Exact Results in Quantum Theory

Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This changed with the recent work of Dragan and Ekert, who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM), since they require introducing non-determinism and wave-like behavior at the fundamental level. In fact, both classical and quantum field theory of tachyons have been constructed. Unfortunately, we will show that the latter theory contains several flaws, mostly caused by adapting incorrect results due to other authors, which puts the aforementioned program in question. In particular, unlike Feinberg, we show that tachyon microcausality violation spoils fundamental features of QFT such as statistical independence of distant measurements, and it negatively affects constructing Lorentz invariant scattering theory of tachyons. Moreover, the Feynman propagator, which was adapted from Dhar and Sudarshan, is shown to violate unitarity, the tachyonic vacuum is unstable due to radiatively generated tachyon self-interactions, and an interpolating tachyon field likely does not satisfy the LSZ asymptotic condition. Our analysis indicates that a covariant QFT of tachyons seems impossible, hence superluminal observers are unphysical and cannot be used to derive QM.