Chapter 20
Tachyons and Causality
For the first part of this chapter, we will keep the Einsteinian Special Theory of Relativity with its critical velocity, the speed of light c L . In ‘A Supplement to the Oxford
English Dictionary’, (vol.VI, Oxford 1986) the tachyon is explained as ‘A hypothetical particle that travels faster than light and has imaginary mass’. We however know
that no particle can ever be accelerated to the speed of light. If we accelerate a particle
moving with a velocity v < c L in the frame o , then all we actually do is to give
the particle a velocity v in its actual rest system
during a short time interval
t. According to the composition of velocities (194) (with c L in place of c o for the
outside observer), the velocities v and v result in the velocity w observed in o ,
with which the particle moves after having being accelerated,
w =
v + v
1 + v vv/c
2
L
,
which always is smaller than c L , as one can easily verify. This is true in any case, even
if we repeat this process as often as we wish asserting as much energy as possible
on a particle.
The remaining logical possibility would be that tachyons must move with super
light velocity exclusively, as we have already stated in Chap. 17. However, it is not to
see how to get hold of such particles. And would not the tachyons perhaps moving
with ‘infinite velocity’ through space give us a chance, hereby completely ignoring
the whole Special Theory of Relativity, of carrying out synchronisation of clocks in
an arbitrary frame by ‘instantaneous action’ without making use of any velocity at
all? One other important objection that needs to be clarified will be illustrated by
means of a short detective story.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_20
219
Tachyons and Causality
For the first part of this chapter, we will keep the Einsteinian Special Theory of Relativity with its critical velocity, the speed of light c L . In ‘A Supplement to the Oxford
English Dictionary’, (vol.VI, Oxford 1986) the tachyon is explained as ‘A hypothetical particle that travels faster than light and has imaginary mass’. We however know
that no particle can ever be accelerated to the speed of light. If we accelerate a particle
moving with a velocity v < c L in the frame o , then all we actually do is to give
the particle a velocity v in its actual rest system
during a short time interval
t. According to the composition of velocities (194) (with c L in place of c o for the
outside observer), the velocities v and v result in the velocity w observed in o ,
with which the particle moves after having being accelerated,
w =
v + v
1 + v vv/c
2
L
,
which always is smaller than c L , as one can easily verify. This is true in any case, even
if we repeat this process as often as we wish asserting as much energy as possible
on a particle.
The remaining logical possibility would be that tachyons must move with super
light velocity exclusively, as we have already stated in Chap. 17. However, it is not to
see how to get hold of such particles. And would not the tachyons perhaps moving
with ‘infinite velocity’ through space give us a chance, hereby completely ignoring
the whole Special Theory of Relativity, of carrying out synchronisation of clocks in
an arbitrary frame by ‘instantaneous action’ without making use of any velocity at
all? One other important objection that needs to be clarified will be illustrated by
means of a short detective story.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_20
219