Researchers at the Hong Kong University of Science and Technology claim to have established that time travel is impossible. More specifically, they claim to have established that an individual photon (the smallest unit of light) may not travel faster than the speed of light (introducing the obvious question of how could it if it is light) and that this precludes anything from going backward in time.
Per the article:
"The study, which showed that single photons also obey the speed limit c, confirms Einstein's causality; that is, an effect cannot occur before its cause," the university said.
The findings have been published in the U.S. peer reviewed journal, Physical Review Letters.
But with god nothing is impossible...
In this experiment there's a medium which delays some parts of a wave packet and speeds up others at the same time (like here in 2000). The conclusion seems to be that a lens made out of this material cannot be used to look into the future.
As unfortunate as this is, our current time travel technology is not affected: we can still use high velocity to go to the future and maybe wormholes etc. to come back.