Well, we have (virtual) particles that can travel backwards in time, without breaking causality. There's no proof that Tachyons exist, they are purely hypothetical, but they are not outright nonsense.
> from https://news.ycombinator.com/item?id=35877402#35886041 : "EM Wave Polarization Transductions" Lt. Col. T.E Bearden (1999) :
>> Physical observation (via the transverse photon interaction) is the process given by applying the operator ∂/∂t to (L^3)t, yielding an L3 output
[and "time-polarized photons"]