lattice parameter. Kröner’s
[50] hypothesis on the inertial mass of a dislocation finds in C. F. v. Weizsäcker’s
analysis its philosophical confirmation. Our general equation of motion (79) for
dislocations can thus be seen from a more general standpoint and is thus better
founded.
Let us consider a kink on a dislocation line, the change of a dislocation line from
one potential minimum to the neighbouring, our solution q
I of the sine-Gordon equation, cf. (111) . Such a kink is nothing other than a sequence of decisions concerning
the occupation of possible lattice positions, the last element of possible forms for the
dislocation line. Hence, the inertial mass m o of a kink relative to the crystal lattice is
a direct consequence of C. F. v. Weizsäcker’s theory of Uralternatives. In Chap. 23,
see Eqs. (296) and (300), we will calculate this inertial mass m o and prove that the
kink does in fact possess all properties of a relativistic particle with respect to the
crystal lattice.
In Chap. 8, we used Newton’s axiomatics to explain the motion of dislocations
relative to the crystal lattice and thus actually discovered the sine-Gordon equation. Dislocations, the ‘linear mispositioning of the ideal lattice’, possess Newtonian
inertia with respect to the lattice. If we therefore consider agglomerates of such mispositioning, or parts of these that represent the objects, the ‘particles’ of the internal
observers, then these also possess inertia with respect to the lattice. If one takes
the elastic deformations, which originate from such dislocation structures, into consideration, then one can calculate that these structures actually generate forces that
energetically influence one another, with the aim of reaching a minimum energy state.
These forces are called configurational forces in the field of continuum mechanics
and can be calculated according to a general law found by J. D. Eshelby [19].
One can also construct, in the boundaries of our model assumptions for internal
observers, equations of motion for the particles of the internal observers. We do not
however intend here on going into the details and problems of such equations of
motion. However, no matter how such equations of motion may look like in detail,
they will be, in the boundaries of our model assumptions, differential equations of
such a type that the motion of a single kink, for example under the influence of
a stress field of other surrounding dislocation structures, would satisfy a certain
path-time law, just as we could exactly calculate the trajectory of a stone thrown up
into the air. We can calculate the position of any particle at any point of time if we
know sufficiently exact the initial conditions. Here, we inevitably get caught up in the