28 Particles and Tachyons
309
space-like vectors with the consequence of a preferred frame in which now the time
component disappears. In our one-dimensional Special Theory of Relativity, only
one single component of the preferred space-like momentum vector P
T
∞ remains,
where we discovered P
T
∞ = m
T
+ c o in (425a). Due to the fact that c o is a constant, the
spatial vector property is completely transferred to m
T
∗ . In our one-dimensional case
only the change of the sign would remain after an inversion according to (433). For
a detailed explanation of the mathematics of Minkowski space, we refer the reader to
A. Papapetrou [99], A. P. French [23]. The mathematical treatment of tachyons in
the framework of Minkowski space can be found in D. E. Liebscher [57].
Up to now, we have only shown that tachyons are compatible with the principles
of the Special Theory of Relativity, and how these can be fitted into the general frame
of this theory. If tachyons actually exist, and if their existence leads to experimentally
proven consequences, then nothing has of yet been said. Only then when we are able
to say more about this question, will we concern ourselves with the causality problem
which is inevitably thrown up in the light of tachyons.
309
space-like vectors with the consequence of a preferred frame in which now the time
component disappears. In our one-dimensional Special Theory of Relativity, only
one single component of the preferred space-like momentum vector P
T
∞ remains,
where we discovered P
T
∞ = m
T
+ c o in (425a). Due to the fact that c o is a constant, the
spatial vector property is completely transferred to m
T
∗ . In our one-dimensional case
only the change of the sign would remain after an inversion according to (433). For
a detailed explanation of the mathematics of Minkowski space, we refer the reader to
A. Papapetrou [99], A. P. French [23]. The mathematical treatment of tachyons in
the framework of Minkowski space can be found in D. E. Liebscher [57].
Up to now, we have only shown that tachyons are compatible with the principles
of the Special Theory of Relativity, and how these can be fitted into the general frame
of this theory. If tachyons actually exist, and if their existence leads to experimentally
proven consequences, then nothing has of yet been said. Only then when we are able
to say more about this question, will we concern ourselves with the causality problem
which is inevitably thrown up in the light of tachyons.