232
21 Violation of Relativity—The Rediscovered Crystal
observer to that of an outside observer, who obviously knows more than his internal
colleague.
It is fascinating to realise that for the internal observer, a kink (or other configurations of dislocations) is an object that possesses energy, that moves through space,
an object that does exactly that what a particle does, a particle with the characteristic
property of individual identity. This individuality is guaranteed by the attribution of
its position described by the space coordinate x at a certain time t. The particle moves
through space according to a well-defined trajectory. We will go into the mathematical details of the physical particle concept for these micro-plastic deformations,
especially for kinks, in Chaps. 22 and 23, see also Günther [37].
The outside observer, who can fixate the crystal and its lattice atoms, sees this
completely differently. This supposed particle, the kink, is nothing other than a certain
structure of missing lattice positions, a quasi-particle as he would state. If this quasiparticle is displaced through the lattice, then what happens is that the same structure
is constructed by other atoms. The outside observer only sees a moving structure.
His individual particles, the lattice atoms, from his point of view, remain stationary
at their original positions. It becomes clear to us that it makes no sense to attribute a
structure an individual identity as the internal observer did.
To illustrate this, we will consider the collision of two kinks which move directly
towards each other with the constant velocity v, just as two balls in snooker would.
This case can be precisely calculated. We however only want to discuss the result
and refer the reader to the calculations made by Seeger [89]. After a certain amount
of time spent by the kinks in rather complicated disorder, a state is achieved in which
both kinks move away from each other, as snooker balls would after a collision. It
would be completely meaningless to ask which of the two kinks move to the right—
as in snooker, the one that came from the right, or the other? Due to the fact that
a structure can be built up from completely different individual lattice atoms, we,
as outside observers, do not see the need to attribute this structure an individuality,
as we do with snooker balls. The internal observer, who has just constructed his
concept of particle individuality, sees this completely differently. Only with difficulty
could he realise that the presumed individuality of his kink is, strictly seen, not
founded on any physical reality, or is at the most founded on a very restricted reality.
The two states—reflection or pass each other—are indistinguishable, because the
‘particles’ are indistinguishable, and they are identical. We remind ourselves that
even in Newton’s mechanics concerning the collision of two particles, such a decision
cannot be made without additional information. Both solutions (51) and (52) are
equally possible.
Maybe this example of kinks in crystals, the ‘particles’ of the internal observer,
is a consolation for those who still cannot accept that even for us ‘outside observers’
the idea of an individual particle cannot be sensibly upheld indefinitely that we also
move into regions, namely if quantum phenomena become relevant, such as for cold
electron and neutron motions for example, where our good old classical idea of
individual particles does not properly reproduce our physical reality.
We will now go one step further and state that we have, with our physics of the
internal observer inside of an infinite crystal, caught ourselves up in v.Weizsäcker’s
21 Violation of Relativity—The Rediscovered Crystal
observer to that of an outside observer, who obviously knows more than his internal
colleague.
It is fascinating to realise that for the internal observer, a kink (or other configurations of dislocations) is an object that possesses energy, that moves through space,
an object that does exactly that what a particle does, a particle with the characteristic
property of individual identity. This individuality is guaranteed by the attribution of
its position described by the space coordinate x at a certain time t. The particle moves
through space according to a well-defined trajectory. We will go into the mathematical details of the physical particle concept for these micro-plastic deformations,
especially for kinks, in Chaps. 22 and 23, see also Günther [37].
The outside observer, who can fixate the crystal and its lattice atoms, sees this
completely differently. This supposed particle, the kink, is nothing other than a certain
structure of missing lattice positions, a quasi-particle as he would state. If this quasiparticle is displaced through the lattice, then what happens is that the same structure
is constructed by other atoms. The outside observer only sees a moving structure.
His individual particles, the lattice atoms, from his point of view, remain stationary
at their original positions. It becomes clear to us that it makes no sense to attribute a
structure an individual identity as the internal observer did.
To illustrate this, we will consider the collision of two kinks which move directly
towards each other with the constant velocity v, just as two balls in snooker would.
This case can be precisely calculated. We however only want to discuss the result
and refer the reader to the calculations made by Seeger [89]. After a certain amount
of time spent by the kinks in rather complicated disorder, a state is achieved in which
both kinks move away from each other, as snooker balls would after a collision. It
would be completely meaningless to ask which of the two kinks move to the right—
as in snooker, the one that came from the right, or the other? Due to the fact that
a structure can be built up from completely different individual lattice atoms, we,
as outside observers, do not see the need to attribute this structure an individuality,
as we do with snooker balls. The internal observer, who has just constructed his
concept of particle individuality, sees this completely differently. Only with difficulty
could he realise that the presumed individuality of his kink is, strictly seen, not
founded on any physical reality, or is at the most founded on a very restricted reality.
The two states—reflection or pass each other—are indistinguishable, because the
‘particles’ are indistinguishable, and they are identical. We remind ourselves that
even in Newton’s mechanics concerning the collision of two particles, such a decision
cannot be made without additional information. Both solutions (51) and (52) are
equally possible.
Maybe this example of kinks in crystals, the ‘particles’ of the internal observer,
is a consolation for those who still cannot accept that even for us ‘outside observers’
the idea of an individual particle cannot be sensibly upheld indefinitely that we also
move into regions, namely if quantum phenomena become relevant, such as for cold
electron and neutron motions for example, where our good old classical idea of
individual particles does not properly reproduce our physical reality.
We will now go one step further and state that we have, with our physics of the
internal observer inside of an infinite crystal, caught ourselves up in v.Weizsäcker’s