Well that's exactly what will happen when anything moves faster than light, it will travel backwards in time. The real question is where is it getting infinite energy to break the light barrier? or are neutrinos the only particles with mass that will not be dragged by the Higgs field?

He said a new particle though. So something other than the neutrinos themselves, I suppose?

It was a neutrino that was discovered moving faster than light at CERN, that is what I was referring to. Tyson also mentioned that it is likely a special type of neutrino already moving faster than light is the one being observed (tachyons). What they think we are seeing is a particle that has been moving faster than light but never accelerated to reach that speed, it has been moving at that velocity all the way since before the beginning of time itself.

A particle moving backwards through time === a particle moving faster than what we have currently established to be the speed of light

My understanding is that it isn't necessarily moving faster but is cheating by moving through a dimension that we can't even draw.

Feynman had particles moving backwards through time as an explanation for something. I'm not sure if he was being totally serious, or using it as an idea to move theory forward.

Anti-particles.