  Since the conventionality thesis rests upon the existence of a fastest causal signal, the existence of arbitrarily fast causal signals would undermine the thesis. If we leave aside the question of causality, for the moment, the possibility of particles (called tachyons) moving with arbitrarily high velocities is consistent with the mathematical formalism of special relativity (see, for example, Feinberg 1967). Just as the speed of light in vacuum is an upper limit to the possible speeds of ordinary particles (sometimes called bradyons), it would be a lower limit to the speeds of tachyons. When a transformation is made to a different inertial frame of reference, the speeds of both bradyons and tachyons change (the speed of light in vacuum being the only invariant speed). At any instant, the speed of a bradyon can be transformed to zero and the speed of a tachyon can be transformed to an infinite value. The statement that a bradyon is moving forward in time remains true in every inertial frame (if it is true in one), but this is not so for tachyons. Feinberg (1967) argues that this does not lead to violations of causality through the exchange of tachyons between two uniformly moving observers because of ambiguities in the interpretation of the behavior of tachyon emitters and absorbers, whose roles can change from one to the other under the transformation between inertial frames. He claims to resolve putative causal anomalies by adopting the convention that each observer describes the motion of each tachyon interacting with that observer’s apparatus in such a way as to make the tachyon move forward in time. However, all of Feinberg’s examples involve motion in only one spatial dimension. Pirani (1970) has given an explicit two-dimensional example in which Feinberg’s convention is satisfied but a tachyon signal is emitted by an observer and returned to that observer at an earlier time, thus leading to possible causal anomalies.