First, the good news for time travelers. Physicists have long recognized that nothing in the laws of physics specifically forbids time travel. As far as they can tell, these laws don’t care whether time is running forwards or backwards; they work just as well either way.
That recognition has spawned numerous studies, some of them surprisingly serious, to test the limits of causality. In this work, physicists have tried everything from bending the fabric of spacetime to exploiting quantum uncertainty to travel back and forth in time. They have even tested some of these ideas. But nothing seems to work. Indeed, some of the schemes require decidedly unphysical conditions that make them unlikely to ever be tested.
But the keenest enthusiasts always fall back on the notion that time travel is still not proven impossible.