29 Tachyons of Plastic Deformation
321
ically, the dependency of x and t in the solution q
T
(x, t) follows simply from
an adapted Lorentz transformation of the time coordinate, thus arises from a state
of simultaneity in a special frame. Physically, such a dislocation motion results in
this special frame by a simultaneous sounding along the complete dislocation line.
For the plastic tachyon, which we external experimenters observe in our laboratory,
e.g. as q
T
∞ (t), the internal observer registers a velocity u = −c
2
o /V from out of a
reference system, opposite to the laboratory, moving with the velocity +V . Because
the momentum P of the tachyon remains positive, if we started from solution (435)
with a positive momentum parameter m
T
∗ , the internal observer states, referring to
the tachyon, that it ‘moves into the past’. Another internal observer moving with
the velocity −V , observes the velocity u = +c
2
o /V for the same tachyon. For both
observers, the elements of the plastic deformation, which move the dislocation from
one potential barrier to the neighbouring, occur in reverse timed order. For the first
observer the procedure with the larger space coordinates occur first, for the second
those with the smaller coordinates occur first. Important is that both solutions of
the internal observers occur according to a corresponding Lorentz transformation
won from q
T
∞ (t), and that these physical solutions also exist for us in the laboratory.
What remains of the ‘tachyon moving into the past’, as registered by some internal observers in certain reference systems, for the external experimenter? The latter
registers not only a simultaneous gliding of the complete line of dislocation from
one potential barrier to the neighbouring, but also such motions where the dislocation elements with positive x-coordinates move ahead faster, and other motions
where those with negative x-coordinates are faster. All three motions are based, for
us observing from the outside, on a simultaneous sounding of the lattice and not on a
localised sounding, whose results would lead us to expect particle solutions of type
(a). In order to mathematically find the formation of the various solutions, we need
to incorporate the external forces F A into our starting equation (79), as done in (53).
This results in an additive stress term on the right hand side of the sine-Gordon equation. The propagation of a localised sounding, the transmission of a signal remains
the privilege of type (a) particles. We can therefore state:
Plastic tachyons cannot transmit signals inside of a crystal.
These situations leads us, in our considerations on tachyons, to ask the question about
the possibility, according to the laws of mechanics, of a collision between a ‘normal’
particle and a tachyon, so that the particle either transfers energy to the tachyon,
or receives energy from it. Only in such a case would it be principally possible to
use a tachyon to transmit a signal or message with its own, extremely large velocity
|u| > c o . We will come back to this question during our discussion on the problems
of causality in the next chapter.
321
ically, the dependency of x and t in the solution q
T
(x, t) follows simply from
an adapted Lorentz transformation of the time coordinate, thus arises from a state
of simultaneity in a special frame. Physically, such a dislocation motion results in
this special frame by a simultaneous sounding along the complete dislocation line.
For the plastic tachyon, which we external experimenters observe in our laboratory,
e.g. as q
T
∞ (t), the internal observer registers a velocity u = −c
2
o /V from out of a
reference system, opposite to the laboratory, moving with the velocity +V . Because
the momentum P of the tachyon remains positive, if we started from solution (435)
with a positive momentum parameter m
T
∗ , the internal observer states, referring to
the tachyon, that it ‘moves into the past’. Another internal observer moving with
the velocity −V , observes the velocity u = +c
2
o /V for the same tachyon. For both
observers, the elements of the plastic deformation, which move the dislocation from
one potential barrier to the neighbouring, occur in reverse timed order. For the first
observer the procedure with the larger space coordinates occur first, for the second
those with the smaller coordinates occur first. Important is that both solutions of
the internal observers occur according to a corresponding Lorentz transformation
won from q
T
∞ (t), and that these physical solutions also exist for us in the laboratory.
What remains of the ‘tachyon moving into the past’, as registered by some internal observers in certain reference systems, for the external experimenter? The latter
registers not only a simultaneous gliding of the complete line of dislocation from
one potential barrier to the neighbouring, but also such motions where the dislocation elements with positive x-coordinates move ahead faster, and other motions
where those with negative x-coordinates are faster. All three motions are based, for
us observing from the outside, on a simultaneous sounding of the lattice and not on a
localised sounding, whose results would lead us to expect particle solutions of type
(a). In order to mathematically find the formation of the various solutions, we need
to incorporate the external forces F A into our starting equation (79), as done in (53).
This results in an additive stress term on the right hand side of the sine-Gordon equation. The propagation of a localised sounding, the transmission of a signal remains
the privilege of type (a) particles. We can therefore state:
Plastic tachyons cannot transmit signals inside of a crystal.
These situations leads us, in our considerations on tachyons, to ask the question about
the possibility, according to the laws of mechanics, of a collision between a ‘normal’
particle and a tachyon, so that the particle either transfers energy to the tachyon,
or receives energy from it. Only in such a case would it be principally possible to
use a tachyon to transmit a signal or message with its own, extremely large velocity
|u| > c o . We will come back to this question during our discussion on the problems
of causality in the next chapter.